Ánapplying numerical methods to study predicting the efficiency of hybrid machining

52 Trang 13 xiii NOMENCLATURE

MINISTRY OF EDUCATION AND TRAINING

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION

FACULTY FOR HIGH QUALITY TRAINING

Ho Chi Minh City, July 2023

CAPSTONE PROJECT ELECTRONICS AND TELECOMMUNICATIONS

ENGINEERING TECHNOLOGY

APPLYING NUMERICAL METHODS

TO STUDY PREDICTING THE EFFCIENCY

OF HYBRID - MACHINING ỨNG DỤNG PHƯƠNG PHÁP SỐ NGHIÊN CỨU DỰ ĐOÁN HIỆU QUẢ CỦA CÁC PHƯƠNG PHÁP GIA CÔNG KẾT HỢP

LECTURER: ASSOC PROF DR PHAM HUY TUAN STUDENT : NGUYEN PHAT DAT

VO HOANG HUY

S K L 0 1 0 9 9 8

HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION

FACULTY FOR HIGH QUALITY TRAINING

GRADUATION PROJECT

Ứng dụng phương pháp số nghiên cứu dự đoán hiệu quả

của các phương pháp gia công kết hợp

Ho Chi Minh City, July 2023

Applying numerical methods to study predicting the

efficiency of hybrid-machining

iii

TRƯỜNG ĐẠI HỌC SƯ PHẠM KỸ THUẬT TP.HCM

KHOA CƠ KHÍ CHẾ TẠO MÁY

Bộ môn: Công nghệ Chế Tạo Máy

CỘNG HÒA XÃ HỘI CHỦ NGHĨA VIỆT NAM

Độc lập – Tự do – Hạnh phúc _

NHIỆM VỤ ĐỒ ÁN TỐT NGHIỆP

Học kỳ II / năm học 2023

Giảng viên hướng dẫn: PGS TS Phạm Huy Tuân

Sinh viên thực hiện:

1 Mã số đề tài: 22223DT275

Tên đề tài: Ứng dụng phương pháp số nghiên cứu dự đoán hiệu quả của

các phương pháp gia công kết hợp

2 Các số liệu, tài liệu ban đầu:

- Các báo cáo liên quan đến mô phỏng gia công, số liệu về chế độ cắt, chế

độ rung trong phương pháp gia công kết hợp

- Thiết bị hỗ trợ rung PZT loại p-225.10

- Mô hình gia công phay có rung hỗ trợ

3 Nội dung chính của đồ án:

- Tìm hiểu tổng quan về công nghệ gia công kết hợp, gia công lai và các

ưu điểm của nhóm công nghệ này;

- Nghiên cứu ứng dụng các công cụ mô phỏng số để dự đoán quá trình

hình thành bavia sau gia công;

- Nghiên cứu ảnh hưởng của rung động tích hợp vào dụng cụ cắt theo một

số chỉ tiêu như: giảm thiểu sự hình thành bavia hoặc cải thiện chất lượng

bề mặt chi tiết;

- Gia công, kiểm nghiệm thực tế (nếu đủ thời gian)

4 Sản phẩm dự kiến

- Báo cáo phân tích kết quả mô phỏng số;

- Kết quả thực nghiệm gia công (nếu đủ thời gian triển khai)

5 Ngày giao đồ án: 03/2023

6 Ngày nộp đồ án: 07/2023

iv

7 Ngôn ngữ trình bày: Bản báo cáo Tiếng Anh  Tiếng Việt 

Trình bày bảo vệ Tiếng Anh  Tiếng Việt 

Địa chỉ sinh viên: 228, Đường số 6, phường Linh Chiểu, Tp Thủ Đức

Số điện thoại liên lạc: 0376398560

Email: 19143123@student.hcmute.edu.vn

Ngày nộp khóa luận tốt nghiệp (ĐATN): 18/07/2023

Lời cam kết: “Tôi xin cam đoan khóa luận tốt nghiệp (ĐATN) này là công trình chính tôi nghiên cứu và thực hiện Tôi không sao chép từ một bất kỳ bài viết nào được công bố mà không trích dẫn đến nguồn gốc Nếu có bất kỳ một sự

vi phạm nào, chúng tôi xin chịu hoàn toàn trách nhiệm”

Tp Hồ Chí Minh, Ngày 18 Tháng 7 Năm 2023

Ký tên

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ACKNOWLEDGEMENTS

First and foremost, we would like to express our gratitude to our mentor Assoc Prof Dr Pham Huy Tuan, for his guidance, valuable advice, and proposing solutions when the problem became difficult and indeed the project would be difficult to complete without his support Our sincere thanks to our colleagues

at the Bosch R&D center, Mr Nguyen Duc Tue, Mr Vu Thu Pham, and Mr Truong Quoc Dung, for their helpful sharing in the field of numerical simulation

to guide our team to complete the thesis We are grateful to our colleagues Mr Nguyen Thai Son at Metkraft, for allowing us to use his workstation to test our numerical simulation models We would like to thank Dr Dang Quang Khoa, MSc Duong Thi Van Anh, and alumnus Pham Huu Day for their assistance during the experiment Finally, we would like to thank our parents for their love and encouragement throughout this process

While implementing the thesis, we couldn't avoid mistakes, although we tried

to complete it by referencing documents, listening, and exchanging ideas Therefore, we are open to receiving the comments of teachers and readers, as their feedback will help us improve our work

Ho Chi Minh City, July 19th, 2023

On behalf of authors Nguyen Phat Dat

vii

ABSTRACT

Nowadays, the accuracy requirements of details of aviation, defense, medical and biochemical fields are increasing more and more Conventional machining methods meet the above requirements but also face many challenges when machining in difficult materials, new materials are not available in the mechanical handbook, and tool wear affects production costs, especially burr formation is a costly charge, deburring process, and cleaning time Vibration-assisted machining has been applied and developed as a solution to the above challenges in recent decades Inheriting from conventional machining, vibration machining uses external energy sources such as amplitude and frequency to change the cutting mechanism, improving machining quality, reducing burr, and tool wear Implementation of vibration-assisted machining depends on structure design, vibration transmission, vibration device, optimization of process parameters, and performance evaluation Therefore numerical methods are used

to predict the performance of vibration-assisted machining to effectively predict and save investment and testing costs, providing insight into the effects of vibrations Moreover, with the goal of numerical simulation application, it will reduce the time and cost of testing equipment Finally, the scope of application

of vibration machining on a broader scale gradually replaces conventional machining in the future

viii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS vi

ABSTRACT vii

TABLE OF CONTENTS viii

LIST OF FIGURES xi

NOMENCLATURE xiii

ABBREVIATION xiv

Chapter 1: OVERVIEW 1

1.1 Background and motivation 1

1.2 Research in Viet Nam 2

1.3 The need of thesis 2

1.4 The scopes and objectives of this thesis 3

1.5 Methodology of this thesis 3

1.6 The structure of this thesis 4

Chapter 2: LITERATURE REVIEW FINITE ELEMENT METHOD IN MACHINING PROCESSES 6

2.1 Introduction finite element method in machining processes 6

2.1.1 Overview of the Explicit Finite Element Method 7

2.2 Automatic time incrementation and stability condition 9

2.2.1 The stability limit 9

2.2.2 Mass scaling to control time incrementation 10

2.2.3 Effect of material on stability limit 10

2.2.4 Effect of mesh on stability limit 12

2.3 Summary 13

Chapter 3: LITERATURE REVIEW OF CUTTING MECHANICS 14

3.1 Introduction 14

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3.2 Mechanics cutting in conventional machining 14

3.2.1 Cutting forces and shear angle 14

3.2.2 Types of chip formation 15

3.2.3 Modeling of chip separation 17

3.3 Vibration-assisted machining 18

3.3.1 Kinematic modeling of VAMILL 18

3.3.2 Tool-workpiece separation conditions in VAM 20

3.4 Summary 22

Chapter 4: NUMERICAL SIMULATION OF CUTTING MECHANISMS IN VIBRATION-ASSISTED MACHINING 23

4.1 Finite element simulation of VAM orthogonal 23

4.1.1 Finite element modeling and material properties 23

4.1.2 Period time and mass scaling 26

4.1.3 Tool-chip friction model 27

4.1.4 Interaction and boundary condition 27

4.2 Model validation between the simulation and experiment 28

4.3 Simulation results and discussion 30

4.3.1 Effect of vibration on shear angle 30

4.3.2 Effect of vibration on chip formation 30

4.4 Conclusion 32

Chapter 5: BURR FORMATION AND CUTTING FORCE INVESTIGATION IN VIBRATION-ASSISTED MACHINING 33

5.1 Finite element simulation of side-milling 33

5.1.1 Finite element model of side-milling 33

5.1.2 Meshing model 34

5.1.3 Interaction and boundary condition 36

5.1.4 Period time calculate 37

x

5.2 Experimental setup 37

5.3 Design of experiments and procedure 39

5.3.1 Introduction to the Taguchi method 39

5.3.2 Entrance downside burr height 39

5.3.3 Cutting force 44

5.3.4 Burr formation 51

5.3.5 Chip morphology in simulation and experiment 54

5.4 Conclusion 55

Chapter 6: CONCLUSION AND RECOMMENDATION 56

6.1 Conclusion 56

6.2 Recommendation 56

REFERENCES 58

xi

LIST OF FIGURES

Figure 1.1 Methodology of the graduation thesis 3

Figure 1.2 Structure of the graduation thesis 4

Figure 2.1 Time integration method in explicit 8

Figure 2.2 Time increment and stability limit in explicit 8

Figure 2.3 The problem description for stability limits 10

Figure 2.4 Part meshing with hexahedron linear element 11

Figure 2.5 Two cases with different time increment 12

Figure 3.1 Merchant’s circle force diagram 14

Figure 3.2 Types of chip formation 16

Figure 3.3 An illustration of node-splitting technique between the tool cutting edge and the node immediately ahead 17

Figure 3.4 Tool tip trajectory in conventional machining 19

Figure 3.5 Schematic diagram of vibration-assisted milling 19

Figure 3.6 Type I tool and workpiece separation during VAMILL 21

Figure 3.7 Type II tool and workpiece separation during VAMILL 21

Figure 3.8 Type III tool and workpiece separation during VAMILL 22

Figure 4.1 Schematic orthogonal diagram 24

Figure 4.2 Orthogonal FE model of VAM 24

Figure 4.3 Meshing model of the workpiece and tool on Abaqus/Explicit 26

Figure 4.4 Tool-chip contact in the sticking zone and sliding zone 27

Figure 4.5 Comparison of cutting force in simulation and experiment [21] 28 Figure 4.6 Flowchart validation of orthogonal cutting simulation 29

Figure 4.7 Comparison the FE results of shear angle in CM and VAM 30

Figure 4.8 Chip formation in simulation with VAM 31

Figure 4.9 Chips without vibration and with vibration 32

Figure 5.1 Side milling model of Al6061-T6 34

Figure 5.2 Meshing process flowchart 35

Figure 5.3 Meshing model of workpiece and cutting tool in side-milling 35

Figure 5.4 Interaction and boundary condition in side-milling 36

Figure 5.5 Period time calculate in side-milling 37

Figure 5.6 Vibration-assisted milling experiment setup 38

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Figure 5.7 The direction of vibraion relation to the feed rate 39 Figure 5.8 Type of burrs in milling 40 Figure 5.9 SN ratios graph and Means graph for entrance downside burr

height 42

Figure 5.10 The milling process for single tooth 44 Figure 5.11 SN ratios graph and Means graph for cutting force 45 Figure 5.12 Cutting force comparison between conventional machining and

vibration-assited machining in FE simulation 47

Figure 5.13 Cutting force deviation between CM and VAM in simulation 48 Figure 5.14 Cutting force between CM and VAM in simulation 49 Figure 5.15 The tool and workpiece contact in VAM at 7th DOE 50 Figure 5.16 The displacement of tool tip between VAM and CM 51 Figure 5.17 Entrance burr height comparison between CM & VAM in

simulation 52

Figure 5.18 Entrance burr height values are measured by ImageJ 53 Figure 5.19 Comparison between simulation and actual machining 54

xiii

NOMENCLATURE

∆𝑡 Stability limit [s]

xiv

ABBREVIATION

C3D4R Linear tetrahedral reduced integration

CFVAMILL Cross-feed vibration-assisted milling

FVAMALL Feed vibration-assited milling

VAMILL Vibration-assisted milling

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CHAPTER 1: OVERVIEW

1.1 Background and motivation

Aluminum alloy (Al6061-T6) is valuable for various automobile applications, automotive parts, and consumer products Furthermore, precision components require more surface roughness, and burr regeneration is necessary to achieve tight tolerances

In conventional machining, Al6061-T6 alloy requires a careful selection of cutting parameters, including the cutting speed, feed rate, depth of cut, tool geometry, and lubrication to optimal surface quality, dimensional accuracy, and tool life [1] The main concern when machining is the phenomenon of chip and burr formation which affects the machined part [2] Despite optimizing parameters, there are still challenges

to understanding the burr formation process

Another method to enhance machining performance in which machining quality and minimizing burr formation can be improved by applying the frequency vibration

of the tool or workpiece is vibration-assisted machining (VAM), which allows for more material to be removed in a shorter amount of time, smooth out the surface and resulting in better surface [3] Compared with traditional machining, vibration-assisted machining can reduce cutting force, reducing run-out in the cutting depth by stabilizing the tool motion and avoiding chatter vibration As a result, a better-machined surface quality can be improved [3] For micromachining, Lu et al [4] analyzed the tool wear and burr formation in vibration-assisted machining can reduce

by decreasing cutting forces, and generating thinner chips

In the conventional machining process, improving and evaluating the influence

of criteria such as stress, residual stress, cutting force, chip morphology, etc., through experiments also require a laboratory setup and is challenging to measure by the experimental method [5] For example, stress can be measured using strain gauges and digital image correlation, and cutting force can be measured using force sensors and dynamometers One other approach is using numerical methods to study cutting mechanism and investigate the above criteria In many cases, numerical simulation and experimental results have a significant difference However, it is still considered

an effective and practical research method [6], not only conventional machining but

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also has studied vibration-assisted machining According to Davim [7] finite element method (FEM) provides insights into material deformation and information about stress, strain, and temperature in the cutting zone, saves the experimental cost, and is suitable for the development of the manufacturing industry Several studies have used FEM to simulate and investigate the burr formation in vibration-assisted machining such as turning, drilling, and milling [8] A few studies from Lu et al (2018) on numerical modeling of 2D cutting with VAM have been reported [9] The FEM model predicts the chip morphology, cutting forces, and residual stress under different parameters in 2D cutting simulation [10] Davoudinejad et al [11] created a 3D finite element model by AdvantEdge (FEM software) to study the effect of helix angle on milling, cutting edge radius on the chip, and burr formation in micro end-milling of Al6061-T6

It is necessary to determine the simulating effect on the machining process input, and output parameters in vibration-assisted machining for Al6061-T6 alloy Thus, this problem can be done by parameter studies with finite element method

1.2 Research in Viet Nam

In Vietnam, FEM machining processes are still early stages The study by Pham

et al (2016) used FEM to study the effect of cutting parameters on the chip shrinkage coefficient and cutting forces in conventional machining of Al6061 with a 2D cutting model [12]

1.3 The need of thesis

Experimental work that requires the accuracy of equipment, and set-up procedures In the product development process, it requires a large number of prototypes when manufacturing, and testing Thus, it requires a lot of resources in terms of time and cost to implement

Another method is the use of numerical methods with computer-aided that could

be substituted for experimental work, reducing the number of prototypes thereby reducing the time Numerical method or finite element method allowing modeling of complex models, and dynamic simulation, large deformation, such as car collisions, machining processes, etc and reducing costs by building numerical simulation models to predict the results Therefore, the authors have conducted this project by applying numerical methods to predict the efficiency of vibration-assisted machining

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1.4 The scopes and objectives of this thesis

This research aims to predict and understand the cutting mechanism of the vibration-assisted machining process through turning, and milling

The scope of research objectives can be summarized as follows:

1 To create a metal cutting model on the finite element method, which employs a Johnson-Cook damage model to describe the orthogonal cutting and 3D cutting in vibration-assisted machining and conventional machining

2 To study the vibration effect on the chip formation during orthogonal cutting, and study the burr formation, cutting force in side milling when machining aluminum alloy by numerical method

3 To study the influence of vibration parameters on chip and burr morphology, cutting force through simulation and design of experiments

1.5 Methodology of this thesis

Figure 1.1 Methodology of the graduation thesis

Vibration-assisted machining

Explicit finite element approach

Cutting mechanics on assited milling simulation

vibration-Cutting process modeling by orthogonal cutting

Morphology of chip, and burr

Cutting mechanics on

vibration-assited milling simulation

Cutting forces, burr size, applications, etc.

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1.6 The structure of this thesis

The thesis is divided into six chapters as shown in Figure 1.2 the brief of chapters is explained as follows:

Figure 1.2 Structure of the graduation thesis

Chapter 1 presents an overview of the research background of the effect of VAM technology on the burr formation mechanism This chapter includes recent research results in VAM Thereby, it shows the need for this topic

Chapter 2 presents general concepts of the implicit and explicit schemes in finite element to simulate VAM, which influences such as the mesh between tool and workpiece, and material properties to the input FE software

Chapter 3 overviews the cutting mechanics, and the types of chip formation typically procedure during the cutting mechanism in conventional machining, and chip separation in vibration-asssited machining

Chapter 4 applies to machining for orthogonal cutting and side milling to understand the cutting mechanism when using vibration in machining This model requires cutting tool geometry, material properties, vibration parameters, contact

Chapter 1 – Overview

Chapter 2 - Literature review FEM in machining processes

Chapter 3 – Literature review of

cutting mechanics

Chapter 6 – Conclusion and recommendation

Chapter 5 – Burr formation and cutting force investigation in assisted machining

vibration-Chapter 4: Numerical simulation

of cutting mechanisms in VAM

5

modelling, and commercial finite element software packages are discussed Reports from a numerical model that is validated to predict the chip, effect of vibration into cutting mechanism when compared to conventional machining and VAM

Chapter 5 reports the height entrance burr formation, cutting force, and the effect of vibration parameters through design of experiments and numerical simulation

Chapter 6 summarizes the research work in this chapter, the conclusion, and the recommendation for future work

2.1 Introduction finite element method in machining processes

The machining process is a dynamic process that involves large deformation and high strain, and analytical techniques still had difficulty producing solutions with adequate accuracy As a solution to this problem, around 1970 [13], the numerical method began to simulate chip formation processes, and temperature in cutting tools

There are two methods to solve in machining process simulation: implicit and explicit

In the implicit, to determine the solution at the time (𝑡 + ∆𝑡) are calculated from quantities at the time 𝑡 and at time (𝑡 + ∆𝑡), and explicit solver every time (𝑡 + ∆𝑡) is calculated from the values at time 𝑡 Both types have been simulated in machining processes [14] Furthermore, the implicit approach requires a length of ∆𝑡 larger than the explicit Therefore the implicit is more computationally expensive

Table 2.1 Comparison of the commerical FE software on cutting process simulation [15]

ABAQUS Lagrange

ALE Euler

Complex solid mechanics Structural mechanics systems

Simulate the mechanics

Multi-physical field analysis

Standard Explicit CAE Design

Mechanical processing Metallurgy

Material processing Civil engineering

Nonlinear structure analysis

Modal analysis

Mentat Parallet Hexmesh

Nuclear power National defence Aerospace Automobile Shipbuilding

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Dynamic response analysis

Static, dynamic contact analysis

ALE Euler

High speed collision Explosion and metal forming

Nonlinear problems of contact

Impact load and material

High speed collision Explosion and metal forming Nonlinear problems of contact- Impact load and material

Automobile safety design

Weapon system design Metal forming

DEFORM

Newton-Raphson Explicit

Environment integrated modeling

Heat conduction Hot and cold molding

Data analysis input

Mesh division and redivision Data transfer calculation

Forging Rolling Extrusion Cold heading Drawing Molding FEM should be performed with the help of computer software, as shown in Table 2.1 the comparison of the software and algorithm in metal cutting simulation Each FE software has different solvers and algorithms Therefore, the results are influenced by the selected software and solver techniques

Overall, choosing the software and solver to use in the machining process simulation

is Abaqus software (Dassault system) with explicit solver

2.1.1 Overview of the Explicit Finite Element Method

Time is an integral part of all physical processes In the explicit FEM time domain is divided into a finite number of time increment and solve unknowns at these specific time points This is called the time integration method

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Figure 2.1 Time integration method in explicit

In Figure 2.2 illustrated time integration by example in milling, when the time would

be divided into many increments from the end mill tool starts machining (point A) to the end

of process (point B) Each time increment is separated by stability limit “∆𝑡”, as illustrated

by the example in Section 2.2 Automatic time incrementation and stability condition

Figure 2.2 Time increment and stability limit in explicit

The explicit algorithm in ABAQUS/Explicit is summarized as follows [17]:

- Step 1: Nodal calculation

∆𝑡

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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

2.2 Automatic time incrementation and stability condition

2.2.1 The stability limit

In previous section, the explicit method approach requires a small time increment size, the time increment size is controlled by the stable time “∆𝑡”, shown in Figure 2.2 Therefore, that procedure only bounded when the time increment is less than stable time increment, also know as CFL (Courant-Friedrichs-Levy) condition [16] The stable time increment can be defined using the shortest element length “𝐿𝑒”, and the dilatation wave speed of the material

𝑐𝑑 = √𝐸

The stability limit is an important consideration in the numerical simulation due to choosing a time increment is smaller than the stability limit, the model will be stable [16] If the stability limit is too large which can lead to inaccurate results because the model wasn’t stable

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2.2.2 Mass scaling to control time incrementation

Mass scaling is a numerical technique to increase the time increment in explicit simulation Hence, this can be upgraded the computational efficiency without affecting to the accuracy of the results Mass scaling works by artificially increasing the density in the model according to Eq (2.5) by increasing “𝜌” which allows for a larger stability limit There are two fundamental approaches used in mass scaling in Abaqus/Explicit: defining a scaling factor directly or defining a desired element-by-element stable time increment for the elements whose mass is to be scaled [17]

2.2.3 Effect of material on stability limit

The material of model affects to the stability limit, in Eq (2.5) its effect on the dilatational wave speed Materials with the following properties will have a smaller stability limit that means more computational time, low density and high wave speed

This example below will demonstrate stability limits and mesh, materials effect to the status stable and unstable of model

Figure 2.3 The problem description for stability limits

All four lateral faces are on rollers, the material is structural steel with the properties shown in Figure 2.3 and displacement 2 𝜇𝑚 is subjected in the free face of part The displacement changes according to the periodic graph with an amplitude of 2 μm, and frequency 1000 Hz

The part was meshed linear brick element (C3D8R), contains 250 elements, and is uniform part with the ratio: 10 x 4 x 4 mesh (seed part = 0.008)

𝜌 = ( 𝑚 )

=

Front View

Side View

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Figure 2.4 Part meshing with hexahedron linear element

The shortest length of 3D solid hexahedron element: 𝐿𝑒 = × 1 −4 (𝑚)

The wave speed of the material using the equation (2.4) in the previous section, and the stability limit in Eq (2.5):

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Less than ∆𝑡𝑠𝑡𝑎𝑏𝑙𝑒 (𝑑𝑡 = 1 5 × 1 −7) Greater than ∆𝑡𝑠𝑡𝑎𝑏𝑙𝑒 (𝑑𝑡 = 1 × 1 −4)

Figure 2.5 Two cases with different time increment

This simple example illustrates the stability limit effect on the stability of the model

In general, the time increment greater than the stability limits the element occurs glassing phenomenon in the mesh element, the model became unstable, and inaccurate

hour-The same example but performed on different materials would take different computational times Instead of steel, the material change to lead material, the wave speed would have changed to 1 11 × 1 3 (𝑚 𝑠) The stable time for the part lead material would

be five times that part steel material

2.2.4 Effect of mesh on stability limit

The stability limit is roughly proportional to the shortest element length “𝐿𝑒” In order

to get accurate results for specific chip and burr formation in the machining process, a fine mesh is often necessary that means “∆𝑡𝑠𝑡𝑎𝑏𝑙𝑒” is very small Therefore, using a uniform mesh (seed part instead of seed edge) is the same element all over the part but wasn’t a good way

if the geometry is complex The goal is to use the finest mesh while still ensuring that the stability limit still not exceeded One recommendation for mesh element quality is to use specialized software for the pre-processing stage like the software Hypermesh from Altair Inc., it is controlled the shortest element length by meshing technique, and another way is an adaptive meshing technique (ALE method)

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2.3 Summary

This chapter provides a comprehensive the explicit finite element method, the technique

to increase computational time but control the stability limit, and the accuracy of the results

1 Explicit requires many small time increments and explicit approaches meet the requirements conditionally stable, which means the time increment might be chosen carefully in order to avoid the unstable, or excessive distortion mesh is a common error

3.2 Mechanics cutting in conventional machining

Orthogonal cutting (2D model) as shown in Figure 3.1 is a type of metal cutting process

in which the cutting tool with a plane cutting face, and cutting edge is perpendicular to the direction of cutting speed It represents only a small segment of the different machining processes such as turning, drilling, milling, etc The orthogonal cutting model is widely applied in metal cutting theory, experimental work, and machining process modeling in simulation due to the simplification of the cutting model, simulated to chip formation, cutting force, cutting thermal, and chip morphology

Figure 3.1 Merchant’s circle force diagram

3.2.1 Cutting forces and shear angle

As Figure 3.1 clarifies the cutting forces suggested by Merchant, also called Merchant’s circle diagram From Merchant’s analytical model, the cutting force 𝐹𝑐, and feed force 𝐹𝑓 can be taken from the Merchant’s circle diagram in Eq (3.1)(3.2), according to [18]:

𝛾𝑛

𝑃

The force components are calculated according to the relationships with shear angle

𝛷, friction angle 𝛽, and the rake angle 𝛾𝑛 In Eq (3.4)(3.5) shows friction force 𝐹 is obtained

by Merchant’s circle, and normal friction force 𝐹 𝑛 [18]

In the metal cutting process, the contact between the cutting tool and workpiece undergoes strict conditions: high velocity, large plastic deformation, high normal load, and the energy released will transform to heat Therefore, the lower friction will be reduced the shear angle, tool wear, and chip sliding easier The friction angle is determined by the friction coefficient in Eq (3.6)

3.2.2 Types of chip formation

There are four characteristic types of chips formed in metal cutting in Figure 3.2 These are continuous chips (a), discontinuous chips (b), segmented chips (c), and continuous chips with the built-up edge (BUE), shown in Figure 3.2 The chip-forming process reflects on the surface roughness, machining parameters, properties of materials, tool geometry, and machining condition

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Continuous chips form when the continuous plastic deformation of material without reaching the breaking point This type of chip is obtained when machining ductile materials such as aluminum, mild steel, and copper In addition, machining a workpiece that has high hardness can produce continuous chips at a low cutting speed Continuous chips with BUE are formed when machining ductile materials under high friction along the tool and chip interface, the addition of chip material deposition in layers is referred to as the built-up edge with the ability to strain hardening

Figure 3.2 (b) shows the discontinuous chip formation, there are small segments when the material of the workpiece undergoes strain, causing a fracture that occurs in the primary deformation zone and leads to forming the small segments Discontinuous chips can be obtained when machining brittle materials or ductile materials at high speed, and high feed Segmented chips deformed at extremely low cutting speed [18] The segmented chips formation depends on the different physical, and thermal properties of the material

Figure 3.2 Types of chip formation

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3.2.3 Modeling of chip separation

The node-splitting technique is used to simulate the removal of materials, thereby forming the chip [19] In which, the interaction between the cutting tool and the workpiece in contact with each other and the node immediately ahead of the tool cutting edge (node O) will separate the workpiece node (node a) According to the physics criteria discussed in chip formation in the previous section, types of chip formation To form chips, the separated element must be volume conserved The separations of two nodes occur when the value of a physical parameter is predefined, such as stress, or strain at that node or the element A in Figure 3.3

Figure 3.3 An illustration of node-splitting technique between the tool cutting edge and the

node immediately ahead

The basic approach in the FE simulation for chip formation is described as followed:

1 Modeling of the geometry, and definition of the type of geometry

2 Assigned the material properties

3 Mesh design and check the error, warning of mesh

4 Type of simulation, and controlling the stability limit condition

5 Assembly according to the reality of model, definition interaction algorithm, friction coefficient, constraints, and determination boundary conditions

6 Controlling mesh by enhanced stiffness and distortion control

7 Analysis, visualization, and validation of the results

Y

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3.3 Vibration-assisted machining

In conventional machining, the tool and the workpiece interact continuously, resulting

in large cutting forces, rough surface finish, and large burr formation These factors can lead

to the post-processing challenges, such as deburring

Vibration-assisted machining (VAM) is a machining process in which frequencies, and amplitudes with values in Hz, kHz, and micrometers vibration amplitudes are applied to the workpiece or cutting tool to change the cutting mechanism and cause the tool-workpiece to separate periodically As a result, surface quality is improved, reduced burr formation, extended tool life, and the ability to machine difficult-to-machine materials

The trajectory of the tool is more complicated than in conventional machining due to the interaction between the tool and workpiece is constantly changing This chapter focuses

on the separation mechanism between the cutting tool and workpiece in vibration-assisted milling (VAMILL) with vibration in the workpiece

3.3.1 Kinematic modeling of VAMILL

The direction of vibration applied in VAM [10], can be classified into two main directions: Firstly, feed-directional vibration-assisted milling (FVAMILL) in which the vibration is parallel with the feed rate (1D VAMILL), and cross-feed directional vibration-assisted milling (CFVAMILL) in which the vibration perpendicular with the feed rate Secondly, the 2D VAMILL where the vibration is applied in the feed and the cross-feed directions

In Figure 3.4 shows the conventional machining, the mathematical equation of tool tip trajectory without vibration as follows [10]:

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Figure 3.4 Tool tip trajectory in conventional machining

Figure 3.5 Schematic diagram of vibration-assisted milling

The relative displacement of tool tip to workpiece in vibration-assited milling can be express by Eq (3.9):

Table 3.1 The direction of VAMILL according to amplitude value

3.3.2 Tool-workpiece separation conditions in VAM

One of the most features that distinguishes VAM from conventional machining is the separation between tool and workpiece To describe the tool and workpiece separation phenomenon, according to [10] there are three types are decided to contact between tool and workpiece at an instantaneous moment in VAM

Type I in VAMILL occurs in the current tool path when the velocity between the tool and workpiece is greater than zero, the tool will contact the workpiece in position 1 As the tool advances to position 2, the cutting direction component approaches zero which means the tooltip breaks contact with the workpiece In position 3, the velocity between the tool and the workpiece is negative, and the movement opposite directions then the tool is separated from the workpiece At the point in position 4, the velocity is positive the tool has regained contact with the workpiece

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Figure 3.6 Type I tool and workpiece separation during VAMILL

Type II in VAMILL occurs when vibration displacement in the instantaneous cutting thickness direction is larger than the instantaneous uncut chip thickness In position 1, the vibration displacement is smaller so the tool is still in contact with the workpiece But in position 2, the vibration displacement is the same as the instantaneous uncut chip thickness and leads to break contact with the workpiece In position 3, the cutting tool exceeds the workpiece, and until the vibration displacement is equal to the instantaneous uncut chip thickness in position 4, the tool will regain the workpiece

Figure 3.7 Type II tool and workpiece separation during VAMILL

Type III in VAMILL is caused by vibration overlaps in some regions with the surface contour by the previous cutting path Hence, in that region, the tool break contact with the workpiece, and discontinuous chips are formation

Type 1

1 4

3 2

Workpiece feed direction

Tool rotation

Tool-workpiece separation Current tool path

𝜔

Type 2

Workpiece feed direction

Tool rotation

Without vibration

1

22

Figure 3.8 Type III tool and workpiece separation during VAMILL

During VAMILL processes, the tool and workpiece separation type I, II, and III could happen simulstaneouly

2 Compared with conventional machining, the VAMILL movement is more complex, and factors such as cutting force, shear angle, and vibration parameters for chip and burr formation are minimized, etc The application of the finite element method is carried out to study the above problem, by predicting the behavior of the material during VAMILL

Type 3

Workpiece feed direction

Tool rotation 𝜔

1 2

Without vibration

Tool-workpiece separation

Wavy surface generated by previous tool path (s)

Current tool path

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CHAPTER 4: NUMERICAL SIMULATION OF CUTTING MECHANISMS IN VIBRATION-ASSISTED MACHINING

This chapter presented the influences of frequency, and amplitude upon the motion

of the cutting tools in orthogonal cutting, material Al6061-T6 according to the Johnson-Cook fracture, and damage ducticle model The results in the orthogonal cutting model show that the cutting mechanism in VAM, and the shear angle to cutting forces, chip forming by vibration at the tool

4.1 Finite element simulation of VAM orthogonal

4.1.1 Finite element modeling and material properties

Finite element modeling (FEM) is widely used in the aluminum alloys machining process to understand the tool and workspace separation, chip, and burr formation, detailed information temperature, stress, and strain which are difficult to measure or require specialized equipment by experiments The orthogonal schematic diagram is in Figure 4.1 model of orthogonal cutting was established by Abaqus/Explicit 2022, and the unit used is SI (mm) The cutting tool insert CCMW

09 T3 04-H13A (supplier Sandvik) has ° rake angle and ° clearance angle, radius

4 𝜇𝑚 Orthogonal simulation provides a visual perspective of the movement in VAM and more computational time efficiency than 3D simulation

The overall dimensions of the workpiece are 3 mm in length, 0.7 mm in height,

1 mm in width, and Al6061-T6 as material The details of material parameters are specifically in Table 4.1 In machining, most of phenomena occurs in the primary and secondary deformation zones Thus, the workpiece was sliced into two areas: the contact area between the cutting tool and the workpiece is fined-mesh, and the remaining area is coarse mesh

The number of elements for the workpiece was approximately 142500 elements, element hex-dominated C3D8R (8-node linear brick) with structured mesh generation technique Compared with the workpiece, the cutting tool material has a higher hardness than the workpiece Thus, the cutting tool can be specified as a rigid body The number of elements for the cutting tool was approximately 24489 elements, element hex-dominated with free mesh generation technique The illustrates meshing model in Figure 4.3