MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING STUDYING THE PRINCIPLES OF BURR FORMATION IN HYBRID MACHININ
OVERVIEW
Introduction
Aluminum alloy 6061 is composed of several elements, including approximately 0.63% silicon, 0.096% copper, 0.091% zinc, 0.466% iron, 0.179% manganese, 0.53% magnesium, 0.028% titanium, 0.028% chromium, with the remaining portion being raw aluminum Adding silicon enhances the alloy's strength and ability to withstand high temperatures Copper improves both strength and corrosion resistance Zinc contributes to better casting properties and acts as a strengthening agent Iron, present in small amounts, can impact the alloy's mechanical properties Manganese improves strength and aids in achieving a favorable grain structure during casting Magnesium plays a significant role in enhancing strength, corrosion resistance, and weldability Titanium and chromium, in small quantities, contribute to grain refinement and improved resistance against stress corrosion cracking [1]
Aluminum alloy 6061 is a widely utilized grade of aluminum alloy that finds applications in various industries Its versatility and availability in different forms, such as plates, tooling plates, bars, and extrusions, make it a popular choice for commercial and industrial projects The alloy exhibits favorable characteristics, including good strength, corrosion resistance, and weldability, contributing to its widespread use To obtain the desired surface quality, dimensional accuracy, and tool life in conventional machining of Al6061-T6 alloy, careful selection of cutting parameters is essential These parameters include cutting speed, feed rate, depth of cut, tool geometry, and lubrication [2]
Vibration-assisted machining (VAM) is a favored method among researchers for investigating high-quality surface improvements and burr reduction in machining Although VAM has demonstrated its effectiveness in numerous cases, there are situations where complete burr elimination may not be achieved To address this, researchers focus on optimizing cutting conditions and utilizing assisted vibration energy during the machining process [3] By carefully selecting cutting parameters and incorporating vibration energy, these techniques aim to minimize burr formation further and enhance the overall machining outcome It is possible to use the FEM software to simulate the chip formation, burr formation, and surface quality of the workpiece to predict the effectiveness of machining In this case, researchers are likely to limit the
2 range of input factors instead of experiments in all these FEM is a tool that is economics in R&D fields and this is developed now and in the future
For instance, Isbilir [4] utilized Abaqus/Explicit software to simulate the drilling process of Ti6Al4V workpieces Their study focused on factors such as thrust force, torque, burr size, and workpiece stress Similarly, İrfan Ucun employed DEFORM 3D software to create a 3D finite element model for simulating the drilling process of Al7075-T6 alloy The objective of the study was to validate the model by investigating the thickness of burrs and the influence of cutting conditions on their formation In the field of milling simulation, Li [5] conducted research on optimizing simulation time for milling processes involving aluminum 6061 Their study aimed to improve simulation efficiency while maintaining accurate results Chen et al [6] developed an orthogonal model to examine chip formation and cutting forces in VAM simulation Their study focused on analyzing the impact of VAM on machining processes.
Motivations for topic selection
Nowadays, the removal of burrs following machining processes, particularly in drilling operations, has become of utmost importance However, there are instances or specific positions where eliminating burrs remains challenging Figure 1.1 provides an academic representation of a specific case that demonstrates the inability to eliminate the formation of an exit burr
Figure 1 1 The drilling hole and burr
The selection of suitable cutting conditions, including speed, feed rate, and depth of cutting, is essential for facilitating the easy removal of burrs using water pressure Making appropriate choices for these parameters is crucial in ensuring efficient elimination of burrs Regarding VAM drilling, researchers globally are actively investigating VAM to assess its potential superiority over conventional machining methods
One approach utilized to determine suitable cutting modes involves conducting experiments using predefined cutting parameters and assessing the effectiveness of VAM in drilling However, it is crucial to acknowledge that setting up well-equipped technology labs and investing in machining equipment incurs significant costs Instead of experimental work, Computer-Aided Engineering (CAE) is another way to predict the effectiveness of machining Designing the machining model is unnecessary, which reduces the funds for experiments As a result, the author decides to select CAE to predict the behavior of burr in the drilling process rather than experiments
Scopes and Objectives
This capstone project mainly focuses on analyzing and understanding the mechanisms underlying conventional drilling and vibration drilling models Because of the resource limitation, the author only examines the outcome trend instead of exacting these The research can be succinctly summarized as follows:
1 Using the Finite element method – Abaqus software to study the exit burr formation
2 Find out the trend of exit burr formation in various cutting conditions by Abaqus/Explicit, which recommend the range for experiment works
3 Compare this to the trend of exit burr formation in convention drilling and VAM drilling.
Structure of thesis
Chapter 1: An overview of the thesis, an introduction highlighting the motivation and reasons for selecting the topic, a description of the experimental methodology, and an outline of the scope and objectives of the thesis
Chapter 2: Identify the factors studied in the simulation as the response variables, outcomes, and their levels It illustrates how to measure the outcomes Introduction of the Taguchi method in experiments
Chapter 3 Overview of the Explicit principle in Abaqus, cutting mechanisms
FEM applied in the drilling machining
Chapter 4 Report to the exit and entrance burr formation in the drilling process in convention and VAM Predict the trend of burr formation
Chapter 5 Summarize the findings Present the conclusion, suggest a plan for addressing the identified issues model, and offer direction for future research
Hybrid machining process
Kapil et al [7] referred hybrid machining involve combining multiple machining processes to overcome limitations and achieve improved performance By integrating different methods, hybrid machining addresses challenges such as limited material removal rates, surface quality issues, and the machining of complex workpieces This approach combines traditional machining processes like milling, turning, or drilling with non-traditional methods such as laser machining or electrochemical machining Another aspect of hybrid machining involves integrating additive manufacturing with subtractive processes, combining the advantages of both approaches
Benefits of hybrid machining include increased material removal rates, enhanced surface quality, improved machining flexibility, process optimization, and potential time and cost savings However, challenges exist in terms of process integration, tooling requirements, and the complexity of optimizing parameters
Hybrid machining is a rapidly evolving field with ongoing research and development aimed at exploring new process combinations, optimizing parameters, and expanding application possibilities The goal is to enhance machining capabilities and meet the evolving demands of modern manufacturing industries
Brehl [8] defines vibration-assisted machining as a technique that involves applying controlled vibrations during the machining process to improve cutting performance and machining outcomes It has gained significant attention as a solution to challenges like tool wear, chip control, and surface quality, which concern the effects of vibration-assisted machining on cutting performance, such as reducing cutting forces, improving chip control, enhancing material removal rates, and impacting tool wear and tool life It would also examine the influence of vibration parameters, such as amplitude, frequency, and direction Surface quality and dimensional accuracy are important considerations in machining The review would discuss how vibration-assisted machining affects surface roughness, surface integrity, and dimensional stability It would highlight the mechanisms by which vibrations help reduce surface defects like built-up edge and chatter marks
Modeling and optimization techniques used in vibration-assisted machining would be another focus of the review This would include analytical, numerical, and
7 experimental methods employed to understand the process and optimize vibration parameters Techniques like finite element analysis, analytical modeling, and response surface methodology would be explored.
Burr formation, measuring, and calibration method
2.2.1 Factors affect the burr formation
Saunders [9], in the majority of metal cutting operations, the emergence of burrs is observed as the cutting tool completes its exit from the workpiece These exit burrs pose a challenge as they require supplementary manufacturing steps to effectively address them, including disassembly and deburring procedures
The model for burr formation encompasses five distinct elements, namely cutting force modeling, thermal modeling, stress modeling, evaluation of a failure criterion, and simulation of material removal In this thesis, the thermal factor is skipped
In order to create a comprehensive model for burr formation, it is essential to have precise the cutting forces exerted during drilling These cutting forces are responsible for applying loads to the finite element model Specifically, during drilling, the thrust force is distributed as a directed pressure on the top surface of the material located in front of the drill
Figure 2 2.a Stress in chip formation, b Burr formation in drilling process
After the drill penetrates the workpiece, the material present in front of the drill sustains the applied thrust force, allowing the cutting process to persist The cutting operation proceeds until the maximum normal stress at point B (as depicted in Figure 2.2) attains the ultimate stress level of the material Subsequent to the failure at pointB, the remaining material undergoes deformation and bends over, resulting in the formation of a burr with a height denoted as Rf
2.2.2 Factors affect to the thrust force
In the research article “Analysis of the effects of process parameters on exit burrs in drilling using a combined simulation and experimental approach”, Lauderbaugh [10] explored the effect of three factors: feed rate, spindle speed, and geometry cutting tools
In that research, the feed rate is a factor that has the most influence on burr height
In this thesis, all simulations use the same geometry cutting tool The feed rate and the spindle speed are variable in conventional drilling In VAM drilling, two factors amplitude and frequency, are added in
The thrust force is a critical factor influencing burr formation In this thesis, it is imperative to conduct simulations to analyze the outcomes of the thrust force Subsequently, a comparison is made with previous results obtained from other simulations or experimental studies To ensure accurate results, the material properties and contact parameters are carefully calibrated Once the calibration process is completed, the cutting condition and geometry cutting tool parameters are systematically varied in order to facilitate new simulations
Chang [11] used to perform experiment that the simulation and experiment in 6061 VAM drilling Author determined that the thrust force in VAM is smaller than convention The thrust force results obtained from the experiments were compared to the corresponding simulation resultsare represented by solid data points, while the experimental data is depicted by hollow circular data points The maximum deviation observed between the experimental and simulation results was 10% Notably, a reduction of 16% in the thrust force was achieved when the vibration frequency was set to 10 kHz This paper presents a thrust force model to predict the thrust force during vibration-assisted drilling of aluminum 6061-T6 The model incorporates plowing force and strain rate-dependent shear strength to provide more accurate predictions than the existing model The results of 72 drilling experiments with TiN-coated standard twist drills are reported, and the predictions from the developed thrust force model are compared with the experimental results The comparison demonstrates that the maximum deviation between the predictions and the averaged values of the experimental measurements is only 7% using the proposed model
Li et al [12] investigated VAM drilling with the frequency range (100 – 1000Hz) and amplitude (0.003 – 0.0035 mm) They supposed that an elevated vibration frequency has been determined to correlate with a reduction in burr height When comparing the burr height values between conventional drilling (CD) and the optimized low-frequency vibration-assisted drilling (LFVAD) technique, a substantial decrease ranging from 52.75% to 53.16% was observed
Influence of factors in burr height
Chen [13] supposed that the feed rate in drilling refers to the speed at which the drill advances into the workpiece It is a critical factor in the drilling process and has a direct impact on the formation of burrs Analyzing the relationship between feed rate and burr height is crucial for optimizing drilling operations and achieving the desired surface quality When the feed rate is increased during drilling, it can lead to an increase in burr height This is primarily because the higher feed rate results in increased cutting forces, causing the cutting tool to push the material upward and create raised edges around the drilled hole The magnitude of the burr height increase depends on various factors, such as the material being drilled, drill geometry, cutting conditions, and the stability of the setup Experimental investigations are conducted to study the influence of feed rate on burr height These experiments involve testing different materials at varying feed rates, and the resulting burr heights are carefully measured and analyzed The empirical data obtained from these experiments help to establish the relationship between feed rate and burr height
Zhang [14] supposed cutting speed, denoting the rotational velocity of the drill bit during micro drilling, plays a crucial role in burr formation Higher cutting speeds have the propensity to generate more heat and induce material softening, which can lead to the creation of larger burrs Therefore, conducting an investigation into the effect of cutting speed on burr formation is essential to establish an optimal range that simultaneously minimizes burr size and ensures efficient productivity
Liao [15] Vibration-Assisted Machining (VAM) drilling has been shown to enhance drilling performance through the reduction of cutting forces, improved chip evacuation, and enhanced surface quality A notable advantage of VAM drilling is its ability to effectively decrease burr formation This is achieved by utilizing the oscillatory motion of the cutting tool to facilitate chip segmentation, thereby preventing the formation of lengthy chips that contribute to burr generation Consequently, this technique leads to diminished burr height and improved hole quality, particularly in materials prone to burr formation like titanium alloys Researchers commonly conduct
11 experimental studies to explore the impact of different vibration frequencies on drilling performance, surface integrity, and burr formation
Generally, higher vibration frequencies are inclined to promote chip segmentation, resulting in smaller chip sizes and smoother material flow This, in turn, aids in minimizing burr formation However, it is important to note that the optimal frequency range for reducing burr height may vary depending on the specific material and drilling conditions
Li [16] conducted a series of experiments to analyze the effects of vibration- assisted drilling on two main aspects: reducing drilling force and improving hole quality They investigated how vibration assistance, achieved through oscillatory motion, can effectively decrease drilling forces compared to conventional drilling methods The study also focused on enhancing hole quality by minimizing burr formation and improving surface finish The experimental data and analysis presented in the paper demonstrate the positive outcomes of vibration assistance in achieving these goals Additionally, the authors found that the frequency of vibration was the most significant factor influencing burr formation
Zhang [17] provides valuable insights into optimizing vibration parameters to improve the surface quality of drilled holes in titanium alloy The study specifically investigates how vibration amplitude affects the surface quality of drilled holes in titanium alloy Through experiments, the authors varied the vibration amplitude between
10 and 30 um and measured the surface roughness values of the drilled holes The results indicated that increasing the vibration amplitude resulted in a decrease in surface roughness, indicating an improvement in the surface quality of the drilled holes
Similarly, other the study examined the impact of different vibration amplitudes, ranging from 5 to 20 um, on the surface quality and burr height in vibration-assisted drilling (VAM) The results demonstrated that increasing the vibration amplitude led to a decrease in surface roughness and waviness values, indicating an improvement in the surface finish of the drilled holes [18]
Experiment planning
In the field of science, it is essential to conduct practical experiments to gather data and knowledge about an object or process These experiments help in obtaining accurate information and identifying the most suitable research direction for the problem being studied Through the process of experimentation, the characteristics of the research object are analyzed and evaluated, resulting in precise and reliable data Analyzing and processing this data provides researchers with a deeper understanding and knowledge of the object, allowing them to identify its fundamental characteristics and establish relationships between its parameters using mathematical equations and graphs This comprehensive understanding obtained through mathematical models and graphical representations enables researchers to apply their knowledge to various real-world applications
Performing practical experiments is crucial as it lays the foundation for all research and development in engineering, especially in the field of optimization Nowadays, a combination of theoretical research and practical experiments is commonly employed Theoretical research helps in understanding the underlying principles and processes, while practical experiments validate and supplement the results obtained from theoretical studies, leading to a better understanding of the underlying mechanisms Experimental planning is a crucial method used to achieve predetermined goals in research Proper planning ensures that the output obtained is sufficient and accurate, providing clear answers to the research questions and enhancing our understanding of the research object [19]
The four factors simulation is divided into three levels in Table 2.1
In this experiment, the output or response variable is factors that affect burr height in the drilling process These are exit burr height, entrance burr height and thrust force
𝐹 𝑡 Table 2.3 indicates all factors in experiments
Table 2 2 Input and response variable
Level of factors Response variable
When planning an experiment, selecting an appropriate experimental design is of utmost importance as it directly affects the experimental process and the resulting outcomes In the case of qualitative or quantitative experiments involving a single factor, it is relatively straightforward to control the number of experiments based on the objectives and scope of the study However, for more complex experiments that involve the examination of multiple factors (combinations of qualitative and quantitative factors), determining the necessary number of experiments becomes more challenging
In such cases, a one-factor experimental model is insufficient, and the use of a multifactor model becomes necessary
An experimental model aims to identify the optimal values for parameters while considering the factors involved and their respective influences It also minimizes the number of experiments required One notable approach to address this challenge is the Taguchi method, which was proposed by Genichi Taguchi, a Japanese statistician and engineer The Taguchi method utilizes orthogonal arrays, similar to factorial designs, but follows a rigorous process that allows for conducting fewer experiments while obtaining more reliable data
The fundamental concept behind the Taguchi method is to identify the key technological factors that maximize efficiency by detecting and mitigating the effects of disturbances These factors, referred to as input variables, impact the results in two directions: one direction brings the results closer to the desired goal, known as the
"Signal," while the other direction causes the results to deviate from the target, known as "Noise." The evaluation of the signal-to-noise ratio (S/N) serves as an effective indicator for assessing and selecting parameters Parameter sets with higher S/N ratios are considered more favorable, while those with lower S/N ratios are considered less desirable [20]
Based on the type of problem at hand, there are 3 distinct methods available to calculate the signal-to-noise (S/N) ratio [21]
Average of rate of S/N for each level of every factor:
In this case, it is possible to select orthogonal L9 table with four factors and three levels
No Speed Feed rate Frequency Amplitude
FINITE ELEMENT METHOD IN DRILLING PROCESS
Cutting parameter and cutting force
3.1.1 Geometry for drilling and cutting parameter
Drilling is a machining process utilized to generate or expand circular holes in solid materials by means of a rotary drill bit The drill bit, often featuring multiple cutting points, is brought into contact with the workpiece and rotated at considerable speeds, ranging from hundreds to thousands of revolutions per minute This rotational motion causes the cutting edge of the drill bit to engage with the workpiece, effectively removing material in the form of chips during the drilling operation In figure 3.1 shown the cutting geometry for drilling [22]
During the chip removal stage in drilling, the cutting speed relies on the tool's rotary motion This speed is quantitatively described by an equation that captures the relationship between the rotational movement of the tool and the resulting cutting speed:
1000 (m/min) (3.1) where d is the diameter of drilling bit, n is the velocity of drill
The feed (s) in drilling represents the axial distance traveled by the drill during a single cycle It is typically measured in millimeters per revolution Drills typically consist of two cutting edges or teeth, and the feed rate can be specified in terms of the number of teeth (z), indicating the amount of feed per tooth: sz = s/z = s/2 (mm/rev) (3.2)
The feed velocity corresponds to the axial speed at which the drill progresses during drilling:
The given parameters allow for the formulation of equations relating to chip thickness per tooth (h), width (b), and feed per tooth (a) Assuming that the drill angle (α) and tool angle (θ) are such that θ = α/2, and a is equal to half of the drill diameter (d), the following equations can be defined:
Figure 3 1 Cutting geometry for drilling
When drilling, the forces responsible for chip removal include the cutting force (Fsz), feed force (Fvz), and radial force (Frz) The cutting force exerted on each cutting edge can be broken down into longitudinal and radial directions, as illustrated in Figure 3.2 The longitudinal forces primarily contribute to the feed force, which is an important factor in the process
𝐹 𝑠𝑧 = 𝐴 𝑠𝑧 𝑘 𝑠 (𝑁) (3.6) where Asz is the cutting face, ks is specific feed force
The specific feed force (𝑘 𝑠 ) is determined by several factors, including the material type, feed velocity, and tool wear To accurately incorporate these influences, additional correction factors are introduced and combined with the basic specific feed force (𝑘 𝑥 )
𝑘 𝑠 = 𝑘 𝑥 𝑘 𝑤 𝑘 𝑟 ℎ −𝑚 (𝑁 𝑚𝑚⁄ 2 ) (3.7) The specific feed force directly related to the basic cutting face of the tool (𝑘 𝑥 ) The influence of tool wear is quantified by the correction factor (𝑘 𝑤 ) The depth of cut is represented by the parameter (h), while the correction factor (m) accounts for the impact of the material type Additionally, the correction factor (𝑘 𝑟 ) encompasses all other relevant influences on the specific feed force
The factor 𝑘 𝑠 accounts for the impacts of material type, feed velocity, and tool angle (θ) on the drilling process, as illustrated in Figure 3.1 It quantifies the relationship between these factors and the specific characteristics of the cutting face (𝐴 𝑠𝑧 )
𝐴 𝑠𝑧 = 𝑑ℎ (𝑚𝑚 2 ) (3.8) where d is the diameter of drill bit
As a result, feed force 𝐹 𝑠𝑧 yields
𝐹 𝑠𝑧 = 𝑘 𝑥 𝑘 𝑤 𝑘 𝑟 𝑑(𝑓 𝑧 𝑠𝑖𝑛𝜃) 1−𝑚 (3.9) where fz ẳ up=n feed per tooth and
The parameter αfv is determined by a function that considers both the feed velocity (u) and the influence of tool wear, which is characterized by the correction factor 𝑘 𝑤 Tool wear is primarily caused by the mechanical and thermal stresses
19 occurring in the contact area between the cutting edges and the workpiece, resulting from friction during the drilling process.
Kinetics of VAM drilling
Figure 3.3 show the direction of vibration in drilling In general, the vibration is applied for workpiece
Figure 3 3 Drilling model with vibration
The overall displacement z in figure 3.4 is determined by the sum of two factors: the displacement attributed to the feed (𝐹𝑛𝑡) and the displacement associated with vibration, 𝐴𝑠𝑖𝑛(2𝜋𝑓𝑡) + 𝐹𝑛𝑡:
𝑧(𝑡) = 𝐴𝑠𝑖𝑛(2𝜋𝑓𝑡) + 𝐹𝑛𝑡 (3.11) where A and 𝑓 are the vibration amplitude (mm) and frequency (Hz), respectively; F is the feedrate (mm/rev); n is the spindle speed (rev/sec); and t is the time (s) Similarly, the instantaneous velocity is:
In order to determine the axial uncut chip thickness, which plays a vital role in the estimation of cutting forces, it is imperative to observe and measure the maximum depth of material removal precisely at the specific rotational location of interest, zmax(θ)
Transform the 2πnt to θ, the equation 3.10 will be expressed:
(3.13) zmax(θ), the axial position can be determined by observing the location of the cutting lips before the current instance In the case of a two-flute drill, where the cutting lips are separated by a distance of π radians, the axial positions of all the cutting lips prior to the current moment are equivalent to z(θ-mπ) Where m is a positive integer
Figure 3 5 Geometry of VAM drilling
The resulting forces for the i th element can be expressed by 2 formula that [23]:
𝐹 𝑝𝑥 = 𝜇 𝑐 𝐹 𝑝𝑡 (3.16) where Fpt is the plowing force in thrust direction, Fpx is the plowing force in horizontal direction, fsp is the experimentally determined specific plowing force,μc is the mean friction coefficient of the tool–work interface, ΔVi is the displaced volume
FEM in machining process
The Finite Element Method (FEM) provides a favorable alternative to address the challenges of time and cost involved in machining experiments By utilizing FEM, it becomes possible to reduce the lengthy duration and high expenses associated with conducting physical experiments Moreover, it is essential to recognize that experimental tests hold validity within the specific conditions under which they are performed and are reliant on the precision and accuracy of the equipment used in the experimentation process [24] In the realm of machining process simulation, two methods are commonly employed: implicit and explicit The implicit method entails calculating the solution at a given time point (t + Δt) using variables from both the current time (t) and the future time (t + Δt) Conversely, the explicit solver determines the values at each time step (t + Δt) exclusively based on the current time values (t) Both of these methods have been extensively utilized in simulating various machining processes [25] Additionally, the implicit approach in machining process simulation requires a larger time step (∆t) compared to the explicit method As a result, the implicit method is computationally more costly and resource-intensive
The literature contains a multitude of publications that document various simulations of machining processes, encompassing different software applications, dimensional parameters, and other pertinent aspects For a comprehensive overview, Table 3.1 [26] provides a detailed reference
Figure 3 6 Path of tool model
Table 3 1.Some machining researches using finite element method
Turning Ti-6Al-4V titanium alloy
Turning Ti-6Al-4V titanium alloy
Ti15V3Cr3Al3Sn titanium alloy
ANSYS TM 7075 aluminium alloy, AISI
John et al [32] DEFORM TM
Lauro et al [33] ANSYS TM
Drilling Ti-6Al-4V titanium alloy
Overview of the Explicit Finite Element method
The term "increment time" within the context of Abaqus refers to the size of the time step utilized in the simulation It represents the interval at which the simulation progresses and the associated calculations are performed The selection of the increment time in Abaqus is influenced by various factors, including the complexity of the problem, the desired level of accuracy, and the computational resources available Typically, a trade-off between accuracy and computational efficiency is considered, where smaller time steps provide more precise results but require higher computational resources, while larger time steps may sacrifice some accuracy in favor of reducing computational costs Ultimately, the determination of the increment time in Abaqus is based on the specific requirements and constraints of the simulation under consideration
Figure 3.7 visually depicts the commencement of the drilling process at position
A, with the drill bit subsequently advancing to point C after a specified total time,
Figure 3 7 Increment time in Explicit t
26 denoted as t To effectively simulate this process, the total time, t, is divided into several smaller increment time intervals In the context of the simulation, each time increment is separated by a stability limit referred to as "∆t" This ensures that the simulation remains stable and reliable throughout the progression of time
Abaqus/Explicit employs a central difference rule to explicitly integrate the equations of motion over time This integration process utilizes the kinematic conditions at one increment to calculate the kinematic conditions at the next increment At the beginning of each increment, the software solves for dynamic equilibrium, which is defined by the nodal mass matrix, M, times nodal accelerations, ü(t), being equal to the net nodal forces The net nodal forces are determined as the difference between the external applied forces, P, and the internal element forces, I:
The methodology for determining the accelerations at the beginning of the current increment (time t) involves the following computational steps:
Step 1: Nodal calculation a Dynamic equilibirum:
𝑢̈(𝑡) = 𝑀 −1 [𝑃(𝑡) − 𝐼(𝑡)] (3.19) The nodal mass matrix, 𝑴, times the nodal accelerations, 𝒖̈, equals the total nodal forces (the difference between the external applied forces, 𝑷, and internal element forces, 𝑰) [17] b Integrate explicitly through time
Step 2: Element calculations a Compute element strain increment, 𝑑𝜀, from the strain rate, 𝜀̇ b Compute stresses, 𝜎 c Assemble nodal internal forces
Step 3: Set 𝒕 + ∆𝒕 to 𝒕 and return to Step 1
Influence of factors in simulation result
3.4.1 Stable time and step time
It is vital to define the stable time in Explicit simulation The determination of the stable time increment involves considering the minimum element length (Le) and the dilatation wave speed (cd) of the material [35]
The wave speed "cd" mentioned in Equation (3.20) is a characteristic of the material, where "E" denotes Young's modulus and "ρ" represents the mass density of the material
The stability limit plays a crucial role in numerical simulations as it affects the selection of the time increment Ensuring that the chosen time increment is smaller than the stability limit is essential to maintain the stability of the model [36] In simulation, the step time Δt must smaller than the stable time On the other hand, the simulation process will appear some error such as “excessively distorted elements”, “the ratio of deformation speed to wave speed exceeds 1.0000 in at least one element” (figure 3.8)
In explicit, it is good to select the small step time, it means the smaller step will make higher accuracy of result However, it reduces the computational cost
Figure 3 8 Error in step time larger than stable time
In [27], Mass scaling is a numerical technique employed in explicit simulations to improve computational efficiency while maintaining result accuracy Its purpose is to increase the time increment by artificially raising the density in the model, as specified in Equation (2.5), through the adjustment of the "𝜌" value This adjustment enables a larger stability limit In Abaqus/Explicit, two fundamental approaches are utilized for mass scaling: direct definition of a scaling factor or specification of a desired element- by-element stable time increment for the elements requiring mass scaling
Joshua [37] predicted chip morphology predicted by the u-LAG models using element sizes of 0.01 mm and 0.06 is presented The model with 0.06 mm elements did not generate a chip due to the complete removal of larger elements near the cutting edge (figure 3.9a), indicating the need for a more refined sacrificial layer of elements in this methodology This suggests that a finer mesh is necessary compared to the other methodologies investigated in this study to achieve chip formation On the other hand, the model with 0.01 mm elements did produce a chip (figure 3.9b); however, its radius of curvature was significantly smaller than that observed in the experiment, indicating a discrepancy between the simulation and experimental results
Figure 3 9a) Workpiece with element size 0.06 mm and b) Workpiece with element size 0.01
RESULT OF BUR FORMATION IN SIMULATION
Design the 3D drilling simulation model
Figures 4.1(a) and 4.1(b) illustrate two perspectives of the actual drilling model, where the workpiece is situated between two plates and a bench vise In order to simulate the drilling process accurately, it is necessary to transform this model into a 3D representation that solely includes the workpiece and the tool The resulting 3D simulation model is presented in Figure 4.2 Considering the constraints of available resources, it is crucial to optimize the computational cost by reducing the number of elements in the workpiece To achieve this, a workpiece size of Φ7x0.1mm and the twist drilling bit size Φ5, helix angle 140° is selected (figure), enabling a total element count ranging from 100,000 to 200,000 elements This approach strikes a balance between computational efficiency and maintaining an acceptable level of accuracy in the simulation
Figure 4.2 depicts the simulation model converted from figure 4.1, the fixture is replaced by static condition in workpiece (restrict 6 DOF) So as to reduce elements number, the top view section of workpiece is circle
Figure 4 1 a) ISO metric view of drilling model and b) Front view of drilling model a) b)
Figure 4 2 a) ISO metric view of simulation drilling model and b) Front view of simulation model
The Johnson - Cook constitutive model is utilized to accurately capture the plastic flow behavior of the workpiece materials It incorporates essential factors such as strain hardening, strain rate strengthening, and thermal softening effects, making it highly suitable for simulating metal cutting processes Moreover, the J – C damage model is employed to accurately characterize material damage and enable the differentiation between the chip and the workpiece during the cutting simulation The flow stress equation is represented by equation 4.1 and the J – C damage criterion equation 4.2 The table 4.1 to 4.3 shown all the parameter of the Al6061 –T6 in simulation σ̅ = [A + B (ε) n ] [1 + C ln( ε̇ ε̇ 0 ) ] [1 - ( T−T r
A: yield stress of the material under reference deformation conditions (MPa) B: strain hardening constant (MPa) n: strain hardening coefficient
C: strain rate strengthening coefficient m ↔ thermal softening coefficient
Tm : melting temperature of the material ε̇ 0 : reference strain rate (1/s) ε̇ ↔ equivalent plastic strain normalized with a reference strain rate ε ↔ plastic equivalent strain ε̅f = [D1 + D2 𝑒 (𝐷 3
Tm: melting temperature of the material ε̅f: failure plastic strain for damage initiation ε̇ p : equivalent plastic strain rate ε̇0: plastic strain rate
𝑝 σ 𝑒 : ratio between hydrostatic pressure to equivalent stress
Table 4 1 Physical parameter of AL6061-T6
Parameter Density (kg/m 3 ) Young’s modulus (MPa) Poisson’s ratio
Table 4 2 Parameter of the Johnson - Cook constant in Al6061-T6
Table 4 3 Ductile damage of Al6061-T6 by the Johnson-Cook model
In this model, to reduce the simulation time, the mesh hexagonal - dominated C3D8R is applied, the element size is 0.03 mm and the element number is 180,000 elements So as to get higher accuracy result, the mesh size should be smaller than feed per tooth Generally, the mesh size usually is selected equal 30% feed rate In the tool, it is applied the tetra element C3D4R, elements is around 2000 elements Figure 4.3 shown the meshing model
Figure 4 3 Meshing in drilling model
The surface-to-node approach was employed to establish the kinematic surface interaction between the cutting tool and workpiece Within this approach, a specific node representing the cutting zone in the workpiece was highlighted in yellow The tool surface served as the master surface, while the workpiece surface acted as the slave surface To ensure accurate dynamic explicit simulation, the shear friction stress required for the simulation is derived using the equation 4.3 [38], the friction coefficient of 0.3 was incorporated into the simulation to account for the frictional forces between the tool and workpiece surfaces τ = μ ∙ σn (4.3)
Where: μ is friction coefficient σn is the contact stress
4.1.5 Boundary condition and first results to calibrated
The boundary condition in convention drilling and VAD is presented in figure 4.5 to 4.7
Figure 4 5 Boundary condition of cutting tool
Figure 4 6 Boundary condition of workpiece in COM
In cutting condition speed 2000 rpm, feed rate 0.1 mm/rev, the tool is applied the longitude feed rate 3.4 mm/s and rotation about cutting tool axis 209.44 rad/s and other factors equal zero (Figure 4.5) In terms of workpiece, all displacement equal zero (Figure 4.6)
Figure 4 7 Boundary condition of workpiece in VAD
On the other hand, in VAD boundary condition in workpiece that is vibration in longitude the cutting tool with frequency 1000 Hz and amplitude 0.002 mm Other factor equal zero (figure 4.7)
The boundary condition in simulation is refer to the [11] and [3] reference The thrust force of revolution 1000 rpm, the feed 0.06 mm/rev in simulation is 145.4 N (figure 4.5) and the thrust force in experiment of [11] is around 128N (figure 4.6) The error number is calculated:
Table 4 4 Validation the simulation thrust force with experiment result
Reference Experiment force (N) Average thrust force in simulation
Figure 4 8 Thrust force at S= 1000 rpm, f = 0.06 mm/rev
Figure 4 9 Thrust force comparison between simulation and experiment
Besides, the exit burr height in the simulation is 0.164 mm, the experimental average burr height in [11] is 0.2 mm
Table 4 5.Validation the simulation Burr height with experiment result
Average burr height in simulation
Figure 4 10 Burr height in simulation
Figure 4 11 Burr height comparison between simulation and experiment
The simulation was conducted over a period of 336 hours, which have no computationally efficient process
Comparision of burr height (mm)
The cutting condition refer some article journal and depend on the ability of CNC VMC-650 machine and pzt, the cutting condition is selected from [3] The simulation reduce 140 hours per simulation In order to optimize the simulation time and achieve cost-effectiveness, adjustments were made to the boundary conditions table 4.6
Table 4 6 Table of cutting parameter
Vibration Frequency (Hz) 1000, 1250, 1400 Vibration Amplitudes (àm) 2, 4, 6
The period time is calculated by equation:
Figure 4 12 Period time of drilling
Where: a is time which the drill the remain chip is remove (s) b is the thickness of workpiece (mm) d is distance between minimum diameter - drill bit and maximum diameter - drill bit fph is feed per time (mm/s).
Result in simulation
The simulation is conducted by HP Z4 G4 workstation computer whose configure in CPU 10 cores with maximum frequency 4.3 GHz, the average simulation time for each cutting condition is 24 hours with the mass scaling for each increments is 5e-7 b
All parameters will be classified in Table 4.7 to determine their levels They are refering to the reference [3] In order to assess the different levels of each parameter and improve computational cost efficiency, the feed rate parameter has been adjusted to a higher value compared to its initial setting
Table 4 7 Level of all parameter
Because a minimum height criterion is imposed on both the entry and exit hole burrs to ensure their adherence to specified standards, the lower than better (formula 2.2 in section 2.4 recommended) will be selected to condition to compare with all parameters The orthogonal array will be formed, as shown in Table 4.8
No Speed (rpm) Feed rate (mm/rev) Frequency (Hz) Amplitude (àm)
It is essential to measure the burr height The software ImageJ is used for examining the burr height in simulation Figure 4.10 – 4.11 Firstly, it is vital to set the scale by sketching a line equal to the thickness of the sample and filling the actual thickness of the workpiece into the set scale table Figure 4.10 Then sketch a line from the original to the lowest position burr, and select a measure to get the result Figure 4.11
Figure 4 13 ImageJ in burr height measurement of CM in condition cutting 4000 rpm, feed rate 0.2
Figure 4 14 Result of burr height in CM at speed 4000rpm, feed rate 0.2
In this way, table 4.9 shows all the burr heights of all parameters in VAD
Main effect plot for Means
S (RPM) F (mm/rev) A (àm) f (Hz)
Table 4 9.Simulation result for exit burr height and S/N ratio
Exit burr height Noise signal S/N
S (rpm) F (mm/rev) f (Hz) A (àm)
Figure 4 15.a) Means graph for exit burr height, b) SN ratios graph for exit burr height Table 4 10 Factors effect exit burr height
S (rpm) F(mm/rev) f (Hz) A (àm)
Main effort for noise ratio
S (RPM) F (mm/rev) A (àm) f (Hz) b)
The influence of various factors on the cutting force signal-to-noise (S/N) ratio was determined and presented in Table 4.10 This analysis involved plotting the SN ratios, as illustrated in Figure 4.12(b) The results indicate that the spindle speed (S) contributed 48.77% to the overall effect on the exit of the burr height, while the feed rate (F) accounted for 32.23% Additionally, the frequency (f) factor contributed 14.15%, and the amplitude is 4.85% to the overall impact
Table 4 11.Simulation result for entrance burr height and S/N ratio
No Factor Entrance burr height (mm)
S (rpm) F (mm/rev) f (Hz) A (àm)
Figure 4 16.a) Means graph for entrance burr height, b) SN ratios graph for entrance burr height
Mean effect plot for Means
S (RPM) F (mm/rev) A (àm) f (Hz)
MAIN EFFORT FOR NOISE RATIO
S (RPM) F (mm/rev) A (àm) f (Hz) a) b)
Table 4 12.Factors effect entrance burr height
S (rpm) F(mm/rev) f (Hz) A (àm)
The influence of various factors on the cutting force signal-to-noise (S/N) ratio was determined and presented in Table 4.12 This analysis involved plotting the SN ratios, as illustrated in Figure 4.13(b) The results indicate that the spindle speed (S) contributed 23.85% to the overall effect on the entrance burr height, while the feed rate (F) accounted for 26.65% The frequency (f) factor also contributed 3.85%, and the amplitude is 35.98% to the overall impact
4.2.3 Compare the exit burr in VAD to CD
Figure 4 17 Comparison burr formation between VAM and COM
Figure 4.14 shown comparison between the burr formation in some cutting condition
Conclusion in result
This study utilizes numerical methods to predict the efficiency of vibration- assisted machining accurately The simulation model is carefully constructed under ideal conditions, considering material parameters measured at room temperature
COMPARISON BETWEEN EXIT BURR HEIGHT VAM AND COM
Moreover, the numerical method is extended to predict the development of drilling burr formation, comparing all statuses of workpieces in different cutting conditions, and applying the Taguchi method to evaluate the influence of machining-related factors
1 The frequency and amplitudes in VAM drilling in simulation at a frequency range (1000 – 1400) slightly affect the exit burr height However, the exit burr formation in VAM is evident compared to COM
2 The amplitude is the most influence on the entrance burr formation; the entrance burr in VAM is lower than COM
3 The exit burr height tended to decrease and clear when the frequency is higher The numerical simulation results of burr formation offer a means to predict the effectiveness of vibration-assisted machining This study demonstrates that machining at higher speeds, along with lower feed rates and higher frequencies, leads to a reduction in burr height
CONCLUSION AND RECOMMEDATION
Conclusion
Overall, based on the results obtained from the project, the following conclusions can be drawn:
1 The numerical methods are utilized to predict the interaction process between the cutting tool and the workpiece in vibration-assisted machining Additionally, these methods allow for the evaluation of the impact of burr height in both conventional machining and vibration machining, enabling a comprehensive analysis of the process
2 It can be seen that effectiveness of applying the numerical to limit the range of cutting condition and support to predict result instead of addressing the numerous experiments, save the cost in R&D field
3 In order to anticipate the effects of vibrations before conducting experimental trials, a numerical simulation model is constructed This model serves as a valuable tool in predicting the potential outcomes and provides guidance for the experimental layout By utilizing the simulation data, informed decisions can be made regarding the experimental setup and subsequent data collection.
Recommendation
The primary objective of this thesis, which involved the application of numerical methods to forecast the efficiency of vibration-assisted machining, has been satisfactorily accomplished Nonetheless, it is essential to acknowledge the existing limitations within the scope of this study Consequently, the following recommendations are outlined for future investigations in this area:
Investigate factors affect to the wear of tool, predict the tool life by FEM
Balance of computational cost and high accuracy result is the issue in this topic The model should be study the method for this
In machining, the heat is form because of fiction, the next research can be concentrate on the thermal factor and predict the machining result
[1] Reddy Sreenivasulul, Chalamalasetti Rao, "Effect of drilling parameters on thrust force and torque during of aluminum 6061 alloy - based on taguchi design of experimanets," Journal of Mechnical Engineering, vol Me 46, 2017
[2] Aamir, M., Tolouei, M.,&Nazir, S., "Machinability of A2024, Al6061, and Al5083 alloys using multi - hole simutaneous drilling approach," Journal of Manufacturing Processes, pp 387 - 396, 2020
[3] A B A P S S Mohammad Uddin, "Evaluating Hole Quality in Drilling of Al
[4] Ozden Isbilir, Elaheh Ghassemieh, "Finite Element Analysis of Drilling of Titanium Alloy," Procedia Engineering 00, pp 1877 - 1882, 2011
[5] Guohe Li, Meng Liu & Shanshan Zhao, "Reduced computational time in 3D finite element," Machining Science and Technology, pp 558 - 584, 2021
[6] Wanqun Chen & Lu Zheng & Xiangyu Teng & Kai Yang & Dehong Huo, "Finite element simulation and experimental investigation on cutting," The International
Journal of Advanced Manufacturing Technology, vol Volume 105, p 4539–4549,
[7] Kapil Gupta, Neelesh K Jain, and R F Laubscher, "Hybrid Machining Processes: Perspectives on Machining and Finishing," anufacturing Science and Engineering,
[8] T D D.E Brehl, "Review of vibration-assisted machining," Precision Engineering, vol 32, no 3, pp 153-172, 2008
[9] L L Saunders, "A Finite element model of exit burrs for drilling of metals," Finite
Elements in Analysis and Design, vol 40, no 2, pp 139-158, 2003
[10] L K Lauderbaugh, "Analysis of the effects of process parameters on exit burrs in drilling using a combined simulation and experimental approach," journal of materials processing technology, vol 209, no 4, pp 1909-1919, 2009
[11] Simon S.F Chang; Gary M Bone, "Thrust force model for vibration-assisted drilling of aluminum 6061-T6," International Journal of Machine Tools & Manufacture, vol 49, no 16, pp 1070-1076, 2009
[12] Shaomin, Li; Deyuan, Zhang; Daxi, Geng; Zhenyu, Shao; Hui, Tang, "Modeling and drilling parameters optimization on burr height using," The International Journal of Advanced Manufacturing Technology , vol 101, pp 2313-2325, 2018
[13] Chen, Q., Li, X., Zhang, L., "Influence of Feed Rate on Burr Height in Drilling: Experimental Investigation and Modeling," Journal of Manufacturing Science and
[14] Zhang, L., Zhang, M., Wang, Q., & Li, X., "Investigation of Cutting Parameters on Burr Formation in Micro Drilling of Aluminum Alloy," Journal of Materials Processing Technology, vol 257, pp 19-28, 2018
[15] X Z B L W & Z L Zhang, "A study on surface integrity and burr formation in drilling of titanium alloy with vibration-assisted machining," The International
Journal of Advanced Manufacturing Technology, vol 96, no 9-12, pp 4707-4714,
[16] Li, H., Li, C., Li, Y., & Cui, X., "Experimental investigation on the effectiveness of vibration-assisted drilling in reducing drilling force and improving hole quality," The International Journal of Advanced Manufacturing Technology, vol
[17] Zhang, W., Li, H., & Guo, Y., "Effect of vibration amplitude on surface quality in vibration-assisted drilling of titanium alloy.," The International Journal of Advanced Manufacturing Technology., Vols 1-4, no 94, pp 167-177, 2018
[18] Smith, J., Johnson, A., & Brown, C, "Influence of vibration amplitude on surface finish in vibration-assisted drilling of aluminum alloys.," Materials and Manufacturing Processes., vol 35, no 9, pp 1085-1093, 2020
[19] G T K Lien, Quy hoạch thực nghiệm (Các phương án quy hoạch thực nghiệm), Đa Nang: Đai hoc Da Nang, 2009
[20] T V Khiem, "Phương pháp Taguchi và ứng dụng trong tối ưu hóa chế độ," Tạp chí Cơ khí Việt Nam, pp 76-82
[21] N H Loc, Giáo trình quy hoạch thực nghiệm, Ho Chi Minh: Đại Học Quốc Gia,
[22] Emir Esim, S ahin Yıldırı, "Drilling performance analysis of drill column machine," Neural Comput & Applic, vol 28, pp 79-90, 2016
[23] D Wu, "A new approach of formulating the transfer function for dynamic," ASME
[24] O J Astakhov VP, Metal cutting mechanics finite element modelling, London: Springer, 2008
[25] F K A Klocke, "Finite Element Method (FEM)," in Manufacturing Processes 1
5TH edition, Springer, Berlin, Heidelberg., 2011
[26] J P Davim, "Finite element method in machining," in Modern manufacturing engineering, Springer, 2015
[27] S V Zanger F, "Investigations on mechanisms of tool wear in machining of Ti- 6Al-4V using FEM simulation," Procedia CIRP 14th CIRP conference on modeling of, vol 8, pp 158-163, 2013
[28] S Y B J Dandekar CR, "Machinability improvement of titanium alloy (Ti-6Al- 4V) via LAM and hybrid machining," Int J Mach Tools Manuf 50:174–182, 2010 [29] A N R A S V Muhammad R, "Numerical modelling of vibration-assisted turning of Ti-15333," Procedia CIRP 1, pp 347-352, 2012
[30] D J Maranhão C, " Finite element modelling of machining of AISI 316 steel: numerical simulation and experimental validation," Simul Model Pract Theory 18, pp 139-156, 2010
[31] S H N M e a Amini S, "FEM analysis of ultrasonic-vibration-assisted turning and the vibratory tool," J Mater Process Technol, pp 43-47, 2008
[32] S K B N e a John MRS, "Finite element method-based machining simulation for analyzing surface roughness during turning operation with HSS and carbide insert tool," Arab J Sci Eng 38, pp 1615-1623, 2013
[33] B L J T e a Lauro CH, "An approach to define the heat flow in drilling with different cooling systems using finite element analysis," Adv Mech Eng 2013, p
[34] O J S T Schulze V, "FE analysis on the influence of sequential cuts on component conditions for different machining strategies," Procedia Eng, no 19, pp 318-323, 2011
[35] D Systèmes., Getting Started with Abaqus: Interactive Edition., 2014
[36] S R & G L Wu, Introduction to the explicit finite element method, Hoboken: Wiley, 2012
[37] H G S A.-S S G Joshua Priesta, "3D finite element modelling of drilling: The effect of modelling method," CIRP Journal of Manufacturing Science and Technology, pp 158-168, 2021
[38] P K A, "Simulation and experimental investigation of drilling," International Journal of Lightweight Materials , pp 197-205, 2018
[39] Mehdi Nosouhi, Reza Nosouhi, Hossein Paktinat, Saeid Amini., "Finite Element Analysis and Experimental Investigation on the," Journal of Modern Processes in
Manufacturing and Production, vol 6, pp 23-34, 2017.