GENERAL INTRODUCTION
Introduction
In the modern manufacturing landscape, traditional machining methods are increasingly inadequate due to the rise of advanced equipment and technologies This has led to the development of various non-conventional machining techniques, including Electron Beam Machining (EBM), Plasma Arc Machining (PLM), Laser Beam Machining (LBM), and Electrical Discharge Machining (EDM) EDM, in particular, is widely used for machining hard and brittle metals in industries like aerospace and automotive While it offers exceptional capabilities for a diverse range of metals, it faces challenges such as low material removal rates and subpar finishing To address these issues, increasing the current can improve machining time, though it may result in higher surface roughness and increased electrode wear Consequently, vibration-assisted machining methods have been introduced to alleviate these drawbacks.
For the reasons mentioned above, I decided to carry out the topic “Optimizing technological parameters for vibration-assisted electrical discharge machining (VAEDM)” for my graduation thesis
Several studies relating to this topic have been carried out nationally and internationally
This machining method is innovative and relatively unknown in Vietnam, indicating a significant opportunity for further research and studies in this area.
In their research titled “Design and Fabrication of Vibrating Electrode for Vibration-assisted EDM,” authors Hoang Trung Kien, Ta Nguyen Minh Duc, and Nguyen Hoai Nam presented findings at the 2019 International Conference on System Science and Engineering (ICSSE) The study utilized a vibration tool featuring a serial-chain-with-two-flexure-hinge mechanism and PZT to induce beneficial vibrations during the EDM process Experimental results demonstrated that controlled parameters significantly influenced machining performance, while surface roughness showed minimal dependence on vibration amplitude Additionally, vibration frequency had no impact on machining time due to the short-cutting travel involved.
In 2020, a group of undergraduate students (Le Dat Hung, Nguyen Thanh Huong, Nguyen Manh Dinh), instructed by Dr Hoang Trung Kien, implemented research, namely
The study investigates the effects of vibration on the Electrical Discharge Machining (EDM) process using drilling-EDM SINITRON to create 3-millimeter-deep holes Various input parameters, including current (I), frequency (F), and vibration amplitude (A), were systematically altered to assess their impact The findings indicate that processing time can be optimized by utilizing low frequencies and high amplitudes with low current Specifically, a significant reduction in processing time of 33% was achieved with parameters set at I = 4A, F = 100Hz, and A = 7 µm Additionally, a 10% decrease in processing time was noted with I = 8A, F = 200Hz, and A = 7 µm, while another 33% reduction was observed with I = 20A, F = 1000Hz, and A = 2 µm.
In contrast to previous studies that applied vibration to the tool or electrode, research by Hao Tong, Yong Li, and Yang Wan in 2008 focused on applying vibration to the workpiece holder at a frequency of 6000Hz and an amplitude of 3 micrometers This innovative approach significantly enhanced machining efficiency by eighteen times and improved dimensional accuracy by 10.5 micrometers compared to conventional methods.
In 2018, M Y Tsai, C S Fang, and M H Yen implemented research, namely
“Vibration-assisted electrical discharge machining of grooves in a titanium alloy (Ti-6A-4V)”
A recent study published in The International Journal of Advanced Manufacturing Technology introduces an affordable auxiliary tool vibration device designed to enhance the efficiency of deep groove electrical discharge machining (EDM) The research involved machining titanium alloy samples (Ti-6Al-4V) using both conventional EDM and vibration-assisted EDM techniques, employing copper, copper-tungsten, and graphite tool electrodes The vibration-assisted EDM was conducted at frequencies of 40, 90, and 140 Hz, revealing that the material removal rate was significantly higher compared to traditional EDM with copper and copper-tungsten electrodes Notably, an optimal vibration frequency of 90 Hz was identified for achieving improved surface roughness Additionally, the machining time for a 9-millimeter groove was reduced by 200% when using vibration assistance compared to unassisted methods.
In 2019, K P Maity and M Choubey conducted research on "Vibration-assisted EDM, Micro-EDM, and WEDM," revealing significant findings Their study concluded that the application of vibration enhances the machining efficiency of EDM and micro-EDM processes.
3 vibration is applied on either tool or workpiece Second, the higher frequency with lower vibration amplitude allows superior machining effectiveness
A study titled “Effects of processing parameters on processing performances of ultrasonic vibration-assisted micro-EDM,” conducted by Qixuan Xing, Zhenyang Yao, and Qinhe Zhang, was published in The International Journal of Advanced Manufacturing Technology in 2021 This research explores the use of ultrasonic vibration-assisted micro-electrical discharge machining (micro-EDM) to enhance the efficiency and precision of creating micro-holes with a high depth-to-diameter ratio in titanium alloy The technique improves the effective discharge ratio during machining and aids in the removal of erosion products Notably, when the ultrasonic amplitude was set to 6 µm, the material removal rate (MRR) increased by 2.4 times, while the relative tool wear rate (TWR), taper angle, and overcut (OC) were reduced by 65.8%, 73%, and 32%, respectively, compared to traditional non-ultrasonic vibration-assisted micro-EDM methods.
In 2016, Eckart Uhlmann and David Carlos Domingos conducted research on vibration-assisted EDM machining of seal slots in high-temperature resistant materials for turbine components Their study focused on innovating and optimizing die-sinking EDM machining to create high aspect ratio cavities in the nickel base alloy MARM247 using graphite electrodes By implementing a unit with piezoelectric actuators, they explored the effects of vibrations on the EDM process, particularly the correlation between electrical parameters and machine tool control The evaluation of workpieces produced through this technique revealed that they met quality criteria, achieving a surface roughness of Ra = 6.4 µm and minimal sub-surface damage and fracture length of less than 100 µm.
The needs of the topic
In the digital age, vibration-assisted machining has gained significant attention and application worldwide, enabling the efficient machining of various materials that were previously challenging to process Despite its advantages, this innovative technique remains largely unfamiliar in Vietnam, resulting in limited research and high equipment costs.
To ensure the highest quality products with optimal surfaces and precise dimensions, it is crucial to establish specific parameters Unfortunately, many factories and workshops often rely on the default settings provided by manufacturers, which can compromise the final output.
Optimizing technological parameters for vibration-assisted electrical discharge machining (VAEDM) addresses inefficiencies stemming from accumulated experiences that require significant time investment This approach introduces engineers, especially those in mechanical fields, to the innovative concept of vibration-assisted machining, enhancing productivity and effectiveness in their work.
Scientific and practical significance
− This topic contributes to the knowledge of non-traditional machining methods in the mechanical field in Viet Nam, particularly on Vibration-assisted Electrical discharge machining methods
− It examines the impacts of vibration on the surface roughness, tool wear rate, and material removal rate in the VAEDM process
Manufacturers can enhance product quality while keeping costs low by optimizing parameters for machining hard-to-machine materials, resulting in improved performance, reduced production time, and minimized expenses.
Research’s objectives and scopes
− To assess the impacts of high frequency-vibration on the performance of the EDM machining method
− To find the optimal machining parameters of the vibration-assisted EDM
− Machining on SKD 11 work-pieces and copper electrodes
− Machining several experiment trials with machining parameters:
• Pulse-On time: 30 às, 45 às, and 60 às;
• Frequencies: 100 Hz, 800 Hz, and 1200 Hz;
• Vibration amplitudes: 0.5 àm, 1,5 àm, and 2.5 àm
− All experimental trials, surface measuring, and weighing processes are implemented in practical workshops at HCMC University of Technology and Education h
Methodologies
To enhance research methodologies in electrical discharge machining and vibration-assisted machining solutions, it is essential to leverage high-quality documentary resources available online, including scientific studies, reports, articles, and relevant books.
− Design methodologies: using CAD software such as Inventor, AutoCAD, and Creo for modeling the vibration module, fixture, workpieces, and electrodes
In our analysis methodologies, we meticulously record all relevant data, including surface roughness, time, and weight This information is then inputted into Excel for initial calculations, such as tool wear and material removal rates Subsequently, we utilize Minitab software for a comprehensive assessment of the data analysis.
THEORETICAL FOUNDATION
Introduction of Electrical Discharge Machining (EDM)
Electrical discharge machining (EDM), often referred to as spark machining or wire erosion, is a non-conventional technique that utilizes electrical discharges to eliminate material from conductive workpieces Unlike traditional machining methods, EDM operates without direct physical contact between the tool, or electrode, and the workpiece, allowing for precise material removal.
There are three typical types of Electrical Discharge Machining They are Die sinking EDM, Wire EDM and Hole drilling EDM
Die sink EDM, also referred to as Ram, sinker, traditional, volume, or cavity-type EDM, is a precision machining technique that utilizes electrodes made of graphite, copper, or tungsten This method involves a servo-motor controlling the vertical movement of the electrode towards the workpiece, effectively eroding material to create intricate three-dimensional shapes and features.
Wire EDM, or wire erosion, is a precision machining technique commonly employed in the production of extrusion dies This process operates on principles akin to traditional methods, but utilizes a highly electrically charged wire to shape the metal, allowing for intricate designs and high accuracy in die manufacturing.
7 varies in diameter from 0.05 to 0.35mm) that serves as the electrode or cathode WEDM is very useful for products with remarkably tight tolerances or tiny features
Hole drilling EDM utilizes a cylindrical electrode made of copper or brass to create precise, tiny, and deep holes in a workpiece This method outperforms traditional drilling techniques by eliminating the need for a deburring stage, making it ideal for producing deep holes that can be up to 250 times the diameter of the electrode With electrode diameters ranging from 0.25 mm to 4.7 mm, hole drilling EDM is particularly suited for applications requiring high accuracy and depth.
2.1.3 Construction of Sink EDM machine:
A sink EDM machine comprises some principal components:
• DC pulse generator: This is a power source for the machining operation It converts the AC power supply into a high pulsed DC supply
The EDM process requires a reservoir of dielectric fluid, such as de-ionized water or non-conductive lubricating oil, to effectively dissipate heat generated during discharge and to remove eroded metal particles.
The tool electrode serves as a replica of the desired shape to be created on the workpiece and is connected to the negative terminal of the power supply Typically made from materials like graphite, copper, tungsten, brass, and their alloys, the electrode plays a crucial role in the machining process.
• Servo-motor: is used to control the feed of the tool, which moves the tool vertically, and maintains the desired gap between the tool and workpiece
• Spark generator: supplies adequate voltage for spark generation and maintain its discharge
The EDM (Electrical Discharge Machining) technique utilizes the erosion of metal from a workpiece through a series of spark discharges between a tool and the workpiece When two current-carrying conductors, known as the anode and cathode, come into close proximity, an electric arc is created, resulting in the erosion of a small amount of metal at the contact point, which produces debris This discharge generates significant heat, causing the metal in the spark zone to melt and evaporate The process is repeated until the desired shape of the workpiece is achieved.
In the electrical discharge machining (EDM) process, the workpiece is connected to the positive terminal, known as the anode, while the electrode connects to the negative terminal, functioning as the cathode A precise gap of 0.005mm to 0.05mm is maintained between the tool and the workpiece, allowing sparks to occur when they are in close proximity The electrode's shape mirrors the desired impression on the workpiece, enhancing the machining accuracy To optimize efficiency, both the electrode and workpiece are submerged in a reservoir of dielectric fluid, which plays a crucial role in the EDM process.
• Used in the following applications: Aerospace; Medical; Electronics; Semiconductor
- It can produce complex shapes, which cannot be produced by other conventional machining methods
- Tolerance of ± 0.005 can be achieved
- Good surface finish can be obtained economically, up to 0.2 microns
- There is no distortion, or vibration between tool and workpiece, as there is no physical contact between tool and workpiece
- Material removal rate (MRR) is very slow
- High excessive tool wear during machining
- This process is solely applicable to the metallic or conductive material h
Introduction of Vibration-assisted machining
The rising demand for components made from hard and brittle materials, including glass, steel alloys, and advanced ceramics, has rendered traditional machining methods like grinding and polishing inadequate In response, innovative techniques such as vibration-assisted machining have emerged to effectively address contemporary market challenges.
Vibration-assisted machining is a cutting-edge technique that incorporates a module generating high-frequency vibrations with small amplitudes to enhance the machining process By fine-tuning critical cutting parameters, including amplitude and frequency, the cutting tool intermittently interacts with the machining table This results in reduced machining forces, thinner chips, and ultimately leads to improved surface finishes, greater accuracy, and minimal burr formation.
Vibration-assisted machining has been applied universally to traditional machining methods such as milling, drilling, grinding, etc It has gained several noticeably beneficial aspects
• Material removal rate (MRR), machining effectiveness, and cutting tool life are considerably increased, reducing machining time
• As brittle machining material, the depth of cut also improves, but we still gain the desired cutting conditions and high-quality surface finish
• When turning operation, the VAM method contributes to the reduction in concentrated stress and cutting force
Figure 2.5 Effect of Vibration-assisted method on surface finish applied in milling operation
When milling operation, as the VAM module is applied, it creates thinner chips and heat yielded through the process, which remarkably improves surface roughness h
Based on the frequency of vibration, VAM principle can be divided into two main types
• Resonance system: This system can solely operate at discrete frequencies greater than
20 kHz and yield displacement amplitudes less than 6μm
• Non-resonance system: This system can operate at the range of operating frequencies
(1 kHz – 40 kHz), and amplitudes yield ten folds greater than the resonance system
Furthermore, VAM can be divided into two types based on the mode of vibration, as shown in Figure 2.6
• 1-Dimensional VAM: This system operates in offset planes of the work-piece surface corresponding to the shear force
The 2-Dimension VAM enhances tool motion by introducing an elliptical pattern, where the major axis represents the cutting force and the minor axis signifies the thrust force.
Figure 2.6 1D and 2D “Elliptical” vibration cutting [1] h
Introduction of Vibration-assisted Electrical Discharge Machining
EDM, a non-conventional machining technique, is ideal for achieving high precision in machining hard-to-machine materials and intricate shapes However, challenges arise during the process due to inadequate debris removal, leading to frequent contact between the tool electrode and the workpiece, which destabilizes the machining The presence of debris can also cause electrical shorting, further complicating the process To address these issues, the introduction of vibration-aided techniques enhances debris removal by creating vibrations that effectively flush out material from the gap, resulting in improved process stability and significantly reduced machining time.
Figure 2.7 Illustration for the mechanism of machining of vibration-assisted EDM [2]
The frequent separation of the tool from the workpiece during machining cycles effectively removes debris, leading to consistent electric discharge and an 11% increase in material removal rate, while reducing relative tool electrode wear by 21% Additionally, a quantitative comparison of machining times reveals that vibration-assisted micro EDM techniques, characterized by higher frequency and larger amplitude vibrations, significantly reduce machining times compared to traditional methods.
Figure 2.8 Comparison of machining time with and without vibration-assisted technique [2] h
Introduction of Piezoelectric
In 1880, French physicists Jacques and Pierre Curie discovered piezoelectricity, a phenomenon where applying pressure to quartz and certain crystals generates an electrical charge This remarkable effect came to be known as the piezoelectric effect.
The Piezoelectric Effect refers to the ability of certain materials to produce an electric charge when subjected to mechanical stress The term "Piezoelectricity" is derived from the Greek words "piezein," meaning to squeeze or press, and "piezo," meaning to push.
Reversibility is a key characteristic of piezoelectric materials, indicating that those which demonstrate the direct piezoelectric effect—producing electricity under applied stress—also display the inverse piezoelectric effect, generating stress in response to an applied electric field.
There are two types of the piezoelectric effect
When piezoelectric material is placed between the two metal disks and is exerted by compressing or stretching force, which leads to the generation of electricity
Figure 2.9 Direct piezoelectric effect mechanism [6]
The piezoelectric effect occurs when a voltage potential is generated across a material, such as a piezo crystal sandwiched between two metal disks This setup allows charges to be collected by the metal plates, producing electricity akin to a small battery This phenomenon, known as the direct piezoelectric effect, is utilized in various applications, including microphones and pressure sensors.
14 sensors, hydrophones, and a variety of other sensing devices utilize the direct piezoelectricity
The piezoelectric effect is a reversible phenomenon, known as the inverse piezoelectric effect, where the application of electrical voltage to piezoelectric materials converts electrical energy into kinetic movement.
Figure 2.10 Inverse piezoelectric effect mechanism [6]
Piezoelectric materials are capable of generating electrical energy when subjected to mechanical stress, such as compression or extension Conversely, applying a voltage to these materials results in mechanical deformation.
In order to produce the piezoelectricity effect, all piezoelectric materials must not be conductive They can be separated into two groups: crystals and ceramics
Piezoelectric materials can be classified into several primitive branches such as [7]
• Naturally occurring biological piezoelectric materials such as human bone, tendon, cellulose, collagen, deoxyribonucleic acid
• Naturally occurring piezoelectric crystals such as quartz (SiO2), Rochelle’s salt (NaKC4H4O6 ã 4H2O), topaz, tourmaline group minerals, etc
• Synthetic piezoelectric ceramics such as lead zirconium titanate, PZT (Pb[ZrxTi1 − x]O3 0 ≤ x ≤ 1), barium titanate (BaTiO3), potassium niobate (KNbO3), bismuth ferrite (BiFeO3), zinc oxide (ZnO), etc
• Synthetic piezoelectric polymers such as poly (vinylidene fluoride) ((CH2-CF2)n), co- polymers of PVDF such as poly (Vinylidenefluoride - co - Trifluoroethylene) P (VDF- TrFE), polyimide, odd-numbered polyamides, cellular polypropylene, etc h
Figure 2.11 Branches of Piezoelectric materials [7]
Due to the unique patterns of piezoelectric materials, there is an array of applications that benefit from their use The applications of piezoelectricity consist of below aspects: [8]
• Actuators in Consumer Electronics (Printers, Speakers)
• Nano-positioning in AFM, STM
The electric cigarette lighter exemplifies the igniter field by utilizing a button press to activate a spring-loaded hammer, which strikes a piezoelectric crystal This action generates a high voltage, allowing electric current to flow across a small spark gap, effectively heating and igniting gas Additionally, most gas burners and ranges incorporate a piezo-based ignition system for efficient lighting.
Figure 2.12 An application of piezoelectricity in daily life
The industrial sector contributes its applications with piezoelectric sensors and actuators for a wide range of uses Some typical applications comprise:
The piezoelectric actuator (PEA) is a highly effective and commercially available device designed for precise control of minute displacements, ranging from 10 picometers (pm) to 100 micrometers (μm) The relationship between the input voltage and the resulting elongation is crucial for its functionality.
Piezoelectric stacked or multi-layer actuators are created by layering piezoelectric plates, with the stack's axis aligned to the direction of linear motion generated when a voltage is applied This configuration ensures that the electric field within the ceramic plates is parallel to the polarized direction, enabling effective actuation.
All the elements are connected in parallel as shown in Figure 2.13 h
In this project, we use Piezo P-225.10 PICA
Table 2.1 Technical data of Piezo P-225.10 PICA
Introduction of flexure hinges
A flexure or elastic hinge is a mechanism made up of rigid bodies linked by compliant elements, engineered to create precise geometric motion when force is applied This type of hinge is created by machining a rigid body into a thin section that serves as a bending joint between two thicker components.
The flexure hinge is primarily categorized into two main types: Primitive and Complex flexure hinges Within the Primitive flexure hinge category, there are three sub-levels: single-axis, dual-axis, and multi-axis flexure hinges.
Single-axis flexure hinge is designed for compliant mechanism with 2D motion on a plane Whereas, 2-axis or multi-axis flexure hinge is applied in 3D motion, with more complexity
This project will concentrate exclusively on single-axis flexure joints with relative motion on a plane, avoiding more complex designs Below, we outline several typical types of 1-axis flexure joints.
Figure 2.16 illustrates various types of flexure hinges designed for achieving rotational motion with a single degree of freedom, including the leaf-type hinge, cross leaf-type hinge, prismatic crossed hinge, notch hinge, and multi-trapezoidal or butterfly hinge [9].
• Pros: There are tons of reasons for the use of compliant mechanisms [10]
− Part count: using flexible components instead of springs, pins, and conventional rigid hinges, which is a contributor to the remarkable reduction in the number of components
− Price reduction: owing to their reduction in the number of parts and a simple fabricating method, the compliant mechanism can be relatively affordable to the manufacturers
Conventional mechanisms often suffer from dimensional precision loss due to backlash and wear caused by the mechanical interactions of connecting components like pins, clutches, and screws In contrast, compliant mechanisms experience minimal distortion, as they rely on fewer or no mating parts, ensuring greater accuracy and reliability.
− Superior performance: compliant mechanisms comprise less moveable joints, such as pin, clutch, screw, and slide joints, which diminish friction and the requirement for the lubrication process
• Cons: Besides its potential benefits, still exist several challenges: [10, 11]
Compliant mechanisms are often subjected to cyclic loading, making it crucial to assess the fatigue life of their components This evaluation ensures that failures do not occur during operation, allowing for the reliable performance of designated tasks.
Elasticity is essential for compliant mechanisms, as these materials must deform and revert to their original shape However, elastic materials often lack the necessary strength, which limits the effectiveness of compliant mechanisms in applications where strength is a critical requirement.
− Amplitude restriction: the movement caused by the compliant hinge is limited by the strength of the deflecting elements Obviously, a compliant hinge cannot provide a continuous rotating motion like a pin joint h
Taguchi method
Dr Taguchi of Nippon Telephones and Telegraph Company in Japan has devised a method based on " ORTHOGONAL ARRAY " trials that results in much decreased " variance
The Taguchi Method effectively integrates Design of Experiments with the optimization of control parameters to achieve optimal outcomes By utilizing Orthogonal Arrays (OA), it facilitates a systematic approach to conducting a minimal yet balanced set of tests, ensuring reliable results in the experimentation process.
Dr Taguchi's Signal-to-Noise ratios (S/N), which are log functions of desired output, serve as objective functions for optimization, aid in data interpretation, and anticipate optimal results
When there are an intermediate number of variables (3 to 50), minimal interactions between variables, and just a few variables contribute significantly, the Taguchi technique is applied properly
The Taguchi method is a systematic approach for assessing and enhancing products, processes, materials, equipment, and facilities This methodology aims to improve key attributes while reducing defects by analyzing the primary variables that influence the process and refining designs or methods to achieve optimal results.
There are 8 steps in Taguchi Method [12]
1 Determine the main functions, side effects, and failure modes
2 Determine the noise factors, testing conditions, and quality of characteristics
3 Determine the objective functions to be optimized
4 Determine the factors and their level
5 Identify the orthogonal array matrix experiment
6 Devise the selected matrix experiment
7 Analyze the data, optimal levels and performance from the software results
8 Verify the experiments and plan the future action
The Taguchi technique classifies problems into two categories: Static and Dynamic Static issues lack a Signal component and are optimized using three Signal-to-Noise ratios: smaller-the-better, larger-the-better, and nominal-the-best In contrast, Dynamic problems include a Signal component and are optimized through two Signal-to-Noise ratios: Slope and Linearity.
In this project, we solely conduct the Static problems Here are three formulas to compute the S/N ratios
(2.5) u: order number of measuring time n: number of experiments
− Emphasize a mean performance characteristic value close to the goal value rather than a value within specified specification limitations, which improves quality of the product
− Simple and uncomplicated to applied in different engineering fields
− Owing to the discrete figures, so the outcomes are approximately optimal
− Are not able to add in constrain conditions
− Solely address single-target problems h
2.6.4 Selection of orthogonal array matrix experiment
To select an orthogonal array matrix experiment, it is essential to compute the degrees of freedom among the factors, as well as the number of factors and levels In this project, we simplify the process by choosing the number of experiments based on the guidelines provided in Table 2.2 [13].
Table 2.2 Selection of orthogonal array [13]
DESIGN OF VIBRATING TOOL (INHERITED)
Design process
The design process of this module is implemented as following steps: [21]
Begin by designing the concept using Inventor software, focusing on the flexure hinge, the module's crucial component Next, utilize Ansys software to assess key parameters, including natural frequency and displacements along the X, Y, and Z axes Evaluate the advantages and disadvantages of each design option to identify the most optimal solution.
• Re-designing the above-selected concept for optimizing the design parameters
• Parameterizing design variables and constrain conditions, and then establish the objective functions
• Optimizing the design variables on Ansys software by Response Surface Optimization (RSO) in order to multi-objective optimization
• Selecting the most optimal design for machining.
Conceptualizations
The PZT will be centrally assembled and electrically insulated from the EDM's electrode using two POM plastic encapsulation components Vibration from the PZT is transmitted to the EDM's electrode through a compliant mechanism, allowing for vertical displacement along the Z-axis In this design, the flexure hinge serves as the housing for the module.
Flexure hinge design
Various design options for compliant mechanisms include rectangular-parallelepiped shapes, disc shapes, spring shapes, and cylinders with zigzag flexures To analyze critical parameters such as vertical displacement along the Z-axis and natural vibration frequencies, Ansys software is utilized These factors are crucial in the design process to prevent resonance phenomena.
• Option 1: Rectangular-parallelepiped-shape model
Figure 3.2 Rectangular-parallelepiped-shape model [21]
Although this kind of shape are easy for manufacturing, its vibration frequency just reaches 321 Hz (Figure 3.2.c), besides, there are the emergences of other displacements of
→ This does not meet the requirement
Disc-shape model is superior in generating high vibration frequency roughly 6511
Hz, but its manufacturing process is quite sophisticated and its total weight is also considerable
→ This is not the most optimal option because of the above-mentioned reasons
• Option 3: Cylinder-spring-shape model
Figure 3.4 Cylinder-spring-shape model [21]
Cylinder-spring-shape model yields quite low vibration frequency just at approximately 223 Hz (Figure 3.4.c) Moreover, there is the appearance of undesired displacements along X, and y axes
→ This does not meet the requirement
Zigzag-shape flexure hinge generates vibration frequency at about 529 Hz (Figure
3.5.c) Besides, this kind of structure may yield rotation movement about Z axis
Figure 3.6 Zigzag-shape model with 3 joints [21]
However, when reducing the number of joints from7 to 3, the vibration frequency may experience an increase from 52 Hz to 1493.2 Hz (Figure 3.6.c)
Figure 3.7 One-side-zigzag and Symmetric-zigzag model
Furthermore, these flexure hinges should be placed symmetrically (Figure 3.7.b) aiming to restrict the rotation movement about Z-axis h
Figure 3.8 Symmetric-zigzag-shape model [21]
➔ In conclusion, the symmetric-zigzag-shape model would be chosen for this project, because it can yield the vibration frequency at up to 1493.2 Hz (Figure 3.8.c)
3.3.2 Optimizing the symmetric-zigzag flexure hinge
The 7075-T6 Aluminum alloy, composed of zinc, copper, and magnesium, is chosen for module manufacturing due to its exceptional mechanical properties This lightweight material offers high durability, fatigue strength, and resistance to wear and heat, making it a preferred choice in the automotive, aerospace, and mechanical industries.
Table 3.1 Chemical compositions of 7075 Aluminum alloy
Table 3.2 Mechanical properties of 7075-T6 Aluminum alloy
• Dimensional parameters of flexure hinge
After implementing tests for static, dynamic, and undesired displacement along X, and
Y axes by using Ansys software, we achieved: h
Natural vibration frequency 1656 Hz Figure 3.12c
Equivalent stress max 67.92Mpa