AOI機台之結構最佳化與熱補償設計

國立臺灣大學工學院機械工程學研究所 碩士論文

Department of Mechanical Engineering College of Engineering

National Taiwan University Master Thesis

AOI 機台之結構最佳化與熱補償設計 Structural Optimum Design and Thermal Compensation Design of an AOI Machine Structure

馬嘉宏 Chia-Hung Ma

指導教授：鍾添東 博士 Advisor: Tien-Tung Chung, Ph.D.

中華民國 99 年 7 月

July, 2010

Acknowledgments

感謝指導教授鍾添東老師三年來的辛勤指導與教誨，使本論文得以順利完 成。也感謝口試委員范光照老師與劉正良老師對本論文的細心指正，使得本論文 更臻完善。

回首研究所生涯並不如大部份人順遂。在經歷更換指導教授的事件，幸虧當 時的錦德學長在我還沒進入此研究室，便已開始給我鼓勵。進入研究室後也並非 事事順心，多虧研究夥伴小家、子揚、稍微、Jaran、嘟嘟、僅僅、Coolken、烏龜 等人，大家互相提攜與照顧，才能順利一路走到今天。同時也感謝前後幾屆學長 姐、學弟妹的陪伴，不管是後門、三國或是飛龍都有我們共同的回憶。要謝的人 太多了，只好老梗的謝個天了。

最後要感謝我的父母、家人與女友元真，從不曾因為延畢的事情指責我並安 慰我，讓我的心裡總是充滿溫暖。謹以此論文獻給每個關心我的人。

Structural Optimum Design and Thermal Compensation Design of an AOI Machine Structure

Abstract

This paper studies the optimum design and thermal compensation design of a high precision automatic optical inspection (AOI) machine structure. First, the structure of AOI machine is introduced. A parametric program for AOI machine is developed to generate solid models of the AOI machine automatically. Then, structural characteristics of the AOI machine are analyzed by the finite element analysis (FEA) and obtained by experiments. Structural responses, such as deformation of the base frame and inspection lens tip, of the original structure are analyzed. An integrated program is also developed by combining solid model generation, FEA simulation, response approximation and numerical optimization searches. Using this integrated program, optimum design of the machine base and moving parts of AOI machine are conducted. The results of optimum design improve the structural characteristics of the AOI machine structure. After the temperature distribution experiment, the thermal deformation of the AOI machine can be analyzed by FEA. Finally, a thermal compensation design is proposed to compensate this thermal error.

Keywords: Automatic optical inspection, structural optimum design, finite element analysis, thermal compensation design

AOI 機台之結構最佳化與熱補償設計

摘要

本文主要探討高精度自動化光學檢測(automatic optical inspection, AOI)機台結

構的最佳化設計與熱補償設計。首先，介紹一種現有的 AOI 機台結構，並發展一

套參數化實體模型繪圖程式以自動化更新此機台結構模型之主要設計參數。接著 透過有限元素分析(finite element analysis, FEA)與實驗，得到此機台之結構特性。

現有機台結構之各種結構響應(structural response)，諸如機台底座與檢測模組之變 形量等，便可經由分析取得。一整合型最佳化程式亦被提出。此程式包括了四個 部份：實體模型產生、有限元素分析模擬、行為響應近似模型產生與最佳化數值

搜尋等。利用此整合型最佳化程式，對此 AOI 機台之底座結構與移動件分別進行

最佳化設計。此最佳化之結果，將可改善底座結構與移動件之結構特性，如結構 剛性增強與輕量化等。另經由溫度分佈實驗得到機台於工作達到穩態時之溫度分 佈，便可利用有限元素分析得到機台之熱變形情形。最後提出一熱補償設計，來 改善此熱膨脹變形情形。

關鍵詞：自動化光學檢測、結構最佳化設計、有限元素分析、熱補償設計

Table of Contents

Abstract V

摘要 VII

Table of Contents IX

List of Figures XI

List of Tables XV

List of Symbols XVII

Chapter 1 Introduction 1

Chapter 2 Theory and Development of AOI Machine Structure 17 2.1 Evaluation of Heat Generation and Air Convection Coefficients 17 2.2 Thermal Deformation Analysis of AOI Machine Structure 20

Chapter 3 Analysis of AOI Machine Structure 25

3.1 Structure of AOI Machine 25

3.2 Parametric Design of AOI Machine Structure 26 3.3 Finite Element Model of AOI Machine Structure 28 3.4 Structural Deformation Analysis and Experiments 31

3.5 Deformation Due to Inertial Force 33

3.6 Modal Analysis and Modal Test 35

3.7 Concept of Structural Optimum Design Program 40

Chapter 4 Optimum Design of AOI Machine 43

4.1 Modified Design for AOI Machine Base 43

4.2 Beam-Shell Finite Element Model for AOI Machine Base and Optimization 45 4.3 Modified and Optimum Design for X-axis Beam of AOI Machine 48 Chapter 5 Thermal Compensation Design of AOI Machine 53

5.1 Temperature Distribution Analysis 53

5.2 Thermal Deformation Analysis 58

5.3 Thermal Compensation Design 61

Chapter 6 Conclusions and Perspectives 67

6.1 Conclusions 67

References 71 Appendix A Parametric Solid Model Design by SolidWorks 75

A.1 SolidWorks API by Visual Basic of MicroSoft Visual Studio 2005 75

A.2 Code Description 76

Appendix B Instruction of the Structural Optimum Design Program 79 B.1 The description of Structural Optimum Design Program 79 B.2 The Description of Optimum Design Problem Setting 79 B.3 The Optimum Design Problem Solver Setting 80

B.4 The Approximation Setting 80

B.5 The Optimum Integrated Environment Setting 80 B.6 The Macro program for structural analysis of AOI machine 80 B.7 The Example of Optimum Design Problem Setting 82

VITA(作者簡歷) 85

List of Figures

Figure 1-1 Configuration of on-line AOI machine in production line 2

Figure 1-2 1/10 scale crane rig in laboratory 3

Figure 1-3 Modified finite element model of crane 3 Figure 1-4 Simplified gantry robot configuration 4 Figure 1-5 Alternative cross-sectional shapes for various loading 5 Figure 1-6 Stress distribution on the vertical ribs in the modified structure 5 Figure 1-7 Symbolic representation of a dual-drive gantry system 6 Figure 1-8 Structural bionic design of stiffening ribs 7 Figure 1-9 Composite X-axis beam for the next generation LCD detecting machine 8 Figure 1-10 Finite element models of (a) the aluminum system and (b) the

foam-composite sandwich system 9

Figure 1-11 The foam-composite sandwich structures 9 Figure 1-12 Measurement of thermal effect on slide-guide 10 Figure 1-13 Spindle, motor and housing under thermal stresses 11 Figure 1-14 Operating sequence of the mechanism when temperature changes 12 Figure 1-15 Elevation view of load cell temperature compensation system 13 Figure 1-16 A section view of an optical assembly 14 Figure 1-17 Invention involving four interfaces used in a lens mount 15 Figure 2-1 A simple illustration of thermal expansion 20 Figure 3-1 Structure of a general gantry type AOI machine 25

Figure 3-2 GUI parametric design program 27

Figure 3-3 Parametric design of AOI machine structure 28 Figure 3-4 SOLID95 3D 20-node structural element in ANSYS 29

Figure 3-5 Boundary conditions of AOI machine 30

Figure 3-6 Mesh model of AOI machine 31

Figure 3-7 Static deformation experiment set up 32 Figure 3-8 Mitutoyo digimatic indicator 543-563 32

Figure 3-9 The simulation result 33

Figure 3-10 The inspection unit moves along X-axis and Y-axis 34 Figure 3-11 Displacement distribution due to inertial force (Load Case 1) 35 Figure 3-12 MPC184 slider constraint geometry 36 Figure 3-13 Boundaries of the AOI machine modal analysis 37

Figure 3-14 Mode shapes of AOI machine by FEM 38

Figure 3-15 The laser doppler vibrometer 39

Figure 3-16 The laser doppler vibrometer principle schematic 39

Figure 3-17 Mode shapes of AOI machine by LDV 40

Figure 3-18 Flow chart of the optimization program 41

Figure 4-1 Modified design of AOI machine base 44

Figure 4-2 Simplified finite element model after modified design 46 Figure 4-3 Parameters in the cross-section of X-axis beam 49 Figure 4-4 Loadings and boundary conditions of X-axis beam optimum design 50 Figure 4-5 Iterative procedure of light weight optimum design 50 Figure 4-6 Iterative procedure of structural reinforcement optimum design 52

Figure 5-1 Infrared position on spectrum 54

Figure 5-2 The energy is sum of emission, reflection and transmission 54

Figure 5-6 Final temperature distribution 56 Figure 5-7 The boundary conditions of temperature distribution analysis 57 Figure 5-8 The result of temperature distribution analysis by ANSYS 58 Figure 5-9 Compare temperature distribution result of FEM with experiment 58 Figure 5-10 The thermal deformation of AOI machine in Y-dir 59 Figure 5-11 The thermal deformation of X-axis beam in X-dir 60 Figure 5-12 The thermal deformation of X-axis beam in Y-dir 60 Figure 5-13 The thermal deformation of X-axis beam in Z-dir 61 Figure 5-14 X-axis beam schematic diagram in thermal expansion 62 Figure 5-15 Thermal compensation design concept 63 Figure 5-16 Thermal compensation design concept 63 Figure 5-17 Local view of the design and principle 64 Figure 5-18 The relationship of θ and legs of right triangle 65 Figure 5-19 Thermal compensation design schematic diagram with four plates 66

List of Tables

Table 3-1 Material properties of AOI machine 29

Table 3-2 Maximum deformation due to inertial force 34 Table 4-1 Static analysis of modified machine base design 45 Table 4-2 Design variables for the machine base 48 Table 4-3 Light weight design variables for X-axis beam 50 Table 4-4 Structural reinforcement design variables for X-axis beam 51

List of Symbols

G rate of heat generation

g& rate of heat generation per unit volume

V volume of heat generation medium h coefficient of convection heat transfer k coefficient of thermal conductivity

Lvp characteristic length of the geometry

Nu Nusselt number

Ra Rayleigh number

Pr Prandtl number

Gr Grashof number

g gravitational acceleration β coefficient of volume expansion

T film f temperature T temperature s of surface

T ∞ temperature of the fluid sufficiently far from the surface ν kinematic viscosity of the fluid

Lhp

characteristic length of horizontal plate Ahp surface area of horizontal plate

P hp perimeter of horizontal plate Lhsp

characteristic length of horizontal square plate

ahsp

length of horizontal square plate Lhcp

characteristic length of horizontal circular plate Dhcp diameter of horizontal circular plate

C constant

m constant ρ density of fluid

V mean fluid velocity

d diameter of tube

μ _{dynamic viscosity}

εT _{thermal strain}

ΔT temperature change α coefficient of thermal expansion

σ _stress

axial

P axial force

A bar cross section area of the bar

ε _strain

δ bar length change of bar

Lbar bar length

E modulus of elasticity

xr design vector )

(x

F r objective function )

(x g_i r

i constraint th

nc number of constraints )

x(x U r

maximum deformation in X direction )

y(x U r

maximum deformation in Y direction )

b(x

V r volume of base frame

) L(x U r

deformation at the inspection lens tip )

XB(x

V r

volume of the X-axis beam

ΔTXb average temperature variation of X-axis beam ΔTLMs average temperature variation of linear motor stator L0 origin length of X-axis beam and linear motor stator LXb X-axis beam lengths by thermal expansion

LLMs linear motor stator lengths by thermal expansion α Xb thermal expansion coefficient of X-axis beam αLMs thermal expansion coefficient of linear motor stator θ bevel angle of thermal compensation design

α A thermal expansion coefficient of box and plate with I-shaped cross sections

α B thermal expansion coefficient of plate with rectangle-shaped

H0 origin height of box and plates

HA height of box and plate with I-shaped cross sections by thermal expansion

HB height of plate with rectangle-shaped by thermal expansion ΔT box temperature change of box

n number of plates in a box

Chapter 1 Introduction

Due to the low profit rate, traditional industries have lost their competitiveness in the past two decades. The emerging technologies and hi-tech industries took advantage in meanwhile, and traditional industries are replaced by them as the key role of promoting the Taiwan economy growth, such as the IC, PC/NB, LCD, communication, MEMS and so on. In the hi-tech industries field, both the main on-line fabrication equipment as well as the off-line inspection equipment is indispensable to guarantee product quality. The on-line AOI equipment is to add AOI machines into production line, such that the AOI machine can full check all production in process. Configuration of on-line AOI equipment in production line [1] is shown as Fig. 1-1. The AOI equipment is the necessary tool in detecting the dimensions and the defects of the hi-tech components, in accordance with the trend of high throughput and high resolution.

The AOI equipment is imported in most domestic hi-tech industries. It consists of the integration of mechanical-electrical-optical-information technologies for technology need. Through the integration of its strong background in mechatronic technology in positioning stages with the optical image processing techniques, it is possible to promote a new AOI industry in Taiwan. The main reason to promote the AOI research for the coming years in Taiwan is because the market requirements are huge not only in domestic need but also in global need. IC, PCB, LCD, Communication, and MEMS parts are the focused industrial applications [2].

Figure 1-1 Configuration of on-line AOI machine in production line [1]

This paper studies regarding two topics about AOI machine. One is about the structure of AOI machine (gantry and base,) and another is about thermal compensation design.

To improve the structure of gantry and base, J.J. Wu develop a finite element model for a 1/10 scale crane rig in the laboratory, as Fig. 1-2 shown, so that one may predict the dynamic behavior of the scale crane rig based on the relevant features of the developed finite element model. The finite element model is then modified, according to the experimental results, using various techniques. It has been found that the new

crane rig with satisfactory accuracy [3].

Figure 1-2 1/10 scale crane rig in laboratory [3]

Figure 1-3 Modified finite element model of crane [3]

Jochen M. Rieber proposed a series automatic control methods for a compliant two-axes mechanism, as shown in Fig. 1-4. The investigation demonstrates how high-precision manufacturing tasks can be optimized by the integration of robot link design and control system design. A trade-off between mass reduction and motion time reduction is shown via a simulation study related to an industry-grade prototype gantry robot [4].

Figure 1-4 Simplified gantry robot configuration [4]

D.R. Griffiths proposed a method combined genetic algorithm and shape optimization to determine the optimal cross-section of beams, subject to various loading conditions. The initial test case is the evolution of an optimal I-beam cross-section, subject to several load cases, as shown in Fig. 1-5. It is shown that the methods developed lead to consistently good solutions, despite the complexity of the process [5].

Figure 1-5 Alternative cross-sectional shapes for various loading [5]

Mathivanan studies on the dynamic behavior of a machine base for crankshaft pin milling machine. Design modifications are proposed to optimize the number of the ribs used and its thickness based on the static and dynamic analysis of the assembly, as shown in Fig. 1-6. A comparison between the existing and modified base structure which is reinforced with the concrete, is also discussed [6].

Figure 1-6 Stress distribution on the vertical ribs in the modified structure [6]

J. Gomand proposed that Industrial control of Dual-Drive Moving Gantry Stage Robots is usually achieved by two independent position controllers, as shown in Fig.

1-7. A physical dynamic lumped parameters model of an industrial robot based on structural, modal, and Finite Element Method analysis is proposed, experimentally identified and validated [7].

Figure 1-7 Symbolic representation of a dual-drive gantry system [7]

Based on the configuration principles of biological skeletons and sandwich stems, Ling Zhao proposed a machine tool column with stiffening ribs inside was designed using structural bionic method, as shown in Fig. 1-8. After the lightening effect was verified by finite element simulation, scale-down models of a conventional column and a bionic column were fabricated and tested. Results indicate that the bionic column can reduce the maximum static displacement by 45.9% with 6.13% mass reduction and its dynamic performances is also better with increases in the first two natural frequencies [8].

Figure 1-8 Structural bionic design of stiffening ribs [8]

S. C. Jung design an imperfection detecting machine which has composite–aluminum hybrid beam structure with high-modulus carbon/epoxy composites in order to enhance dynamic stiffness and damping capacity of the structure.

New designs of beam structure are also proposed for the next generation inspecting system which has much longer beam length, as shown in Fig. 1-9. Parametric study for composite X-axis beam system and optimization scheme of joint inserts are performed in the designing process [9].

Figure 1-9 Composite X-axis beam for the next generation LCD detecting machine [9]

In order to enhance structural robustness of microfactory machine elements, Ju Ho Kim proposed the foam-composite sandwich structure. Unidirectional carbon/epoxy prepreg as skin materials and PVC foams as core materials were used to construct the sandwich structures, as shown in Fig. 1-10. and 1-11. The total mass of the sandwich column system was 1 kg whereas the mass of the current aluminum system was 2.6 kg.

From the vibration tests it was found that the newly designed sandwich column system had 1.5 times higher natural frequency [10].

Figure 1-10 Finite element models of (a) the aluminum system and (b) the foam-composite sandwich system [10]

Figure 1-11 The foam-composite sandwich structures [10]

To consider about thermal effect on machines, Sun-Kyu Lee proposed the effects on machine slide-guide contact conditions caused by thermal deformation, as shown in Fig. 1-12. Since a slide guide as a large friction surface, the motion is greatly influenced by thermal distortion caused by heat generation in the ball nut and the bearing support, during machining processes. This can investigate the typical behavior of the friction coefficient in response to both the external load and the linear speed [11].

Figure 1-12 Measurement of thermal effect on slide-guide [11]

E. Creighton proposed a spindle growth compensation scheme that aims towards reducing its thermally-induced machining errors. A FEA is conducted on the spindle assembly. This FEA correlates the temperature rise, due to heating from the spindle bearings and the motor, to the resulting structural deformation. It is expected to reduce its thermally induced spindle displacement by 80% [12], as shown in Fig. 1-13.

Figure 1-13 Spindle, motor and housing under thermal stresses [12]

A. Gelman proposed passive thermal compensation mechanism is intended for maintaining the stability of performance parameters of an optomechatronic system over a wide operating temperature range, as shown in Fig. 1-14. This allows the mechanism described herein to act as a motion amplifier. The amplifier Input is a small dimensional change in the links, caused by temperature change and its output is the rotational motion of the output link. The amplification is according to the rules of lever dynamics [13].

Figure 1-14 Operating sequence of the mechanism when temperature changes [13]

Mark Stern proposed a load cell temperature compensation system for accurately measuring a force load applied to an external member during environmentally varying temperature values. It includes a standard load cell which is rigidly mounted on a load cell mounting plate, as shown in Fig. 1-15. The load cell mounting plate is fixedly secured to the external member which has an external force load applied thereto. The temperature compensation system further includes a force load application mechanism which transmits a predetermined force load to the load cell. In this manner, temperature variations applied to the external member will be compensated for by compensation system and not read as a load force applied to the external member [14].

Figure 1-15 Elevation view of load cell temperature compensation system [14]

Michael J. proposed an athermalized optical assembly includes a laser beam source, such as a laser diode, and a collimator lens which are together mounted in an active thermally-compensated structure, as shown in Fig. 1-16. The difference in the coefficient of thermal expansion (CTE) of each compensation ring is chosen such that the flexure plate kinematic hinge is passively operated to approximately compensate for thermal shifts in system focal length while maintaining radial and angular alignment of the lens relative to the laser diode source, so as to provide controlled axial movement of the collimating lens [15].

Figure 1-16 A section view of an optical assembly [15]

Donald R. proposed a passive mechanical system that unwanted positional shifts between two objects, such as lenses, are precisely compensated during thermal changes, as shown in Fig. 1-17. Materials with differing coefficients of thermal expansion and angled interfaces transforms a longitudinal dimensional change into a fine transverse dimensional change to precisely control movement as a function of temperature thereby maintaining, e.g., lens focus [16].

Figure 1-17 Invention involving four interfaces used in a lens mount [16]

This paper aims at providing a structural optimum design and a local thermal compensation design for AOI machine. First, the structure of AOI machine is introduced.

Secondly, the static analysis of AOI machine is performed by considering the effect of inertial force. Thirdly, various types of base design are proposed to improve the structural strength of AOI machine. Based on the analysis, the structural optimum design is performed to provide a suitable design for AOI machine base. Fourthly, the optimum designs of moving part are also performed to both reduce weight and deformation separately. Fifthly, the temperature distribution analysis is proposed by considering operating conditions, and the thermal deformation analysis is also performed. Finally, there is a new thermal designs proposed for reducing the thermal deformation generated by the difference in the coefficient of thermal expansion of X-axis beam and linear motor stator.

Chapter 2 Theory and Development of AOI Machine Structure

2.1 Evaluation of Heat Generation and Air Convection Coefficients

This paper refers to the book of HEAT TRANSFER [17] for the thermal analysis.

A medium through which heat is conducted may involve the conversion of electrical, nuclear, or chemical energy into heat energy. In heat conduction analysis, such conversion processes are characterized as heat generation. The rate of heat generation in medium may vary with time as well as position within the medium. When the variation of heat generation with position is known, the total rate of heat generation in a medium of volume V can be determined from:

∫

= _V gd

G & V (2-1)

In the special case of uniform heat generation, as in the case of electric resistance heating throughout a homogeneous material, the relation in Eq. 2-1 reduces to G =g&V, where _g& is the constant rate of heat generation per unit volume.

Natural convection heat transfer on a surface depends on the geometry of the surface as well as its orientation. It also depends on the variation of temperature on the surface and the thermo-physical properties of the fluid involved. The simple empirical formulations for calculating the coefficient of convection heat transfer h in natural convection are divided into two parts, vertical plate part and horizontal plate part. For vertical plates, the formulations can be expressed as Eq. 2-2 to Eq. 2-4.

L Nu h k

vp

= (2-2)

( )

[

]

6 2 1

1

Pr 492 0 1

387 825 0

0 . /

Ra . .

Nu = + +

(2-3)

( )

Pr ₂

3

− ×

=

×

= ^∞

v L T T Gr gβ

Ra ^{s vp} (2-4)

where k is coefficient of thermal conductivity, L_vp is characteristic length of the geometry, Nu is Nusselt number, Ra is Rayleigh number, Pr is Prandtl number, Gr is Grashof number, g is gravitational acceleration, β is coefficient of volume expansion, T is temperature of surface, _s T_∞ is temperature of the fluid sufficiently far from the surface, and ν is kinematic viscosity of the fluid. Noting that all fluid properties are to be evaluated at the film temperature ( )

2 1

+ ∞

= T T

T_{f s} .

However, the characteristic length L_hp of horizontal plates is different than vertical plates and it can be calculated from:

hp hp

hp P

L = A (2-5)

where A is the surface area and _hp P is the perimeter. Note that _hp L_hsp =a_hsp/4 for a horizontal square surface of length a , and _hsp L_hcp = D_hcp/4 for a horizontal circular surface of diameter D .

of horizontal plates by Eq. 2-5, the simple empirical formulations for calculating the coefficient of convection heat transfer h in natural convection are similar to the formulations of vertical plates and it can be expressed as Eq. 2-6 to Eq. 2-8.

L Nu h k

hp

= (2-6)

Ram

C

Nu = × (2-7)

( )

Pr

Gr ₂

3

− ×

=

= ^∞

v L T T

Ra gβ ^{s hp} (2-8)

where the values of the constants C and m depend on the geometry of the surface and the flow region, which is characterized by the range of the Rayleigh number. The constant C is 0.54 and the value of m is 1/4 in this paper.

Flow in a tube can be laminar or turbulent, depending on the flow conditions. Fluid flow is streamlined and thus laminar at low velocities, but turns turbulent as the velocity is increased beyond a critical value. It certainly desirable to have precise values of Rayleigh numbers for laminar, transitional, and turbulent flows. Under most practical conditions, the flow in a tube is laminar for Ra< 2300, turbulent for Ra >10000, and transitional in between. The Reynolds number is defined as Eq. 2-9.

μ ρ^Vd Ra=

(2-9)

where ρ is the density, V is the mean fluid velocity, d is the diameter of the tube, and μ is the dynamic viscosity.

The average Nusselt number for turbulent flow across tubes can be expressed

n

CRam

Nu = Pr (2-10)

d Nu h= k

(2-11) where Rayleigh numbers Ra can be defined by Eq. 2-9. Noting that C =0.023,

8 .

=0

m , and n=0.3 are given in this paper for cooling condition.

2.2 Thermal Deformation Analysis of AOI Machine Structure

Changes in temperature produce expansion or contraction of structural materials, resulting in thermal strains and thermal stresses. A simple illustration of thermal expansion is shown in Fig. 2-1, where the block of material is unrestrained and therefore free to expand [18]. When the block is heated, every element of the material undergoes thermal strains in all directions, and consequently the dimensions of the block increase.

Figure 2-1 A simple illustration of thermal expansion [18]

) (ΔT α

ε_T = (2-12)

in which α is a property of the material called the coefficient of thermal expansion.

Since strain is a dimensionless quantity, the coefficient of thermal expansion has units equal to the reciprocal of temperature change. In SI units the dimensions of α ^{can be} expressed as either 1/K (the reciprocal of kelvins) or 1/°C (the reciprocal of degrees Celsius).

In general, the force per unit area is called the stress and is denoted by the Greek letter σ . Thus, the axial force Paxial acting at the cross section is the resultant of the continuously distributed stresses. Assuming that the stresses are uniformly distributed over cross section, the resultant must be equal to the intensity σ times the cross-section area A_bar of the bar. Therefore, the stresses can be expressed as:

bar axial

A

σ = P (2-13)

This equation gives the intensity of uniform stress in an axially loaded, prismatic bar of arbitrary cross section shape. When the bar is stretched by the forces P_axial, the stresses are tensile stresses; if the forces are reversed in direction, causing the bar to be compressed, the stresses are compressive stresses.

As already observed, a straight bar will change in length when loaded axially, becoming longer when in tension and shorter when in compression. Therefore, a unit length of the bar will have an elongation equal to 1/L_bar times δ . This quantity is _bar called the elongation per unit length, or strain, and is denoted by the Greek letter ε^. The strain is given by the Eq. 2-14. If the bar is in tension, the strain is called a tensile

compression, the strain is a compressive strain and the bar shortens.

bar bar

L

ε = δ (2-14)

Many structural materials, including most metals, wood, plastics, and ceramics, behave both elastically and linearly when first loaded. Consequently, the stress-strain curves begin with a straight line passing through the origin. When a material behaves elastically and also exhibits a linear relationship between stress and strain, it is said to be linearly elastic.

The linear relationship between stress and strain for a bar in simple tension or compression is expressed by the Eq. 2-15 and is called Hooke’s law. Noting that E is a constant of proportionality known as the modulus of elasticity for the material. The modulus of elasticity is the slope of the stress-strain diagram in the linearly elastic region.

Eε

σ = (2-15)

If the material follows Hooke’s law, the strains produced by the stresses σ_x^, σ , y

and σ_z acting independently are superimposed to obtain the resultant strains ε_x^, ε , y

and ε_z. Thus, the following equations for the strains in tri-axial stress can be expressed as Eq. 2-16. Noting that ν is Poisson’s ratio and E is the modulus of elasticity.

( )

[ ]

⎪⎧ x = σx −νσy +σz

ε E1

( )

[ ]

( )

[ ]

( )

[ ]

⎪⎪

⎪

⎩

⎪⎪

⎪

⎨

⎧

+ +

−

=

+ +

−

=

+ +

−

=

αΔT σ

σ ν E σ

ε

αΔT σ

σ ν E σ

ε

αΔT σ

σ ν E σ

ε

y x z z

x z y y

z y x x

1 1 1

(2-17)

Ordinary structural materials expand when heated and contract when cooled, and therefore an increase in temperature produce a positive thermal strain. Assuming that the material is homogeneous and isotropic and that the temperature increases ΔT is uniform throughout the block. This equation can calculate the increase in any dimension of the block by multiplying the original dimension by the thermal strain. If one of the dimensions is L_bar , then that dimension will increase by the amount.

bar bar

T

bar =ε ×L =α×ΔT×L

δ (2-18)

) (α ΔT E

Eε

σ = _T = × (2-19)

Chapter 3 Analysis of AOI Machine Structure

In order to determine the specification of the AOI machine, a finite element analysis was performed. The structure of AOI machine is introduced. Finite element model of AOI machine structure is also proposed. Due to the inertial force produced from moving parts during detection process, the analysis of AOI machine is conducted to understand the characteristics of AOI machine structure. The result of analysis is also verified by experiment result.

3.1 Structure of AOI Machine

An AOI machine is generally composed of a base, a X-axis beam, a Y-axis beam, and the inspection unit. The AOI machine to be analyzed in this paper has gantry type structure as shown in Fig. 3-1. The gantry structure is mounted on a base and the devices under test are placed on the base.

Figure 3-1 Structure of a general gantry type AOI machine

3.2 Parametric Design of AOI Machine Structure

Based on the parametric design and feature tree, SolidWorks utilizes a parametric feature based approach to create models and assemblies. In a solid model, there are a lot of parameters in every feature. But not all parameters are interested by designers. The graphic user interface (GUI) is proposed to show the interesting parameters. Designers can update the shown parameters of model by GUI dialog conveniently. In this section, two kinds of parametric design programs are developed by Microsoft Visual Basic language. One is for AOI machine structure with GUI and the other is for any cad model from SolidWorks by executables (EXE files).

The GUI parametric design program includes several parts: menu items, schematic diagram, eDrawing viewer, file control and design parameters, as shown as Fig. 3-2.

This program can update not only the length, width and height of whole machine, but also the cross section detail dimensions of X-axis beam, Y-axis beam and base frame.

There are a total of 31 parameters. Based on this GUI parametric design program, designer who has no 3D modeling capability can update the CAD model parameters easily. The origin machine and double width of machine are shown in Fig. 3-3.

The other way to update the model parameters is the executables. In this paper, two executables are developed. They are controlled by command line arguments. Designers can update parameter by command “SW_PChange <part_name.sldprt>

<parameter_name> <value>” and export ACIS model by command “SW_OutputSAT

Figure 3-2 GUI parametric design program

(a) Present AOI machine structure

(b) AOI machine structure with double width Figure 3-3 Parametric design of AOI machine structure

3.3 Finite Element Model of AOI Machine Structure

The solid model is transformed in the form of ACIS SAT, and then it is imported into finite element analysis software. Solid95, the structural second order element [19]

as shown in Fig. 3-4, is used for modeling of AOI machine. Material properties are listed in Table 3-1.

X-direction and Y-direction.

Figure 3-4 SOLID95 3D 20-node structural element in ANSYS [19]

Table 3-1 Material properties of AOI machine

Component Material name Young’s modulus (GPa)

Poisson’s ratio

Density (g/cm^3) X-axis beam, stage

and inspection unit AL6061 68.9 0.33 2.7

Junction plate AL7075 71.7 0.33 2.81

Linear guide S50C 195 0.29 7.86

Y-axis beam S45C 205 0.29 7.85

All other parts SS41 205 0.29 7.85

Figure 3-5 Boundary conditions of AOI machine

Tetra mesh was mainly used for mesh processing. Element number is between 55,000 and 60,000. After giving material properties and boundary conditions, a finite element mesh model is built, as shown in Fig. 3-6. One static FEM computation takes about 90 second at a computer equipped with Intel core 2 quad Q6600 CPU and 2 GB RAM.

Figure 3-6 Mesh model of AOI machine

3.4 Structural Deformation Analysis and Experiments

Since the effect of gravity cannot be removed, the deflection due to self weight cannot be measured. To ensure the accuracy of the finite element model, an experiment is conducted by adding loads to AOI machine. The AOI machine is applied static 10kg per time at the upper middle point as the circle in figure, until the load reaches 50 kg, as shown in Fig. 3-7. The digimatic indicator of Mitutoyo, 543-563, is used to measure the deformation. It has 2.5μm accuracy and 0.5μm resolution, as shown in Fig. 3-8. This experiment had been conducted three times and digital indicator was used to measure deformation at specific points. The deformation versus load is linear.

Figure 3-7 Static deformation experiment set up

(a) A front view of 543-563 (b) Specifications of 543-563 Figure 3-8 Mitutoyo digimatic indicator 543-563

After comparing experiment results with FEM simulation results, if results are coherent, then the finite element modal is reliable. Since the result of deformation experiment 18.01μm corresponds with the result of FEM deformation 19μm as shown in Fig. 3-9, the FEM analysis error is 5.21%. Therefore, this finite element model can

Figure 3-9 The simulation result

3.5 Deformation Due to Inertial Force

During the detection process, the inspection unit needs to move back and forward rapidly along X-axis, both the inspection unit and X-axis beam have to move back and forward rapidly along Y-axis, as Fig. 3-10 shown. The maximum acceleration of the inspection unit will reach 0.5g. Hence, when considering high precision, the effect of inertial force must be taken into consideration. There are two loading cases should be considered. Load case one is that the inspection unit moves along X-axis with the acceleration of 0.5g. Load case two is that the inspection unit and X-axis beam move along Y-axis with the acceleration of 0.5g, as Table 3-2 shown.

After taking the effect of inertial force into consideration, the simulation is

displacement distribution of AOI machine is performed, too. In load case one, the maximum deformation of base is 12.45μm, and the maximum deformation of whole AOI machine is 34.02μm, as shown in Fig. 3-11. On the contrary, in load case two, the maximum deformation of base is 7.07μm, and the maximum deformation of whole AOI machine is 23.91μm.

Figure 3-10 The inspection unit moves along X-axis and Y-axis

Table 3-2 Maximum deformation due to inertial force

Inertia loading Acceleration Max. deformation Deformation of base Load case 1,

(0.5g, 0, 0) 34.02μm 12.45μm

Figure 3-11 Displacement distribution due to inertial force (Load Case 1)

3.6 Modal Analysis and Modal Test

The purpose of modal test and modal analysis is to find out the natural frequencies and mode shapes of the structure. Not only the inspection unit of AOI machine moves back and forward during the detection process but also the others pumps, which fixed the objects by atmospheric pressure, and ball screws, which control the position of inspection unit, give the AOI machine structure steady oscillation forces back and forward. If the frequencies of this oscillation force are similar with any natural frequency of the structure, the structure may cause resonance. The detection accuracy will be affected. In this section, the modal test of AOI machine is proposed, and the modal analysis is also proposed to verify with each other.

For the accuracy of modal analysis, multipoint constraint element MPC184 is used, since there is one DOF between the X-axis beam and Y-axis beams by sliders. In

constraints like rigid link, rigid beam, slider, spherical, revolute, universal and slot. In this case, the MPC184 slider constraint is used, its geometry is as shown as Fig. 3-12.

The node I is expected to lie initially on the line joining the node J and K.

Figure 3-12 MPC184 slider constraint geometry [19]

Since there is no related displacement between machine base and ground, the four corners of the base bottom are fixed. Furthermore, X-axis beam is fixed with Y-axis beams by two angle plates for regular constraints, as shown as Fig. 3-13. Other boundaries and constraints are as the same as said in section 3-3. The results of the modal analysis about the X-axis beam of AOI machine are obtained by FEA. Less than 1000 Hz, natural frequencies of the AOI machine X-axis beam are 141Hz, 349Hz, 391Hz, 635Hz, 685Hz and 794Hz. The mode shapes of AOI machine at 141Hz, 349Hz, 635Hz and 794Hz are shown in Fig. 3-14.

Figure 3-13 Boundaries of the AOI machine modal analysis

(a) Mode shape of X-axis beam at 141Hz

(b) Mode shape of X-axis beam at 349Hz

(c) Mode shape of X-axis beam at 635Hz

(d) Mode shape of X-axis beam at 794Hz Figure 3-14 Mode shapes of AOI machine by FEM

The LDV (laser doppler vibrometer) is used to measure the natural frequencies and mode shapes of the AOI structure. LDV is a velocity measuring instrument, as shown in Fig. 3-15. The measurement principle of LDV is as follows: first, LDV injects a He-Ne laser, then the laser separates to reference beam and measurement beam by the spectroscope; second, the measurement beam reflects from vibrating object, therefore its wave length is initially 633 nm and variation after reflection; third, the detector detects sum of the reference beam and reflected measurement beam to compute the vibration frequencies of vibrating object; as shown as Fig. 3-16.

Figure 3-15 The laser doppler vibrometer [20]

Figure 3-16 The laser doppler vibrometer principle schematic [20]

The boundary conditions are set as previously described. The results of the modal test about the X-axis beam of AOI machine are measured by LDV. Less than 1000 Hz, natural frequencies of the AOI machine X-axis beam are 131Hz, 324Hz, 375Hz, 582Hz, 645Hz and 724Hz. The mode shapes of AOI machine at 131Hz, 324Hz, 582Hz and 724Hz are shown in Fig. 3-17. Compared with the results of modal test and modal analysis, the maximum error is about 9.7%. It means that this FEM model is suitable to analyze with suitable boundaries.

(a) Mode shape of X-axis beam at 131Hz

(b) Mode shape of X-axis beam at 324Hz

(c) Mode shape of X-axis beam at 582Hz

(d) Mode shape of X-axis beam at 724Hz Figure 3-17 Mode shapes of AOI machine by LDV

3.7 Concept of Structural Optimum Design Program

is written in Microsoft Visual C++ language. By parametric design program (SolidWorks API) and parametric analysis (ANSYS APDL), this program can update parameters of models, analyze automatically, and then execute sensitivity analysis and optimization. After several iterations, an optimal solution can be received.

Figure 3-18 Flow chart of the optimization program

Chapter 4 Optimum Design of AOI Machine

This chapter aims at developing optimum design of the AOI machine structure.

First, many modified base structures are proposed in order to reduce the deformation due to inertial force and increase the structural stiffness of the AOI machine base in both X-axis and Y-axis direction. Then a more suitable model is selected to carry out optimization. During the process of optimization, the finite element model will be calculated hundred or thousand times. Therefore, the finite element model of machine base is rebuilt by beam-shell to reduce the calculation time. By using this beam-shell model, optimum design variables for cross section can be received.

The inspection unit and X-axis beam are the moving parts during the inspection process, as shown in Fig. 3-10. The moving parts usually accelerate and decelerate substantially. The inertial force acting on the AOI machine is multiplied the mass of moving parts by 0.5g. Reducing the weight of moving parts can decrease the inertial force effectively while remain the acceleration of moving parts; or remain the same inertial force while increase the acceleration of the moving parts.

4.1 Modified Design for AOI Machine Base

The deformation of AOI machine base due to inertial force can be reduced by adding diagonal beams and oblique beams to the base. Five modified designs of AOI machine are proposed as shown in Fig. 4-1. The simulation results of modified design are listed in Table 4-1.

(a) Inner-oblique (b) LR-diagonal 1

(c) LR-diagonal 2 (d) LR-diagonal 3

Table 4-1 Static analysis of modified machine base design Model Volume changed

(%)

Max def. of base (µm)

Def. changed (%)

Present model --- 7.07 ---

Inner-oblique 1.87 6.65 -5.94

LR-diagonal 1 4.62 3.37 -52.33

LR-diagonal 2 9.07 2.20 -68.88

LR-diagonal 3 13.69 1.30 -81.61

Y-dir

LR-diagonal V 3.20 1.27 -82.04

According to above analysis, conclusions can be made as following:

y The structural stiffness is weak if the base frame consists of vertical beams only.

y The deformation in Y-axis can be reduced 80% by adding diagonal beams on left side and right side of the base.

y The total volume of machine base is increased slightly.

4.2 Beam-Shell Finite Element Model for AOI Machine Base and Optimization

It takes hundred or even thousand times of analysis to finish structural optimization.

In order to reduce total process time, ANSYS beam189 and shell93 are used to rebuild finite element model. In this way, a simplified model with loadings and boundary conditions is built, as shown in Fig. 4-2.

Figure 4-2 Simplified finite element model after modified design

This simplified finite element model has about 4,600 nodes and 28,000 D.O.F. and only takes 5 second to finish one analysis. Although this model can reduce calculation time effectively, it should also guarantee the accuracy of this model during static analysis. By comparing analysis results of two models, the error of simulation results between simplified beam-shell mesh model and solid mesh model is about 11%.

Therefore, simplified model can be used to find optimum solution during optimization process, and it can also assure the accuracy of the simulation.

The numerical optimization problem can be written in the following form:

x F that Such x

Find r, (r)→min

The optimization problem of the AOI machine is formulated by selecting three geometric parameters ( x_i,i = 1,2,3) of the rectangle tube’s cross section as the design variables. x ,₁ x₂ are the width and length of the rectangle tube, x is the thickness of ₃ rectangle tube. The best modified design has diagonal-V steel structure in left side and right side of the base, as shown in Fig. 4-2. The constraints include the upper and lower limit of design variables and the displacement due to inertial force. According to the performance of modified design, the displacement due to inertial force is less than 0.5 times of original displacement in both X-axis and Y-axis direction, i.e. the structural stiffness in both X-axis and Y-axis direction is doubled. The optimization problem is formulated as:

) 5 . 0 7 ( 5 . 3 ) (

; ) 5 . 0 12 ( 6 ) (

; 3 6

6 . 1 1 ; 0 2

; 1 200

20

min )

( ) (

,

×

<

×

<

<

<

<

<

<

<

→

=

m m y x

U m

m x x

U

mm x

mm x

x mm x

mm to Subject

b x V x F

that Such x

Find

μ μ μ

μ ^r

r r r

r

(4-2)

where Ux(xr)is the maximum deformation in X direction, Uy(xr)is the maximum

deformation in Y direction, Vb(xr) is the volume of base frame. After numerical searches of the structural optimization program, the optimum values are listed in Table 4-2. The ideal size for cross section of rectangle tube that calculated by optimum program is 67 x 67 x 1.6. By decreasing thickness in X-axis direction and increasing width to 67 mm, this design can strengthen the structural stiffness in X-axis. On the contrary, the structural stiffness decreased in Y-axis direction as the thickness and width both decreased. However, the structural stiffness decreased in y-axis can be improved

With this optimum design, the structural stiffness is doubled and total volume of base can be decreased 31.2% to 23,151cm^3 (original volume is 33,658cm^3). By using standard part of square tube 60 x 60 x 3.2, this structural stiffness of modified design, compared with original design, becomes 2.47 times in X-axis direction and 5.2 times in Y-axis direction, and 10.5% of the base weight is reduced.

Table 4-2 Design variables for the machine base

Parameter Initial value Optimum value

x1 125 mm 66.9 mm

x2 75 mm 66.9 mm

x3 2.3 mm 1.6 mm

Ux 12.45 μm 6 μm

Uy 7.07 μm 1.92 μm

Vb 33,658 cm^3 23,151 cm^3

4.3 Modified and Optimum Design for X-axis Beam of AOI Machine

In order to decrease the weight of moving parts of AOI machine, selecting the total volume of X-axis beam as the object function. The optimization problem of the AOI machine is formulated by selecting four geometric parameters (x_i,i= 1, 2, 3, 4) of X-axis beam as the design variables. x₁, x₂, x are the thicknesses in the cross-section ₃ of x-axis beam, x is the side length of the square in the middle as shown in Fig. 4-3. ₄ The constraints follow the general aluminum extrusion limit for large-scale platform.

The thickness of dimensions should not be less than 5mm. To avoid the geometrical error, three design variables should not be larger than 30mm simultaneously. Moreover,

larger than the original deformation of inspection unit (45.6μm). The optimization problem is formulated as:

m x

U

mm x

mm mm

x x x mm

to Subject

x V x F

that Such x Find

L

XB

μ 6 . 45 ) (

120 20

; 30 ,

, 5

min )

( ) (

,

4 3

2 1

<

<

<

<

<

→

=

r

r r

r

(4-3)

where U (x)

L

r is the deformation at the inspection lens tip, V (x)

XB

r is the volume of

the X-axis beam. After calculation by using optimization program, the optimum values are listed in Table 4-3. The iterative procedure is shown as Fig. 4-5. The total volume of X-axis beam can be decreased 26% to 6,464cm^3 (original volume is 8,753cm^3.)

Figure 4-3 Parameters in the cross-section of X-axis beam

Figure 4-4 Loadings and boundary conditions of X-axis beam optimum design

Table 4-3 Light weight design variables for X-axis beam Parameter Initial value Optimum value

x1 6 mm 7.069 mm

x2 18 mm 11.253 mm

x3 15 mm 7.619 mm

x4 60 mm 58.69 mm

VXB 8,753 cm^3 6,464 cm^3

UL 45.6 μm 45.6 μm

To reinforce the structural stiffness of AOI machine, selecting the deformation of lens at the same boundary condition and loadings as object function. The behavior constraint is the total volume of X-axis beam (8,753cm^3), while other settings remain the same. The optimization problem is formulated as:

3 4

3 2 1

8753 )

(

120 20

; 30 ,

, 5

min )

( ) (

,

cm x

V

mm x

mm mm

x x x mm

to Subject

x U x F

that Such x Find

XB

L

<

<

<

<

<

→

=

r

r r r

(4-4)

After calculation by using optimization program, the optimum values are listed in Table 4-4. The iterative procedure is shown in Fig. 4-6. The deformation of the lens can be decreased to 37.1μm (18.6% reduction).

Table 4-4 Structural reinforcement design variables for X-axis beam Parameter Initial value Optimum value

x1 6 mm 11.09 mm

x2 18 mm 15.19 mm

x3 15 mm 9.07 mm

x4 60 mm 67.71 mm

VXB 8,753 cm^3 8,753 cm^3

UL 45.6 μm 37.1μm

Figure 4-6 Iterative procedure of structural reinforcement optimum design

After numerical searches of the structural optimization, 26% of the x-axis beam weight can be reduced when the deformation of lens remains the same, or 19% of the lens deformation is reduced meanwhile the volume remains the same. Hence, the inspection unit can be moved with a higher acceleration, then the AOI machine can use linear motor with lower power as actuator, or a better image quality can also be acquired during the inspection process.

Chapter 5 Thermal Compensation Design of AOI Machine

In the chapter, the temperature distribution of AOI machine under the temperature distribution becoming steady state is detected by an infrared thermometer and the thermal couple. After the experiment results are obtained, the temperature distribution can be very closely simulated in ANSYS. Since the temperature distribution is re-performed in ANSYS, the thermal deformation analysis can also be executed.

According to the result of thermal deformation analysis, a thermal compensation design is proposed to compensate the thermal error of the AOI machine.

5.1 Temperature Distribution Analysis

For detecting the temperature distribution of AOI machine under the temperature distribution become steady state, the infrared thermometer is used. It measures the temperature using blackbody radiation emitted from detected object that the wave length range of this radiation is about 0.7μm ~ 1mm (infrared), as shown in Fig. 5-1.

Therefore infrared thermometer can measure the temperature from a distance (non-contact). By knowing the surface emissivity and energy emitted by the detected object, the temperature of object can be determined.

Figure 5-1 Infrared position on spectrum [21]

Although the infrared thermometer is detecting the energy from the object surface, the energy is not only emitted from object. The energy is sum of emission, reflection and transmission by the surface, as shown in Fig. 5-2. So that not all surfaces are suitable for infrared thermometer measurement, such as: transmission with infrared, shining surface (metal) and other surface with high reflection. Adding tapes with knowing emissivity can solve this problem and get accuracy result.

shown as Fig. 5-3 and 5-4. After machine switch on, the environment temperature is 25.3℃. The experiment is measured until the temperature stabilized, spent a total of 5 hours. The initial and final temperature distributions are shown as Fig. 5-5 and 5-6.

Figure 5-3 The arrangement of temperature distribution experiment

Figure 5-4 Measuring the X-axis beam of AOI machine

Figure 5-5 Initial temperature distribution

As the results show that the temperature of X-axis beam ranges from 26.2℃ to 27.1℃. Note that there are some red color regions on linear motor stator in Fig. 5-6. In general, red region means higher temperature but the linear motor stator has shining surface which is not suitable to measure temperature by an infrared thermometer because of the reflection. Here the thermal couple is used to measure the temperature of stator. The results show that the temperature of linear motor stator ranges from 27.5℃

to 33.5℃.

After the experiment results are obtained, the temperature distribution can be very closely simulated in ANSYS. The boundary conditions and the result are shown in Fig.

5-7 and 5-8. The temperature of the X-axis beam ranges from 26.3℃ to 27.3℃. For verifying the result from FEM and experiment, a series of temperature numerical at X-axis beam from end to mid are captured, as shown as Fig. 5-9. In this figure, it shows that the FEM result is very close to experiment result.

Figure 5-7 The boundary conditions of temperature distribution analysis