Diamond turn machining  theory and practice

Introduction

The Need: Fabricating Smooth Surfaces

Every morning, we engage with a fundamental optical component: the common mirror Constructed from flat float glass with a smooth surface and a metallic reflective coating, it effectively reflects visible light The crucial smoothness of its surface, achieved by floating liquid glass in a molten tin bath, prevents scattering of optical rays, preserving their intensity and focus For optimal reflection and transmission, surface undulations must be smaller than the wavelength of light In engineering, applications extend beyond visible light to include wavelengths from infrared to X-rays, where the required surface smoothness becomes increasingly stringent, particularly for X-ray mirrors that demand surface undulations at the Angstrom level Additionally, complex surface shapes are essential for certain applications, ensuring electromagnetic waves reflect off the top surface without penetrating the glass.

Such engineering applications demanding surface smoothness include:

Defense forces utilize specialized instruments that harness the infrared (IR) segment of the electromagnetic spectrum for enhanced night vision capabilities Additional defense technologies encompass helmet-mounted display systems, head-up displays, virtual reality systems, avionics, and various imaging systems essential for both air and land defense operations.

X-ray beam deflections necessitate the use of highly polished curved surfaces in silicon An essential technology in this process is diamond turning, which serves as a critical precursor to the final optical polishing required for mirror fabrication Companies such as Zeiss in Europe are currently producing these advanced mirrors.

Diamond turning technology is essential for producing medical optical products that enhance vision, both externally and for implants used within the body These optical elements are primarily crafted from polymers, utilizing either direct diamond turning or diamond-turned inserts for injection molding, enabling mass production Numerous companies specialize in manufacturing these items, including ophthalmic implants, mobile camera lenses, and progressive lenses.

Smooth surface - specular reflection Rough surface - diffuse reflection

For effective electromagnetic (EM) wave reflection, the surface must have undulations that are one order lower than the wavelength of the incoming EM wave Similarly, for successful transmission, it is essential to have such surfaces on both sides of the component.

Complex geometries with demanding surface smoothness needed in a variety of applications from space and defence to medical.

Diamond turning plays a crucial role in the production of large mirrors essential for telescope applications These telescopes are frequently developed through international collaborations among multiple countries.

Space technology relies on diamond turning technology to produce specialized rocket components that demand high-precision smooth surfaces Recent advancements in avionics are focusing on achieving precision surfaces from titanium substrates.

• Medical products such as many structural implants require very smooth surfaces for optical, tribological reasons and also for better integration with the body.

The requirements of reflection, transmission, index of refraction, disper- sion and index gradients also demand the use of varied engineering materi- als (Table 1.1).

The current challenge lies in processing a diverse range of materials—ranging from ductile to brittle and soft to hard—to achieve optically smooth surfaces with complex geometries Machining and abrasive grinding/polishing are the established manufacturing processes known for delivering precise dimensions, tolerances, and surface smoothness.

Complex shape needed for a typical X-ray mirror.

Materials to be Processed for Fabricating Components Interacting with EM Waves

Visible Spectrum Infrared Spectrum X-Ray Beams

ZnSe and ZnS Silicon, Germanium Chalcogenides

Silicon highlights the limitations of traditional machining processes in achieving the high-quality smooth surfaces required for advanced applications To address these shortcomings, modifications have been proposed, leading to the development of a new process known as DTM (Direct Tooling Method).

Conventional Machining and the Need to Go Beyond

Machining processes such as turning, milling, drilling, and boring are essential for shaping raw materials by removing unwanted material to achieve desired forms These processes create new surfaces through the impact of cutting tools that move relative to the workpiece, utilizing brute force for material removal The precision of 3D tool movement allows for the creation of complex shapes with high dimensional accuracy and tolerance control A rigid machine holds both the cutting tool and the workpiece securely while providing controlled cutting and feed motions The interaction between the tool and the material results in shear and fracture, which, along with the tool's motion irregularities and geometry, leaves distinctive marks and surface undulations on the finished product.

The sharpness of cutting tools, typically ranging from a few to tens of micrometers, significantly influences shear-fracture interactions at the tool's cutting edge Tools made from hard materials like multigrain carbides, ceramics, and polycrystalline diamond face challenges in controlling edge profiles, which can leave distinct marks on the work surface Machine tools equipped with various linear and rotary slides often experience unavoidable vibrations due to rigid metal-to-metal contacts, leading to variations in tool edge motions and resulting in surface imperfections Despite efforts to mitigate these issues, achieving optimal surface finishes in precision machining remains a challenge, with typical roughness values of several micrometers falling short of the stringent requirements for IR, visual, and UV/X-ray optical components, which demand machining precision of ±0.1 μm, surface finishes better than 0.01 μm Ra, and a ratio of error tolerance to machined precision of 10–6.

The transition from conventional precision machining to ultra-precision machining (UPM) is a gradual process that relies on the intelligent use of advanced tooling, high-precision equipment, effective processing algorithms, and strict environmental controls Additionally, implementing error compensation procedures is crucial to ensure that components meet rigorous quality standards.

To effectively address the requirement for surface smoothness in machining, it is essential to move beyond traditional machining processes and seek comprehensive improvements across all aspects of the field This necessity has led to the development of diamond turn machining (DTM), a new approach that promises significant advancements in achieving superior surface quality.

Diamond Turn Machining (DTM)

Diamond turn machining (DTM) is an ultra-precision machining process distinguished by its ability to produce surfaces with nanometer-level roughness and submicron form tolerances This process excels in creating micro-structured surfaces, such as those found in diffractive optical elements, across a variety of materials, including ductile, semi-ductile, and brittle substances like silicon The effectiveness of DTM stems from the precise interaction of diamond cutting tools, controlled lathe operations, and stringent machining protocols, all aimed at achieving optimal surface quality Characterized by surface profile deviations measured in submicrons and roughness in nanometers, DTM requires a unique combination of cutting tools, process conditions, machine tools, motion control, fixtures, and measurement techniques to meet the rigorous standards necessary for next-generation precision instrumentation.

For effective shearing action, a cutting tool must possess a sharp and uniform edge with waviness and edge radius measured in nanometers Achieving such precision is feasible only with hard single crystal materials like diamond, where specific crystallographic planes and directions can be meticulously selected This process demands significant expertise for local development and contributes to higher tooling costs.

To achieve a high-quality machined surface free from indentation and fracture, particularly in brittle materials, it is crucial to ensure smooth chip formation This can be accomplished by maintaining ductile-regime machining conditions, which require keeping the chip load cross-section dimensions below a critical threshold Additionally, inducing compressive stresses through the cutting edge radius and utilizing negative rake angles plays a significant role in achieving these conditions.

To achieve optimal cutting and feed motion, it is crucial to mount tools and work materials with minimal holding stresses on high-precision, vibration-free sliding bearing systems, both linear and rotational One effective method for ensuring smooth motion is to eliminate mechanical contact between moving elements by introducing a small gap filled with temperature-controlled pressurized fluids, such as air or oil However, the design and manufacture of these specialized bearing systems can be challenging, resulting in significant capital investment.

Diamond turning has recently showcased a unique characteristic involving the simultaneous, high-speed coordination of spindle motion and the z-direction feed axis This chiseling-like dynamic along the tangential cutting path enables the creation of intricate textured features essential for applications like diffraction gratings However, this coordinated motion can lead to undesirable overlapping of the tool path on previously machined surfaces, as it typically avoids the intermittent motion seen in milling To effectively harness this technique, sophisticated built-in controls and custom programming strategies are often necessary to achieve specific textures.

Diamond turning necessitates the use of specialized high-precision fixtures to securely hold the work material and cutting tool, often utilizing vacuum systems for fine adjustments The dynamics of these fixtures are crucial in minimizing vibration effects during the process Any errors in tool holding or dynamics can result in significant damage and deterioration of the workpiece's surface quality, ultimately reducing the lifespan of the valuable precision diamond tool.

• The fine surface generated requires high precision metrology sys- tems that can verify whether the needed tolerances have been attained

To optimize diamond turning processes, it is essential to address any discrepancies between the desired and achieved surface geometries This can be accomplished by making necessary adjustments to the process conditions, whether in-line or off-line, ensuring a seamless loop of continuous improvement.

In the mid- to late 1970s, the first specialized diamond turning machines (DTMs) were developed by Lawrence Livermore National Labs in the United States These machines range in size from small to very large, and since their inception, the technology has significantly advanced, leading to the availability of commercial products primarily from the United States, United Kingdom, and Japan Ongoing research in the field of diamond turning continues globally, with notable contributions from countries such as Japan, Hong Kong, India, China, South Africa, the United States, the United Kingdom, and various European nations.

Diamond turning machining (DTM) is driven by the need for miniaturization in electronic circuitry and precision components, responding to global demands for smaller, high-volume commercial products Advances in machine design, controls, and tooling have enabled the production of complex surface shapes, achieving submicron surface figure errors and nanometer-level roughness This deterministic approach enhances accuracy and surface quality by minimizing operational randomness through effective monitoring and control The collaboration of diverse scientific and technological disciplines has enriched DTM processing, particularly in ultra-high-precision machining and optical instrumentation development DTM has revolutionized aspheric shape creation, overcoming limitations of traditional optical fabrication and offering new possibilities for various applications in research and industry.

The development of ultra-precision components using advanced equipment and novel diamond tools is a costly endeavor, yet the optical production industries have successfully adopted DTM processes by optimizing their workflows and resource utilization Over the past two decades, global DTM activities have surged, driven by various applications that leverage this technology to achieve their goals Key factors influencing effective DTM operations include the material properties of the workpiece, the condition and environment of the DTM equipment, the geometry of diamond tools, machining parameters, and the capabilities of metrology equipment Additionally, aspects such as diamond tool setup, equipment dynamics, and thermal management during DTM significantly impact outcomes A comprehensive understanding of DTM operations and associated challenges can only be gained through dedicated efforts in developing precision components via DTM.

Diamond turn machining (DTM) is a specialized machining process that stands out in the industry for its unique capabilities This book introduces the term DTM, although it is also commonly known as diamond turning, single point diamond turning (SPDT), or ultra-precision machining in existing literature Throughout this book, the term DTM will be consistently used to refer to these processes.

Place of DTM in the Process Chain

Components requiring high surface smoothness often utilize the DTM process The production chain begins with the creation of the rough shape through conventional bulk processing methods, such as casting.

Conventional machining processes, such as milling and turning, are used for semi-rough shaping, followed by the DTM process to achieve the desired form and surface finish Depending on the type of electromagnetic wave interaction anticipated, a polishing process may be necessary.

The requirement for surface smoothness is closely linked to the type of electromagnetic (EM) wave interacting with the surface For components interacting with infrared (IR) waves, processing through Diamond Turning Machining (DTM) is sufficient, as the mid-spatial frequencies present on a DTM surface do not significantly affect performance However, components that necessitate the reflection and transmission of visible light are sensitive to these mid-spatial frequencies and cannot accommodate them.

Microwaves Visible Ultraviolet X-rays Gamma

DTM + polish + ion beam figuring (iterative)

Surfaces that interact with infrared waves can be effectively processed using DTM, whereas surfaces that interact with visible light necessitate additional polishing Furthermore, surfaces that deflect X-ray beams require multiple iterations of polishing and measurement following DTM processing to achieve optimal results.

Final product with smooth surface

The manufacturing process of optical components involves a typical chain that begins with deterministic cutting and feed motion paths in Direct Tooling Methods (DTMs) These components undergo subsequent loose abrasive polishing to achieve isotropic surface characteristics While the DTM process ensures precise form control, polishing enhances local surface smoothness, which is crucial for optical surfaces in X-ray instrumentation that require strict slope and roughness control This process often includes multiple iterative polishing and measurement cycles following DTM, and may necessitate specialized techniques like ion-beam figuring for fine material removal, further ensuring the desired geometric form.

Summary

This chapter explores the diamond turn machining (DTM) process, highlighting its role in achieving smooth surfaces on various materials, including metals, polymers, and semiconductors It discusses the limitations of traditional machining methods, which led to significant modifications in machine structure, cutting tool materials, geometry, and motion control, ultimately resulting in the development of ultra-precision DTM This niche process, also known as single-point diamond turning, offers distinct advantages in shaping components to achieve optically smooth surfaces, both flat and complex, making it an essential technique in modern manufacturing.

Diamond Turn Machines

Introduction

Diamond turn machines (DTMs) are ultra-precision devices capable of producing surfaces with nanometric accuracy The quality of these surfaces is influenced by both the machine's inherent quality, which can be controlled during the manufacturing process, and inaccuracies from various process variables Therefore, constructing machines with exceptional accuracy is crucial for achieving ultra-precision machined surfaces While the machine-building process is well-established globally, only a limited number of manufacturers specialize in diamond turn machines due to the stringent accuracy requirements.

This chapter offers valuable insights into the construction of diamond turn machines, beginning with an overview of the different types available It then explores the key characteristics and capabilities of these machines, detailing their components, the technologies utilized, and the environmental factors that influence their performance Additionally, a typical specification sheet for a diamond turn machine is included to provide a comprehensive understanding of its features.

Classification of Diamond Turn Machines

Diamond turn machines are classified based on their number of axes and configurations, similar to other machines This classification method is one of the most common ways to categorize diamond turn machines.

Figure 2.1 shows the schematics of the same.

Type A machines resemble traditional lathe machines, allowing for simultaneous programming of both the X-axis, which holds the headstock and spindle, and the Z-axis, which carries the tool This capability enables the creation of axi-symmetric features, and with the right fixtures, off-axis parabolic surfaces can also be produced on these machines.

Type B machines offer enhanced control over the spindle (C-axis), allowing for the creation of non-axisymmetric features When paired with attachments such as fast tool servos, these machines can produce complex features, including lenslet arrays.

Type C machines feature B-axis control that maintains the cutting tool perpendicular to the work surface, making them ideal for machining spherical surfaces In contrast, Type D machines resemble milling machines but utilize a fly tool mounted on a spindle for their operations.

Requirements of Diamond Turn Machines

Ultra-precision machining processes aim to achieve surface profiles with deviations of just a few nanometers or less Minimizing deviations from the desired profile is crucial for enhancing the quality and performance of precision-engineered components.

Type B Spindle C head Tool post

Classification of diamond turn machines.

Diamond turn machines are designed to achieve precise surface profiles with deviations as low as a few tens of nanometers To accomplish this level of accuracy, meticulous attention is given to all aspects of machine construction Key elements influencing surface deviations are highlighted in Figure 2.2, which compares both conventional precision machines and diamond turn machines.

Diamond turn machines achieve surface accuracy within tens of nanometers, significantly surpassing conventional precision machines that typically reach accuracies better than 1 micrometer The inaccuracy contributions from machine tools are considerably lower in diamond turn machines, as they effectively control and compensate for tool and process variable inaccuracies However, achieving extreme accuracy in diamond turn machines necessitates meticulous attention during the machine-building process Key factors influencing the accuracy of diamond turn machines include various operational parameters and design considerations.

• Positional accuracy and repeatability of moving elements

2.3.1 Positional Accuracy and Repeatability of Moving Elements

Positional accuracy is the degree of agreement between the targeted value and the programmed value of the moving slides and spindle; repeatability is

Tool setting accuracy 10 sharpness Tool 3

Several factors contribute to the inaccuracies observed on generated surfaces in diamond turn machines Achieving a positional accuracy within tens of nanometers is a key objective in their design Generally, diamond turn machines demonstrate positional accuracy and repeatability that surpasses conventional precision machines by two to three orders of magnitude However, these performance metrics can be influenced by various factors that impact the overall effectiveness of the diamond turning process.

• Degree of freedom of moving elements

• Geometrical accuracy of the axis of moving element and its datum

• Scale, drive and feedback elements

Ensuring that a moving element has freedom of movement only in the desired direction is crucial for eliminating errors For instance, X-axis movement should allow translation solely along the X-direction while restraining all other degrees of freedom Figure 2.3 illustrates the various degrees of freedom across all three axes and highlights the necessary freedoms for the X-axis and spindle As shown in Figure 2.3a, errors can arise from unconstrained degrees of freedom, including clearances between moving components, geometric inaccuracies in sliding surfaces, and friction among parts Therefore, to achieve precise X-axis movement, it is essential to eliminate the five degrees of freedom—Y, Z, x, y, and z—while similarly constraining undesirable freedoms in other axes to minimize various errors.

Schematic diagram showing desirable degrees of freedom for (a) X-axis slide and (b) spindle.

Diamond Turn Machines experience spindle inaccuracies such as pitch, yaw, and roll, which impact their performance Additionally, errors stemming from datum inaccuracies, scale discrepancies, and feedback system limitations further compromise the machine's positional accuracy.

Loop stiffness in a diamond turn machine reflects the equivalent stiffness values of various machine components during the machining process In Type A machines, the elements contributing to loop stiffness can be represented in a specific manner.

– Work piece – fixture – spindle – headstock – X-axis table – X-axis guide- ways – bed – Z-axis guide ways – Z-axis table – tool post – cutting tool – work piece.

The cutting force F acting at the tool – work piece interface is related to mass (m), acceleration (x), damping coefficient (c), velocity (x), stiffness (k) and deflection (x); and it is represented by the following equation:

Joint stiffness between two elements can be modeled using springs with specific stiffness values, while damping elements are represented by dampers During machining, forces at the tool-workpiece interface are transmitted through these elements in both directions Different elements experience varying deflections under the same force, leading to an unbalanced loop stiffness that alters the cutting tool's path.

Cutting force (F) k tool k tool-post k guideways k work-piece k fixture k spindle k headstock k’ guideways c 1 c 2 c 3

Work-piece Chip k - Stiffness c - Damping k Z-table k X-table

Loop stiffness of various elements of a diamond turn machine.

The loop stiffness of a machine is influenced by the individual stiffness and damping values of its components, with any variations leading to vibrations and chattering on the machined surface For instance, altering the clamping length of the tool shank affects the tool overhang and, consequently, the stiffness of the tool shank, resulting in deflection at the tool tip and chatter on the surface Therefore, selecting appropriate materials and geometries for machine elements to achieve balanced loop stiffness is crucial in the design of diamond turn machines Additionally, the damping characteristics of components like slides and bearings significantly impact loop performance, as different types of bearings—such as sliding surfaces, linear motion guideways, aerostatic, and hydrostatic bearings—exhibit varying damping properties, which influence the selection of other elements in the loop stiffness.

Thermal drift significantly impacts the performance and accuracy of diamond turn machines, primarily due to heat generated by drivers and friction from spindle rotation and slide movement This phenomenon leads to differential expansion of machine components, resulting in undesirable effects such as altered clearances between spindle bearing surfaces and table slides, as well as changes in spindle length and headstock height Such expansions can adversely affect the position and orientation of the rotational axis, ultimately influencing the size and shape of the machined components To mitigate thermal drift, proper material selection and cooling arrangements are essential Modern diamond turn machines incorporate embedded temperature sensors and employ compensation strategies to minimize the effects of thermal drift effectively.

Diamond turn machines must produce optical quality surfaces devoid of size and shape deviations, as well as cosmetic defects such as scratches and chatter marks A primary cause of these defects is vibration at the interface between the tool and the workpiece, which also significantly impacts tool life.

• Tool and tool tip vibration

Vibration leads to periodic relative displacement between the tool and workpiece, resulting in deviations from the desired tool path at a microscopic level, which adversely affects surface topography and finish The cantilever design of the tool shank allows for free vibrations at its tip, causing uncontrolled displacements Similarly, diamond turn machine spindles, supported by either aerostatic or hydrostatic bearings, experience axial and radial shifts as well as random tilts, with eccentricity and unbalanced mass contributing to vibration Inhomogeneous workpiece materials can induce additional 'material-induced vibrations', while external vibrations are transmitted through the tool and spindle to the cutting interface Collectively, these factors hinder surface quality, making it crucial to minimize vibrations transmitted to the machining zone, as complete elimination is unattainable.

Characteristics and Capabilities of Diamond Turn Machines

Diamond turn machines (DTMs) exhibit unique behaviors and capabilities that significantly influence their output These machines leverage inherent characteristics to achieve precise material removal As illustrated in Figure 2.6, the minimal movement between the tool and the workpiece allows DTMs to perform extremely small unit removals (UR) of material, facilitating a high level of control over the material removal process.

Vibration on machined surface Vibration amplitude in Y-direction

Vibration amplitude in X-direction àm 3.75

The effect of vibration on the machined surface is significant in precision machining processes Typically, these processes utilize a chip cross-section of 10 μm × 10 μm, while diamond turn machining achieves a remarkably smaller chip cross-section of less than 1 μm × 1 μm This reduction represents just one hundredth of the uncut radius (UR) in traditional precision machining The small UR in diamond turn machining allows for the simultaneous machining and finishing of surfaces, enhancing overall surface quality and precision.

Diamond turning machines excel in achieving nano-regime machining by precisely controlling the machining path, allowing for size tolerances, shape errors, and surface finishes within a few tens of nanometers However, one significant drawback is the excessive tool wear caused by small uncut radii (UR) To produce surfaces with optical quality, it is crucial to minimize vibrations from both external and internal sources, effectively reducing issues like chatter and dig marks The damping characteristics of the bearing elements are vital in significantly lowering vibration amplitudes.

Components of Diamond Turn Machines

A diamond turn machine is constructed by combining various functional components, as depicted in Figure 2.7 The key components and their respective sub-systems are detailed in Table 2.1.

Ability to achieve small movements

Small unit removal of material (UR) and hence better control on the process

Machining of precise surfaces and complex three dimensional geometries

Depth of cut (few nm)

Characteristics and capabilities of diamond turn machines.

Spindle head with integral motor

Optical based tool measurement system

Tool post with fast tool servo

Components of diamond turn machine.

Important Functional Elements and Components of a Diamond Turn Machine

1 Structure and bed Machine frame

2 Positioning Table and guide-ways

Headstock and spindle Motor and drive elements Tool post and tool In-situ tool measurement

4 Sensing Linear scales and rotary encoder

Hall sensor Velocity and acceleration sensors Closed loop feed back

6 Peripheral Pneumatic, hydraulic and electrical devices

7 Special devices Slow tool servo system

Some of the basic differences between the components of a diamond turn machine and other machines are:

Individual components are engineered for exceptional positional accuracy, with diamond turn machines achieving guideway straightness of better than a few hundred nanometers, significantly surpassing the few micrometers typical in conventional precision machines.

• Moving components have thermal equilibrium so as to avoid dif- ferential coefficient of thermal expansion leading to inaccuracies.

• Assembly of the machine components leads towards a high level of accuracy For example, in a headstock assembly, the spindle run-out is of the order of 20–30 nm.

• Drive systems are extremely fast responding.

• Selection of material for each component is done with considerations for inertia, thermal, damping and strength aspects.

Technologies Involved in Diamond Turn Machine Building

The construction of diamond turn machines integrates various advanced technologies to enhance functionality and minimize unwanted noise Key features, such as vibration isolators between the machine bed and the ground, effectively reduce incoming vibrations, while hydrostatic or aerostatic spindle bearings achieve remarkable precision with run-out levels as low as a few tens of nanometers Continuous advancements in technology have transformed the design of these machines; for instance, modern diamond turn machines now utilize linear motors for table movement instead of the traditional ball screw arrangements A comprehensive overview of the technologies employed in different components and subassemblies of diamond turn machines can be found in Table 2.2.

When building diamond turn machines, it's crucial to understand the characteristics of different technologies Hydrostatic bearings are preferable for table guide-ways due to their superior damping properties, while aerostatic bearings excel in thermal stabilization, making them ideal for spindles.

Environmental Requirements for Diamond Turn Machines

Environmental conditions severely affect the accuracy, performance and life of the machine Diamond turn machines are very sensitive for the following environmental conditions:

To mitigate the impacts of environmental factors, diamond turning machines are operated in a controlled clean room environment It is essential to maintain a temperature stability of ±1°C and humidity levels within ±5%, adhering to a clean room classification of 10,000 or better These standards are crucial for minimizing the adverse effects of temperature, humidity, and dust on the machining process.

Various Technologies Employed in Diamond Turn Machine Building

1 Ground–machine interface Vibration isolator

6 Compensation of slide errors and non-symmetric features Slow tool servo [16]

7 Tool position measurement Optical/LVDT

10 Spindle temperature stabilisation Water cooling

11 Scale (table positioning) Linear scale

12 Spindle drive Integral brushless motor

13 Table drives AC linear motors

14 Spindle position monitoring Halls sensor

15 Environment Clean room with temperature and humidity control

To achieve nanometric accuracy in machining components, it is crucial to maintain consistent environmental conditions, as any temperature variation can significantly impact size tolerance, shape, and surface finish Therefore, workpieces are thermally stabilized by ensuring they are kept in uniform environmental conditions prior to the machining process.

Vibration isolators minimize the transmission of ground vibrations to diamond turn machines, but acoustic vibrations still directly affect machine components and the machining zone Therefore, it is essential to effectively control noise levels in the vicinity of the machine to ensure optimal performance.

Sample Machine Specification Sheet

Table 2.3 shows sample specification of a diamond turn machine.

Summary

This chapter provides a comprehensive overview of diamond turn machines (DTMs), detailing their classification and essential functional requirements such as positional accuracy, repeatability, and balanced loop stiffness It also addresses the impacts of thermal and vibration effects on performance Key desirable characteristics, capabilities, and various components involved in the construction of DTMs are discussed, along with the necessary environmental conditions for optimal operation Additionally, a sample specification sheet for DTMs is included to enhance understanding.

Sample Solved Problems

In the diamond turn machining process, it is essential to assess the potential inaccuracy when machining a cylinder with specific parameters: a tool shank cross-section measuring 10 mm by 10 mm, a length of 50 mm, constructed from tool steel, and a Young’s modulus of elasticity of 200 GPa.

Solution 1 Equivalent stiffness of the cutting zone can be calculated by considering the stiffness of the tool as well as the machine, as illustrated in Figure 2.8.

Second moment of inertia of tool shank (I) = bd 3 /12 = 10 −2 × (10 −2 ) 3 /12 8.3 × 10 −10 m 4

Stiffness of tool shank (K t ) = W/δt = 3EI/L 3 = 3 × 200 × 10 9 × 8.3 × 10 −10 / (0.05 3 ) = 398.4 × 10 4 N/m.

Sample Specification of a Diamond Turn Machine

Machine type Diamond turn machine

Machine base Natural/synthetic granite bed

Vibration isolation Pneumatic, weight carrying capacity up to

5000 kg, resonant frequency in both vertical and horizontal direction < 2.5 Hz

Control system Aerotech Model: A3200 (indicative only)

Programing resolution 0.01 nm (linear)/0.0000001 0 (rotary)

Resolution 16 picometer (linear)/0.018 arc-sec (rotary)

Aero static, liquid-cooled Integral brushless motor 16,000 rpm

Form accuracy (P-V) Better than 1.0 nm Ra

Better than 0.1 micron Power requirement

15SCFM @120 PSIGFloor space (W × L × H) 1500 mm × 2000 mm × 2000 mm

Equivalent stiffness (K eq ) can be calculated by using the figure and force equilibrium, which is written as follows:

Note: X is tool displacement with respect to the work-piece.

Deflection due to radial force on tool (δ) = Fr/K eq = 0.2/4.33 = 0.046 μm = 46 nm. This deflection is a tool path deviation with respect to the defined path program.

Thus, the extent of machining inaccuracy can be quantified as 46 nm.

Example 2 During diamond turning of copper alloy, compare inaccura- cies, when cutting edge sharpness (R) varies from 100 nm to 150 nm Assume other parametres are constant.

Solution 2 Let equivalent stiffness of tool-work-piece = K eq

Referring to Figure 2.9, ploughing force in case of 100 nm sharp tool = F1 σ f b (2Rt) 0.5 = σ f b (200t) 0.5 where, σ f is flow stress.

Accordingly, ploughing force in the case of 150 nm sharp tool, F2 = σ f b

The ratio of inaccuracies due to tool deflection when cutting edge sharp- ness varies from 100 to 150 nm = F1/F2;

Hence, a 150 nm sharp tool leads 1.41 times higher inaccuracy, when it is compared with 100 nm sharp tool.

Sample Unsolved Problems

In a single point diamond turn machining process, maintaining a tool offset error of 10 μm while producing a hemispherical ball with a diameter of 20 mm results in a form accuracy that can be calculated based on the specified parameters Given that other sources of errors are negligible, the precision of the machining process can be effectively assessed by analyzing the impact of the tool offset on the final form of the hemispherical ball.

Q2 During diamond turn machining, compare inaccuracies when it is applied on aluminium (flow stress = 140 Mpa) and brass (flow stress 300 Mpa) Assume other parametres are constant.

In diamond turn machining, the vibration isolation can be calculated using specific parameters for achieving smooth cylindrical surfaces The tool shank has a cross-section of 10 mm × 10 mm and a length of 50 mm, made from tool steel with a Young’s modulus of elasticity of 200 GPa The radial force (Fr) applied is 0.2 N, while the tangential force (Ft) is 0.15 N Additionally, the stiffness of the machine tool (Km) is 50 N/μm These parameters are essential for determining the effectiveness of vibration isolation in the machining process.

Mechanism of Material Removal

Introduction

In engineering, material processing to achieve specific shapes, sizes, and surface finishes can be accomplished through top-down, bottom-up, or combined approaches The top-down method involves machining bulk materials with tools such as cutters and lasers to remove excess material, while the bottom-up approach adds material through processes like electroforming and additive manufacturing Each method has its advantages and disadvantages; for instance, machining often leaves residual tensile stresses on surfaces, whereas bottom-up techniques may lack product homogeneity Understanding the mechanisms of material removal and addition is crucial for controlling process variables to enhance product quality, including strength and accuracy Diamond turn machining (DTM), a material removal process, shares similarities with conventional machining but has unique parameters that significantly impact product quality This chapter explores key aspects of material removal mechanisms in DTM.

• Micro- and nano-regime cutting

Comparison of Deterministic and Random Machining Process

DTM (Diamond Turning Machining) is a process that removes minimal material from pre-shaped components, functioning as both a machining and finishing technique In this context, machining and finishing are used interchangeably The interactions between the tool and workpiece during either tool-based or abrasive-based machining significantly influence the quality of the finished surface Key quality factors such as shape, size, and surface finish are determined by the employed process, making it essential to comprehend the characteristics and behaviors of finishing processes to achieve the desired surface quality Finishing processes can be broadly classified based on their specific characteristics.

Figures 3.1 and 3.2 illustrate examples of two distinct classes of processes, with Figure 3.1 depicting a typical deterministic process known as the turning process, which involves unit removal (UR).

Schematic of deterministic finishing process: Turning.

The material removal mechanism can be accurately regulated by adjusting process parameters such as depth of cut, feed per revolution, and cutting velocity Furthermore, precise control over the tool path allows for the machining of intricate surfaces This deterministic approach to tool path travel, combined with a predictable material removal rate, facilitates the efficient achievement of the desired component size and shape In turning processes, the typical material removal rate (MRR) can be mathematically expressed.

MRR d f v= mm /min 3 (3.1) where d = depth of cut in mm; f = feed in mm/revolution; v = cutting velocity in mm/min.

The lapping process, illustrated in Figure 3.2, is a typical random process characterized by variable material removal rates across different locations on the surface This process occurs simultaneously at multiple tool-workpiece contact points, making it challenging to predict the precise material removal rate, which varies in a nonlinear manner Additionally, tool path control on the work surface is not feasible, limiting the lapping process to finishing only simple geometries The average material removal rate (MRR) for flat lapping can be described using Preston’s equation.

AverageMRR∝Pv dT dt= / (3.2) where P = pressure, v = Volume; T = thickness in mm; and t = time in min.

Motion of lapping plate Work-piece Lapping plate

Work-piece Lapping plate ickness of material removed

Schematic of random finishing process: Lapping.

The lapping process offers superior flatness and surface finish due to its area averaging capability and control over cutting forces, unlike deterministic processes that leave a distinct lay pattern on surfaces Additionally, machine inaccuracies are evident in surfaces finished by deterministic methods, while random finishing techniques, such as lapping, effectively eliminate the impact of these inaccuracies.

Both deterministic and random finishing processes have distinct advantages and disadvantages Key characteristics and capabilities of these processes are outlined in Table 3.1 This discussion primarily focuses on DTM, which is categorized as a deterministic finishing process.

Cutting Mechanisms for Engineering Materials

Engineering materials are primarily categorized into ductile and brittle types, with their failure modes providing insight into the material removal process Understanding these mechanisms is crucial, as machining aims to effectively remove material from the work surface to achieve the desired surface qualities.

Key Characteristics and Capabilities of Deterministic and Random Finishing Processes

Characteristics Path controlled Force controlled

Location of point of material removal is controllable Material removal by area averaging Few process parametres Large number of process parametres

Faster process Slow and tedious process

Machine needs to be precise, as its signature is transferred to generated surface

Machine need not to be precise, as its signature is not transferred to generated surface

Lay pattern is generated on finished surface No lay pattern is generated on finished surface Capabilities Precisely controllable MRR Difficult to control MRR

Complex surface generation is possible Only generation of simple surfaces like flat and spherical surfaces are possible

Size control is possible Size control is not possible

Finish impaired by lay pattern Extremely high surface finish

Mechanism of Material Removal materials Material removal mechanism is generally affected by the fol- lowing factors:

• Work material and its properties

• Tool material and its properties

• Relative position between the work-piece surface and tool

• Relative motion between the work material and tool

Figure 3.3 depicts the process of material removal in ductile materials Numerous factors play a significant role in the material removal mechanism and subsequently affect the quality of the generated surface.

In the machining of ductile materials, the moving tool compresses the material, causing it to slide along the shear zone and transform into chips through plastic deformation, which are then removed from the parent material The specific cutting energy required for material removal varies based on the defect density in the shear zone; as the uncut chip thickness decreases, defect density diminishes, necessitating higher specific cutting energy for chip removal The desired shape of the component is achieved by carefully controlling the tool path, with various factors influencing the ductile material removal process summarized in Table 3.2 The specific cutting energy for machining ductile materials can be estimated using a specific equation.

Specific Cutting Energy=G e ( − 2π W a / ) (3.3) where G = modulus of rigidity, W = dislocation width and a = interatomic spacing.

The tool nose radius is the most crucial factor influencing the cutting mechanism of a material As the uncut chip thickness (t c) shifts from above to below the threshold value, the cutting mechanism transitions from shear cutting to ploughing and finally to rubbing, depending on the tool edge radius (r) This relationship is illustrated schematically in Figure 3.4, while Table 3.3 outlines the material removal mechanisms associated with varying levels of cutting edge sharpness.

When the uncut chip thickness exceeds the critical chip thickness (t c), plastic deformation dominates, leading to chip formation from the displaced work material In contrast, when the uncut chip thickness falls between the critical threshold and the level that induces pure elastic deformation, elastic deformation prevails, resulting in ploughing action without material removal If the uncut chip thickness is below the pure elastic deformation threshold, the tool merely rubs against the work surface, again without removing material Additionally, as the uncut chip thickness approaches certain critical values, the rake angle of the tool shifts from positive to negative, creating a dead metal zone that increases cutting force, specific cutting force, and specific cutting energy This phenomenon, where specific cutting force or energy rises with decreasing uncut chip thickness, is referred to as the size effect Furthermore, the mechanism of material removal transitions from shearing to ploughing and ultimately to rubbing as the a/r ratio decreases for a given uncut chip thickness.

Factors Affecting Ductile Material Removal

Material flow back characteristic and rubbing of finished surface with tool

Cutting tool Cutting edge radius Minimum achievable uncut chip thickness Cutting tool angles/geometries/ orientations Hot hardness

Tool rubbing on the finished surface

Machining parametres Uncut chip thickness Rubbing/ploughing/cutting

Machine Precision Minimum uncut chip thickness

Transfer of machine signature on finished surface

The cutting mechanism for machining brittle materials involves an indenter, or cutting tool, applying pressure normal to the machining surface, which leads to the formation of lateral and median cracks after a certain penetration depth As these cracks intersect, material removal occurs, resulting in the generation of discontinuous chips This process is visually represented in Figure 3.6 Additionally, the maximum theoretical specific cutting energy for machining brittle materials can be calculated using a specific equation.

Section: A-A (not to scale) a/r a- uncut chip thickness r- cutting edge radius (sharpness)

Effect of tool nose radius on cutting mechanism (a) Tool nomenclature (b) Shearing (c) Ploughing (d) Rubbing (e) Cutting mechanism for different a/r ratio.

Effect of Cutting Edge Radius on Cutting Mechanism

Increasing cutting edge radius r 1 r 2 r 3 t 1 Cutting Ploughing Rubbing t 2 Ploughing Rubbing – t 3 Rubbing – –

Material removal in both ductile and brittle materials can be illustrated through the multigrain material removal process, as depicted in Figure 3.7 This process occurs at the macro level, where material is removed as the failure line advances along the grain boundaries The resistance to plastic deformation is approximately equal to the material's shear strength Additionally, a reduction in grain size leads to an increase in the number of grain boundaries, which enhances the resistance to material removal.

Formation of discontinuous chips in brittle material processing (a) Initial deformation of mate- rial (b) Crack formation (c) Chip formation.

Length of median crack from top surface Length of lateral crack from top surface

Micro- and Nano-Regime Cutting Mechanisms

As the uncut chip thickness decreases, material removal occurs across the grains rather than along the grain boundaries, leading to a significant increase in resistance due to reduced defect density along the failure path Defects such as dislocations and vacancies within the grains are crucial in determining this failure path When the uncut chip thickness transitions from micro to nano levels, the diminished defect density results in a substantial increase in resistance to material removal, which ultimately impacts tool life.

Typical material separation path Grain boundary

Typical material separation path within

Sub-grain material removal leads to deterioration in machining processes A typical graph illustrates the relationship between uncut chip thickness and specific cutting energy, highlighting that at the atomic level, the specific cutting energy corresponds to the atomic bonding force.

Figure 3.10 shows various regions for a typical cutting process Regions I,

II and III represent the regions corresponding to nano cutting, micro cutting and macro cutting, respectively.

Abrasive-based micro- and nano-finishing processes differ from traditional single point machining by gradually removing only the projecting peaks of a surface until they are completely smoothed out As the peaks are eliminated, the rate of material removal decreases Figure 3.11 illustrates the various stages of this process, with Figure 3.11a depicting the interaction between an abrasive particle and a micro-irregularity peak, while Figure 3.11b shows a chip partially sheared off the peak At this stage, the abrasive particle and chip are connected through secondary bonding forces As the shear plane length diminishes along the cutting path, the material resisting force becomes less than the secondary bonding force, ultimately facilitating the chip's removal.

Molecular dynamics simulation (MDS) is crucial for understanding material removal behavior at the nanometer scale, especially when experimental techniques are ineffective due to uncut chip thickness A typical MDS illustrates tool-workpiece interaction, revealing three atomic layer regions: the Newtonian layer, the thermostat layer, and the boundary layer In the Newtonian layer, atoms adhere to Newton's second law of motion, governed by specific pair interactions.

Uncut chip thickness (in microns)

Specific cutting energy (in GPa)

Effect of uncut chip thickness on specific shear energy.

Grain boundary Dislocation (movable) Precipitant

Points defects range (Atomic cluster) [1 nm–0.1 àm]

Dislocation range (0.1 àm–10 àm) Micro-crack range

Macro, micro, and nano cutting regions.

Possible path of abrasion to get another chip

Interaction due to secondary bonding force

Abrasive particle material removal involves several stages: initially, the abrasive makes contact with the workpiece, followed by the shearing of peaks, which results in the formation of chips When two atoms approach each other, they experience inter-atomic forces derived from pair potential, facilitating atomic movement The Verlet algorithm is utilized to calculate the velocity and position of these atoms, while thermodynamic properties are determined by conserving the number of atoms, volume, and energy within the Newtonian region As atomic movements occur, any increase in local temperature is regulated by a thermostat layer, ensuring uniform temperature among the atoms in this region Additionally, atoms in the boundary layer provide fixed boundary conditions, and Molecular Dynamics Simulations (MDS) play a crucial role in visualizing and analyzing these interactions.

• Shear plane and chip formation

• Interaction between two bodies like work material and tool

Figures 3.12b and 3.12c illustrate the MDS (Minimum Defect Size) for varying ratios of uncut chip thickness to tool edge radius, utilizing copper as the work material and single crystal diamonds as the tool material Additionally, Figures 3.12d and 3.12e present MDS for different ratios of uncut chip thickness to tool edge radius, providing further insights into the relationship between these parameters.

Uncut chip thickness, a = 10 Å Cutting edge sharpness, r = 0 (Sharp cutting edge), Cu

Chip formation due to shear plane deformation a/r = 0.5, a = 10 Å, r = 20 Å, Cu

No shear plane Adhesion with tool at rake and flank face a = 10 Å, r = 0, (Sharp cutting edge), Si

Adhesion with rake and flank face Deformed layer

(a) MDS layers; (b) MDS for Cu with sharp tool; (c) MDS for Cu with finite tool sharpness; (d) MDS for Si with sharp tool and (e) MDS for Si with finite tool sharpness.

Mechanism of Material Removal sharpness, when silicon (Si) and single crystal diamonds are used as work material and tool material, respectively.

Ductile Regime Machining of Brittle Materials

Under specific cutting conditions, brittle materials can exhibit ductile behavior, particularly when the uncut chip thickness is below a critical threshold value (t c), which varies by material In this scenario, the material in front of the cutting tool is removed as a continuous chip through plastic deformation If the defects generated ahead of the tool do not reach the finished surface, the resulting machined surface remains free of defects This defect-free condition is attainable when the uncut chip thickness is less than t c Blake and Scattergood identified this critical depth parameter, which influences the transition from plastic flow to fracture along the cutting edge They noted that due to the complex interactions between tool geometry, machining parameters, and material response, significant material removal often occurs through fracture, even under ductile-regime conditions Typical values of t c for various materials are detailed in Table 3.4, while Figure 3.12d illustrates the ductile regime machining of silicon with an uncut chip thickness below t c.

In case of brittle materials, threshold chip thickness is expressed by the following equation [25]: t a E H

Threshold Uncut Chip Thickness for Different Brittle Materials

Threshold Uncut Chip Thickness ( t c ) in nm Reference

Nano crystalline, binderless tungsten carbide 165 [29] where a = constant depends on materials; E = elastic modulus; K c = fracture toughness of the material; and H = hardness of the material.

Machining of Polymers

Precision polymer optics play a crucial role across various industries due to their unique properties While traditional methods like injection moulding, compression moulding, and extrusion often fall short in meeting the stringent requirements for optical applications, precision machining through tool-based processes becomes essential Polymers are generally softer, less strong than metals, less rigid, have low density, act as thermal insulators, and exhibit increased viscosity at elevated temperatures The structure of typical amorphous polymers includes randomly distributed polymer chains in one type, while another type features long polymer chains organized in a regular arrangement.

Metals and ceramics exhibit high rigidity, which helps resist distortion on machined surfaces In contrast, polymers have lower resistance to cutting forces, leading to significant distortion of the machined surface The unique properties of polymers greatly influence the quality of the generated surface during machining.

The glass transition temperature (Tg) marks the critical range at which polymers shift from a rigid to a pliable state, occurring significantly below their melting temperature.

Randomly oriented polymer strand Uniformly oriented polymer strand

Viscoelasticity refers to the unique property of polymers that display both viscous and elastic behavior during deformation This characteristic means that the deformation of polymers under stress is time-dependent; when mechanical stress is constant, the strain continues to increase over time Conversely, when a constant deformation is applied, the stress experienced by the material relaxes gradually.

At a specific temperature, each polymer exhibits a unique relaxation time, which is influenced by its vibrational, rotational, and translational movements As the temperature rises, the relaxation time diminishes, leading to a softer and more ductile polymer.

During the machining process, polymers exhibit the following three dis- tinct behaviours:

• Elastic or rubber like state

• Liquid or fluid flow state

Machining polymers resembles the machining of other engineering materials; however, the temperature increase during the process leads to unique behaviors Initially, when the temperature is below the glass transition temperature (Tg), the material removal occurs through brittle fracture Once the temperature surpasses Tg, the behavior shifts to ductile shear plastic deformation.

The glass transition temperature (Tg) varies based on the polymer type and the extent of cross-linking among its strands Polymers are formed when monomers are connected through covalent or ionic bonds Additionally, many polymer strands are interconnected by ionic bonds or weaker Van der Waals forces, which can be described using the Lennard-Jones potential.

In the material removal process, inter-atomic spacing (r) plays a crucial role, influenced by constants σ and ε that are specific to the physical properties of the materials This process involves the sliding of polymer strands against one another, as well as shearing and cutting of these strands.

Major problems encountered during polymer precision machining include

• Reattachment of fine chips on the finished surface

• Melting of the finished surface

• Dimensional distortion of the component due to mechanical and thermal effects

Summary

This chapter explores the mechanisms of material removal across macro and micro domains, focusing on various finishing methods for engineering materials such as ductile, brittle, and polymers It also covers the material removal processes in diamond turning, including micro- and nano-scale machining, along with insights from molecular dynamic simulations.

Sample Solved Problems

To calculate the specific cutting energy during diamond turn machining of a copper alloy, use the following parameters: the rigidity of the copper alloy (G) is 45 GPa, Poisson’s ratio (ν) is 0.28, inter-planar spacing (d hkl) is 0.288 nm, inter-atomic spacing (a) is 0.2556 nm, and the cutting edge sharpness of the diamond tool is 5.0 μm.

Solution 1 Here, the cutting edge sharpness of the tool is of the order of a few microns (i.e 5 μm) In this case, chip deformation depends on the dis- location mechanism and hence ‘Peierls stress’ shall be used to compute flow stress for the chip formation Dislocation width (W) = d hkl /(1 – ν) = 0.288/

Shear stress to move dislocation (τ p ) can be calculated using ‘Peierls stress’ formulation for the chip ‘flow stress’ as follows: τ p =G e ( − 2 π W a / ) Eexp[(−44 7/ ) ( × 0 4 0 2556/ )]1 2 ××10 − 3 GPa1 2 MPa.

Or, τ p = 131.2 Mpa Thus, the required specific cutting energy (ϒ) = energy to deform (or strain energy due to shear stress). ϒ =τ p 2/ G2 1 2 90 000 0 192 2/ , = MPa=0 192 J/cm wher3, ee MPa1 =1J/cm 3

In diamond turn machining of a copper alloy, the specific cutting energy can be calculated using the following parameters: the rigidity of the copper alloy is 45 GPa, with a Poisson's ratio of 0.28 The inter-planer spacing is 0.288 nm, and the inter-atomic spacing is 0.2556 nm The cutting edge sharpness of the diamond tool is 50 nm It is assumed that the specific cutting energy at the nanometric scale is 90% of that at the atomic scale.

Solution 2 Required shear stress at the atomic scale (theoretical shear stress) τmax = G/2π Therefore, shear stress to flow the material (τ) = 0.9 τmax 0.9 × 45/2π GPa = 6.44 GPa.

Thus, the required specific cutting energy (ϒ) = energy to deform (or strain energy due to shear stress): ϒ =τ2/ G2 =6 44 90 0 4608 2/ = GPaF0 8 MPaF0 8 J/cm3; w where MPa1 =1J/cm 3

Example 3 During diamond turn machining of ductile (copper) and brittle

In this study, we analyze the specific cutting energy of silicon and copper materials, utilizing key parameters such as the rigidity of copper (G Cu) at 45 GPa, a Poisson’s ratio (ν) of 0.28, an inter-planer spacing (d hkl) of 0.288 nm, and an inter-atomic spacing (a) of 0.2556 nm The rigidity of silicon (G Si) is noted to be 5 GPa The machining process is assumed to occur under ductile conditions, resulting in crack-free surfaces, with the diamond tool maintaining a cutting edge sharpness of 200 nm.

Solution 3 In the case of copper, the required shear stress can be calcu- lated using ‘Peierls stress’:

Shear stress to move dislocation (τCu) = G Cu e (–2πW/a) = 45 exp [(–44/7) × (0.4/0.2556)] = 45 × 2.915 × 10 –3 GPa Or, τCu = 131.2 MPa.

Thus, the required specific cutting energy (ϒCu) = energy to deform (or strain energy due to shear stress): ϒCu =τCu 2 /2G Cu 1 2 90 000 0 192 2 / , = MPa=0 192 J/cm 3 ;; where MPa1 =1J/cm 3

Thus, the required specific cutting energy in copper (ϒCu) = 0.192 J/cm 3

Silicon undergoes deformation primarily through ductile shear, allowing it to flow without creating cracks or a substantial number of dislocations Consequently, the shear stress in silicon can be approximated as the theoretical shear stress, calculated using the formula τSi = GSi / (2π^5) and resulting in a value of approximately 158,245 MPa.

Thus, the required specific cutting energy in silicon (ϒSi) = 1,582.45 J/cm 3

In the diamond turn machining of ductile copper and brittle silicon materials, the specific cutting energy is compared using key parameters: the rigidity of copper (G Cu) is 45 GPa with a Poisson's ratio (ν) of 0.28, while its inter-planer spacing (d hkl) is 0.288 nm and inter-atomic spacing (a) is 0.2556 nm For silicon, the rigidity (G Si) is 125 GPa, with a Poisson's ratio (ν) of 0.24, a dislocation width of 0.25 nm, and an inter-atomic spacing (a) of 0.23 nm The machining process is assumed to occur in a ductile mode, resulting in crack-free surfaces, utilizing a diamond tool with a cutting edge sharpness of 5.0 μm.

Solution 4 As cutting edge sharpness of the diamond tool = 5.0 μm, mate- rial deformation will take place because of dislocation movement in both cases.

In the case of copper, required shear stress can be calculated using ‘Peierl’s stress’:

Shear stress to move dislocation (τcu) = G Cu e (–2πW/ a) = 45 exp [(–44/7) × (0.4/0.2556)] = 45 × 2.915 × 10 –3 GPa Or, τcu = 131.2 Mpa.

Thus, the required specific cutting energy (ϒCu) = energy to deform (or strain energy due to shear stress): ϒCu=τcu 2 /2G Cu1 2 90 000 0 192 2 / , = MPa=0 192 J/cm 3

Silicon deforms through ductile shear, allowing it to flow under dislocations without cracking, as the cutting edge radius is only a few microns Consequently, the shear stress can be accurately calculated in this scenario.

Shear stress to move dislocation (τSi) = G Si e (–2πW/a) = 125 exp [(–22/7) × 0.25/0.23] = 4.1 GPa. ϒSi=τSi 2 /2G Si=0 06724 GPag 24 MPag 24 J/cm 3

Sample Unsolved Problems

To calculate the specific cutting energy during the diamond turn machining of an aluminum alloy, we utilize the following parameters: the rigidity of the aluminum alloy (G) is 25 GPa, the Poisson’s ratio (ν) is 0.26, the inter-planar spacing (d hkl) is 0.3 nm, the inter-atomic spacing (a) is 0.25 nm, and the cutting edge sharpness of the diamond tool is 5.0 μm.

To calculate the specific cutting energy during diamond turn machining of an aluminium alloy, we utilize the following parameters: the rigidity of the aluminium alloy is 25 GPa, the Poisson’s ratio is 0.26, the inter-planer spacing is 0.3 nm, the inter-atomic spacing is 0.25 nm, and the cutting edge sharpness of the diamond tool is 50 nm It is assumed that the specific cutting energy at the nanometric scale is 90% of the atomic scale.

In the diamond turning process of ductile materials like aluminium and brittle materials such as silica, the specific cutting energy is influenced by various parameters For aluminium, with a rigidity of 25 GPa, a Poisson's ratio of 0.26, an inter-planer spacing of 0.3 nm, and an inter-atomic spacing of 0.25 nm, the cutting is performed in a ductile mode, resulting in crack-free surfaces In contrast, silica exhibits a higher rigidity of 50 GPa The sharpness of the diamond tool, measured at 100 nm, plays a critical role in optimizing the cutting energy during machining.

Q4 During diamond turn machining of ductile (aluminium) and brittle

This study analyzes the specific cutting energy of silica and aluminium materials by comparing their mechanical properties The rigidity of aluminium is measured at 25 GPa, with a Poisson’s ratio of 0.26 and an inter-planer spacing of 0.288 nm, while its inter-atomic spacing is 0.25 nm In contrast, silica exhibits a rigidity of 50 GPa, a Poisson’s ratio of 0.16, a dislocation width of 0.25 nm, and an inter-atomic spacing of 0.22 nm The machining process is assumed to occur under ductile conditions, resulting in crack-free surfaces, with a diamond tool cutting edge sharpness of 5.0 μm.

Tooling for Diamond Turn Machining

Introduction

The Diamond Turn Machining (DTM) process is a specialized machining technique essential for achieving fine form and surface finishes required in optical applications This precision relies on stringent requirements for cutting tool materials and geometry, as the surface finish is influenced by the chip formation mechanism and deformation near the cutting edge Maintaining uniformity in this mechanism across the cutting path is crucial for consistent surface quality, with tool sharpness at the nanoscale being vital Such sharpness is typically achievable only with single crystal materials like diamond, as polycrystalline aggregates fall short The machined surface's form is also contingent on the tool edge geometry; any deviations from the intended design due to wear or fabrication issues can compromise the final output Therefore, precise fabrication of cutting tools with controlled edge waviness is essential This chapter highlights the necessity for specialized cutting tools in the DTM process, detailing their fabrication, setup in DTM machines, and addressing concerns related to tool wear and the economic aspects of the process.

Tool Materials and Their Requirements

For the DTM (Direct Tooling Machining) process, cutting tools must meet specific requirements similar to conventional machining, including sufficient hardness, toughness, and resistance to wear and chemicals While a variety of conventional cutting tools are available, they often fail to achieve the surface finish required by DTM due to challenges in maintaining the cutting edge's sharpness, smoothness, and uniformity The cutting edge, formed by the intersection of the rake and clearance faces, is characterized by two radii: the nose radius and the edge radius To perform effectively in DTM, the cutting edge must exhibit fine surface finish and precise form tolerance, both along and across its length Typically, the cutting edge spans several millimeters in length but only a few tens of nanometers in width, with circular shapes defined by the aforementioned radii Form tolerance along the edge is often described as waviness, while sharpness across the edge lacks explicit specifications The fabrication of cutting tools for DTM poses significant challenges due to the required precision, with waviness and edge radii dimensions ranging from hundreds of nanometers to tens of nanometers.

Commercially successful cutting tool materials for conventional machining, such as carbides, polycrystalline diamond (PCD), polycrystalline cubic boron nitride (PCBN), and ceramics, consist of aggregates of smaller particles bonded together with a binder These aggregates exhibit fairly isotropic properties due to the random orientation of the individual particulates The microstructure of these poly-granular or poly-crystalline materials contributes to their effectiveness in machining applications.

Schematic explaining nose radius and edge radii in a cutting tool.

Diamond turn machining faces challenges in achieving a smooth cutting edge due to the granular aggregates that create protrusions at the meeting faces, which cannot be effectively smoothed at the nanometric scale A potential solution is utilizing single crystal materials for the cutting edge, as this limits protrusions to atomic spherical forms However, single crystals exhibit anisotropic properties, and many cannot be grown to suitable sizes for cutting tools While materials like carbides, ceramics, and CBN can only reach micrometre sizes, diamond stands out as it can be grown or found in larger sizes, offering excellent hardness and abrasive wear resistance, albeit with varying properties across different crystal planes The anisotropic nature of diamond presents a significant challenge in selecting the optimal crystallographic orientation for cutting edge fabrication, an issue not encountered in conventional machining tool production.

Single Crystal Diamond Tools

Diamond stands out as the most effective single crystal material for cutting tools in the DTM process Both synthetic and natural diamonds are utilized in the production of these tools, with many users expressing a preference for natural diamonds Commercial single crystal diamond (SCD) tools are readily available for purchase, catering to the needs of various companies in the industry.

Schematic explaining the difference between PCD and SCD (a) Single crystal tool and (b) poly crystalline tool.

DTM processes depend on suppliers like the UK-based Contour Diamond and Japan-based ALMT Diamond Corporation for their regular operations These companies also perform relapping on used or worn SCD tools, allowing SCD tool inserts to undergo multiple relaps before they are ultimately discarded.

Diamonds utilized in DTM cutting tools are sourced from either natural deposits or synthetic production, with synthetic diamonds created through a CVD process, offering flat surfaces with known crystallographic planes for precise geometric shaping Natural diamonds, often aesthetic rejects from the jewelry industry, typically come in an unfaceted raw form but may contain defects that hinder their performance as cutting tools Brownish hues in diamonds signify residual stresses that can lead to chipping during machining, while carbon spots indicate a tendency for hole formation in the crystals Additionally, irregularities in natural crystal growth result in property variations, complicating the selection process for tool manufacturers They also face challenges in identifying the correct crystallographic planes and orientations within the raw crystal, necessitating careful fixturing during the processing stages to ensure optimal tool performance.

Single crystals exhibit anisotropic properties due to the unique arrangement of their atoms, and diamond is a prime example Understanding how different crystallographic orientations and directions influence these properties is crucial for selecting the optimal plane and direction for the rake face, flank face, and cutting edge of cutting tools.

Diamond's structure consists of a tetrahedral arrangement of sp³ hybridized carbon atoms, where a central carbon atom bonds with four adjacent atoms In the face-centered cubic (FCC) arrangement of carbon atoms, four tetrahedra are positioned within alternating sub-cubic cells, forming the unit cell of diamond.

This unit cell structure allows for the examination of key crystallographic planes and directions, yet there has been limited exploration into the optimal planes for cutting tool applications Notably, certain diamond planes, particularly the {111}, {110}, and {100} families, have been extensively studied for their properties related to abrasive wear and friction.

The questions that come up then are the following:

• Which of these crystallographic planes should be the rake face of the cutting tool?

• Which of these crystallographic planes should be the clearance faces? Clearance often forms in multiple planes.

Tooling for Diamond Turn Machining

• In which direction on the rake face plane should the cutting edge be fabricated? Cutting edge, often being nonlinear, is normally along, i.e tangential to, multiple directions.

Abrasive wear and the friction coefficient are crucial properties that depend on the crystallographic structure of materials The ability of diamond crystals to resist abrasive wear is essential for effectively shaping them into cutting tools Given that diamond is the hardest natural substance, the most effective method for shaping it involves using other diamonds as abrasives.

Take an FCC arrangement of C atoms; unit cell divided into 8 equal cubes C 1 to C 8

One C-atom placed in sub-cube C 1

One C-atom placed in sub-cube C 3

One C-atom placed in sub-cube C 5

One C-atom placed in sub-cube C 7

Schematic showing how carbon atoms are arranged in a diamond Imagine an FCC cell of

To create a structured arrangement of carbon atoms, divide the space into eight equal cubes Position a carbon atom at the center of four specific cubes (C1, C3, C5, and C7) and establish tetragonal bonds with the three nearest face-centered atoms and one nearest edge atom.

C 5 Family of (111) planes Family of (110) planes Family of (100) planes

In diamond cubic structures, the {111} family of planes is the most resistant to abrasion, with the direction being the hardest to process, making it ideal for cutting tool surfaces despite requiring extensive processing times Conversely, the {100} family of planes is the softest, with the direction being the easiest to abrade Understanding these properties is crucial for the effective fabrication of cutting tools, as it is essential to accurately position and secure the diamond crystal in the optimal plane and direction for enhanced performance Experimental data supporting these findings is readily available.

The friction coefficient is a critical property in cutting tool design, as the cutting edge must be shaped to ensure that chip flow aligns with the direction of the lowest friction While this principle is important, it cannot be strictly applied due to the curvature of cutting edges and the varying chip flow directions during the tool-normal machining process Experimental data, particularly for diamond-on-diamond interactions, can provide some insights, but comprehensive data on the tribological behavior of different engineering materials against diamond in machining conditions is lacking Additionally, the cutting edge radius is a key factor, as it is the most vulnerable part of the tool, prone to micro-fracture and wear, necessitating further research into edge geometries and optimal configurations such as crystallographic planes and directions.

Schematic summarising the various soft crystallographic directions (shown with black arrows) to abrade diamond.

Effective tooling for diamond turn machining, including features like chamfers and lands, is essential for enhancing edge strength and preventing chipping To achieve precise edge control in diamond crystals, it is crucial to address the fabrication challenges associated with these advanced techniques.

The surface finish of diamond tools significantly affects their performance, with crystallographic factors influencing their resistance to abrasive wear and resulting in different roughness patterns For optimal functionality, the rake face of diamond tools should possess a very smooth, sub-nanometric roughness and exhibit isotropic characteristics to accommodate any chip flow direction Achieving this ideal surface finish necessitates multiple polishing processes.

Sub-surface damage caused by the abrasive fabrication process significantly affects the performance of cutting tools in the DTM process This damage can be identified through chemical etching of the diamond in a thermally assisted, oxygen-rich environment Each abrasive method leaves distinct surface patterns and sub-surface stresses Therefore, polishing should be conducted in multiple stages to ensure that the damage from each step is effectively eliminated in the following step.

Tool Geometry

Diamond tools are commercially available in a variety of macro-geometrical shapes – both standard shapes and customised shapes Some common geom- etries routinely used are shown in Figure 4.6.

The most common cutting edge shape is triangular with the nose radius at one apex of the triangle Other edge shapes include:

• Flat rectangular shape used in grooving applications with custom- ised groove widths down to a few micrometres

• Two straight cutting edges meeting at an obtuse angle – used for nano-milling

Schematic showing (top view of the rake face, showing cutting edges) various geometries in which diamond tools are available.

• Single arc cutting edges – used for milling

• Multiple discontinuous connected arcs – used for nano-milling applications

In addition to the advanced cutting profile, key geometrical parameters include Top Rake Angle, Cylindrical/Conical Edge, Tool Nose Radius, Cutting Arc, Offset Angle, Included Angle, Front Clearance, Second Clearance, Primary Depth, Diamond Depth, Total Cutting Height, and Tool Nose Waviness Clearance angles play a crucial role in chiseling complex micro-geometries using fast tool servo (FTS) and slow tool servo (STS) applications, as they limit the cutting tool's interaction with previously machined surfaces While larger clearance angles facilitate the creation of intricate micro-arrays in optics, they can also weaken the cutting edge, which is critical since diamond is brittle and subjected to significant stresses during interrupted cutting Typically, zero rake angles are employed with SCD tools, but negative rake angles are often necessary for machining brittle materials like silicon and germanium to ensure ductile regime machining If a negative rake cannot be achieved within the diamond crystal, the tool holder seating surface can be inclined to achieve the required angle.

The cutting edge must be exceptionally smooth, maintaining a consistent profile with edge profile tolerances typically measured in fractions of micrometers This precision is known as controlled waviness of the tool.

Edge waviness of diamond tools

Controlled waviness Non-controlled waviness

Waviness in the tool nose radius.

Tooling for Diamond Turn Machining

Commercial suppliers also supply tools without the waviness being con- trolled for less demanding applications Any form errors on the cutting tool will duplicate on the machined surface (Figure 4.8).

Diamond Tool Fabrication

The standard configuration of a single crystal diamond (SCD) tool utilized in diamond turning machines (DTM) features a diamond crystal that is brazed onto a tool holder This design is frequently employed in applications such as face-turning, grooving, and ultra-precision milling.

Tool form error gets transferred to the work machined surface.

Schematic of the typical structure of a single crystal diamond tool and holder.

The fabrication of diamond crystals involves several critical steps, including determining the type and quality of the diamond, identifying its crystallographic orientation, and shaping the surfaces to achieve the desired geometry for the rake face, nose radius, and edge radii Synthetic diamonds typically come with a known crystal orientation, while natural diamonds require single crystal x-ray diffraction for orientation identification After positioning the crystal in a specially designed fixture, a diamond abrasive grinding wheel is used to create a flat rake face, followed by grinding the clearance faces with a bonded abrasive wheel The precise creation of the nose radius is executed using a rotating fixture, while controlling edge waviness and polishing techniques, often kept as trade secrets, are refined through experimental methods.

The tool holder, constructed from steel or a molybdenum alloy, is essential for housing the diamond crystal Proper alignment of the nose radius center with the tool holder's center is crucial, along with the correct orientation of the rake face plane relative to the tool holder base To ensure optimal performance, the tool holder is frequently ground and polished for flatness and perpendicularity, and may also be coated with a Ni/Cr finish.

Brazing diamond onto a substrate is crucial for tool fabrication, as the strength of the brazed joint significantly impacts the tool's performance during DTM machining With brazing temperatures often exceeding 1000°C, there is a risk of diamond graphitisation, which can compromise its structure To mitigate this issue, brazing can be performed under lower pressures and in inert gas atmospheres, raising the graphitisation temperature from 1000°C to as high as 1600°C Interestingly, some localized graphitisation at the brazed interface can enhance joint strength While metals do not diffuse into diamond, the formation of stable carbides by adding elements like Ti, Cr, Ta, and Si to brazing alloys facilitates effective bonding These alloys, known as active brazing filler metals, include systems such as Cu-Ag-Ti and Cu-Sn-Ti, enabling successful brazing of diamond to various materials.

Tooling for Diamond Turn Machining or Ni-Cr-B are common brazing filler metals for joining diamonds to met- als and ceramics.

Tool Wear

Diamond tools, like those used in conventional machining, experience wear during the DTM process, impacting the tool's finite lifespan and significantly affecting the economic viability of processing materials such as silicon and germanium Tool wear types in conventional machining include flank wear, crater wear, and edge chipping, but the DTM process is more sensitive to wear, allowing only minimal degradation Unlike conventional machining, crater wear is rare in diamond tools, with edge radiusing, edge chipping, and groove formation being more prevalent High temperatures and carbon atom diffusion lead to accelerated wear of diamond tools when machining ferrous alloys, prompting attempts to mitigate this issue; however, commercial success remains limited Tool wear influences not only the quality of the machined surface but also the cutting mechanism, making ductile regime material removal conditions particularly sensitive to tool degradation.

Tool wear, while observed using scanning electron microscopy, is often measured using optical metrology techniques One such technique used and reported is coherence correlation interferometer (CCI) (e.g Taylor Hobson CCI

The method of measuring variations in interference fringes allows for the assessment of the vertical position of optical elements above the surface being scanned, crucial for analyzing tool wear This technique captures sample images of both new and worn tools, highlighting the importance of tracking the nose radius profile to determine waviness deviations from an ideal circular arc Continuous CCI measurements throughout the diamond cutting tool's life enable the observation of wear progression over machining time, as demonstrated in a case study involving single crystal silicon Here, the waviness increased from approximately 3 μm in the unused state to over 12 μm after 200 cycles, indicating significant edge chipping that deepened and widened along the cutting edge A correlation between the tool's waviness change and machining time underscores the relationship between tool wear and operational duration.

Measuring tool edge radius, typically in the range of tens of nanometers or less, becomes increasingly difficult as machining time progresses Initial estimates have been derived from side images of straight cutting edges obtained through scanning electron microscopy, which only provide measurements of the imaged plane More advanced methods, such as atomic force microscopy (AFM), have been employed to assess the edge radius both directly and indirectly However, challenges arise in locating the edge during AFM measurements, and interactions between the AFM tip and the edge can lead to measurement inaccuracies.

Length = 0.4448 mm Pt = 3803 nm Scale = 10,000 nm

Profile of the nose radius used to determine waviness.

Worn tool is area is magnified in every image to measure and identify the worn area

Coherence correlation interferometry images of a diamond tool edge.

Tooling for Diamond Turn Machining

Progress of waviness with machining time.

Impression of the cutting edge radius

AFM measurements of tool edge radius.

Tool Setting in DTM

Errors in setting the diamond tool on DTM equipment can lead to surface imperfections, notably the ogive error In the traditional DTM face-turning process, the workpiece rotates around the spindle axis, creating an axially symmetric surface from the tool's path The ogive error occurs when the tool path does not align with the central rotational axis, often due to challenges in accurately determining the tool tip height and the center of the tool nose radius.

Summary

Single crystal diamond remains the premier cutting tool in the DTM process due to its exceptional hardness and flexibility, allowing for precise carving of rake faces and cutting edges on specific crystallographic planes This material provides the ultra-sharp cutting edge essential for achieving high optical quality surfaces in various engineering applications While challenges persist in machining ferrous alloys, diamond effectively meets most optical processing requirements However, advancements in producing large single crystals of alternative materials, such as cubic boron nitride for cutting tools, have not been reported, limiting options for processing materials unsuitable for diamond machining.

Tool setting error can lead to errors in the surface generated.

Tooling for Diamond Turn Machining

Unsolved Problems

1 Describe the various steps involved in the diamond tool fabrication process.

2 Conceive the design of a fixture which allows transfer, without loss of orientation, of the diamond crystal from the single crystal x-ray diffraction equipment to the abrasive polishing machine.

3 Draw a thumbnail sketch of a diamond tool and label some impor- tant geometrical parametres.

4 Describe the various soft and hard crystallographic directions of abrasion in the diamond cubic structure.

DTM Process Parametres and Optimisation

Introduction

Diamond turn machining excels in producing optical-quality surfaces with precise nano-regime control over size, shape, and finish It is widely used for manufacturing components in optical molds, astronomical telescopes, IR optics, avionics headgear, and laser optics, utilizing materials such as nickel, aluminum alloy, silicon, germanium, polymers, and copper This machining process requires specific grades and geometries of single crystal diamond tools, along with optimal process parameters like speed, feed, and depth of cut to achieve defect-free surfaces However, the dual challenge of generating flawless surfaces while controlling size and shape, alongside minimizing tool wear, presents significant difficulties in diamond turn machining.

To effectively address these challenges, it is crucial to comprehend the impact of various input parameters on the diamond turning machining process and their significance concerning different output parameters This chapter provides a concise discussion on this topic.

Diamond Turn Machining Process and Parametres

Each diamond turn machine exhibits unique behavior and does not operate uniformly for the same tool-work material combination The natural frequency of the machine, which can lead to chattering, varies between machines, highlighting the necessity to map and optimize the behavior of diamond turn machines under different process conditions The diamond turn machining process typically follows a specific sequence, as illustrated in Figure 5.1, which outlines the various input and output parameters involved.

• Selection of a diamond turn machine whose characteristics like positional tolerance, stiffness, thermal drift etc are known (Known behaviour);

• Material on which the surface is to be generated (Known properties);

• Selection of tool grade, geometry and the crystal orientation suitable for the component geometry and material (Known parametres);

• Clamping method for the work-piece considering elimination of footprint error and stability of holding (Known methods);

• Size, shape and surface finish

• Geometry (TNR, cutting edge radius, rake and clearance angles)

• Fast tool servo parametres Chapter 5

DTM Process Parametres and Optimisation

• Selection of optimised process parametres like speed, feed, depth of cut, cutting direction, coolant, parametres of fast tool servo etc

Following the above steps leads to achieve the below-mentioned outcomes during diamond turn machining:

• Generate surfaces free from cosmetic defects, vibration and ther- mal effects; and control their size, shape and surface finish value (Process should be controlled to achieve this objective)

• Predictable and minimum tool wear (Wear prediction models are essential)

With these objectives in mind, various process parametres and their effects will be discussed in the following sections.

In diamond turn machining, the spindle is responsible for holding either the workpiece or the fly cutter, maintaining a constant speed throughout the process This consistent spindle speed is crucial to prevent acceleration and mitigate the effects of inertial forces on the machined surface Consequently, the cutting velocity varies, starting from zero at the spindle's axis and reaching its maximum at the largest radial distance from the workpiece's axis This controlled spindle speed leads to precise machining results.

The process facilitates material removal through the relative movement between the tool and the workpiece, allowing for the precise achievement of the desired shape, size, and surface finish of the component.

• Enables maintaining the required level of productivity by control- ling the material removal rate.

Diamond turn machining distinguishes itself from other machining processes by not requiring higher spindle speeds to achieve superior surface quality, thanks to its sharp cutting edge For instance, fast tool servo machining operates at just a few revolutions per minute However, to enhance material removal rates, higher spindle speeds are essential Yet, exceeding optimal spindle speeds can lead to increased tool wear, resulting in size and shape variations in the workpiece, as well as altering the material removal mechanism Research has demonstrated the correlation between spindle speed and surface finish across various materials, indicating that surface finish variations are influenced not only by tool wear but also by factors such as induced vibrations and increasing thrust force Consequently, determining the optimum spindle speed necessitates trial machining on specific materials.

Tool wear effect Surface finish

Spindle speed Machine characteristics Vibration effect

Effect of spindle speed on surface finish.

Optimum Spindle Speed for Various Materials

Work-Piece in mm Top Rake Angle in Degrees Tool Nose

Radius, mm Spindle Speed, rpm

DTM Process Parametres and Optimisation

The main goal of diamond turn machining is to accurately shape components to meet specific size, shape, surface finish, and reflectivity requirements by managing the feed path However, this process often results in the formation of micro-helical grooves on the surface, which can negatively impact surface quality Overall, the feed rate plays a crucial role in influencing these factors.

• Unit removal (UR) of material

• Quality of the machined surface in terms of surface finish, vibration effects, etc.

Optimizing the feed rate is crucial for enhancing the material removal rate and reducing cycle time, especially when machining large components or high-volume batches The unit removal of material, proportional to the chip's cross-sectional area, varies with feed, impacting efficiency in the manufacturing process.

Achieving optical quality on machined surfaces is a critical requirement in diamond turn machining To meet this goal, it is essential to regulate several process parameters, particularly the feed rate The surface finish value in any single-point machining process can be quantified using a specific equation.

Surface finish PV( )= f 2 /8R (5.1) where f = feed per revolution and R = tool nose radius.

However, this equation has been modified by many researchers and some of these results are shown in Table 5.2.

Feed force generated during machining increases with feed rate and is given as:

Feed forceF f =C A V f f f =C d b V f f =C d b n f f (5.2) where C f = constant; A f = cross-sectional area of chip; d = depth of cut; b width of chip; V f = feed velocity; n = rotational speed; and f = feed rate.

Increased feed force leads to greater tool wear, resulting in more pronounced size and shape errors on the machined surface As illustrated in Figure 5.3, the feed significantly impacts these outcomes Additionally, Figure 5.4 highlights how both the depth of cut and feed influence the length of the nano-cutting region, as shown in Region 1 Generally, a longer nano-cutting region correlates with a decline in surface finish quality.

(Trends are indicative only) Feed

Effect of feed on various output parametres.

Achievable Surface Finish Values in DTM

Peak to valley, R max = ( f 2 /8R) where f = feed rate, R = tool nose radius [9]

R th = ( f 2 /8R) + t/2 (1 + t R/2) [35] where t = min undeformed chip thickness

R th = ( f 2 /8R) + t/2 (1 + t R/2) + k 1 k 2 r n H/E k 1 = coefficient in relation to the elastic recovery, k 2 = coefficient denoting the size effect, H = Vicker’s hardness, E = modulus of elasticity, r n = tool cutting edge radius

DTM Process Parametres and Optimisation

The depth of cut (DOC) has a minimal impact on surface quality, as illustrated in Figure 5.4, where changes in DOC do not significantly alter the proportion of chip length in the nano-cutting region (Region 1), resulting in consistent surface finish values However, it is important to note that the material removal rate increases with a higher DOC.

The length of the tool shank overhang significantly influences its stiffness and the resulting surface quality of the machined part As illustrated in Figure 5.5, there is a clear relationship between the achievable surface finish and the tool shank overhang Stiffness remains optimal until the overhang exceeds a certain length, beyond which it begins to decrease, leading to a deterioration in surface finish Single crystal diamond tools, known for their brittleness, are particularly sensitive to variations in shank overhang; deviations from the optimal length can result in damage to the cutting edge and even breakage of the tool tip.

Effect of feed and depth of cut on nano-cutting length.

Heat generated at the machining zone is carried away by

The smaller cross-sectional area of the chip allows it to carry away a larger proportion of the heat generated during machining Additionally, diamond tools, known for their excellent heat conductivity, transfer significant heat away from the workpiece To prevent thermal damage to the machined surface, it is crucial to minimize heat transfer to the workpiece while maximizing heat removal through the chip and tool, which is influenced by the materials' volumes and thermal conductivities The most effective method for reducing heat transfer to the workpiece is using coolant, particularly mist coolant, which efficiently removes heat as latent heat The resulting chips are lightweight, longer, and often in powder form, increasing their tendency to adhere to the finished surface and potentially causing damage.

• Adhesion, where part of it gets cold welded to the generated surface and it becomes difficult to remove these chips, without impairing the quality of the surface (Figure 5.6a);

Effect of tool shank overhang on surface finish.

DTM Process Parametres and Optimisation

• Abrasion, which generates digs and scratches on the machined sur- face and causes cosmetic defects (Figure 5.6b);

• Interference, where long chips get curled on the tool and break the tool tip.

To address these challenges, the coolant nozzle is strategically oriented to effectively remove chips from the machined surface, while the coolant is blended with appropriate additives to reduce the adhesion between the chips and the surface being machined.

5.2.6 Clamping Method and Footprint Error

Clamping force can cause unwanted strain on the workpiece, leading to distortion of the machined surface upon removal This elastic deformation, known as footprint error, occurs when the clamping is released In the diamond turning machining industry, there are primarily two methods of clamping employed to mitigate these effects.

• Flexible clamping, either by direct mounting of the work-piece on the vacuum chuck or using a suitable fixture;

• Rigid clamping of the work-piece with a suitable fixture

The first method involves securing the work-piece on the machine spindle with a vacuum chuck This can be done by either directly attaching the work-piece to the vacuum chuck or by mounting a fixture that holds the work-piece onto the vacuum system.

Signal A = SE2 EHT = 2.00 kV WD = 5.8 mm Stage at T = 0.0º Mag = 30.00 KX 1 àm

Chip particles adhered to surface Scratch on work surface

Signal A = SE2 EHT = 2.00 kV WD = 5.8 mm Stage at T = 0.0º Mag = 17.96 KX 1 àm

Adhesion of chips and the presence of digs and scratches on the finished surface can significantly affect the quality of the workpiece Vacuum chuck clamping offers flexibility to accommodate variations in cutting forces due to material inhomogeneity, minimizing shock loading on the cutting edge and enhancing tool life In contrast, rigid clamping holds the workpiece firmly without flexibility, making it the preferred choice for larger or non-axially symmetric components.

Vibration Related Issues

Vibration significantly impacts the surface quality in diamond turn machining, as highlighted in Chapter 2 Both material-induced and machine-induced vibrations affect the interface between the tool and workpiece, leaving distinct marks on the finished surface Key sources of these vibrations include the spindle bearing element and any existing imbalances.

Generated surface Clamp and reaction blocks Fixture

Vacuum chuck Interface Work-piece Spindle

Clamping methods (a) Direct vacuum clamping of work-piece (b) Vacuum clamping of the fixture with work-piece (c) Rigid clamping method.

The DTM process parameters and optimization involve critical factors such as spindle rotation, fluctuations in pneumatic and electrical power supply, table bearing elements, material inhomogeneity, cutting force, and external vibrations Analyzing vibrational signals through power spectral density (PSD) provides insights into vibration sources, with a typical PSD of a diamond-turned surface finish illustrating these effects Initially, machine and process-related factors dominate vibration generation, while tool wear becomes more significant over time Stability lobe diagrams, created from tap testing data, are essential tools for identifying stable speeds based on the specific configuration of the machine, cutting tool, tool holder, and tool overhang.

Thermal Issues in Diamond Turn Machining

During machining, input power is transformed into heat energy, which is then dissipated through the chip, tool, coolant, and workpiece This transmitted heat can adversely affect both the tool and the workpiece, leading to potential damage.

A: Machine tool effect B: Process effect (feed) C: Material effect

The surface finish profile of diamond-turned surfaces is influenced by various factors, including process dominance, machine tool effects, and tool wear Accelerated wear due to pressure and heat in the machining zone can significantly impact the quality of the finished surface If heat is not effectively dissipated from the workpiece, it can compromise the surface integrity, leading to various types of damage.

• Change in the mechanical and metallurgical properties of the sur- face layer including:

• Swelling of material affecting the dimensional tolerance and shape error

The intense heat generated during machining travels with the cutting point, allowing for modeling and visualization of its impact on various materials, which aids in optimization Materials with poor thermal conductivity, such as polymers, experience more significant thermal effects compared to metals like copper and aluminum alloys Additionally, materials with low thermal diffusivity, like germanium used in thermal imaging cameras, are particularly susceptible to thermal damage, necessitating extensive preventive measures to protect the finished optical surface.

• Selecting proper machining sequence for enabling the finishing pass to remove the previously thermally damaged layer;

• Preventing generation of excessive heat due to tool rubbing with the finished surface

The quality of a diamond-turned surface is influenced by various factors that dynamically impact tool wear To achieve optimal surface quality and extend tool life, it is crucial to optimize process parameters Additionally, considerations of vibration and thermal effects are essential in the pursuit of the desired surface finish.

For smaller batch production, extensive experimentation for optimization can be costly, making it essential to utilize existing guidelines and data from the literature Key factors to consider during the optimization process are outlined in Table 5.3.

DTM Process Parametres and Optimisation

This chapter explores the impact of different diamond turning machining parameters on key outcomes such as surface quality and tool life It also highlights important considerations for optimizing these parameters, as well as the effects of vibration, thermal conditions, and clamping methods on the quality of the machined surface.

In diamond turn machining of a convex-hemispherical surface on a 15 mm diameter copper shaft, the diamond tool has a nose radius of 1.5 mm and a cutting arc angle of 120° The Z-axis represents the axis of rotation, while the X-axis indicates the radial direction To find the locus of the diamond tool and the equation of the generated surface, one must determine the initial and final coordinates of the diamond tool during circular interpolation, while neglecting the effects of machine and tool stiffness as well as elastic recovery of the work material.

Radius,R 2 7 5/ = mm radius of the diamond tool,; r=1 5 mm

AB is a circular arc (quarter size of a circle) with center O and radius R; hence, the equation for path AB can be written as:

Work material Fixed by designer

Machine Capacity and capability of the machine

Tool grade and geometry Tool manufacturer catalogue and data base

Method of clamping Footprint error

Speed Stability lobe for the system and tool life

Feed Surface finish and tool life

Depth of cut Tool life and productivity

Coolant and nozzle position Surface quality and tool life

Similarly, the equation of path CD can be written as;

This is the locus of the diamond tool.

The initial point of the tool C = (9,0,0) and the final point of the tool D = (0,0,9).

R o can be written as the value of X at the specified value of Z using Equation 5.3:

Using Equation 5.5 the circle of Figure 5.9b can be written as:

X 2 +Y 2 =( )R o 2 =(R 2 −Z 2 )=>X 2 +Y 2 +Z 2 =R 2 ;orX 2 +Y 2 +Z 2 V.225 This is the equation of the DTM turned surface.

To determine the equation of the diamond-turned surface created by machining a convex-hemispherical copper shaft, we consider a radial misplacement of the diamond tool by 0.010 mm The copper shaft has a diameter of 15 mm, while the diamond tool features a nose radius of 1.5 mm and a cutting arc angle of 120° For this analysis, we neglect the effects of machine and tool stiffness, as well as the elastic recovery of the work material, with the Z-axis representing the axis of rotation and the X-axis indicating the radial direction.

From Figure 5.10a, the equation of the circular path AB can be written as:

(a) Schematic for tool movement along a circular interpolation to machine hemispherical shape and (b) cross-sectional view along M-M on the X-Y plane at a specific Z-value.

DTM Process Parametres and Optimisation

This X can be represented as the radius of Figure 5.10b Hence, the equa- tion of the diamond turned surface can be formulated using Equation 5.6 as

The locus of the diamond tool during the diamond turning process of a convex-hemispherical surface on a 20 mm diameter copper shaft can be determined by considering the tool's nose radius of 1.0 mm and a cutting arc angle of 120° The generated surface equation can be derived while neglecting the influences of machine and tool stiffness, as well as the elastic recovery of the work material In this setup, the Z-axis represents the axis of rotation, while the X-axis indicates the radial direction, facilitating a precise analysis of the machining process.

To determine the locus of the diamond tool for generating a concave mirror on aluminum with a radius of curvature of 300 mm, we consider a mirror diameter of 15 mm and a diamond tool with a nose radius of 2.0 mm, cutting at an arc angle of 120° For this analysis, we neglect the impact of machine and tool stiffness, as well as the elastic recovery of the aluminum material The Z-axis is assumed to be the reference for this operation.

The article discusses a schematic illustrating the tool's movement during circular interpolation to create a hemispherical shape, incorporating eccentric error in the tool's positioning It also provides a cross-sectional view along the M-M line on the X-Y plane at a designated Z-value, with the axis of rotation aligned with the X-axis, which represents the radial direction The analysis aims to determine the initial and final coordinates of the tool's path.

To determine the equation of the diamond-turned surface produced by machining a convex-hemispherical surface on a copper shaft with a diameter of 15 mm, it is essential to account for a radial misplacement of the diamond tool by 0.050 mm The diamond tool features a nose radius of 1.5 mm and operates with a cutting arc angle of 120° For this analysis, we will neglect the effects of machine and tool stiffness, as well as the elastic recovery of the work material, while assuming the Z-axis serves as the axis of rotation.

X-axis is the radial direction.

Summary

This chapter examines how different parameters of diamond turning machining influence outcomes such as surface quality and tool life It also highlights key considerations for optimizing these parameters, along with the impacts of vibration, thermal conditions, and clamping methods on the quality of the machined surface.

Sample Solved Problems

In diamond turn machining of a convex-hemispherical surface on a 15 mm diameter copper shaft, the locus of the diamond tool and the generated surface can be determined by considering the tool's nose radius of 1.5 mm and a cutting arc angle of 120° By neglecting the effects of machine and tool stiffness, as well as the elastic recovery of the work material, we can establish that the Z-axis represents the axis of rotation while the X-axis indicates the radial direction The initial and final coordinates of the diamond tool for circulation interpolation during this machining process can be calculated based on these parameters.

Radius,R 2 7 5/ = mm radius of the diamond tool,; r=1 5 mm

AB is a circular arc (quarter size of a circle) with center O and radius R; hence, the equation for path AB can be written as:

Work material Fixed by designer

Machine Capacity and capability of the machine

Tool grade and geometry Tool manufacturer catalogue and data base

Method of clamping Footprint error

Speed Stability lobe for the system and tool life

Feed Surface finish and tool life

Depth of cut Tool life and productivity

Coolant and nozzle position Surface quality and tool life

Similarly, the equation of path CD can be written as;

This is the locus of the diamond tool.

The initial point of the tool C = (9,0,0) and the final point of the tool D = (0,0,9).

R o can be written as the value of X at the specified value of Z using Equation 5.3:

Using Equation 5.5 the circle of Figure 5.9b can be written as:

X 2 +Y 2 =( )R o 2 =(R 2 −Z 2 )=>X 2 +Y 2 +Z 2 =R 2 ;orX 2 +Y 2 +Z 2 V.225 This is the equation of the DTM turned surface.

To determine the equation of the diamond-turned surface generated from machining a convex-hemispherical copper shaft with a diameter of 15 mm, we consider a diamond tool that is radially misplaced by 0.010 mm The tool has a nose radius of 1.5 mm and operates with a cutting arc angle of 120° For this analysis, we neglect the effects of machine and tool stiffness, as well as the elastic recovery of the work material The Z-axis is designated as the axis of rotation, while the X-axis represents the radial direction.

From Figure 5.10a, the equation of the circular path AB can be written as:

(a) Schematic for tool movement along a circular interpolation to machine hemispherical shape and (b) cross-sectional view along M-M on the X-Y plane at a specific Z-value.

DTM Process Parametres and Optimisation

This X can be represented as the radius of Figure 5.10b Hence, the equa- tion of the diamond turned surface can be formulated using Equation 5.6 as

Questions and Problems

The locus of the diamond tool during the diamond turning process of a convex hemispherical surface on a 20 mm diameter copper shaft can be determined by analyzing the tool's movement, with a nose radius of 1.0 mm and a cutting arc angle of 120° In this scenario, the Z-axis represents the axis of rotation, while the X-axis indicates the radial direction By neglecting the influences of machine and tool stiffness, as well as the elastic recovery of the work material, we can derive the equation of the surface generated during machining, which reflects the precise geometry of the finished convex hemispherical shape.

To determine the locus of the diamond tool for generating a concave mirror on aluminum with a radius of curvature of 300 mm, we consider the specifications: the diameter of the aluminum mirror is 15 mm, the nose radius of the diamond tool is 2.0 mm, and the cutting arc angle is 120° For this analysis, we neglect the effects of machine and tool stiffness, as well as the elastic recovery of the work material, while assuming the Z-axis is aligned appropriately.

The article discusses a schematic illustrating tool movement during circular interpolation to create a hemispherical shape, incorporating eccentric error on the tool It also includes a cross-sectional view along the M-M line on the X-Y plane at a designated Z-value, highlighting the axis of rotation and the X-axis as the radial direction The focus is on determining the initial and final coordinates of the tool's movement throughout the machining process.

To determine the equation of the diamond-turned surface generated after machining a convex-hemispherical surface on a 15 mm diameter copper shaft, we consider the radial misplacement of the diamond tool by 0.050 mm The nose radius of the diamond tool is 1.5 mm, and the cutting arc angle is 120° For this analysis, we neglect the effects of machine and tool stiffness, as well as the elastic recovery of the work material, while assuming the Z-axis as the axis of rotation.

X-axis is the radial direction.

Tool Path Strategies in Surface Generation

Introduction

In the DTM process, generating a new surface requires both cutting and feed motions, similar to traditional machining The cutting motion creates high momentum interference between the tool and workpiece, effectively shearing or fracturing material for removal Typically, the workpiece is mounted on a rotating spindle, while the feed motion supplies new material to the cutting tool at a slower, orthogonal speed The coordination of these two motions in various configurations results in the creation of different geometrical surfaces during the DTM process.

Diamond turn machining produces two main types of surfaces: rotationally symmetric and rotationally asymmetric Rotationally asymmetric surfaces can exhibit fine micro-textured features, such as those found in diffractive optic elements The symmetry axis refers to the central axis around which the part is rotated during the diamond turn machining process Although a surface may appear symmetric initially, it may not be rotationally symmetric; rotating it around the central axis reveals varying surface features at different radial positions.

Rotationally symmetric parts are typically manufactured through conventional turning processes, but DTM (Dynamic Tool Motion) is also capable of producing these components In addition, DTM has evolved to routinely create rotationally asymmetric parts, which necessitate a different coordination of tool and work surface movements When producing rotationally symmetric parts, the tool's position is independent of the part's rotational angle, while for rotationally asymmetric parts, the tool's position is directly linked to the part's angular position on the rotating spindle The following sections will detail the tool paths used for both types of shapes in DTM.

Tool Paths for Symmetric Macro Shapes

The diamond turn machining process primarily utilizes a face turning operation similar to conventional turning methods In this process, the workpiece rotates around the spindle axis while the tool moves perpendicularly to this axis The tool's feed motion typically occurs within a plane that includes the spindle axis, ensuring precise machining.

A typical DTM (Dual Tool Machine) features a 2-axis system that allows for simultaneous control The tool feed motion is generally not synchronized with the spindle rotation, which operates at either a constant speed or in a monotonically increasing manner.

This article illustrates the differences between rotationally symmetric and asymmetric shapes, highlighting an example where a planar surface features off-centered convex lens protrusions Additionally, it discusses a section of the surface filled with tiny features measuring tens of micrometers, emphasizing the intricate details that contribute to the overall design.

Tool feed path motion is in XZ plane

Tool motion path View along Y-axis

Tool motion path for symmetric shapes involves spindle rotation to provide cutting motion while the tool moves in the XZ plane to generate the necessary geometry.

Tool path strategies in surface generation involve adjusting the speed of the cutting tool to maintain a constant tangential speed at its tip This adjustment can lead to the production of features that are naturally rotationally symmetric around the axis In a typical Direct Tooling Machine (DTM) setup, this results in the creation of shapes that are symmetrical about the axis, which can include both spherical and aspherical forms, such as elliptic and parabolic shapes.

To achieve a symmetrical surface, material is systematically removed, starting with the creation of a flat planar face through a face turning operation This process involves removing a disc-shaped volume of material from the workpiece, which occurs in a slowly peeling spiral pattern When visualizing this, imagine the spindle at rest while the cutting tool rotates and moves in a feed motion, tracing a spiral path from the outer edge towards the center This spiral material removal technique is applicable even on curved surfaces, such as spheres, resembling the way one would peel the skin off an orange The mathematical representation of this spiral path can be quantified for precision in machining.

Consider the DTM operation of facing a flat surface such as in Figure 6.3 Assuming that the spindle revolving speed is N (rev/s), and the radial

Total volume of material to be removed

Process can be viewed as the tool moving in a spiral path scratching the stationary work-piece

The face turning operation, a fundamental process in DTM, effectively removes material in a uniform thickness spiral to create symmetrical shapes, such as a planar surface This technique remains applicable even on curved surfaces, like spherical shapes When the tool feed is set at f mm/rev, the cutting tool follows an Archimedes spiral path, represented in polar notation as r = fθ.

The spiral path of the tool can be expressed mathematically as 2πθ, where r ref indicates the starting position from which the tool moves radially inward To determine the x and y coordinates of this spiral path, one can use the origin located at the center of the spindle axis at an appropriate point.

2 (6.3) assuming that the tool starts from an outer point (defined using R ref ) and spirals inwards For the flat surface, z is zero or a constant.

For a spherical surface with radius R, the trajectory forms a three-dimensional spiral This path features a varying z-coordinate, expressed as z = z_ref ± √(R² - r²), where z_ref denotes the reference point from which the tool begins its movement.

The rotationally asymmetrical nature of the feature indicates that z is not dependent on θ For a parabolic surface of revolution defined by a constant value of a, the z-coordinate varies with r, remaining independent of θ.

For practical path execution with a rotating spindle, and radial feed path, set θ = 0 Then r = x, and the controller determines the position x and then based on this, the z-coordinate for tool motion.

For non-analytical surfaces, a method can be implemented by projecting onto a flat surface (XY plane) and utilizing a feed rate in the x-direction to create an Archimedes spiral path This involves identifying a discrete set of points in polar coordinates (r, θ) The z-coordinate at these points is determined using the provided data or a non-parametric relationship By selecting sufficiently close points (r, z) with θ set to zero due to spindle rotation, linear interpolation or alternative methods, such as spline-based interpolation, can be applied to achieve the desired results.

Tool Path Strategies in Surface Generation controller sophistication and encoder resolution) to fill in the gaps between the points for tool movement.

Understanding the concept of spiral motion paths is crucial for visualizing the creation of asymmetrical shapes by synchronizing tool feed motion along the Z-axis with spindle rotation on the C-axis This article focuses solely on finishing path motions, while rough cut motion paths and their related algorithms can be sourced from standard CNC literature.

Tool Paths for Producing Asymmetric Macro Shapes

In this section, we will explore the necessary tool feed motion paths required to create the asymmetrical shape illustrated in Figure 6.1b Specifically, we will examine how to achieve effective cutting motion by rotating the workpiece around the spindle's central axis.

In standard operation of a DTM machine, the spindle's rotational position (θ) is fixed, allowing only for programmed complete revolutions at a specific rate Additionally, the tool feed motion occurring in the XZ plane is independent of the spindle's rotation.

Z-axis If tool motion, in the XZ plane, is represented as a function of time as XZ(t) and spindle motion as θ(t), then under usual conditions, XZ(t) ≠ f(θ(t)) There is a mild form of synchronisation that happens, when the spindle speed is altered based on the X-position of the tool, to maintain constant sur- face cutting speed – however, this form of synchronisation does not involve controllable rotational position of the spindle; it merely changes spindle rota- tional speed with time based on where the tool is.

The DTM machine now features a controllable spindle rotation, introducing a third axis of control (C axis) alongside the X and Z axes, allowing for simultaneous manipulation of all three axes This advancement enables precise control over the angular position of the spindle, represented as XZ(t) = f(θ(t)) As illustrated in Figure 6.4, when the spindle rotates from position θ1 to θ2 at a constant speed, the tool's position can be adjusted from (x1, 0, z1) to (x2, 0, z2) in a coordinated manner This simultaneous control of the spindle's angular position and the tool's coordinates is essential for crafting rotationally asymmetrical shapes, emphasizing the importance of maintaining a variable θ rather than setting it to zero.

The synchronization of the spindle rotational axis (θ) with tool motion (x and z) can be achieved through two methods The first method involves utilizing the existing Z-axis motion slide in the DTM machine to move the entire slide, which holds the tool, in harmony with the spindle rotation Alternatively, the second method introduces an additional W-axis motion for the cutting tool, which operates in conjunction with the existing Z-axis movement, allowing for synchronization of the W-axis with the C-axis.

W-axis in combination with the Z-axis is coordinated with the C-axis

The synchronization of the entire Z-axis slide is referred to as slow tool servo, which is ideal for creating rotationally asymmetric features In contrast, coordination of a high-speed short-stroke W-axis is known as fast tool servo, essential for producing micro-features Recent advancements have introduced hybrid methods that effectively combine both the Z-axis slide and fast tool servo for enhanced performance.

The slow tool servo (STS) concept utilizes the existing motion of the Z-axis slide to synchronize with spindle rotation, enabling the creation of rotationally unsymmetrical features on a work surface This innovative surface generation technique is effective for surfaces with gradual changes in features For example, consider a flat circular disc featuring a hemi-cylindrical protrusion with an exaggerated radius R along its diameter, illustrating how the cylinder typically blends into the disk.

Schematic illustrating spindle synchronisation with X and Z axes As the spindle rotates from angle θ 1 to θ 2 , simultaneously the tool position can be changed from (x 1 ,0,z 1 ) to (x 2 ,0,z 2 ) synchronously.

Tool Path Strategies in Surface Generation surface with another concave fillet radius (not shown here) Clearly this fea- ture is rotationally not symmetric.

To create the desired surface, the tool can be visualized as following a spiral motion path, with the z-coordinate varying based on the angle θ around the Z-axis The origin is positioned at the center of the flat region of the disc, and as the spindle rotates by an angle of 2α, the tool traces a helical path from A to C During the rotation along arc CC, the tool maintains a constant z-position at z = 0 Subsequently, it continues along the helical path CA, where the z-coordinates vary, before returning to a nearby point A” with a constant z = 0 The coordinate changes as the tool moves from point B to B1 on the cylindrical surface can be expressed through specific equations.

Tool moves from B to B 1 for a rotation θ

B 1 lies on circle z 2 + y 2 = R 2 Hence, F 1 B 1 = √(R 2 – x 2 tan 2 θ)

The article describes a hypothetical rotationally unsymmetrical surface featuring a flat disc with a hemi-cylindrical protrusion extending along its diameter The protrusion's radius is exaggerated for clarity, although in reality, it is typically larger and smoothly transitions into a concave fillet radius that connects to the disc.

In the context of cylindrical protrusions, the relationship is defined by the equation Z = R² - x² tan²θ, where R represents the radius and θ is the angle set to zero when the cylinder's axis aligns with the XZ plane during rotation Achieving this motion requires synchronizing the spindle rotation with the Z-axis, as the controller monitors the rotational angle and calculates the corresponding x- and z-coordinates accordingly.

In the context of slow-tool servo motion for cutting tool path generation, sampling points for non-analytical surfaces in symmetrical shapes are crucial As the spindle rotates, the z-direction movement of the cutting tool must be controlled using these sampling points and their interpolation Two common methods for selecting these points during spindle rotation are the constant angle sampling strategy (CASS) and the constant-arc-length sampling strategy (CLSS) CASS involves selecting equal angular increments, where the intersection of the Archimedes spiral with these angles serves as sampling points This method leads to a denser concentration of points near the center and a sparser distribution further out, with point density varying based on radius Employing a finer angle is essential for minimizing error in the cutting process.

Constant angle Constant arc-length

# of points per revolution = 360/∆θ # of points = spiral arc length/∆s

Two types of azimuth sampling methods.

Tool path strategies for surface generation often lead to an excessive number of redundant points near the center during interpolation between peripheral points Although easier to implement, the CASS method generates a high volume of point data for large optics, which can overwhelm CNC controllers and reduce spindle speeds due to the increased number of points per spindle revolution A viable solution to this issue is the constant arc method, which selects samples based on equal arc-length spacing along the spiral path, effectively optimizing data handling and improving efficiency.

Implementing the constant arc method presents challenges due to the varying number of points per spindle revolution based on the tool's position Recent advancements in sampling point selection, such as the combination of CASS and CLSS methods, have emerged These sampling strategies and interpolation techniques significantly impact surface accuracy, particularly in slow and fast tool servo systems.

Tool Paths for Producing Micro-Features

The slow tool servo system enables the creation of axially unsymmetrical features through a rotational cutting motion around a fixed axis; however, it faces limitations due to the synchronous movement required between the Z-axis slide system and the rotating spindle C-axis The Z-axis slide system, comprising the table, tool fixture, and tool, has significant mass, making it challenging to execute rapid back-and-forth motions Such quick movements are essential for generating features with steep slopes or small sizes, known as micro-features This is exemplified in Figure 6.7, where the left feature, larger with gradual slopes, shows minimal change in the Z-coordinate during tool traversal, while the right feature, smaller with sharper slopes, exhibits a more pronounced Z-coordinate change over a narrow spindle rotational angle.

For efficient and rapid Z-direction movements of the cutting tool during brief spindle rotations, implementing a dedicated actuator for the tool is advisable This approach allows for the movement of a smaller mass, rather than the entire Z-axis slide system, enhancing performance The proposed system incorporates an additional small parallel motion along the Z-axis, optimizing the cutting process.

W-axis) and being synchronously controlled with the C-axis, is called the fast tool servo (FTS) system.

The FTS system, often sold commercially as an attachment to the DTM machine, allows rapid acceleration and deceleration of the cutting tool in the

Z-axis to move synchronously to the fast rotating spindle C-axis that provides the needed cutting motion Such rapid motions are commonly achieved with a piezo-actuated linear actuator system on which the cutting tool and holder can be mounted (Figure 6.8).

A typical commercial system features a W-axis travel of several hundred micrometers at a frequency of approximately 200 Hz, allowing for a movement of around 300 micrometers along the Z-axis in just 5 milliseconds With a spindle rotational speed of 1000 rpm, the tool can retract and advance by 300 micrometers during a 6° spindle rotation, enabling precise handling of sharp slopes in machining applications.

Small micro-features, like those shown on the right, are produced through rapid back-and-forth movements of the Z-axis and C-axis, necessitating shorter angular swings This contrasts with the larger, small-slope features depicted on the left, which require different motion dynamics for their generation.

FTS in a DTM machine setup.

Tool path strategies in surface generation are essential for creating complex micro-array features The FTS system has proven effective in generating these intricate designs on DTM machines, making it suitable for various optical applications.

Newer strategies that combine FTS and STS systems [44] and those with long-stroke, multi-axis adaptations of the FTS (explained later in Chapter 9) have also recently evolved.

Tool Normal Motion Path

The cutting tool edge profile and its uniformity are essential for preserving the machined surface geometry Cutting tools can be acquired with either controlled or uncontrolled waviness in their cutting edges, where uncontrolled waviness results in varying edge-profile errors Tool wear further alters the cutting edge profile, leading to deviations from the intended machined surface To mitigate these errors, additional axes of motion, such as rotational movement around the Y-axis (B-axis), can be employed Implementing tool-normal cutting motion allows for consistent contact of the cutting edge with varying surface curvatures throughout the tool's motion path.

Ensuring that the same region of the cutting edge maintains contact, throughout the motion path.

The normal motion tool necessitates synchronization between the B-axis, X-axis, and Z-axis, enabling the tool to move effectively in the Z-plane while tracking the surface normal This alignment ensures that the tool's orientation remains consistent with the surface, allowing the same area of the cutting tool to maintain contact throughout its motion path This approach offers several significant advantages.

Uncontrolled waviness in tools can lead to a consistent cutting region, which helps maintain a uniform work surface This stability ensures that any variations in the cutting edge do not negatively impact the machined surface quality Furthermore, since this error is fixed, it may even be possible to compensate for it effectively.

• In case of controlled waviness tool, having a B-axis rotation helps in utilising different regions of the cutting edge and hence spread the wear evenly leading to longer tool life.

Deterministic Surface Generation

All mechanical machining, grinding, and polishing processes involve material removal through a scratching action, which requires the tool or workpiece to move in a specific direction and speed In machining and grinding, this motion typically follows a consistent direction, often achieved through rotation, leading to observable scratches on the surface known as the lay pattern Surface grinding creates straight line grooves, while face turning produces a spiral scratch pattern, reflecting the tool's spiral motion path.

Lay patterns caused by deterministic tool motion paths The patterns are scratch marks caused by abrasive/tool motion paths.

Tool path strategies in surface generation create specific lay patterns on a component's surface, resulting from deterministic surface generation influenced by the tool's motion paths These predetermined paths lead to anisotropic surfaces, meaning the surface characteristics vary depending on the observer's direction Consequently, the topology of the surface appears distinct when viewed from different angles.

Surface frequencies can negatively impact performance in visible optics, while their effect in infrared optics may be less significant This interference arises from the interaction of wavefronts with various spatial frequencies on the surface Surface roughness is typically assessed using a surface profiler, which can collect spatial data closely enough to identify these frequencies through Fourier analysis, allowing for the evaluation of power spectral density (PSD) For instance, a flat optical component machined at a feed rate of 4 micrometers per revolution will show a PSD peak at a spatial frequency of 250 mm⁻¹ Surface frequency components are categorized into low spatial frequency (LSF), mid-spatial frequency (MSF), and high spatial frequency (HSF), with LSF characterized by parameters like form and power, HSF defined by roughness, and MSF involving waviness, ripple, smoothness, and slope errors.

Deterministic tool motion paths can lead to the formation of mid-spatial frequencies (MSF) on produced surfaces The presence of these MSF can cause various optical effects, including hazing, a subtle decrease in the range of shades in darker areas, and uneven texture in out-of-focus regions of an image.

MSF errors arise from the rapid formation of desired shapes on workpieces, but they can be minimized through the use of arbitrary motion paths during surface scratching for material removal Loose slurry abrasive polishing processes effectively achieve these random motions, allowing for slow form generation while eliminating MSF on surfaces Consequently, visible optical components typically undergo polishing after direct-to-metal (DTM) processes, whereas infrared optical components may not require additional processing if tolerances are lenient To address deterministic marks and mitigate MSF's impact on optical performance, fast tool servo systems are adapted to incorporate random motions alongside regular sliding movements.

Summary

This chapter explores the tool motion paths utilized in the DTM process for generating various optical surfaces The face-turning process, commonly employed in DTM, can be represented as an Archimedes spiral motion, resulting in axially symmetric features By synchronizing axis movements, both large gradual-slope and small micro steep-slope non-symmetric features can be produced with STS and FTS systems Additionally, the tool motion paths in DTM inherently create deterministic surfaces with mid-spatial frequency components While FTS systems can help minimize errors, subsequent polishing is often necessary, especially for visual optics components.

Randomised loose abrasive polishing processes

Slow process to generate form and finish

Highly deterministic tool path scratching in SPDT

Faster process to generate form High MSF error

Low and high MSF errors are related to the type of ultra-precision machining processes.

Tool Path Strategies in Surface Generation

Questions and Problems

1 Explain and differentiate slow tool servo and fast tool servo systems in a diamond-turn machine.

2 Why is spindle-axis synchronised movement needed to generate rotationally asymmetric parts in a diamond-turn machine?

3 Describe the various spatial frequencies on a surface and their con- sequences on optical performance.

4 Correlate MSF and tool motion paths.

5 A hypothetical surface to be generated using a slow tool servo sys- tem is shown in Figure 6.13 The surface is a cylindrical disk with a right-angled half-cone protrusion lying with its axis along one of the radii Write the generic coordinate variation for X and Z as a func- tion of rotational angle θ for a finish turning pass on this surface.

Application of DTM Products

Introduction

Ultra-precision machining has revolutionized the manufacturing of large optical elements, such as mirrors and lenses used in astronomy, which were once crafted manually, requiring significant time and expertise The introduction of precision machining techniques, including diamond turn machines, has transformed the finishing process into a deterministic operation, enhancing quality and significantly reducing cycle times This advancement has not only benefited the production of optical components but has also opened new opportunities in the biomedical sector Additionally, the demand for ultra-precision components in aerospace and military applications has driven the development of specialized machines capable of creating complex surfaces with exceptional accuracy The advancements in precision machining equipment, particularly diamond turn machines, have enabled the widespread use of polymer optics in everyday and advanced applications This chapter explores the diverse applications of diamond turn machining across various industries.

Diamond Turn Machining Applications

Diamond turn machining caters to a wide range of application areas Major groups of components that can be machined by DTM are categorised as follows:

• Metal molds for polymer optics

Diamond turn machining (DTM) is essential for producing a diverse range of components, particularly in optics, which include both polymer and metal types For small batch production, polymer optics are directly machined using DTM, while metal molds machined by DTM facilitate high-volume polymer optic production In contrast, metal optics rely solely on machining techniques without molding This precision machining method is widely applied to UV, broadband, and IR optics, as well as to ultra-precision components where stringent size control, shape accuracy, and surface finish are critical.

Applications in the Optical Domain

Optics can be categorized by their construction materials, light behavior on surfaces, and wavelength domains The classifications of optics produced through diamond turn machining are illustrated in Figure 7.1, while Figure 7.2 presents the fundamental optical elements amenable to this machining technique Additionally, Table 7.1 summarizes the characteristics of these optics along with the necessary diamond turn machining facilities for their production.

The following equation describes the functional relationship between optical scattering and surface roughness [45]:

Light rays Focal point Fresnel lens

The equation defines total integrated scattering (TIS BP) as a function of several variables: R 0 represents the theoretical reflectance of the surface, R q denotes the RMS roughness, θ i indicates the angle of incidence, and λ is the wavelength of light.

As the wavelength decreases, the scatter on optical surfaces increases, making it essential for surfaces intended for visible range applications (400 to 700 nm) to maintain a lower surface roughness value.

Diamond Turn Machineable Optical Elements

Spherical lens Focuses light into a point (projection, collimation, imaging, ophthalmic) [radius of curvature, shape error]

Cylindrical lens Focuses light into a line (beam shaping and ophthalmic) [radius of curvature, shape error]

Aspherical lens Reduces or eliminate spherical aberration and astigmatism (ophthalmic, projection, collimation, imaging)

(reflection) It has periodic structures like grooves to diffract light into several beams travelling in different directions (beam splitter, beam shaper, hologram) [groove shape accuracy, spacing, depth]

2-axis DTM With fly cutting

(transmission) Reduces spherical abrasions (collimation, e.g light house, collection, e.g solar collector, low cost magnification) [focal distance, diameter, prism width, wedge angle, collecting angle]

Aspherical diffractive optics It has diffractive features on aspheric surface

Removes spherical and chromatic abrasions (imaging, broadband illumination sources) [sag at any radial distance, conic constant, curvature, aspheric terms, groove shape accuracy, spacing, depth]

Lenslet array Concave or convex spherical or aspheric micro lenses in a plane (Shack–Hartmann sensor, beam homogenisation for projection systems) [aspheric parametres, pitch]

3-axis DTM Fast tool servo

Freeform optics Non-symmetric surface forms (LED reflector, HUD, progressive spectacle, torics, off-axis parabola) [free form shape parametres]

3-axis DTM and slow tool servo(or) 4-axis DTM with fly cutting

The application of DTM products varies significantly across different wavelength ranges, particularly in the infrared (IR) range of 700 nm to 1 mm and the ultraviolet (UV) range of 10 nm to 400 nm Surfaces designed for 193-nm wavelength applications must be significantly smoother than those for visible applications to meet the same scattering specifications Diamond turn machining excels in producing surface roughness of less than 5 nm, effectively satisfying the requirements for both visible and IR applications However, for UV applications, additional super finishing may be necessary to minimize scattering further.

Polymer Optics Products

Polymer optics encompass a variety of applications, including LED optics, light reflectors, freeform optics, infrared optics, imaging optics, display optics, and street light illumination Additionally, they play a crucial role in IR and UV optics as well as ophthalmic lenses Typical examples of these polymer optics can be seen in Figure 7.3a and b.

Mold Inserts for Polymer Optics

Metal molds play a crucial role in the injection molding process for mass-producing polymer optics The high-quality components required for optical products necessitate an exceptionally accurate and precise manufacturing process for the molds Consequently, the master mold must be crafted with meticulous attention to detail, ensuring optimal size, shape accuracy, and surface finish To enhance durability, electroless nickel with a higher phosphor content is applied as a coating, typically ranging from 250 to 500 microns, on steel or stainless steel substrates, which are subsequently diamond turned for superior precision.

Polymer optics products come in various sizes, including both small and large components These optical elements, as outlined in Table 7.1, are typically manufactured using metal molds To create intricate mold inserts through Direct Tooling Manufacturing (DTM), specialized accessories such as slow tool servo and fast tool servo are employed.

Metal Optics

Metal optics is a significant field where Diamond Turning Machining (DTM) plays a crucial role Reflective mirrors, essential for applications such as lasers and astronomy, are typically crafted from materials like copper and aluminum alloys These mirrors, often designed as conic sections, demand precise control over both shape and surface finish The manufacturing process utilizes advanced 2- or 3-axis diamond turning machines to achieve the necessary specifications.

IR Optics

Infrared and near-infrared optics play a crucial role in night vision and thermal imaging across diverse sectors such as defense, aerospace, automotive, and medical fields Primarily, these optics are of the transmission type, though reflective IR optics are utilized in certain applications Most infrared optics are crafted from semiconductor materials, including silicon and germanium, with a smaller number made from glass and polymers.

Typical metal optics (a) Typical off-axis parabolic mirrors (b) Typical planner aluminium alloy mirror (c) Large size aluminium alloy mirror for space application.

Diamond Turn Machined Ultra-Precision Components

Precision optics demand stringent control over form, figure, and finish, while numerous engineering products prioritize size control as a key requirement Additionally, many engineering items, such as drums for flat-screen TV panels and high-precision ball bearings, necessitate both shape and size control Figures 7.6a, b, and c illustrate various engineering products that have been finished using diamond turn machining.

Major Diamond Turn Machining Application Areas

Diamond turn machining is extensively used in three major areas, namely, aerospace and defence, industrial and biomedical applications [46,47] Table 7.2 shows the major areas and some specific applications.

Typical IR optics (a) Typical germanium optics (b) Typical silicon optics (c) Typical silicon diffractive optics.

Typical diamond turn machined industrial products (a) Typical linac cavity (b) Typical flat precision spacer (c) Typical light concentrator with flange.

DTM's most popular products encompass a diverse range of optical and medical devices, including HUD lenses, astronomy mirrors, high-precision image intensifier tubes, and intraocular cataract lenses (IOL) They also offer low vision aids, mobile camera lenses, night vision goggles, progressive lenses, orthopedic ball-socket joints, hip joints, knee joints, and components for nuclear fusion.

Materials Machinable by DTM

Diamond turn machining is an efficient process applicable to metals, polymers, and crystals, allowing for precise finish machining that achieves the desired surface finish and shape while minimizing tool wear Some of the most commonly used materials in this technique include various metals and synthetic polymers.

Metals that can be diamond turn machined are

Copper, brass, aluminum alloys, electroless nickel, bronze, copper beryl- lium, tin, antimony, silver, gold, zinc, magnesium, lead and platinum.

Polymers that can be diamond turn machined are [48–50]

PMMA offers excellent chemical and scratch resistance, while polycarbonate is known for its impressive impact strength and temperature resistance Polystyrene stands out for its low cost and high transparency Polyetherimide provides high thermal, chemical, and impact resistance along with a high refractive index Cyclic olefin copolymer boasts a high modulus and low moisture absorption, and cyclic olefin polymer is characterized by its completely amorphous structure and high chemical resistance Additionally, nylon and acrylonitrile butadiene styrene are notable materials in this category.

Application Areas of Diamond Turn Machining

Aerospace and Defence Industrial Biomedical

Missile system Laser Dental imaging

Heads up display (HUD) Heads up display (HUD) Medical imaging

Helmet mounted display (HMD) Automotive Molecular imaging

Security Display and projections Medical laser devices

Biometrics Solar energy Hip joint

Crystals that can be diamond turn machined are [48,49]

Barium Fluoride (BaF2), Cadmium Telluride (CdTe), and Cesium Bromide (CsBr) are key materials used in various optical applications Additionally, Cesium Iodide (CsI) and Chalcogenide Glass play significant roles in photonics Other important compounds include Gallium Arsenide (GaAs) and Germanium (Ge), which are crucial for semiconductor technology Lithium Fluoride (LiF) and Magnesium Fluoride (MgF2) are known for their optical properties, while Potassium Bromide (KBr) and Potassium Chloride (KCl) serve in infrared applications Silicon (Si) and Sodium Chloride (NaCl) are widely utilized in electronics, and Thallium Bromoiodide (KRS-5) is notable for infrared optics Lastly, Zinc Selenide (ZnSe) and Zinc Sulfide are essential materials in laser technology and imaging systems.

Summary

This chapter explores the diverse applications of diamond turn machining (DTM), emphasizing its significance in optical machining Key applications include polymer optics, mold inserts, metal optics, and other ultra-precision engineering products It also outlines the various optical elements and materials such as metals, polymers, and crystals that can be effectively diamond turned.

DTM Surfaces – Metrology – Characterization

Introduction

Precision engineering encompasses two essential aspects: deterministic fabrication and error-free metrology A prime example of this is diamond turn machining (DTM), which highlights the importance of ensuring that fabricated components meet both dimensional accuracy and surface quality standards within specified tolerances.

A major branch of qualification of DTM-generated components involves surface metrology and surface characterization Often these two terms, metrology and characterization, are used without differentiation in between

[51] However, it is pertinent not to complicate these issues This can ably be done by a comprehensive discussion and clear understanding of the surface features as per desired quality criteria.

Metrology involves measuring the geometrical and surface features of manufactured components, while characterization takes a comprehensive approach to evaluate how these features deviate from specifications This analysis considers the interrelationship of features and provides insights for potential reductions through process optimization The importance of qualifying precision surface quality, in relation to geometrical specifications and surface characteristics, is illustrated in the precision component development cycle by DTM.

DTM enables the rapid and efficient production of high-precision surfaces However, similar to other precision machining methods, it is essential to qualify and quantify the results of the DTM process to ensure accuracy and reliability.

DTM-generated precision surfaces are evaluated based on their dimensional accuracy and surface quality criteria This assessment determines whether the components meet specified geometrical dimensions within the required tolerances Figure 8.2 illustrates the standard evaluation methodology for precision components produced through DTM.

Apart from the departures from the geometrical dimensions (as indicated in Figure 8.2), the features of DTM-generated precision components and

Qualification Precision optics – Opto-mech modules – Mech modules

Waviness – figure error (ΔZ vs X in terms of Pt, Pq)

Surface finish (roughness in terms of Ra, Rt)

Form – shape error (in terms of ΔR, ΔK)

Evaluation outline of DTM-produced precision components and surfaces.

DTM Surfaces – Metrology – Characterization surfaces depart from the prescribed surface parametres [52] in terms of form, figure and finish quality criteria (Figure 8.3).

The primary surface feature detected by a scanning probe is the smoothness or roughness, which is essential for surface analysis Following this, the examination of the deviation of the surface's fabricated locus from its intended locus provides insights into shape and figure errors.

Global DTM operations primarily focus on creating rotationally symmetric surfaces through turning and facing techniques These processes are recognized for producing near-accurate surfaces that adhere closely to specified nominal values, ensuring high precision and maintaining surface quality within designated tolerances However, various factors contribute to significant inherent processing errors in DTM processes, with major issues affecting surface quality stemming from material inconsistencies.

DTM turnable precision conics A, spherical; B, elliptic; C, parabolic; and D, hyperbolic profiles.

The curved line shows the desired profile; the double dimpled curve shows the waviness; the second double dimpled curve shows the waviness with roughness spikes.

This chapter primarily addresses the measurement challenges associated with surfaces generated by DTM, while also acknowledging the significance of work-piece characteristics, machining parameters, tool geometry, tool placement, and machining and metrology protocols, which are discussed in greater detail in other sections of the book.

Surface Quality

The study of surface errors requires both qualitative and quantitative analysis, particularly for precision surfaces produced by DTM processes, which include planes, spheres, and conics Designers formulate the geometry and surface features based on the intended performance of each component within the overall system However, any variations in geometry and profile can significantly impact performance, making it essential to understand the dimensional parameters and surface characteristics, as well as the errors that may arise Specifically, DTM-generated precision conic surfaces are characterized by their radius of curvature, conic constant, and useful aperture, which can be expressed in terms of sag (z) relative to the useful aperture (r).

The base curvature of a surface, denoted as 'c', is the inverse of its radius of curvature at the vertex The conic constant 'k' plays a crucial role in defining the surface's shape, where a positive value indicates an oblate ellipsoid rotating around its major axis, while a negative value between -1 and 0 signifies a prolate ellipsoid rotating around its minor axis.

0 (sphere); –1 (parabola), < –1 (hyperbola); while A i corresponds to the con- stants of higher order conic terms.

The conic is defined by the locus of tool interaction on the workpiece around its rotational axis, influenced by its base radius of curvature (RoC) and conic constant k In the design and machining process, various issues can arise, both practically and theoretically Changes in the designated base radius or the desired conic constant, or both, can lead to unintended results This may result in a surface that deviates significantly from the intended design or a surface that only partially meets the desired specifications.

DTM Surfaces – Metrology – Characterization profile error popularly known as form error The genesis of this form error and its elimination/reduction is discussed elsewhere in this book.

Optimizing the DTM process helps maintain the specified values of RoC and k within acceptable tolerance ranges, significantly reducing form error However, the surface profile may still deviate from the desired locus, exhibiting variations in the number of peaks and valleys, as well as their amplitudes and spatial distributions across the useful aperture These deviations in peaks and valleys can greatly impact surface quality and overall performance DTM practitioners often combine these two types of surface errors—form error and figure error—into a broader category known as "waviness."

The DTM process excels in achieving superior surface smoothness compared to other physical material removal methods, thanks to its controlled machining forces and reduced vibrations However, even with these advantages, DTM-generated precision surfaces exhibit minimal roughness, referred to as finish error This roughness arises from inherent irregularities in the production process, such as cutting tool characteristics and feed rates, and is also influenced by the material composition and heat treatment.

In DTM-generated surface texture evaluation, it is essential to distinguish between form error, figure error, and finish error Form error refers to the overall deviation of the surface shape from the intended design, while figure error involves the presence of peaks and valleys that deviate from the datum while maintaining the basic shape Roughness is characterized by localized amplitude variations from the peaks and valleys within a specified sample length Understanding the transition point where waviness decreases and finish error begins is crucial for single-point diamond turning teams, as is recognizing when roughness starts to affect waviness.

Quantification of Surface Errors

Identifying surface errors is straightforward, but quantifying them in universally accepted terms poses a significant challenge This process requires precision to eliminate any potential for error during derivation, analysis, and optimization.

To ensure a consistent evaluation of surface quality, a standardized approach is essential This involves the introduction of a comprehensive set of parameters, each with distinct definitions and clear boundaries Notably, surface texture parameters play a crucial role in characterizing surface quality by measuring both waviness and roughness effectively.

Surface Texture

Understanding surface texture is crucial for classifying and quantifying various parameters of surface characteristics Surface texture refers to the deviations from the intended surface profile, influenced by the machining method, material, and final application This deviation profile, which varies in frequency and magnitude, defines the 'lay' of the machined surface and encompasses form error, figure error, and finish error To effectively quantify surface profile errors, it is essential to define and explain the various parameters of surface texture The science of surface characterization integrates multiple disciplines, yet its methodologies are often overlooked Key questions must be addressed before characterizing a surface, including the machining process used to create the precision surface and the geographical location of the surface in question.

Lay (Direction of dominant pattern)

3-D perspective of DTM surface with lay, waviness and roughness.

DTM Surfaces play a crucial role in metrology and characterization, focusing on their intended deployment It's essential to consider whether these surfaces will work alongside other precision surfaces Additionally, understanding the specific application area for these precision surfaces is vital Finally, the processes involved in utilizing DTM Surfaces significantly contribute to their effectiveness in various applications.

The choice of characterization methodology and equipment is primarily influenced by the answers to initial queries Historically, the location of surface characterization activities determined the preferred surface parameters; for instance, average roughness (Ra) was favored in the United States, while mean roughness depth (Rz) was more common in Europe However, with the global development and distribution of precision products, geographical considerations have diminished in importance Despite this shift, quality criteria remain intact, leading to a rise in popularity for certain surface texture parameters while others have become obsolete The pursuit of improved surface quality continues and is expected to intensify in the future.

Diamond turning is a key precision fabrication technique used to create high-quality surfaces for various applications, particularly in optics While most diamond-turned surfaces are utilized in optical systems, they also serve critical roles in consumer instrumentation, security, biomedical devices, automotive instrumentation, societal tools, avionics, and strategic sectors To assess the surface texture of these diamond-turned components, a contact profilometer is commonly employed, which scans the machined surface using a stylus of specific geometry.

A contact profilometer utilizes a diamond or ruby stylus mounted on a scanning arm to measure the surface profile of precision-machined components, including various shapes such as planes and conics During the scanning process, the stylus moves linearly across the surface, detecting vertical displacements caused by imperfections This data is then compared against the intended surface profile, specifically analyzing the sagitta (depth) values against aperture values The resulting error profile highlights discrepancies between the actual and designated profiles, providing insight into the texture variations of the surfaces.

A well-chosen combination of stylus geometry, stylus scan logistics, compatible profilometer electronics, standardized metrology protocols, and suitable surface analysis software is essential for accurately computing the surface texture of precision machined surfaces While contact profilometry offers significant advantages in surface metrology, it is also important to consider its drawbacks for a comprehensive assessment of surface characterization Further details will be provided later.

Surface Texture Parametres

The surface texture of any precision machined component can be defined into two broad constituent components in terms of their spatial wavelengths [55–59].

Longer wavelengths create the 'waviness' realm, influenced by macro-level factors, whereas shorter wavelengths fall into the 'roughness' domain, resulting from the tooling and machining processes.

Waviness and roughness of surfaces can be effectively controlled by the quality of tooling and the skill level of the operator, as well as the functional requirements of the components In addition to spatial wavelengths, the frequencies and magnitudes of deviations from a baseline significantly influence surface texture quantification The precision machining and metrology community has introduced over 100 parameters to describe surface texture, making it essential to approach the quantification of surface texture with caution and foresight, considering factors such as machining processes, measurement methods, and application contexts.

DTM Surfaces play a crucial role in metrology and characterization, as the precision of the surface significantly influences the expression of its texture It is essential to consider specific parameters that consolidate all surface data into a single value, highlighting the importance of careful application and interpretation to ensure accurate results.

To grasp the quantified aspects of precision machined surface texture, it is essential to understand the relevant surface texture parameters This discussion will encompass the origins, applications, popularity, and common usage of surface parameters and attributes Given that many DTM-processed surfaces are typically analyzed using a stylus-based profilometer, we will delve into the terminology associated with surface characterization in detail.

Surface: The boundary of the processed work-piece medium, which separates from the surrounding medium.

Profile: A two-dimensional slice through an area of the machined surface.

Surface texture: The topography of a surface composed of cer- tain deviations (including roughness and waviness as discussed earlier).

Parametres: The features of the surface texture expressed in terms of either the occurrences of profile departures (from the locus of the profile) or in terms of their magnitudes.

The filtration process is essential for selecting specific wavelength ranges of surface profile deviations, effectively isolating peaks and valleys This methodology for surface profile characterization relies on a well-defined filtration technique that assesses the magnitudes and spatial distributions of these features along the profile's locus Specialized software codes, designed specifically for profilometers, facilitate this filtration process, ensuring accurate surface characterization.

The primary profile is obtained by eliminating the surface form from the surface profile, capturing all deviations from the intended profile This includes both large wavelength figure errors and small wavelength roughness The primary profile serves as the foundation for assessing all primary parameters.

The waviness profile represents the surface profile by encompassing all deviations with large wavelengths from the designated profile, while excluding smaller wavelength deviations, known as roughness.

Roughness refers to the surface characteristics resulting from indentations on the topography of a material, primarily due to machining processes and inherent material traits It is important to note that roughness does not include waviness or form errors.

The unfiltered primary profile (P-profile) represents the true measured surface profile, while filtering according to ISO 11562/ISO 16610-21 yields the waviness profile (W-profile) and the roughness profile (R-profile) The cut-off λc is the variable used to distinguish between waviness and roughness, with profile types identified by the letters P, R, or W.

Areal: A three-dimensional surface area of the surface under consideration.

Stylus instrument: It enables two-dimensional tracing of a surface

The stylus is traversed normal to the surface at constant speed.

Traced profile: The enveloping profile of the real surface acquired by means of a stylus instrument The traced profile consists of form deviations, waviness and roughness components.

The surface scan comprises two key components: profile length details and profile departures, which include aspects like waviness and roughness To effectively assess the profile for any violations, it is essential to establish the length parameters, including total scan length, evaluation length, and sample length.

Unfiltered and filtered profiles of surface texture.

Traversing length: It is the overall length traveled by the stylus, when acquiring the traced profile.

Evaluation length: The portion of the traversing length, which is con- sidered for the analysis of the surface.

Sampling length: The portion of the evaluation length considered for assessment and evaluation of roughness (with pre-decided wave- length), also known as the cut-off length.

The cut-off is a crucial variable that defines the boundary between waviness and roughness profiles based on wavelength This value is chosen according to the surface of the workpiece, considering factors such as peak-valley distribution and anticipated roughness It's important to recognize that varying cut-off lengths can yield different surface texture values Additionally, selecting the correct cut-off is specific to the application, and proper lengths should be determined by the interaction area with mating components, material properties, and the scale of physical phenomena involved.

Spatial Parametres

Surface texture parameters are classified as spatial parameters, defined by evaluation length and the periodicity characteristics of the surface's reference line.

Amplitude Parametres

In consonance with the spatial parametres, another series of surface texture parametres are classified under the broad category of amplitude parametres, the

Allowance for run-up Allowance for overtravel

The scanning of surface length involves key parameters, including amplitude, which is measured from a defined reference line It is crucial to have a clear definition of this reference line, as both spatial and amplitude parameters collectively determine the profile errors of the surface Understanding the type of texture parameter, whether it is waviness or roughness, is essential, as it is dictated by the profile deviation.

The average height parameter is a measure of surface texture, calculated by averaging the height estimates from various sampling lengths using either arithmetic or RMS methods To accurately represent the roughness profile, five different sampling lengths are utilized for this averaging process.

Extreme height parameter refers to the maximum height magnitudes derived from the total amplitude of the highest peaks and lowest valleys on a surface This parameter is crucial for assessing the quality of precision surfaces produced during machining To evaluate a surface's suitability for specific applications, it is typically analyzed over the total evaluation length rather than just the sampling length Often, this parameter influences the choice of machining processes to ensure compliance with required surface quality tolerances and the acceptance of the finished surface.

Over the years, numerous surface texture parameters have developed across different working groups, resulting in increased confusion and misunderstanding Therefore, it is essential to focus on surface texture parameters that align with the specific application requirements and quality standards of the surfaces in question.

In order to give a practical insight to DTM surface characterization, let us review the most commonly considered surface texture parametres: Pt, Pq, Ra and Rt.

The peak-to-valley profile amplitude error (Pt) is a crucial parameter in evaluating surface characteristics and determining quality acceptance or rejection Pt represents the total amplitude of the highest peak and the deepest valley across the entire evaluation length of the primary profile of a DTM surface This measurement is particularly significant in precision optical surface generation, which is essential for various instrumentation applications Figures 8.9 and 8.10 illustrate the profile analyses of two distinct DTM surfaces.

Figure 8.9 illustrates a DTM-generated surface featuring a high profile error (Pt) of 1.74 μm, evaluated over a length of 49 mm In contrast, Figure 8.10 depicts a well-turned surface with a significantly lower profile error of 0.33 μm, assessed over a 47 mm length.

DTM surfaces in metrology are characterized by surface profile errors similar to the PV error in optical metrology, typically measured against the mean wavelength of the visible spectrum, which is 0.633 μm A quality optical surface generally exhibits a profile error that is a fraction of this wavelength For instance, the DTM surfaces illustrated in Figures 8.9 and 8.10 show surface errors of approximately 2.7 λ and 0.52 λ, respectively The suitability of these surfaces for specific applications ultimately determines their quality, rather than the exact numerical values of the errors The Pt value plays a crucial role in the acceptance or rejection of optical components, significantly impacting the future of the industry developing DTM components.

DTM surface with small Pt value: 0.33 μm and Pq: 43 nm over 47 mm evaluation length.

DTM surface with large Pt value: 1.74 μm and Pq: 0.3 μm over 49 mm evaluation length.

Pq, or average amplitude error, is a crucial parameter in assessing surface quality, specifically the root-mean-square (rms) profile error, which measures deviations from a specified surface profile While Pq is commonly used in optical design specifications to qualify surface quality, it represents an average of all amplitude variations, including peaks and valleys, which may not fully capture the surface texture's true nature This averaging can obscure process-induced errors that affect the profile Therefore, to accurately validate both the machining process and the finished component, it is recommended to consider the maximum surface profile error, known as Pt Ultimately, the relevance of the rms profile error depends on the specific application of the surface in question.

Surface roughness, represented by the average roughness parameter Ra, is a critical quality metric in precision machining due to its wide acceptance and utility across various applications Over the years, numerous parameters have been developed to quantify surface roughness, influenced by geographical factors, available skill sets, and advancements in precision metrology Aligning machining and metrology processes with a standardized parameter enhances clarity and consistency in evaluating surface quality Ra effectively serves this purpose by calculating the arithmetic average of amplitude variations from the mean line over a specified sample length This approach is applicable across multiple domains in precision engineering, as illustrated by the roughness profile of a DTM surface over an evaluation length of 12.8 mm.

DTM surface with small Ra: 14 nm and large Rt: 248 nm over 12.8 mm evaluation length.

The selection of sample lengths for analyzing surface roughness varies significantly depending on the application and operational level For instance, typical sample lengths differ in the R&D stage, prototype production, and large volume production, with values of 0.025 mm, 0.08 mm, and 0.8 mm, respectively Additionally, the roughness quality criterion of surfaces generated by DTM is determined by their intended application, similar to the assessment of surface profile error (Pt).

Rt represents the total surface roughness value, calculated as the sum of the highest peak's amplitude and the deepest valley's amplitude within a designated sample length of the DTM surface across the entire evaluation length.

In surface characterization, distinguishing between roughness and waviness is crucial For instance, a surface may exhibit a low average roughness of 14 nm while having a peak roughness value of 248 nm, indicating significant spikes that can distort the overall roughness profile These high peaks can be overlooked in standard averaging methods, yet they play a vital role in shaping the waviness profile and can greatly influence the Pt value if located at critical points Therefore, it's important to create a DTM surface that maintains not only a favorable average roughness but also a controllable Rt value to minimize the impact on Pt.

Power Spectral Density

The roughness profile of a DTM-generated surface is typically represented by the arithmetic average of the amplitudes of localized peaks and valleys over a specified sample length However, this method overlooks the spatial distribution of these features across the entire scan length, potentially resulting in different roughness profiles sharing the same arithmetic value while exhibiting distinct surface textures This limitation creates an inaccurate representation of the DTM surface Consequently, the power spectral density (PSD) has emerged as a universally accepted surface roughness parameter in recent years.

The Power Spectral Density (PSD) quantifies the entire roughness profile by analyzing both the vertical magnitudes and the spatial distribution of peaks and valleys It is derived from the Fourier transform of the autocorrelation function of the roughness profile, encompassing both vertical components and spatial characteristics For a comprehensive understanding of PSD, further details can be found in other sections of this book.

Tolerance

Tolerance refers to the allowable error in system parameters, particularly in DTM-generated components where dimensional and surface texture parameters, such as waviness and surface roughness, are crucial These tolerances are typically minimal since DTM is the final machining process The required tolerances depend on the component's application, and factors like machining process, work-piece material, and tool geometry influence waviness and roughness Waviness tolerances are often represented as fractions of the mean visible wavelength (λ: 0.633 μm), including peak-to-valley (Pt) or root-mean-squared (rms) deviations Surface roughness can cause scatter, which must be minimized based on application needs While achieving tight tolerances in diamond-turned components can be challenging and costly, a careful assessment is essential to determine if the investment in maintaining these tolerances is warranted.

Waviness tolerances for injection molded components made from DTM-generated precision inserts are typically generous for non-imaging applications, often measured in microns In contrast, MIL grade DTM components designed for imaging applications require tighter tolerances, specifically λ/3 to λ/4 Consumer optics can accommodate roughness tolerances of a few tens of nanometers (Ra), whereas DTM components intended for space applications must maintain low roughness levels, ideally below 10 nm (Ra < 10 nm).

Surfaces with the same Ra, but with different roughness profiles.

Metrology by Stylus-Based Profilometres

The testing of diamond-turned surfaces involves analyzing form, figure, and finish errors, collectively known as surface deviations To evaluate these deviations, peak-to-valley value (P-V) and root-mean-square value (rms) are the most widely accepted parameters For a more detailed characterization, advanced parameters like polynomial coefficients are also employed The characterization of aspheric surfaces encompasses two main tasks: measuring surface roughness and assessing surface deviations Various roughness measurement techniques are available, including total scattering, angle-resolved scattering, mechanical and optical profiling, atomic force microscopy, white light interferometry, and confocal laser scanning microscopy, each with its unique advantages and limitations Typically, a nanoscale surface profiler is used for surface roughness characterization, while an interferometer is utilized to measure surface deviations across the entire precision surface.

Surface roughness is typically measured using profilometers, which can be mechanical or optical Mechanical profilometers utilize a stylus that physically contacts the surface, while optical profilers employ a non-contact optical beam Each type has its own advantages and disadvantages depending on the application Stylus-based profilers have been widely used to assess the statistical properties of smooth optical surfaces and are effective for measuring MEMS, semiconductor devices, optical thin films, and surface finishes A typical profilometer includes a small-diameter stylus, a gauge or transducer, a traverse datum, and a processor As the stylus traverses the surface, it records the variations in height, which are converted into a signal by the transducer and processed to create a visual profile with roughness metrics.

Touch-probe profilers are inherently destructive as their stylus tip traverses the specimen's surface, leaving marks behind They provide a linear data scan, which only detects rotationally invariant errors Furthermore, contact profiling techniques tend to smooth surface data, leading to reduced data bandwidth Additionally, stylus methods are unable to assess index inhomogeneities in glass or detect assembly errors in lens systems.

Sources of Errors in Surface Quality

The diamond turning process is characterized by minimal machining forces on the workpiece, optimized interaction between diamond tools and the material, and minimal material removal As a result, macro-machining conditions have a limited impact on the surface quality of diamond-turned surfaces Instead, the micro-machining process introduces specific sources of surface deviations.

The surface quality of diamond-turned components is influenced by four key factors: the properties of the work-piece material, the DTM equipment and machining conditions, the tooling parameters, and the protocols for machining and metrology While the first three factors have been covered in detail elsewhere in this book, this chapter focuses on the surface errors that arise from protocol violations during various stages of precision component development using DTM These stages include tool setting, work-piece holding and handling, machining, and metrology, as illustrated in Figure 8.13.

Surface errors – genesis setting Tool

Non-uniform thermal distribution figure Form errors

Random machining parametres Metrology protocol violation

Tilt Random scan force and speed figure Form finish errors

Ogive Error

In diamond turning operations, precise tool-setting is crucial for achieving high-quality surface generation Proper alignment of the precision tool, workpiece, fixture, and vacuum chuck must be maintained within sub-micron error margins Any misalignment, whether in the vertical (Y-axis) or horizontal (X-axis) direction, can lead to significant surface errors and shape discrepancies in the finished component.

Misalignment of the diamond tool in the vertical axis can lead to significant issues during machining When the tool's center is positioned below the chuck's center, it results in an undercut workpiece, creating a cylindrical shape with a diameter twice the gap between the diamond tool and the vacuum chuck Conversely, if the tool's center is above the chuck's center, the workpiece becomes over-cut, forming a cone at its center with a diameter also twice the gap between the two centers Proper alignment is crucial to avoid these undesirable outcomes.

Misalignment of the diamond tool along the horizontal axis, referred to as x-offset, can lead to a conic error known as ogive error in the precision surface after machining This error occurs similarly to the height misalignment of the tool center relative to the vacuum chuck's center, manifesting in either under-cut or over-cut modes Understanding ogive error is crucial, as it is one of the primary shape errors that must be minimized for improved machining accuracy.

An ogive refers to the rounded, tapered end of a two-dimensional or three-dimensional object It can exhibit ogive error when a circular arc-shaped surface is generated around a rotational axis, with the error's magnitude influenced by the offset between the generating curve vertex and the axis of symmetry For instance, a surface without ogive error is illustrated in Figure 8.14a However, if the tool center fails to align with the chuck's center in the x-direction, the resulting x-offset will lead to an under-cut ogive error, which can be visualized as a gothic dome.

When the tool moves past the chuck's center in the x-direction, the x-offset of the tool can cause an over-cut ogive error, resulting in a double-gothic artifact at the center of the workpiece.

Ogive error can occur even with optimal conditions, such as precise coordination between the tool and work-piece, near-parallelism of the rotating work-piece and the generated circular arc, and absence of tool wear or machining effects This error, whether under-cut or over-cut, can damage the tool and reduce its lifespan, while also affecting the tolerances of precision components produced through diamond turning by impacting waviness error Therefore, it is crucial to evaluate ogive error during tool setup and implement measures to minimize it, ensuring compliance with the component's tolerance criteria Additionally, diamond tool x-offset can lead to opposite ogive errors in convex and concave profiles, resulting in distinct W-shape and M-shape waviness patterns at the profile center.

Metrology Errors

Diamond turning typically results in a precision-machined surface when proper precautions are observed throughout the machining process However, errors can occur during workpiece handling, potentially leading to damage Therefore, meticulous care is essential to ensure the integrity of the component.

Axis of rotation Axis of rotation

(a) Surface without ogive error (b) Surface with under-cut ogive error (c) Surface with over-cut ogive error.

M-Shapes and W-Shapes at the Work-Piece’s Centre Due to Ogive Error

Ogive Error at the Work-Piece’s Centre Profile Tool Stopped Before Spin Axis Tool Past Spin Axis

DTM Surfaces – Metrology – Characterization is essential for ensuring the precision of diamond-turned components A significant source of surface errors can arise during the surface characterization stage, even when diamond turning is performed under optimal conditions with minimal tool wear Despite ideal machining parameters, unacceptable surface quality, such as waviness, may still occur This issue often stems from the surface characterization process itself For instance, when a precision-machined workpiece is characterized using a contact profilometer, it involves carefully removing the workpiece from its vacuum chuck or fixture, which can impact the accuracy of the measurements.

Proper placement of the workpiece and its fixture under the profilometer's stylus is crucial for accurate surface analysis Setting the default force of the stylus ensures consistent scanning, while selecting the vertex point based on surface curvature is essential for precise measurements Inputting design data into the metrology code generates the target surface, and choosing appropriate scan, evaluation, and cut-off lengths is vital for effective analysis Performing a linear scan and analyzing the resulting data are key steps, but mistakes at any stage can lead to flawed surfaces or misrepresented profiles, potentially resulting in an unacceptable surface despite having an acceptable profile error.

The release of a component from a vacuum chuck, with or without its fixture, can significantly alter its profile due to pressure changes, resulting in form errors related to radius of curvature and conic constant As illustrated in Figure 8.15, the extent of holding errors varies across different materials during diamond turning operations These holding errors can greatly affect both profile error metrology and compensation To mitigate this issue, employing an appropriate fixture during diamond turning is essential, as it helps maintain the workpiece's form despite changes in vacuum pressure.

Vacuum off Vacuum on Part released

The next essential step in DTM surface characterization is positioning the component under the profilometer, ensuring proper alignment to avoid surface tilt, as illustrated in Figure 8.16 Modern post-scanning analysis software often includes a tilt removal option, which should be used carefully to determine whether the tilt originated during fabrication or from improper placement on the profilometer If the component is non-parallel or trapezoidal, it must be machined to achieve parallelism relative to the vacuum chuck before diamond turning the desired surface profile However, this machining process may reduce the work-piece's thickness, necessitating adequate thickness allowances on the blank to ensure optimal results.

When scanning a workpiece with a stylus, three potential issues can arise: improper stylus force, unsuitable scanning speed, or a combination of both These problems can lead to surface damage from scratching due to excessive force or cause the stylus to skip over the profile's peaks and valleys from insufficient force Ultimately, these errors result in rejected components or inaccurate measurements.

At the metrology stage, positioning errors can occur when the workpiece is incorrectly aligned under the profilometer, leading to a lateral shift of the component's vertex This misalignment can result in significant complications and inaccuracies in measurement outcomes.

Unequal clear aperture measurements and misregistration of the fabricated conic profile with the intended target result in discrepancies in the base radius of curvature (RoC) and conic constant Consequently, the conic presented for analysis differs from the fabricated version, leading to significant profile errors Figures 8.16 and 8.17 illustrate these anomalies.

The lateral positioning of the workpiece may not influence the waviness of a flat machined component; however, it will impact the evaluation of its functional aperture For conical and spherical components, any shift in placement can significantly alter the analysis.

DTM components placed under the profilometer with a skewed base.

DTM surfaces in metrology can experience significant waviness errors at the characterization aperture and vertex To mitigate these errors, it is essential to ensure proper cresting of the component's vertex during profilometer measurements.

Thermal Effects and Metrology

During machining, the interaction between the work-piece and the diamond tool generates significant thermal energy as the tool shears through the material While coolant helps remove heat from the tool-job interface, some heat remains trapped in the work-piece due to its thermal diffusivity With repeated machining cycles, the temperature at the tool-job interface increases, leading to a Gaussian thermal profile that causes material bulging and surface profile distortion To address this deterioration, a process must be established to compensate for the heat-induced changes, which includes calculating the heat generated in the work-piece and conducting thermal modeling in a steady state.

The model's generalization to the transient state involves validating it by measuring the temperature at the tool-job interface and computing the changes in the surface profile due to thermal accumulation in the workpiece This process varies across different zones of the workpiece and among materials based on their thermal properties, such as diffusivity and expansion, as well as the specified tolerances of the components being machined The thermal flux generated leads to swelling in the workpiece, which can result in hysteresis losses after recovery, ultimately causing a deterioration in the surface profile characterized by increased surface waviness and roughness.

Profile change due to vertex shift during profilometry.

Error Compensation Techniques

Improving surface quality is largely influenced by design requirements and the correction processes used in developing precision components Achievable roughness is affected by machine dynamics and tool geometry, while reducing waviness remains a key challenge Effective waviness correction involves selecting the appropriate diamond tool and monitoring its wear, optimizing machining parameters, controlling the machining process, and following established machining-metrology protocols However, despite these efforts, some waviness persists on the workpiece, necessitating further reduction to meet stringent surface quality tolerance limits This can be achieved through a tool path compensatory approach, which involves adjusting the tool path based on the existing waviness to minimize its impact.

In the tool path compensatory approach, metrology initiates the compensation process by analyzing the workpiece's sagitta variation in relation to its aperture, as outlined in the sag table during the diamond turning stage Waviness, or profile error, refers to the discrepancy between the designed and fabricated profiles, specifically the deviation of sagitta from the design specifications concerning the aperture Tool path compensation addresses this sag deviation by adjusting the prescribed tool path, resulting in a new path that incorporates the negative waviness component This adjustment aims to achieve a near-zero waviness surface in the subsequent machining process.

Tool path compensation Surface scan data

Schematic of profile error compensation.

DTM surfaces play a crucial role in metrology and the characterization cycle, assuming that tool dynamics remain relatively stable across successive machining cycles While achieving zero error in a single compensatory cycle may be unrealistic, it is possible to reduce waviness to acceptable levels within two to three machining cycles.

This approach is effective for correcting figure errors but not for form errors, which require a different strategy due to the dynamics of tool geometry during machining Waviness reduction relies heavily on accurately characterizing the diamond-turned workpiece surface, making it essential for the metrology process to provide a precise surface profile, free from errors introduced during characterization Proper handling of the workpiece after diamond turning and adherence to a standardized metrology protocol are crucial The success of developing precision surfaces hinges on both the fabrication process, such as diamond turning, and the surface characterization methods employed Therefore, studying surface quality presents both challenges and significant rewards.

This chapter provides insights into the qualification of precision components developed by DTM, focusing on geometrical dimensions and surface features Depending on the application of the precision component, the required and achieved precision levels, along with the specified tolerance ranges, are critical DTM practitioners are encouraged to thoroughly explore surface characterization and leverage on-field experiences Ultimately, the knowledge and skills gained from this process will significantly enhance real-life problem-solving capabilities.

Summary

This chapter focuses on the qualification of components produced by Direct Tooling Manufacturing (DTM), emphasizing its role in the fabrication process It discusses essential aspects of dimensional measurements and surface characterization, including form, figure, and finish The chapter explains precision surface metrology processes, detailing surface texture parameters and their relationship to proposed surface quality criteria It also provides an overview of tolerances in DTM, highlighting accuracy and precision requirements achieved through this method Additionally, it covers contact profilometers and precision surface scanning techniques, as well as sources of surface errors encountered during component development The chapter concludes with strategies for enhancing surface quality based on the key criteria of form, figure, and finish.

Advances in DTM Technology

Introduction

This chapter highlights the latest global interests and advancements in the field of DTM, covering various aspects such as machine tool structure, cutting tools, work materials, process monitoring, tool holders, path planning, and coolant effects The emphasis is on applied technological developments rather than fundamental research, with explanations presented in a straightforward manner accompanied by basic schematics to clarify the concepts discussed Figure 9.1 illustrates the recent research areas within DTM.

DTM Process Monitoring

The DTM group at Hong Kong Polytechnic, led by W B Lee, is developing innovative techniques to monitor surface roughness during the DTM cutting process, aiming to correlate force signals with surface profile signals They uniquely quantify surface profiles along a spiral cutting path, in addition to traditional radial measurements By using a centrally placed hole to mark the start and end of the spiral motion and implementing high feeds per revolution to enhance the spirals, they extract surface profiles from maps and temporally match them with force signals Their findings indicate a strong correlation between surface undulations along the spiral path and force variations In a related study, vibration sensors were utilized to collect signals from the DTM process, further demonstrating a significant correlation between vibration signals and surface profile undulations along the cutting path.

Hence, by monitoring the vibration or force signals, clues about variations in surface profile (along the cutting spiral path) can be obtained.

A proposed method for monitoring the lifespan of diamond tools involves measuring changes in the tool's nose radius through taper grooving experiments This process utilizes a non-contact surface profiler to assess alterations in the groove profile However, due to the inevitable elastic recovery, the groove profile may not accurately reflect the tool's nose radius.

Coolant planning Path micro- Tool control holder Tool material Work

Areas of recent research in DTM.

Surface roughness profile along the cutting velocity path (spiral path) shows better correlation to force and vibration signals.

An estimation of elastic recovery has been conducted by applying volume constancy and basic assumptions regarding the groove profile's elastic recovery Experimental tests of this method have produced satisfactory outcomes Nonetheless, the effectiveness of this approach for monitoring tool condition during a DTM process remains to be evaluated.

A sensor fusion approach has been developed for monitoring the DTM process, utilizing a combination of force, vibration, and acoustic emission sensors positioned close to the cutting tool This method collects data from all sensors simultaneously, addressing the complexity of DTM signals that cannot be effectively analyzed using traditional linear and Gaussian signal processing techniques To tackle this challenge, a novel adaptive nonparametric Bayesian Dirichlet process method for fusing sensor signals has been proposed, tested, and compared with alternative fusion methods.

Developments Related to Machine Tools

A proposed architecture for the DTM machine introduces a cutting tool that swings via a rotary arm, rather than moving solely along a linear axis This innovative design features two linear axes and three rotational axes, with two of the rotary motions powered by hydraulic motors The swinging arm enables the cutting tool to perform arc motions in various inclined planes, allowing it to trace spherical surface arcs on a rotating workpiece The necessary plane orientation can be geometrically calculated, and this new approach aims to reduce interpolation errors typically associated with the T-type structure of the DTM.

Signal fusion Vibration sensor DTM part

The integration of multiple sensors in DTM, along with innovative signal fusion techniques, enhances the precision of machine tool architecture A kinematic error model is established to perform sensitivity analysis, focusing on the alignment of two hydraulic motors to minimize the impact of diverse errors.

The Fraunhofer Institute has investigated an innovative approach to dual-sided DTM machining, where both the top and bottom surfaces of a workpiece are machined simultaneously while being uniquely clamped in the center This concept necessitates significant alterations to the machine structure, including the addition of two Z-axis slides flanking a centrally positioned spindle, which must be accessible from both faces The primary goal of this development is to enhance the cost-effectiveness of the DTM process, alongside exploring automation options for tasks such as workpiece loading and tool changes.

The issue of imbalance of spindle continues to attract attention and methods are being devised to study and counteract its effects [74] This work reports

Structure of swing arm DTM machine.

Unique two-sided parallel machining to reduce DTM process times.

Advancements in DTM technology focus on modeling the dynamics of aerostatic spindles to mitigate their effects Research indicates that imbalance can create a star effect on DTM machined surfaces, characterized by radial spokes radiating from the center This phenomenon is linked to the air-hammering effect combined with the influences of air bearing spindles.

Brinksmeier’s group at the University of Bremen is advocating for the implementation of high-speed spindles in the DTM process, which currently necessitates precise spindle balancing This need for accuracy intensifies at elevated speeds, prompting the exploration of innovative methods to address this challenge while simultaneously reducing stiffness in spindle mounts to enhance the sensitivity of unbalanced measurements.

Ongoing efforts are focused on identifying and modeling errors in DTM machines, specifically in their individual components like spindles and slides, as well as in the overall structure These models aim to enhance error compensation and improve form accuracy.

Developments Related to Cutting Tools

A recent study introduces an innovative polycrystalline diamond tool created by aggregating nano-crystalline diamond particles without the use of a binder This new form of the tool demonstrates increased density and an 11% reduction in weight, enhancing its overall performance and efficiency.

Single crystal diamond (SCD) Poly crystalline diamond (PCD) Aggregated diamond nanorod (ADNR)

(Cobalt or SiC as binder) (No binder)

Aggregated diamond nanorod (ADNR) is a groundbreaking material for cutting tools, surpassing single crystal diamond (SCD) in hardness While ADNR exhibits superior fracture toughness, Knoop hardness, and wear coefficient compared to SCD, it has a lower Young’s modulus Additionally, tools made from a similar nano-crystalline diamond form are marketed as offering comparable performance to SCD-based cutting tools, although these claims require further validation.

Recent studies highlight that while new cutting tools excel in DTM machining of brittle materials, their performance deteriorates over time due to tool wear, affecting ductile-to-brittle transitions A simulation model demonstrates that as flank wear progresses, the hydrostatic stress distribution, crucial for preventing crack propagation, becomes disturbed, with fluctuations in stress and a displacement of the highest stress point behind the tool edge This analysis provides insights into maintaining ductile conditions despite tool wear Additionally, researchers at the University of Bremen have developed a novel thermal actuator designed to precisely align multiple diamond cutting tool edges in DTM milling processes, which is essential for improving cycle times By utilizing LED-based infrared heating, the actuator can adjust tool edges from nanometres to hundreds of nanometres, with testing currently underway.

Multiple insert milling tool holder (four SCD inserts)

A unique idea of thermally actuating various inserts in DTM milling process to align the inserts perfectly.

W B Lee’s group in Hong Kong reports [81] a method to optimally choose the best cutting tool suited for a given optical surface to be generated via the DTM process It is known that the cutting tool nose radius influences the form that is generated While having a zero nose radius would be best, it would be practically not feasible; in practice, one would like to have a large possible nose radius to maintain tool strength In order to balance these two conflicting requirements, the group uses ray-tracing models to predict the optical errors that can result from the use of various tool nose radii The form is first predicted for a given nose radius and then fed into the ray-tracing model An optimisation search is then initiated to maximise the nose radius which may provide an acceptable optical error (e.g wave front aberration).

Influence of Coolant in DTM

Several groups are testing the effects of various types of coolants and addi- tives on the performance in the DTM process Some key findings are reported in this section.

Fritz Klocke’s research group at Fraunhofer has discovered that optimizing the coolant used in diamond turning can extend the critical depth of cut, where the ductile-to-brittle transition occurs Taper scratch tests conducted on hard brittle materials, such as tungsten carbide (WC), reveal that certain cutting fluids can increase this critical depth To enhance the efficiency of diamond turning machining (DTM), it is recommended to use customized cutting fluids Additionally, it has been found that the pH levels of the water in the coolant significantly impact the critical depth of cut, as demonstrated in tests involving WC and two types of glass materials.

W B Lee’s group reports [84,85] the use of nano-droplet-enriched cutting fluids (NDCF) in DTM and in taper scratch experiments using diamond tools on 6061 aluminium alloy NDCF is a mix of mineral oil and water with the oil in the form of nano-droplets (Figure 9.8) In DTM experiments con- ducted with NDCF, surface finish is seen to be improved In the taper scratch

Under the influence of non-conventional cutting fluids (NDCF), grooves are reported to be uniform without any plastic deformation bumps, which are typically observed when using conventional cutting fluids This suggests that NDCF possesses superior thinning capabilities, allowing it to penetrate the tool-chip interface effectively, thereby reducing friction and improving chip formation as well as material deformation near the cutting edge.

The challenge of using diamond tools to effectively machine ferrous alloys persists, driving ongoing research for viable solutions Recent studies from Rensselaer Polytechnic highlight the innovative application of graphene oxide platelets in a semi-synthetic cutting fluid, enhancing the performance of PCD tools when machining ferrous alloys.

Mild steel machining with a PCD tool has demonstrated significant improvements, including a 30% reduction in tool wear, a 50% decrease in cutting temperatures, and a 30% reduction in cutting forces X-ray photoelectron spectroscopy (XPS) studies suggest that graphene oxide particles are disrupting the carbon diffusion at the tool-chip interface This promising technique may also be applicable to the DTM process.

Vibration-Based Controlled-Tool Motion

Efforts are underway to enhance the capabilities of the fast tool servo (FTS) system by synchronizing it with the slow-tool servo (STS) to extend tool reach This innovative system integrates the C-axis with the Z-axis slide and FTS, allowing the STS to 'macro' position the cutting tool while the FTS performs precise 'micro' cutting motions at that location Recent reports highlight advancements in programming techniques that effectively combine STS and FTS motion paths, leading to increased versatility in producing complex geometrical shapes However, it is important to note that the dynamic performance of this integrated system remains constrained by the limitations of the STS.

Efforts are underway to enhance the motion stroke of the FTS system, with a new long-range single-axis FTS system utilizing voice coil motors This innovative design features a linear air bearing stage controlled by a closed-loop system that incorporates glass linear encoders The mechanical design is optimized to achieve first and second modal frequencies exceeding 1 kHz, enabling a stroke of up to 30 mm and accelerations nearing significant thresholds.

100 Gs It can be used up to a frequency of 200 Hz.

Conventional oil-water coolant NDCF

Use of nano-droplet enriched cutting fluids in DTM has been reported.

Two-axis FTS systems are increasingly replacing single-axis systems, particularly for applications such as machining dimple patterns on rollers used in large-area hot embossing These advanced systems feature an in-feed axis that moves approximately 40 micrometres perpendicular to the roller axis, alongside a parallel axis with a stroke of 75 micrometres Designed for an operational bandwidth of 1.5 kHz, the 2-axis FTS enhances precision and efficiency in manufacturing processes.

A recent report highlights the innovative use of a 2-axis flexure-based frictionless table system (FTS) aimed at counteracting the deterministic cutting motion typical of the DTM process By introducing pseudo-random vibrations through decoupled motions in two axes, this approach effectively disrupts the spiral feed marks on the workpiece surface A novel surface topography generation algorithm was developed to implement this technique, and experimental tests comparing tool paths with and without these vibrations demonstrated significant improvements Additionally, light scattering tests confirmed that the application of random vibrations reduces the scattering fringes commonly observed on DTM machined surfaces.

Vibrations can be utilized not only for controlling tool motion but also for inducing local loss at the tool-chip interface, thereby reducing wear and cutting forces This method, initially developed to minimize tool wear while diamond turning ferrous materials, has seen limited commercial success, with Delta Optics in Singapore being a notable exception Recently, this technique has shown promise in the diamond turning of titanium alloys, indicating potential advancements in its application.

Vibrations to cause tool-chip intermittent contact losses are largely based

Elliptical vibration cutting involves the tool executing an elliptical motion at high frequencies, where only a small segment of the arc is in contact with the material This technique is typically enabled by resonant mechanical vibration systems using piezo-actuators; however, these systems face challenges such as cross-talk between motion axes and sensitivity to material variations To address these limitations, non-resonant systems have been developed, allowing for 3D motion of the cutting tool through the use of four piezo-stacks, enabling adjustable amplitude, frequency, phase shifts, and acting locations Additionally, a novel approach combines elliptical vibration cutting with an STS system, resulting in double-frequency vibration cutting, which alters the cutting plane's interaction with the workpiece This advancement necessitates the development of new algorithms for tool path generation, innovative tool geometries, and surface prediction techniques.

In summary, the research indicates that strategically induced active vibrations in cutting tools can effectively counteract the impact of other vibrations within the machine tool and process system.

Tool-Path Planning

Innovative tool-path planning techniques are emerging, driven by the need to diamond turn new geometries Additionally, the quest to lower both process-planning and processing costs is advancing the development of novel algorithms for effective tool path generation.

In a notable development, conventional CAD/CAM software is utilized for tool path planning in DTM processes, addressing the high costs associated with DTM-specific CAM software To mitigate these expenses, an application programming interface (API) has been created to integrate with commercial CAD software like SolidWorks This integration enables the creation of spiral tool path trajectories for generating path plans suited for free-form surfaces using FTS/STS systems The effective deployment of this interface facilitates the generation of tool paths, allowing for the fabrication of components with intricate free-form profiles and micro-optic arrays using STS/FTS systems.

A novel tool path planning algorithm has been developed for optical components that require arrays of identical micro-features with discontinuous repetition This innovative approach diverges from the conventional spiral path planning typically used in FTS/STS-based feature generation By creating a virtual spindle axis at each feature within the array, the new algorithm enhances the tool planning process, allowing for more precise and efficient fabrication of optical components.

Elliptical vibration machining has been adopted in DTM in various ways.

Recent advancements in DTM technology highlight the significance of STS/FTS system machines Within this complex framework, micro-optics arrays (MOAs) are now being machined with improved efficiency, facilitating better tool path planning.

A novel method for generating spiral tool paths has been introduced, addressing the issue of unequal spiral spacing commonly encountered when projecting a planar Archimedean spiral onto a work surface This approach involves first creating a surface of revolution that closely matches the workpiece's surface, allowing for the generation of an Archimedean spiral with consistent spacing The surface spiral is then projected along its normal direction onto the target workpiece, significantly reducing spacing variation Comprehensive algorithms have been developed and tested for automating the processes of surface of revolution creation, spiral generation, and projection, yielding promising results on actual work surfaces.

A novel motion planning approach has been developed to machine a Fresnel lens on a cylindrical roller, addressing the limitations of traditional FTS arrangements in DTM machines Typically, these machines synchronize the C-axis and W-axis (Z-axis of the FTS stage) along with the X-axis, resulting in a maximum of three-axis synchronization However, this configuration is inadequate for producing the required Fresnel lens To resolve this issue, the machine has been modified to synchronize the B-axis of the lathe with the C-axis, achieving full synchronization across all four axes This innovative tool path planning method has been successfully implemented to create the essential Fresnel lens on the roller.

A novel approach is introduced for processing standard Fresnel lenses on flat surfaces, leveraging the B-axis This method employs a circular swing of the B-axis along with a specially designed curved tool edge, tailored to accommodate both Fresnel and roller geometries, ultimately enabling the precise generation of Fresnel lens shapes.

Tool path planning algorithms have evolved over time, to optimally use the hardware developments such as 2-axis and 3-axis FTS systems In a

Innovative techniques for crafting complex shapes, like Fresnel arrays on cylindrical roller molds, enhance the traditional DTM process Typically, the feed motion occurs along the X-axis, resulting in an Archimedes spiral motion that is uniformly spaced according to the feed per revolution or angular rotation This article explores whether optimizing the spiral gap can boost cutting efficiency A notable advancement involves a 2-axis FTS, which utilizes an Adaptive Tool Servo (ATS) to refine path planning efficiency In this system, the second axis, aligned with the X-axis, feeds the cutting tool, allowing for micro-motion control based on the workpiece's curvature By adjusting the feed rate according to curvature changes—accelerating at small changes and decelerating at rapid ones—this method significantly reduces cutting points, machining time, and form errors, supported by detailed algorithms tested across various geometries.

Efficient tool path planning is crucial for optimizing machining processes, as highlighted by Rahman’s group at the National University of Singapore They propose a profile error analysis (PEA) that evaluates two strategies—constant angle and constant arc—to assess the desired surface profile By analyzing these methods, the approach that minimizes the number of cutting points while meeting form requirements is selected, ensuring effective and precise machining outcomes.

New Materials and Materials Treatment

As new families of materials are being diamond turned, efforts are in prog- ress in terms of material property alterations, prior/during the process, to suit the DTM process.

Conventional FTS/STS Adaptive FTS

Some unique uses of the FTS system to optimise tool paths and reduce process times.

New aluminum alloys are being developed for optical applications, particularly rapidly solidified cast aluminum alloys with refined microstructures Ongoing DTM-based machinability studies are focused on alloy RSA 905, an optical grade aluminum, through collaboration between researchers in South Africa and Taiwan The findings indicate that surface roughness decreases with increased cut length, achieving minimal surface roughness of just a few nanometers over a 4-km cutting length.

Potassium dihydrogen phosphate crystals can be effectively processed using the DTM method, as noted in recent studies These crystals are characterized by their high water absorption, low fracture toughness, and sensitivity to temperature fluctuations A collaborative manufacturing sequence has been established between China and the United Kingdom, which begins with the DTM process, followed by polishing and ion-beam figuring to achieve the desired shape.

Recent studies on the machinability of a Cu-Cr-Zr alloy, a hard copper alloy utilized in molds, dies, and optical components, highlight its challenges due to hard precipitates and surface oxides Research includes an analysis of chip morphology and tool wear, as well as the examination of acoustic emission signals generated during machining Additionally, the study investigates abrasive and notch wear on diamond tools, providing insights into the machining process of this complex material.

Special treatment of materials to enhance machinability has gained significant attention in conventional machining and has been specifically applied to the DTM process This article investigates the effectiveness of electro-pulse treatment (EPT) on the machinability of titanium alloys, particularly Ti-6Al-4V, which, despite their commercial value, are challenging to machine The customized EPT system subjects titanium-alloy samples to various conditions, primarily focusing on frequency, resulting in reduced grain size and softened material Subsequent diamond turning of the samples reveals that EPT positively influences chip morphology and surface condition, leading to improved chip formation, enhanced surface finish, and extended tool life.

In-situ treatment of materials during machining to enhance DTM has been explored, particularly through the use of laser heating to increase ductility Pioneered by John Patten's group at Michigan State University, this technique involves directing an IR laser beam through a diamond cutting tool to focus on the cutting edge, effectively heating the material in close proximity Tests have shown significant improvements in material removal rates and surface finish Building on this advancement, Precitech, a DTM machine company, has introduced a commercial add-on that enables users to incorporate laser assistance into the DTM process.

In an independent development, W B Lee’s group also has reported [106] the use of a laser beam (100 micrometres in diameter) to treat material ahead of the cutting edge, by a special microscope arrangement.

Tool Holding for DTM

Recent advancements have introduced a hexapod-style parallel kinematic system for positioning and moving cutting tools on DTM machines, aiming to enhance the accuracy of older models while compensating for operational errors This innovative system also facilitates tool-normal machining Due to the unique kinematic motion of the hexapod, new algorithms for tool path generation have been developed Experimental trials, including simple face turning and intricate patterns resembling a compound eye, showcase the effectiveness and practicality of this approach.

AMETEK Precitech, a well-known DTM machine builder, and the German company Levicron GmbH are collaborating to enhance tool and work holding in DTM machining setups, aiming for greater automation in tool and work changes Their advancements include automatic taper clamping systems that achieve an impressive 0.2 micrometre repeatability, static run-outs of 0.6 micrometre or less, and adequate balancing capabilities at spindle speeds reaching up to 60,000 rpm.

Proposed concept of using a hexapod to control the cutting tool position.

Summary

Global advancements in the Direct Tooling Manufacturing (DTM) process are evident, particularly in Europe, where there is a focused effort to enhance economic efficiency by minimizing processing times Significant changes are being proposed, including the adaptation of conventional machining techniques for DTM applications Additionally, innovative solutions are emerging to meet specific machining needs, and this chapter provides an overview of international efforts in this field Notably, research into coolant enhancements has also been explored to optimize the DTM process.

It is seen that in the near future, the DTM process will undergo significant changes to make it more mainstream for adoption in various applications

As in all spheres of technology, it is necessary to have vision, think innova- tively and test these novel ideas.

Questions

1 Besides the developments listed in this chapter, think through and list five possible new directions of developments and research pos- sible in DTM.

2 List five recent developments in conventional machining automa- tion Can you extend them directly to DTM? If not, how would you customise these developments to make them applicable to DTM?

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Page numbers with f and t refer to figures and tables, respectively.

Abrasive particle, for material removal,

Accuracy of DTM; see also Diamond turn machines (DTM) balanced loop stiffness, 15–16, 15f positional accuracy, 13–15, 14f repeatability of moving elements,

Asymmetric macro shapes, tool paths for slow tool servo (STA, 84–87 synchonisation of spindle rotation,

Brittle materials; see also Material removal mechanism about, 30 ductile regime machining of, 39–40, 39t machining mechanism, 33–34, 34f

CAD software, 140 Carbon spots, 50 Characterisation, defined, 105 Chip formation, 34

Clamping method, 71, 72f Coherence correlation interferometry

(CCI), 57, 57f Computer numerical control (CNC) motion paths, 47 Constant angle sampling strategy

(CASS), 86, 87 Constant-arc-length sampling strategy

(CLSS), 86, 87 Contact profilometer, 111, 111f, 112, 125 Controlled-tool motion, vibration-based,

138–140 Coolant in DTM, 70, 71f, 127, 137, 138 Crack formation, 34f

Crater wear, 57 Crystals, diamond turn machined, 102 Cutting edge surface, 48

Cutting mechanisms for engineering materials, 30–35, 33f, 33t; see also Material removal mechanism Cutting tools and development, 135–137, 135f manufacturers and diamonds, 50

Damping, 4, 16, 18, 19, 20Degree of freedom, 14, 14fDepth of cut (DOC), 69, 69fDeterministic finishing processes, 28, 28f

Diamond structure of, 50, 51f tools, 53, 53f tool wear development, 58f turning technology, importance of,

Diamond turn machines (DTM) about, 11 characteristics/capabilities of, 17–18,