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6/01 c:/CIRClDateDuo.p65-p.15

A GE
CAI

A GENERAL FRAMEWORK FOR AUTOMATED
CAD-GUIDED OPTIMAL TOOL PLANNING IN
SURFACE MANUFACTURING

BY

Heping Chen

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Electrical and Computer Engineering

2003

AGEXER.

 

 

 

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ABSTRACT

A GENERAL FRAMEWORK FOR AUTOMATED CAD-GUIDED OPTIMAL
TOOL PLANNING IN SURFACE MANUFACTURING

By

Heping Chen

This dissertation develops a general framework for automated CAD-guided opti-
mal tool planning in surface manufacturing. Surface manufacturing is a process to
add material to or remove material from the surface of parts. Spray painting, spray
forming, indirect rapid tooling, spray coating and polishing are typical applications
of surface manufacturing. Industrial robots are used to implement these processes.
Tool planning of these processes, which builds a bridge between product design and
manufacturing, is crucial for the product quality. Typical teaching methods are not
feasible any more because products are subject to a shorter product life, frequent
design changes, small lot sizes, small in-process inventory restrictions and quality is-
sues. An automated tool planning process (ATPP) is desirable for the tool planning
of industrial robots.

In surface manufacturing, automated tool planning develops a tool trajectory for
a free-form surface based on a tool model such that the given constraints are sat-
isfied. According to the material distribution constraints, the processes in surface
manufacturing can be categorized into two groups: material uniformity and cover-
age. Based on a tool model and material distribution constraints, a free-form surface
is divided into patches. The parameters (the spray width and tool velocity) used
for automated tool planning are determined by optimizing the material distribution
on a plane. Since different material deposition patterns are used in automated tool
planning, comparison between the raster and spiral material deposition patterns are

performed. The raster material deposition pattern is better than the spiral one for

continuous in
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continuous material deposition. After the spray width is determined, an improved
bounding box method is developed to generate a path for a patch using the raster
pattern. The tool orientation is determined using the local geometry of a free—form
surface. Since the material deposited on the free-form surface is less than the de-
sired material thickness, a suboptimal velocity algorithm is developed to optimize
the material thickness deviation. For a free-form surface with multiple patches, an
integration algorithm is deveIOped to integrate the trajectories of the patches. To
verify if a trajectory satisfies the given constraints, a verification model is developed.
The implementation and simulation results show that the developed automated tool
planning algorithm can be applied to generate trajectories for different processes in
surface manufacturing such that the given constraints are satisfied.

To increase productivity and the quality of manufactured products, it is desirable
for industrial robots to run in their optimal conditions subject to some optimization
criteria. Optimal tool planning generates a tool trajectory in surface manufactur-
ing using given optimization criteria. Optimal tool planning for industrial robots
is challenging. Based on the CAD model of a free-form surface, along with a tool
model, constraints and optimization criteria, a general framework for Optimal tool
planning with constant and non-uniform material distribution has been developed for
surface manufacturing. Multi-objective constrained optimization problems are for-
mulated. The implementation and simulation results are consistent with theoretical
analysis. The developed optimal tool planning algorithm can be applied to generate
tool trajectories in surface manufacturing.

The general framework can also be extended to other applications such as di-
mensional inspection and nanomanufacturing. A general framework for automated
tool planning for nanoassembly in nanomanufacturing is developed to manufacture
nanodevices and nanostructures. The algorithm is implemented successfully to man-

ufacture nanostructures using an atomic force microscope (AF M).

For my mother, father, wife and daughter,

their love and support make my dream true.

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foremost. .
Dr. King Xi
mints from '.
a fruitful res.
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like to thank

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Foundat ion

ACKNOWLEDGEMENTS

Foremost, I would like to acknowledge all the invaluable help from my advisor,
Dr. Ning Xi, without whom this would not have been possible. This dissertation
comes from numerous discussions in his office, from his keen insight and guidance in
a fruitful research area, and his support. Not only the knowledge, but also the research
experience and friendship I gained here will be beneficial for the rest of my life. I would
like to thank all my committee members, Dr. Yifan Chen, Dr. Chichia Chiu, Dr.
Erik Goodman and Dr. F athi Salem, who have devoted many hours in the committee
meetings. Their insightful comments and suggestions have enhanced the technical
soundness of this dissertation. I am grateful to my friends and colleagues from the
Robotics and Automation Laboratory and the Ford Motor Company. The discussions
with Dr. Muming Song and Dr. Weihua Sheng substantially contributed to my work
and broadened my knowledge. I would like to express my great appreciation to Mrs.
Carolyn Haines and Mr. Ali Saeed for revising my dissertation. My thanks go to
my family, especially my wife and my parents. Without their years of encouragement
and continuous support, I would not have reached this point. I would like to thank
the Scientific Research Laboratory of the Ford Motor Company and National Science

Foundation for providing financial support for this research.

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TABLE OF CONTENTS

INTRODUCTION
1.1 Background ................................
1.2 Previous Work ..............................
1.2.1 Spray Painting ..........................
1.2.2 Spray Forming ..........................
1.2.3 Rapid Tooling ...........................
1.2.4 Coverage ..............................
1.2.5 Optimal Trajectory Planning ..................
1.3 Motivations and Challenges .......................
1.4 Objectives .................................
1.5 Contributions of the Dissertation ....................
1.6 Organization of the Dissertation .....................

A GENERAL FRAMEWORK OF OPTIMAL TOOL PLANNING

2.1 A General Framework ..........................

2.2 Task Conditions and Requirements ...................
2.2.1 CAD Model ..... l .......................
2.2.2 Tool Model ............................
2.2.3 Task Constraints .........................
2.2.4 Optimization Criteria .......................

AUTOMATED TOOL PLANNING
3.1 A General Framework for Automated Tool Planning ..........
3.2 Determination of Tool Trajectory Parameters .............
3.3 Comparison of Material Deposition Patterns ..............
3.4 Patch Forming Algorithm ........................
3.4.1 Threshold Angle Determination .................
3.4.2 Patch Generation .........................
3.5 Trajectory Generation for 3 Patch ....................
3.5.1 Tool Path Generation .......................
3.5.2 Tool Orientation Generation ...................
3.5.3 Tool Trajectory Generation ...................
3.6 Trajectory Verification Model ......................
3.7 Suboptimal Tool Velocity .........................

TOOL TRAJECTORY INTEGRATION

4.1 Material Distribution in the Intersecting Area of Two Patches

4.2 Optimization Process for a Surface with Two Patches .........
4.2.1 Case 1: Parallel-parallel (PA-PA) Case .............
4.2.2 Case 2: Parallel-perpendicular (PA-PE) Case .........
4.2.3 Case 3: Perpendicular-perpendicular (PE-PE) Case ......

4.3 Optimization Process for a Surface with Multiple Patches .......
4.3.1 Point Case of a Surface with l\=Iultiple Patches .........

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12

14
14
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22
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4.3.2 Line Case of a Surface with Multiple Patches .......... 59

5 IMPLEMENTATION OF AUTOMATED TOOL PLANNING 64
5.1 Optimization Process ........................... 64
5.1.1 Determination of Tool Trajectory Parameters ......... 64
5.1.2 Paint Thickness Optimization for a Surface with Two Patches 65
5.2 Spray Painting .............................. 68
5.2.1 Trajectory Generation and Verification ............. 68
5.2.2 SubOptimal Velocity Verification ................. 74
5.2.3 Comparison with Other Methods ................ 74
5.3 Spray Forming .............................. 76
5.3.1 Trajectory Generation and Verification ............. 76
5.3.2 Suboptimal Velocity Verification ................. 78
5.4 Rapid Tooling ............................... 79
5.4.1 Trajectory Generation and Verification ............. 79
5.4.2 Suboptimal Velocity Verification ................. 81
5.5 Verification of Tool Trajectory Integration ............... 82
5.5.1 Spray Painting .......................... 82
5.5.2 Spray Forming .......................... 85
6 OPTIMAL TOOL PLANNING AND IMPLEMENTATION 88
6.1 Optimal Tool Planning .......................... 88
6.2 Preference Articulation .......................... 90
6.3 Implementation and Results ....................... 91
6.3.1 Optimal Tool Planning with Optimal Time .......... 92
6.3.2 Optimal Tool Planning with Optimal Material Distribution . . 95
6.3.3 Optimal Tool Planning with No Preference Articulation . . . . 98
6.3.4 Optimal Tool Planning with Preference Articulation ...... 101
6.3.5 Comparison among the Methods ................ 104

7 OPTIMAL TOOL PLANNING FOR NON-UNIFORM MATERIAL DISTRI-
BUTION 105
7.1 Optimal Tool Planning for Non-uniform Material Distribution . . . . 105
7.2 Implementation and Results ....................... 107
7.2.1 Optimal Tool Planning with Optimal Time .......... 109
7.2.2 Optimal Tool Planning with Optimal Material Distribution . . 112
7.2.3 Optimal Tool Planning with No Preference Articulation . . . . 115
7.2.4 Optimal Tool Planning with Preference Articulation ...... 118
7.2.5 Comparison among the Methods ................ 121
8 EXTENSIONS OF THE GENERAL FRAMEWORK 122
8.1 Extension to Dimensional Inspection in Manufacturing ........ 122
8.2 Extension to Nanomanufacturing .................... 123
8.2.1 Introduction ............................ 123
8.2.2 Automated Nanomanipulation System ............. 125

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8.2.3 A General Framework ...................... 126

8.2.4 Automated Tool Path Planning ................. 129

8.2.5 Implementation and Testing ................... 136
8.3 Conclusion ................................. 140
CONCLUSIONS 143
9.1 Conclusions ................................ 143
9.2 Extensions to Other Applications .................... 144
MULTI-OBJECTIVE CONSTRAINED OPTIMIZATION 146
A.1 A Multi-objective Constrained Optimization Problem ......... 146
A2 Optimization Method ........................... 146

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5.3
5.4
5.5
5.6
5.7

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6.2

6.3
6.4

7.1
7.2

7.3
7.4

LIST OF TABLES

The implementation results for the two material deposition patterns . 35

The relationship between the spray width and the maximum and the
minimum material thicknesses ...................... 61

The maximum and minimum thicknesses for the three cases when a = 30° 68

The calculated parameters ........................ 71
The simulation results .......................... 71
The simulation results using the suboptimal velocity method ..... 74
The simulation results for fixed gun directions ............. 76
The simulation results .......................... 86
The simulation results .......................... 86
The results for optimal tool planning with optimal time ........ 92
The results for the optimal tool planning with optimal material distri-

bution ................................... 95
The results for for Optimal tool planning with no preference articulation 98
The results for optimal tool planning with preference articulation . . 101
The results for optimal tool planning with optimal time ........ 109
The results for the optimal tool planning with optimal material distri-

bution ................................... 112

The results for the optimal tool planning with no preference articulation115
The results for the optimal tool planning with preference articulation 118

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1.2

1.3

1.4

2.1
2.2
2.3
2.4

2.5

2.6

3.1
3.2
3.3

3.4
3.5
3.6

3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14

3.15
3.16

LIST OF FIGURES

A typical production flow. ........................
The spray painting process using an industrial robot: (a) an ABB robot
and a part; (b) the painting process for a portion of a car hood.

The spray forming process using industrial robots: (a) ABB robots
and a part; (b) the forming process for a pickup truck box. ......
The indirect rapid tooling process using an industrial robot: (a) an
ABB robot and a part; (b) the indirect rapid tooling process ......

The automated CAD—guided optimal tool planning system .......
The optimal tool trajectory planner. ..................
The triangular approximation of part of a car hood ...........
The normals of triangles. v0, v1, v2 and ’03 are the vertices of triangles
A and B ...................................
A tool model. (1) is the fan angle; 8 the spray angle; h the tool standoff;
R the spray radius; r the actual spray distance. ............
A tool profile. ...............................

The automated tool planning system ...................
The automated tool trajectory planner ..................
Material deposition of a point 5 on a plane: (a) one path (b) two paths.
R is the spray radius; :1: the distance of the point 3 to the first path; '0
the tool velocity; and d the overlapping distance. ...........
The material deposition patterns: (a) raster; (b) spiral. ........
The triangular approximation of a plane .................
The generated paths for the two material deposition patterns: (a)
raster; (b) spiral. .............................
The material thicknesses for the two material deposition patterns with
constant velocity: (a) raster; (b) spiral. .................
The optimal material thicknesses for the two material deposition pat-
terns: (a) raster; (b) spiral .........................
Patch forming algorithm ..........................
The material on a plane is projected to a free—form surface. 6”, is the
maximum deviation angle of the free-form surface; 773., the normal of
the plane; and ii,- the normal of a point 3 on the free—form surface. . .
The patch forming process .........................
A patch and its bounding box: TOP, FRONT and RIGHT are the
directions of the bounding box. .....................
The improved bounding box method to generate a path for a patch. .
Part of a tool path and a series sample points ..............
Tool orientation generation. .......................
A tool trajectory on a free‘form surface is projected to form an offset
tool trajectory. ..............................

15
15
17

17

19
20

23
24

25
30
31

32
33
34
35
36
38
40
41
42
42

43

3.17

3.18
3.19

3.20

4.1
4.2

4.3
4.4
4.5
4.6
4.7

4.8

4.9

5.1
5.2
5.3
5.4
5.5
5.6
5.7

5.8
5.9
5.10
5.11

5.12
5.13

5.14
5.15
5.16

5.17
5.18

Material deposition on a free-form surface. 77,- is the normal of a trian-

gle; 7,- the deviation angle from the gun direction; It the desired tool

standoff; h,- the actual tool standoff .................... 44
The trajectory verification model: material projection. ........ 45
Material projection: (a) from 02 to C3; (b) from Cg to a small area on

a free-form surface. ............................ 45
The material thickness projected from a plane to a free-form surface. 48
The material distribution on the intersecting area of two patches. . . 50
(a) Case 1: parallel-parallel case; (b) Case 2: parallel-perpendicular

case; (c) Case 3: perpendicular-perpendicular case. .......... 52
Parallel-parallel (PA-PA) case ....................... 52
Parallel-perpendicular(PA-PE) case .................... 54
Perpendicular-perpendicular (PE-PE) case ................ 57
The Point case. .............................. 59
A surface with three patches: (a) perpendicular path for patch 2; (b)

parallel path for patch 2 .......................... 60
The relationship between the spray width and (a) velocity; (b) the

maximum and minimum material thicknesses. ............. 62
The tool height is increased from the desired tool standoff. ...... 63
The optimized paint thickness on a plane. ............... 65
The Optimized paint thickness for the PA-PA case when a = 30°. . . 66
The optimized paint thickness for the PA-PE case when or = 30°. . . 66
The optimized paint thickness for the PE—PE case when a = 30°. . . 67
The triangular approximation of (a) a car fender; (b) a car door. 69

The generated paths for (a) a car hood; (b) a car fender; (c) a car door. 70
The simulation result of paint thickness for (a) a car hood; (b) a car

fender; (c) a car door. .......................... 72
The ROBCAD simulation system ..................... 73
A part of a gun path ............................ 73
A painted part (part of a car hood) .................... 73
The simulation results of paint thickness using the suboptimal velocity

method for (a) a car fender; (b) a car door ................ 75
A car frame (a) CAD model; (b) The generated path .......... 77
The calculated thickness of a car frame (a) without velocity optimiza-

tion; (b) with subOptimal velocity ..................... 78
The mold for indirect rapid tooling .................... 79
The two perpendicular paths of a mold for indirect rapid tooling. . . 80
The calculated thickness for indirect rapid tooling (a) without velocity

optimization; (b) with velocity optimization. .............. 81
The part with two flat patches when a = 30°. ............. 82
Verification results for the PA—PA case: (a) the path; (b) the paint

thickness. ................................. 83

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6.5

6.6

6.7

6.8

6.9

7.1

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

8.1

Verification results for the PA-PE case: (a) the path; (1)) the paint
thickness. .................................
Verification results for the PE—PE case: (a) the path; (1)) the paint
thickness. .................................
The computed area densities for (a) the PA-PA case; (b) the PA-PE
case; (c) the PE-PE case ..........................

A path is divided into segments ......................
The optimized material thicknesses for the optimal tool planning with
optimal time: (a) the car hood; (b) the car door .............
The optimized velocities for the optimal tool planning with optimal
time: (a) the car hood; (b) the car door. ................
The optimized material thicknesses for the optimal tool planning with
optimal material distribution: (a) the car hood; (b) the car door.

The optimized velocities for the optimal tool planning with optimal
material distribution: (a) the car hood; (b) the car door. .......
The Optimized material thicknesses for the optimal tool planning with
no preference articulation: (a) the car hood; (b) the car door.

The optimized velocities for the optimal tool planning with no prefer-
ence articulation: (a) the car hood; (b) the car door. .........
The optimized material thicknesses for the optimal tool planning with
preference articulation: (a) the car hood; (b) the car door. ......
The optimized velocities for the Optimal tool planning with preference
articulation: (a) the car hood; (b) the car door. ............

Desired non-uniform material thicknesses for: (a) a car hood; (b) a car
door .....................................
The optimized material thicknesses for the optimal tool planning with
optimal time: (a) the car hood; (b) the car door .............
The optimized velocities for the Optimal tool planning with Optimal
time: (a) the car hood; (b) the car door. ................
The optimized material thicknesses for the optimal tool planning with
optimal material distribution: (a) the car hood; (b) the car door.

The Optimized velocities for the optimal tool planning with optimal
material distribution: (a) the car hood; (b) the car door. .......
The optimized material thicknesses for the optimal tool planning with
no preference articulation: (a) the car hood; (b) the car door.

The optimized velocities for the optimal tool planning with no prefer-
ence articulation: (a) the car hood; (b) the car door. .........
The optimized material thicknesses for the Optimal tool planning with
preference articulation: (a) the car hood; (b) the car door. ......
The optimized velocities for the optimal tool planning with preference
articulation: (a) the car hood; (1)) the car door. ............

A general framework for nanomanufacturing ...............

xii

87
88

93

94

96

97

99

102

103

108

110

111

113

114

116

119

120

125

8.2
8.3
8.4
8.5
8.6

8.7

8.8

8.9

8.10

8.11
8.12
8.13
8.14
8.15

8.16

8.17

A general framework for the automated CAD—guided path planning
system ....................................
Tip path planner ..............................
A designed nanopart ............................
The raw data from an AFM ........................
The straight line connection between an object and an destination. 01
and O2 are objects; D1 and D2 destinations; 81 is an obstacle .....
The van der Waals force between an object and an obstacle. R1 and
R2 are the radius of the two spheres, respectively; D is the distance

between the two spheres; Fw van der Waals force; Fc the friction force.

An object may be lost during turns. 01 is an object; D1 a destination
and 81 an obstacle ............................
A virtual object and destination (VOD) connects an object and a des-
tination. 01 is an object; D1 a destination; 81 an obstacle and V1 a
VOD. ...................................
Two VODs connect an object with a destination. 01 is an object; DI
the destination; 31 and S2 are obstacles. ................
(a) Object obstacle; (b) Destination obstacle. .............
The assignment of an object to a destination. .............
Path generation algorithm .........................
The CAD models of two nanostructures: (a) a line; (b) a rectangular.
The AFM images with nanoparticles to manufacture: (a) a line; (b) a
rectangular. ................................
The real-time AFM images in the augmented reality system with man-
ufactured nanostructures: (a) a line; (b) a rectangular. ........
The manufactured nanostructures: (a) a line; (b) a rectangular.

xiii

126
127
128
128

129

130

132

132

134
135
136
137
138

139

 

CHAPTER 1
INTRODUCTION

Surface manufacturing is a process which adds material to or removes material from
the surface of parts. Spray painting, spray forming, indirect rapid tooling, spray
cleaning and polishing are typical examples of surface manufacturing. Industrial
robots are used to implement these processes. The tool planning of these processes
is crucial to satisfy some given constraints. Typical teaching methods are complex,
time-consuming and the material distribution is dependent on the Operator’s skill.
Automated optimal tool planning process (AOTPP) is desirable for planning tra-
jectories for industrial robots. However, AOTPP for industrial robots in surface
manufacturing is a challenging research topic.

This dissertation develops a general framework for automated optimal tool plan-
ning based on the CAD model of a free-form surface, a tool model, given constraints
and optimization criteria in surface manufacturing. The following section gives the
background that related to the research. The remaining sections of this chapter de-
scribe the previous work, motivation, objectives, contributions and organization of

this dissertation.

1. 1 Background

Recent trends have seen new constraints in product manufacturing. Examples of
these constrains are a shorter product life, frequent design changes, small lot sizes,
and reduced in-process inventory. Automation in manufacturing can satisfy these
requirements, while providing flexibility and good quality products at a low cost.
Automation has been studied and implemented successfully in many areas. Some
examples are machining processes, material handling. inspection, welding, packaging,

and surface manufacturing. With a pressing need to upgrade productivity, manufac-

 

turing indu:
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turing industries are turning more and more toward robots. Compared to humans,
robots yield more consistent quality, more predictable output and are more reliable.
Industrial robots are one of the examples of automation equipment. Recent years
have seen rapid deveIOpments in the areas of surface manufacturing using industrial

robots. A typical production flow [1] is shown in Figure 1.1.

 

Product design and manufacturing tools

—M

1

Process planning

1

Manufacturing Processes

1

Products

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.1: A typical production flow.

Product design provides a description of the product in low level simple geometric
entities (faces, edges and vertices), while high level description of entities are de-
sired to plan manufacturing processes in the manufacturing environments. Process
planning builds a bridge between product design and manufacturing and translates
design information into the process instructions to efficiently and effectively manu-
facture products. Tool planning for industrial robots for surface manufacturing, an
example of a process planning, remains a challenging research topic [2, 3]. Since tool
planning translates design information into the tool instructions to manufacture parts,
it greatly affects the quality of the products and the efficiency of the surface manu-
facturing processes [4, 5]. Currently, there are two tool planning methods: manual
and automated.

Manual tool planning (typical teaching methods) is based on manufacturing engi-
neers’ experience and knowledge of production facilities, equipment, their capabilities,
processes, and tools. A manufacturing engineer has to carry out extensive tests on

a work cell to improve a. tool trajectory. This process is complex and very time-

 

 

 

 

consuming. The results vary based on the manufacturing engineers’ skill. It usually
requires the engineers to use a trial-and-error approach to find a good path or tra—
jectory for a surface manufacturing tool. The generated path or trajectory is usually
operator-dependent and error-prone. It is even harder for engineers to figure out a
better path or trajectory when some performance criteria have to be considered. For
example, in the Ford Motor Company’s Aston Martin plant, it takes an experienced
engineer a few weeks to design a trajectory for a car door panel.

Computer aided tool planning (CATP), an automated tool planning process (ATPP),
is desirable for surface manufacturing. CATP, which automatically establishes com-
munications between the CAD model of a part and the product manufacturing pro—
cesses, reduces human labor dramatically and keeps human operators from being
exposed to harmful working environments. Currently automated tool planning re-
ceives little attention and has always caused a bottleneck for surface manufacturing.
Therefore it is essential to develop automated tool planning to replace manual tool
planning. This challenging research topic has been receiving more and more attention

from academia and industry.

1.2 Previous Work

According to the material distribution constraints, the processes in surface manufac-
turing can be categorized into two groups: material uniformity and coverage. Material
uniformity requires that a surface be covered with material to achieve certain amount
of material deposition. Examples are spray painting, spray forming and rapid tooling.
Spray forming and rapid tooling can also be categorized as net shape manufacturing
processes since no machining process is needed for the manufactured parts. Coverage
requires that a surface be covered by material or touched by a tool, such as spray
coating, spray cleaning [6] and polishing. There are only a few reports on automated

tool planning for surface manufacturing.

 

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1.2.1 Spray Painting

Spray painting is an important process in the manufacturing of many products, such
as automobiles, furniture and appliances. Figure 1.2 shows an industrial robot (ABB

robot) used for spray painting.

   

Figure 1.2: The spray painting process using an industrial robot: (a) an ABB robot
and a part; (b) the painting process for a portion of a car hood.

The uniformity of paint thickness on a. product can strongly influence its quality.
Tool planning for spray painting is critical to achieve uniformity of paint thickness
and has been widely studied [7, 8, 9]. Suk et a1. [9] developed an Automatic Trajec-
tory Planning System(ATPS) for spray painting robots. Their method is based on
approximating a free-form surface using a number of individual small planes. Their
simulations showed over and under-painted areas on a painted surface. Asakawa et
al. [7] developed a teachingless path generation method based on the parametric sur-
face to paint a car bumper. The paint thickness was 13 to 28 um while the average
thickness was 17.7 pm. The method to find the spray width and gun velocity was not
reported. Antonio (:1! a1. [10] developed a framework for optimal trajectory planning
to deal with the paint thickness problem. However. the paint gun path and paint

deposition rate must be specified. In practice, it is very difficult to obtain the paint.

 

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deposition rate for a free-form surface. Alternatively, some commercial software, such
as CirnStation [11], IGRIP [12] and ROBCADT‘” / Paint [13]. can generate paint gun
trajectories and simulate the painting processes. However, the gun paths are Obtained
in an interactive way between the users and the software. This tool planning process

is inefficient and error—prone.

1. 2. 2 Spray F arming

Spray forming is used for the glass fiber preforming processes [14]. Figure 1.3 shows

an industrial robot (ABB robot) used for spray forming.

 

(a) (b)

Figure 1.3: The spray forming process using industrial robots: (a) ABB robots and
a part; (b) the forming process for a pickup truck box.

Glass fiber is chopped and applied along with thermoplastic powdered binder to
the preform screen using industrial robots. Positive airflow through the screen holds
the chopped fiber on the screen surface during the entire spray~up routine. When
spray-up is complete, the tool is closed and the preform is compressed to the desired
thickness. Ambient temperature airflow through the screen is then stopped, and hot
air is drawn through the screen in order to melt the binder. After the binder has been

melted, hot airflow is stopped and ambient air is again drawn through the preform,

freezing the binder and setting the preform. The tool is opened and the finished

preform de—molded. The advantages of the technology are:

0 light weight of parts because glass fiber is lighter compared to other materials,

such as steel and cement;
0 low cost because there are no dies as contrasted to the stamping methods;

0 flexibility because robots can be re-programmed to manufacture other parts.

Chavka [14] developed a spray forming system. However, no path planning method
was presented. Based on the CAD model of a building facade, Penin et al. [15]
developed an automatic path planning method to spray glass fiber on a panel with
cement. The fabricated panels can achieve better flex-traction strength and are lighter
weight than conventional concrete panels. The spray width and tool velocity are
determined using some spray rules. The paths are generated by approximating a
curved surface with several planes. No material constraints are specified. The tool
planning for spray forming must satisfy area density (material weight in a unit area)

constraints [14].

1.2. 3 Rapid Tooling

Rapid tooling is a type of rapid prototyping, which is a technology to quickly deliver
a part by an additive, layer-by-layer process based on the CAD model of a mold.
This is a new technology developed to reduce both time and cost. There are different
technologies used for rapid prototyping [16], such as stereolithography (SLA), selec-
tive laser sintering (SLS), room temperature vulcanized (RTV) molding , and rapid
toohng.

Rapid tooling is a process to produce components in a layer-by-h yer (additive)
process in end-use materials. The rapid tooling process has been attracting more

attention lately because it can manufacture tools rapidly at low cost. There are

two technologies for rapid tooling: direct and indirect. Direct rapid tooling directly
makes hard tooling or metallic molds by depositing material on a surface layer-by-
layer (also called layered manufacturing). Indirect rapid tooling makes hard tools or
metallic molds using rapid prototyping parts as patterns. In indirect rapid tooling
[17], molten metal is sprayed on a ceramic mold layer—by—layer until the desired metal
thickness is achieved. Typically indirect rapid tooling is used to make dies or punches
to produce parts. Since there is no machining process needed for the manufactured
parts using the indirect rapid tooling process, it is a net shape manufacturing process.
Figure 1.4 shows an industrial robot (ABB Robot) used for indirect rapid tooling

process.

 

(a) (b)

Figure 1.4: The indirect rapid tooling process using an industrial robot: (a) an ABB
robot and a part; (b) the indirect rapid tooling process.

Some work has been done on path planning for the direct rapid tooling process
[4, 18, 19]. Luo et al. developed software and hardware for a rapid tooling system
[18]. The software includes a slicing algorithm which generates 2D flat contours from
a faceted 3D model and a tool path generation algorithm. Yang et al. [4] studied dif-
ferent scanning strategies for the tool path planning in rapid tooling. An equidistant

scanning algorithm was proposed and implemented. Their methods improved manu-

facturing efficiency and product quality. However, both Luo and Yang’s approaches
only deal with 2D flat contours and are not sufficient to handle free—form surfaces.
There is little research work in the indirect rapid tooling process. Chalmers [17]
demonstrated an indirect rapid tooling process used by the Ford Motor Company. No
tool planning algorithm is reported. For indirect rapid tooling, the material sprayed
on a mold must satisfy material thickness and temperature constraints. Because
the path planning for direct rapid tooling can only deal with 2D contours, it is not
suitable for the tool path planning of indirect rapid tooling since most parts are

free-form surfaces.

1. 2.4 Coverage

Coverage is to cover every point on a surface using a specific tool. Spray coating, spray
cleaning, polishing are typical applications for coverage. There are different methods
to generate paths for coverage. Sheng et al. [20] developed a method to automatically
generate a path such that every point on a surface can be covered. Huang [21]
presented an optimal path planning method to cover a surface by minimizing the
turns. Polishing is necessary to obtain a good surface smoothness as well as to meet
the required dimensional tolerances. Mizugaki [22] developed a path planning method
for a polish robot. Takeuchi et al. [23] discussed polishing path generation using the
CAD model of a surface. Even though these path planning methods can guarantee

the coverage of a surface, the material distribution constraints are not considered.

1.2.5 Optimal Trajectory Planning

To increase productivity and the quality of manufactured products, it is desirable
for industrial robots to run in their optimal conditions subject to given Optimization
criteria. In industry, minimal time of a manufacturing process means high produc-

tivity and low cost. To improve the product quality, the material distribution on a

free-form surface has to be optimized. Hyotyniemi [24, 25] developed a locally con-
trolled optimal trajectory planning system for spray painting robots. Paint thickness,
surface quality and trajectory smoothness are considered to form a multi-objective
optimization problem. However, the method is time-consuming and needs extremely
high computing capacity even for simple surfaces. This makes the method infeasi-
ble. Moreover, the paint gun velocity is not considered as an optimization parameter.
Antonio et al. [8, 10] presented an optimal trajectory planning method for spray coat-
ing. The variation of paint thickness is minimized. Because the optimization process
needs high computing capacity, they developed fast solution techniques [26] to solve
the problem. However, the spray gun path has to be given using teaching methods
by experienced operators. The parametric representation of a surface and a path
is needed for optimization. Although parametric representation is mathematically
accurate, its local nature causes difficulties for path planning [20, 27]. Furthermore,

these optimal tool planning methods are developed for individual process.

1.3 Motivations and Challenges

In manufacturing, computer aided tool planning (CATP) builds a communication
between CAD and CAM [2]. Surface manufacturing, such as spray painting, spray
forming, indirect rapid tooling, spray coating and polishing, need to generate trajec-
tories based on the CAD model of a free-form surface such that the task constraints
can be satisfied. Although some scattered and problem—specific planning algorithms
have been developed, there is no general tool planning method for surface manu-
facturing. Optimal tool planning is hardly addressed. Also the verification of the
generated trajectories is not discussed. Therefore, from a practical point of view, it
is desirable to develop a general framework for automated optimal tool planning in
surface manufacturing.

Due to different tool models and constraints in different processes, it is challenging

to deveIOp a general framework of tool planning for these processes. Since there is no
feedback information available to control industrial robots in surface manufacturing,
tool planning is crucial to the manufacture of high quality products. For material
uniformity, material thickness must satisfy given constraints, but coverage does not
have such a requirement. Some processes, such as indirect rapid tooling, need to
spray a surface many times. These make the development of a general framework for
automated tool planning in surface manufacturing difficult.

Optimal tool planning is even more challenging because:

0 There are many optimization criteria: robot motion, optimal time, material

distribution deviation and material waste.

c There are many adjustable parameters: the tool velocity, tool standoff, tool

orientation and flow rate of material.

1.4 Objectives

Although the processes in surface manufacturing are different, they can be catego-
rized into two groups: material uniformity and coverage. Material uniformity, such
as spray painting, spray forming and indirect rapid tooling, requires the material
distribution on a surface to satisfy given constraints. Coverage, such as spray coat-
ing, spray cleaning and polishing, requires that every point on a surface be covered.
However, both material uniformity and coverage have some commonalities: (a) the
trajectories are generated based on the CAD models, tool models, constraints and
optimization criteria, and (b) the tool trajectory is defined by a six dimensional vector
which specifies the position and orientation of a tool. Therefore, the objective of this
dissertation is to develop a general framework for automated CAD-guided Optimal

tool planning in surface manufacturing.

10

1.5 Contributions of the Dissertation

In this dissertation, a general framework for automated CAD-guided Optimal tool
planning in surface manufacturing has been developed and implemented successfully.

The main contributions of the dissertation are:

0 A general framework for automated CAD-guided optimal tool planning in sur-
face manufacturing has been developed based on the CAD-model of a free-form

surface, a tool model, constraints and optimization criteria.
0 A patch forming algorithm has been developed to satisfy the given constraints.

0 Comparison of different material deposition patterns has been performed. The
performance of the raster material deposition pattern is better than that of the

spiral material deposition pattern for continuous material deposition processes.

0 A theorem has been proven about the relationship between the material distri-

bution and tool velocity.

0 A tool trajectory generation algorithm has been developed such that the given
material thickness constraints can be satisfied. The tool path of a free-form sur-
face is generated using an improved bounding box method. The tool orientation

is determined based on the local geometry of a free-form surface.

0 A tool trajectory integration algorithm has been developed to integrate the tool

trajectories for a surface with multiple patches.

0 A tool trajectory verification model has been formulated to verify the generated

trajectories.

0 An optimal tool planning algorithm has been developed to generate tool trajec-

tories based on the given Optimization criteria.

11

a An optimal tool planning algorithm for non-uniform material distribution on a

free—form surface has been developed and implemented.

0 The general framework has been extended to other applications, such as the
dimensional inspection in manufacturing and nanoassembly in nanomanufac-

turing.

1.6 Organization of the Dissertation

This dissertation describes a general framework for automated CAD-guided optimal
tool planning in surface manufacturing. The tool planning algorithm is developed
for various applications. Implementations and simulations are presented to test the
general framework and verify the generated trajectories. The dissertation includes

the following chapters:

0 Chapter 2 describes a general framework for automated CAD-guided optimal
tool planning of free-form surfaces in surface manufacturing. The CAD model
of a free—form surface, a tool model, task constraints, and optimization criteria

are presented.

0 Chapter 3 introduces a general framework for an automated CAD-guided tool
planning algorithm. The determination of tool trajectory parameters is dis-
cussed. The comparison of different material deposition patterns is reported.
The patch forming algorithm is presented. The trajectory generation algorithm
is developed for a patch. The tool trajectory verification model is presented to
compute the material distribution on a free-form surface. A suboptimal velocity

algorithm is developed.

0 Chapter 4 reports a tool trajectory integration algorithm for a free-form sur-

face with multiple patches. Three cases: parallel-parallel (PA-PA), parallel—

12

perpendicular (PA-PE) and perpendicular-perpendicular (PE—PE), are discussed
for a surface with two patches. A trajectory integration algorithm for a surface

with multiple patches is also presented.

Chapter 5 presents the implementation and testing of the automated tool plan-
ning algorithm. Tool trajectories for different parts in different processes are
generated and verified. The verification of the trajectory integration algorithm

is also performed.

Chapter 6 discusses the general framework for automated CAD-guided optimal
tool planning. An optimal tool planning algorithm for constant material dis-
tribution is developed and implemented. A preference articulation method is
discussed. Implementation of four cases, optimal time, optimal material distri-

bution, no preference articulation and preference articulation, are presented.

Chapter 7 presents the general framework for automated CAD-guided optimal
tool planning with non-uniform material distribution. The developed algorithm
is implemented. Implementation of four cases, optimal time, optimal material
distribution, no preference articulation and preference articulation, are pre-

sented.

Chapter 8 discusses the extensions of the general framework to other processes,
such as dimensional inspection in manufacturing and nanoassembly in nanoman-

ufacturing.

Chapter 9 summarizes the dissertation by giving conclusions and presenting the

extensions of the developed general framework.

13

CHAPTER 2
A GENERAL FRAMEWORK OF OPTIMAL TOOL
PLANNING

In this chapter, a general framework for automated CAD-guided Optimal tool planning
in surface manufacturing is presented. The CAD model of a free—form surface, a tool

model, task constraints and optimization criteria are discussed.

2.1 A General Framework

A general framework for automated CAD-guided optimal tool planning is to generate
an optimal tool trajectory based on the CAD model of a free-form surface, a tool
model, constraints and optimization criteria. Tool planning, also called trajectory
generation, is to plan the tool position, orientation, and velocity for a given process
in surface manufacturing. A general framework for automated CAD-guided optimal
tool planning in surface manufacturing can be formulated as:

Given the CAD model of a free-form surface M, a tool model C, constraints (2 and
optimization criteria \II, find a tool trajectory P such that the constraints are satisfied,
i.e.,

F(M, n, G, o) = r. (2.1)

Figure 2.1 illustrates the automated CAD-guided Optimal tool planning system.
Based on the CAD model of a free-form surface, a tool model, constraints and op-
timization criteria, the optimal tool trajectory planner generates an optimal tool
trajectory automatically for a free—form surface. The optimal tool trajectory is input
to a tool trajectory verification model to verify if it satisfies the given constraints.
The trajectory is also input to ROBCADTM / Paint [13] to simulate the kinematics

constraints and collisions.

14

 

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CAD Model ROBCAD ’"
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Tool Model
a» O
Trajectory
I Constraints "in “ \ \
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Figure 2.1: The automated CAD-guided optimal tool planning system.

The optimal tool trajectory planner is the core of the general framework. Figure

2.2 shows how the planner works.

 

CAD model, tool model, constraints and
optimization criteria

 

 

 

I Automated tool planning

1

I Tool trajectory I

I

I Optimal tool planning I

 

 

 

LOptimal tool trajectory I

 

Figure 2.2: The optimal tool trajectory planner.

Based on the given conditions, such as the CAD model of a free-form surface,
tool model and constraints, a tool trajectory is generated using the automated tool

planning algorithm. Then the optimal tool planning algorithm is applied to generate

15

an Optimal tool trajectory for the free-form surface based on the optimization criteria.

2.2 Task Conditions and Requirements

This section describes the CAD model of a free-form surface, a tool model, task

constraints and optimization criteria.

2.2.1 CAD Model

The CAD model of a free-form surface contains geometric information of the surface.
According to Sheng [28], the representation scheme in 3D modeling can be catego-
rized into parametric and tessellation representations. The parametric representation
is pOpular in CAD modeling. B-Spline, Bezier and NURBS surfaces are some of the
common parametric surfaces used in CAD modeling [29, 30]. The parametric repre-
sentation is mathematically accurate, however, its local nature brings difficulties for
tool planning [27]. The global knowledge of a free-form surface, instead of the local
knowledge, is important for tool planning [28]. Tessellation representation, which is
much simpler, is frequently used to approximate free-form surfaces. With increased
computer processing power, tessellation representation can be very refined and accu-
rate. A triangular approximation of a free-form surface, which has global information
about a free-form surface, is desirable for tool trajectory planning. The error intro-
duced in rendering a free-form surface into triangles can be decreased by reducing the
size of triangles. Therefore, after tessellation, the CAD model of a free-form surface

M can be formulated as:

M-——{T,:i:1,---,N} (2.2)

where T,- is the ith triangle on the free-form surface; N the number of triangles.
Figure 2.3 shows the triangular approximation of a free-form surface.

In CAD design, a free-form surface consists of many low curvature parametric

16

 

1.2.

1.1-

 

 

 

eight (m)

 

   

 
 

1.4

 

; , ‘ 1.2
‘ Y/A 1
Width (m) 0 0.6 0'8 Length 011)

Figure 2.3: The triangular approximation of part of a car hood.

surfaces. The normals of these parametric surfaces may not point to one side of the
free-form surface. Therefore, after a free—form surface is rendered into triangles, the
normals of the triangles have to be adjusted. Here a method is deveIOped to adjust

normals of the triangles.

 

Reference

Figure 2.4: The normals of triangles. v0, v1, v2 and 213 are the vertices of triangles A
and B.

Figure 2.4 shows two neighbor triangles A and B. 7?; and H; are normals of triangles
A and B. In the data structure, a triangle is represented by its three vertices. Each
vertex contains the XYZ coordinates. The normal of the triangle is determined by

the sequence of its three vertices. If the sequence of any two vertices in a triangle

17

is reversed, the normal of the triangle is reversed. Suppose triangle A points to the
same side as a reference direction, which can be determined by the angle between the
normal of triangle A and the normal of the reference. Then triangle A is chosen as
the seed triangle. The normal of triangle A is generated using its three vertices v0,
v1 and v2. The sequence is:

U0—*U1—*’U2—>’U0.

Triangle B, which has a common edge with triangle A (two common vertices), is
found. If the normals of triangles A and B point to one side, the sequences of the
two common vertices in the two triangles must be reversed. For example, if the the

sequence of 110 and v1 in triangle B is

’01 —’Uo—*’U3—’Ui,

the normals of triangles A and B point to the same side since the sequences of v0 and
121 are reversed in the two triangles. There is no need to reverse the sequence of the

two vertices. If the sequence of triangle B is:

U1 —*U3-—*’U0—”U1,

This sequence of 220 and 221 in triangle B is the same as that in triangle A. The
sequence of 210 and 211 has to be changed to reverse the normal of triangle B. This
process continues until all of the triangles with common edges are processed. Then
the newly added triangles are used as seed triangles and the process continues until

there is no triangle left. Then the normals of the triangles are adjusted.

2.2.2 Tool Model

A tool model can be modeled as a spray cone [8, 9, 31, 32, 33] as shown in Figure 2.5.

18

Tool

R Spray cone

 

 

Figure 2.5: A tool model. d) is the fan angle; 0 the spray angle; h the tool standoff;
R the spray radius; r the actual spray distance.

Material particles are emitted from the tool radially within the spray cone with a
fan angle (15. A spray pattern is formed when the spray cone intersects a plane. The
distance from the tool center to the plane is the tool standoff h. The normal of the
plane is parallel to the tool spray direction. The radius of the spray pattern is R,
which is defined as spray radius. 6 is the spray angle and r the actual spray distance.

For material uniformity, the knowledge of the material deposition rate on a spray
pattern is needed. The material deposition rate depends on many parameters, such
as the tool standoff and the flow rate of material. Here these parameters are assumed
to be fixed [9, 10, 31, 32]. There are different profiles of the material deposition rate
[8, 9, 31, 32, 33] used in different processes. Some profiles are quite simple [9] and
others are quite complex [33]. A typical profile of the material deposition rate can be
roughly approximated by parabolic curves [8, 32] as shown in Figure 2.6.

The material deposition rate on a plane can be modeled as:

G = f(r, h). (2.3)

Goodman it et al. [34] presented a method to measure the material deposition rate

19

 

LII- V
.L\. r
IML ...

 

-R ‘0 R >r

 

Figure 2.6: A tool profile.

by spraying a plane. The tool model is valid for coverage if the material deposition
rate is considered to be a constant. For some processes, such as polishing, the tool

model is still valid even though the tool standoff is 0.

2. 2. 3 Task Constraints

A general constraint 9 can be expressed as follows:

9 = {Ma y, Z($,y)),Aqd(:v,y, Z($,y)),w} (24)

where x, y, 2(15, y) are the coordinates of a point on a free—form surface; qd(:r, y, z(:c, y))
is the desired material thickness constraint on the point ; Aqd(:z:, y, z(:r, y)) the ma-
terial thickness deviation from the desired material thickness on the point; to other
constraints, such as material waste, cycle time, reachability, temperature and tool ori-
entation. For example, the temperature on a surface must be kept in a certain range
during a rapid tooling process. For some applications, the tool orientation cannot
change rapidly.

Spray painting, spray forming and indirect rapid tooling require that the tool tra-

jectory planning satisfy material uniforn'iity constraints, i.e., the material sprayed on

20

a free—form surface must satisfy the desired material thickness and material thickness
deviation constraints. Spray cleaning and polishing are examples of coverage. Each
point on a free-form surface must be covered by a spray pattern. Coverage is a spe-
cial case of material uniformity. Therefore the constraints can be expressed using a

general formula, i.e.,

Aqd(:r, y, z(:c, y)) 7é 0 Material uniformity

(May, 2(r,y)) = 1,Aqd($,y, Z($,y)) = 0 Coverage (2-5)

2.2.4 Optimization Criteria

Optimal tool planning is based on the optimization criteria. A general optimization
criterion ‘11 is expressed as:

\p = (x111,\r2,...,\rK) (2.6)

where €11,912, ..., \IIK are K optimization criteria, such as minimum time and optimal

material distribution etc..

21

CHAPTER 3
AUTOMATED TOOL PLANNING

This chapter discusses an automated tool planning system. Based on the CAD model
of a free-form surface and a tool model, an automated tool planning system is de-
veloped such that the given constraints are satisfied. A patch forming algorithm is
presented to generate patches. After patches are formed, a trajectory is generated
for each patch. A trajectory verification model is developed to verify the generated
trajectory. A suboptimal tool velocity algorithm is discussed to minimize the material

thickness deviation.

3.1 A General Framework for Automated Tool Planning

An automated tool planning system is to generate a tool trajectory automatically
based on the CAD model of a free-form surface, a tool model and constraints in
surface manufacturing. The automated CAD-guided tool planning system can be
formulated as follows:

Given the CAD model of a free-form surface 1%, a tool model C and constraints

Q, find a tool trajectory P such that the constraints are satisfied, i.e.,

F(M,Q,G) = r. (3.1)

Figure 3.1 illustrates the automated tool planning system. Based on the CAD model
of a free-form surface, a tool model and constraints, the automated tool trajectory
planner generates a tool trajectory automatically. Here the desired material thickness
is considered to be a constant. The generated trajectory is input to a trajectory
verification model to verify if it satisfies the given constraints. The trajectory is
also input to ROBCADTM / Paint [13] to simulate the kinematics constraints and

collisions.

22

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

CAD Model ROBCAD TM
Tool
I
, Tool Trajectory
Tool Model Trajectory
E? /
[ii/U
Planner
1
_, .__.._.. I I

 

 

Figure 3.1: The automated tool planning system.

The tool trajectory planner is the core of the automated tool planning system.
Figure 3.2 shows how the tool trajectory planner works.

From the given conditions, such as the CAD model of a free—form surface, a
tool model and constraints, patches are formed for the free-form surface using the
patch forming algorithm. Then, a trajectory is generated for each patch using the
tool trajectory planning algorithm. The generated trajectories of the patches are
integrated to form a trajectory for the free-form surface. The suboptimal tool velocity
algorithm is developed to optimize the material distribution deviation. Finally, the
generated trajectory is verified to check if the given constraints are satisfied. This
chapter focuses on the tool trajectory generation for one patch. The tool trajectory

integration is discussed in the next chapter.

23

 

 

 

Given conditions

1

Patch forming algorithm

1

Patches

1

Tool planning algorithm for one patch

1

Tool trajectory for each patch

1

Tool trajectory integration algorithm

1

Tool trajectory for a free-form surface

I
Suboptimal velocity algorithm

1

Suboptimal tool trajectory

1

Tool trajectory verification

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.2: The automated tool trajectory planner.

3.2 Determination of Tool Trajectory Parameters

To generate a tool trajectory for a free-form surface, the spray width and the tool
velocity have to be determined. The spray width and the tool velocity are computed
by optimizing the spraying process on a plane. Figure 3.3 shows material deposition

on a plane.

24

 

 

 

 

 

8 Path
R W
May cone

>
a;
[e

l:
E

——-————d

A/ Path
I

l

|

I

Plane

 

Figure 3.3: Material deposition of a point 3 on a plane: (a) one path (b) two paths. R
is the spray radius; a: the distance of the point 3 to the first path; 12 the tool velocity;
and d the overlapping distance.

The spray width w can be expressed as:

w=2R—d (an

25

where d is the overlapping distance.

Theorem 3.2.1 Given a tool model, the material thickness on a plane is related to
the tool velocity and the overlapping distance. Moreover, the material thickness is

inversely proportional to the tool velocity.

Proof. The material thickness of a point 3 on a plane can be calculated using

the following equation,

T
q. = jg f(r(t))dt (3.3)

where q(s) is the material thickness of point 3; T the total spray time for point 3;
and r(t) the distance from point 3 to the center of the spray cone.

For each point on the plane, there are at most two neighboring paths which
contribute to the material thickness of the point. The material thickness (7(23, d, v) of

the point due to the two paths can be expressed as:

aim) ogng—d
(MW) = chew) + (22(x,d,v) R — d < a: s B (3-4)
92($,d,t’) R<xS2R—d

where a: is the distance of the point to the first path; v the tool velocity; (11(13, v) and
(12(33, d, v) are the material thickness due to the first and second paths respectively.

They can be calculated using equation (3.3),

t1
("11(:r,v)=2/ f(r1)dt OSISR
0

t2
(i2(:1:,d, v) = 2/ f(r2)dt R — d S 1: _<_ 2R — d (3.5)
0

where t1 and t2 are the parameters related to the spray time on point 5 for the first

and second paths respectively; r1 and r2 the distances of the point to the tool centers

26

respectively. t1, t2, r1 and r2 are:

 

_ RZ—zL‘2 _\/R2—(2R—d—;r)2
v v

n = W r2 = x/("vtl'z + (2R — d - an)? (3.6)

 

 

In equation (3.5), let

t = a, (3.7)
v
then it can be written as:
2 ‘3
mm) = ;/ f(ri)dy o s a: g R
o
2 “2
q_2(:1:,d,v) = fi/ f(Té)dy R — d S :1: 3 2R — d (3.8)
0

where

 

t'1= \/RQ—.’L‘2, t’2 = \/R2—(2R—d—a:)2
r] = x/y2+3:2, r; = \/y2+(2R—d—a:)2. (3.9)

 

Therefore, q1(:c, v) and qg(.r,d, v) are inversely proportional to the tool velocity.
From equations (3.4) and (3.8), we obtain that the material thickness on a plane is
inversely proportional to the tool velocity and also related to the overlapping distance.
<1

To find an Optimal velocity v and an overlapping distance d, the mean square
error of the material thickness deviation from the required material thickness qd must
be minimized, i.e.,

min {E1(d,v) = [am—«(M — (i(;1t,d.v))2d.r}. (3.10)

(16 [0.3] ,v

27

The maximum and minimal material thickness deviations from the average mate-
rial thickness have to be minimized because they determine the material thickness
deviation from the average material thickness.

e — 2 - 2
E. .1 , _ mar- + _ m," , .11
del[101,llr?l],v{ 2( ,t) ((1 qd) ((Id (1 l } (3 )

From equations (3.10) and (3.11), a multi-Objective error function is formulated:
E(dw) = (E1(d,v),E2(d,v))T- (3-12)

The no preference articulation method in Appendix A is adopted to solve the
multi-objective optimization problem. From equation (A.4), equation (3.12) can be

transferred to,

min {E(d, v) = /\1E1(d,v) + /\2E2(d,v)}. (3.13)
dE[0,R],v

Lemma 3.2.1 E(d,v) can be minimized by properly choosing the overlapping dis-

tance (1.

Proof. From Theorem (3.2.1), (f(r, d, v) is inversely prOportional to the tool velocity
v. Let:

1
(i(.'1:,d,v) = —p(1:,d). (3.14)
v
Then the maximum and the minimum material thicknesses can be expressed as:

_ 1 _ 1
qmar = _pma.:r(d)a qmin : —pmin(d)- (3'15)
U U

To find minimal E (d, v), first compute

(9E(d. v)

= . .1
(91) 0 (3 6)

28

From equations (3.12), (3.14), (3.15) and (3.16), the following equation is obtained:

/\1 023—0! {12(957dld-T + A2p72nar(d) + Mpgnnwl

(IdIAI f02R—d 10(13 dldx + /\2pmar(d) + AQPmin(d)l.

 

(3.17)

The tool velocity can be expressed as a function of the overlapping distance d. There-
fore, the minimization of E (d, v) is only related to the overlapping distance d. <1
A golden section method [35] is adopted here to calculate the overlapping distance

d and the tool velocity v by iteration.

3.3 Comparison of Material Deposition Patterns

Material deposition on a free—form surface in manufacturing has many applications,
such as surface manufacturing and rapid prototyping (3D printing and layered man-
ufacturing) [4, 19, 36]. These applications can be categorized into two groups, con-
tinuous and discontinuous material deposition. The continuous material deposition
is to deposit material on a free-form surface continuously, such as surface manufac-
turing. For the discontinuous material deposition, the tools can be turned on and off
to deposit material on a surface. Tool path planning for these two processes has been
widely studied and different material deposition patterns have been used. There are
two main material deposition patterns, raster and spiral, as shown in Figures 3.4(a)
and 3.4(b) respectively.

Both the raster and the spiral patterns are implemented in continuous and dis-
continuous material deposition [7, 9, 18, 19, 36, 37]. Kao et al. [36] claims that the
spiral material deposition pattern is preferred for layered manufacturing. However,
they do not report any explanation. Although the two patterns are used in different
applications, there is no comparison to show the performance of the two patterns.
Therefore, to achieve better material distribution, it is desirable to compare the per-

formance of the two patterns in different applications. Here the comparison of the

29

 

 

 

 

”

 

 

 

 

 

 

 

 

 

Figure 3.4: The material deposition patterns: (a) raster; (b) spiral.

two material deposition patterns for continuous material deposition is performed.
The uniformity of material distribution on a product can strongly influence the
quality of the product. Hence, the uniformity of the material distribution is used
as a criterion to justify the two material deposition patterns. Since Optimal tool
planning may affect the uniformity of the material distribution, the Optimal tool
planning algorithm (Chapter 6) is used to generate optimal tool trajectories to obtain
optimal material distribution for the two material deposition patterns. Based on the
CAD model of a surface and a tool model, two trajectories are generated for the
two material deposition patterns. The trajectories are then optimized to obtain the

Optimal material distribution to justify the two material deposition patterns.

A plane, which was rendered into triangles as shown in Figure 3.5, is used to
test the two material deposition patterns. If the material distribution of a material
deposition pattern on a plane is better than that of the other, the same result can be
obtained on a free-form surface.

The parameters used to compute the material distribution are the same as those
in Section 5.1.1. Using the spray width in equation (5.2), the trajectories for the two

material deposition patterns are generated and shown in Figures 3.6(a) and 3.6(b)

respectively.

30

      

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Width (m)

_ —0.3
0'3 —0.4 Length (m)

Figure 3.5: The triangular approximation of a plane.

The material thicknesses for the two paths are calculated based on the constant
velocity in equation (5.2) using the trajectory verification model (3.34). The results
are shown in Figures 3.7(a) and 3.7(b) respectively. The big jump in Figures 3.7(a)
and 3.7(b) is due to the transition of the path as shown in Figures 3.6(a) and 3.6(b).

Then the paths are divided into segments and each segment is divided into 10 small
pieces. The optimal tool planning algorithm ( Chapter 6) is applied to optimize the
velocities to obtain optimal material distribution. The material thicknesses for the
two material deposition patterns are computed and shown in Figures 3.8(a) and 3.8(b)
respectively.

For the raster material deposition pattern, the maximum and minimum material
thicknesses occur at the boundary of the part (Figures 3.7(a) and 3.8(a)) for both
optimal and non—optimal trajectories. This can be compensated by extending the path
outside the part (Section 3.5) or by the neighboring path (Chapter 4) . Therefore,
better results can be achieved for the raster pattern (Section 5.1.2). However, the
maximum and the minimum material thicknesses for the spiral pattern occur at the

corners Of the paths (middle of a part), which cannot be compensated.

31

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0

-1
0.1

 

0.1 0.2

 
 
   
  
  
 

    

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Width (m) _02
-O.3 -0.4
‘0-5 Length (m)
(a)

1‘ .
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.5 o,
O
I

”h

 

—0.1
—0.15

-O.2

Width (m)‘°'25 0"

-0.3
Length (m)

(b)

Figure 3.6: The generated paths for the two material deposition patterns: (a) raster;
(b) spiral.

The results of the material distribution for the two material deposition patterns

are summarized in Table 3.1.

The maximum material thickness for the spiral pattern is larger than that of

32

  
 
 

       
    
   

    

 

 

 

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" ire-researwr". «- -
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Thickness (um)

 

Y (rn)

X (m)

(b)

Figure 3.7: The material thicknesses for the two material deposition patterns with
constant velocity: (a) raster; (b) spiral.

the raster pattern. The minimum material thickness is smaller. This means the
deviation of the material distribution of the spiral pattern is bigger than that of the

raster pattern. The path length of the spiral pattern is also longer than that of the

33

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Figure 3.8: The optimal material thicknesses for the two material deposition patterns:
(a) raster; (b) spiral.

raster pattern. So is the process time. Therefore, it is better to use the raster pattern

in continuous material deposition processes. This is consistent with the fact that the

34

Table 3.1: The implementation results for the two material deposition patterns

 

 

 

 

 

 

 

 

 

 

 

 

 

—~ Optimal Non-Optimal
—- Raster Spiral Raster Spiral
Average (am) 49.9 49.6 51.3 54.1
Maximum (,um) 61.6 68.8 77.1 116.5
Minimum (,um) 37.8 29.5 27.5 30.9
Process time (s) 8.39 8.77 8.84 9.56
Path length (m) 2.8566 3.0894 2.8566 3.0894

 

raster pattern is widely used in automotive manufacturing.

3.4 Patch Forming Algorithm

The process for patch forming is shown in Figure 3.9.

 

Given conditions

1
Threshold angle

1

Patch forming algorithm

1

Patches

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.9: Patch forming algorithm.

Based on a tool model and constraints, the maximum and minimum material
thicknesses on a plane are calculated. A threshold angle is obtained. Patches are

formed using the patch forming algorithm.

35

3.4.1 Threshold Angle Determination

After the material thickness on a plane is optimized, the average, maximum and

minimum material thicknesses are qd, (imam and gm," respectively. Assume that the

total material on the plane is projected to a free-form surface and the maximum

deviation angle of the free-form surface is fith. The maximum deviation angle is

the maximum angle between the normal of every point on the free—form surface and

the normal of the plane. Figure 3.10 shows the material on a plane projected to a

”a
Plane

Free-form surface

a

free-form surface.

a
.3

Figure 3.10: The material on a plane is projected to a free-form surface. fig, is the
maximum deviation angle Of the free-form surface; 17,, the normal of the plane; and

ii,- the normal Of a point 5 on the free-form surface.

Assume the total material is projected to the free-form surface along the normal

of the plane. Without considering the tool standoff variation, the material thickness

at point 3 can be expressed as:

q. = econ/3....) (3.18)

Where q— is the material thickness on the plane. The material thickness q, on the

free-from surface must satisfy the following inequality:

(Tm-incos(,‘3th) S (Is S (imam! (319)

36

 

 

 

If the material thickness g, on the free-form surface satisfies the task constraints,

i.e.,

Iq. — ml S An. (3.20)

then
(Tina: _ Qd .<_ AQd (3'21)
Qd _ (TminC03(fith) S Aqd (3.22)

If equation (3.21) is always satisfied, the threshold angle fit}, can be calculated using
equation (3.22),

— A
M. (3.23)

511. = acos

qmin

This means, for any free-form surface, if the maximum deviation angle 6mm satisfies:

51710:: S fitha (3.24)

the material thickness on the free—form surface can satisfy the material thickness
constraints.
In coverage, the threshold angle B... can be chosen as any value less than 90"

according to equation (3.34).

5’. 4. 2 Patch Generation

After the threshold angle 6.}, is obtained, patches are generated. A patch is expressed

as:

PT,- = {lecos-lmj . a.) < 3..., D(T,-,T.,.) g R,T,- e M, T. e M} (3.25)

37

where PT, is the ith patch; ii,- and 7'27), are the normals of the jth and kth triangles,
respectively; D(Tj, Tk) is the distance between the centers of the j th and kth triangles.

The patch generation process of a patch is shown in Figure 3.11.

 

 

 

 

 

 

 

 

 

 

 

I . Add the first seed
A seed triangle 7 to a patch
I4
V‘

 

Find surrounding triangles

1

Find the deviation angle .6

1

Add the triangle to the patch

More triangles

More triangles in the part

 

 

 

 

 

 

 

 

 

 

 

     

 

     

 

Yes

 

t No
End

 

 

 

 

Figure 3.11: The patch forming process.

The steps for the patch generation are:

Arbitrarily choose a seed triangle as the first triangle of a patch.

Step 1:

Step 2: Find surrounding triangles. The distance between each surrounding triangle
and the seed triangle is less than the spray radius.

Step 3: Calculate the angle between the normal of the seed triangle and the normal of

each surrounding triangle.

38

 

g? “ I'Ml—J'F-‘i

 

 

 

Step 4: Compare the angle with the threshold angle. If it is less than the threshold

angle 6.1,, the triangle is added to the patch.

Step 5: After all Of the surrounding triangles are checked, use each of the newly added

triangles as a seed triangle.

Step 6: Continue the process until no more triangles can be added to the patch.

Step 7: If there are remaining triangles, choose a seed triangle from the remaining tri-

angles.

Step 8: Repeat steps 2-7 to form a patch.

Step 9: If there are triangles left, repeat steps 2-8 for patch generation until there is no

triangle left.

After the process is performed, the free-form surface is divided into one patch or

several patches.

3.5 Trajectory Generation for a Patch

A tool trajectory includes the tool position, orientation, and velocity. The tool posi-
tion is determined by the spray width. After the spray width and the tool velocity

are found, a tool trajectory generation algorithm is developed to generate a tool

trajectory for a free-form surface.

3.5.1 Tool Path Generation

After patches are formed, a tool trajectory can be generated for each patch using
the spray width and the tool velocity. Sheng et al. [20] developed a bounding box
method to generate a path for a patch. A bounding box Of a patch is a box which

contains the whole patch exactly. Figure 3.12 shows a patch and its bounding box.

39

 

 

 

 

 

Figure 3.12: A patch and its bounding box: TOP, FRONT and RIGHT are the
directions of the bounding box.

The FRONT direction of the bounding box is the Opposite direction of the area-
weighted average normal of a patch, The average normal direction of a patch with

N triangles is defined as:

N ..
a, = 21513:“: (3.26)
H Zi=l Sini“

where it, is the average normal of the surface; ii,- and s,- are the normal and the area of

 

the ith triangle (i = 1, ..., N), respectively. All vertices on a patch are then projected
to a plane whose normal is the FRONT direction. The TOP and RIGHT directions
are determined by finding the smallest rectangle which can cover all of the projected
points on the plane.

Since the bounding box method cannot generate a trajectory to follow the contour
Of a patch, an improved bounding box method is proposed here to generate a tool
path for a patch. Figure 3.13 is an illustration of the path generation algorithm using
the improved bounding box method.

The steps for the path generation of a patch are:

Step 1: The patch is cut using a series of top cutting planes. whose normals are the TOP

40

 

 

 

 

 

 

 

 

Figure 3.13: The improved bounding box method to generate a path for a patch.

direction. The distance between the neighboring planes is the spray width. A

series of top intersecting lines LT,- are Obtained, as shown in Figure 3.13.

Step 2: The patch is cut using a series of right cutting planes, whose normals are the

RIGHT direction. A series of right intersecting lines L Rj are obtained, as shown

in Figure 3.13.

Step 3: For each right intersecting line L3,, find the number p,- Of intersecting points
with all of the top intersecting lines. The number p,- is the path number for

the right intersecting line L Rj. The procedure is repeated until all of the right

intersecting lines are processed.

Step 4: Each right intersecting line is divided into p,- segments. A series of points are

obtained. The procedure is repeated until all of the right intersecting lines are

divided.
Step 5: Connect the points along the RIGHT direction to form a path.

One of the advantages of the improved bounding box method is that the tool path

can follow the contour of a free-form surface.

41

3.5.2 Tool Orientation Generation

The tool orientation is determined based on the local geometry of a patch. Figure 3.14

shows the tool orientation generation.

Tool moving direction Part

Over-spray point

 

 

 

Tool path

Spray cone

 

 

Figure 3.14: Part of a tool path and a series sample points.

At each sample point, triangles whose distance to the sample point is less than

the spray radius are found as shown in Figure 3.15.

 

Figure 3.15: Tool orientation generation.

The average normal of these triangles is calculated using equation (3.26). After
finding the average normal, the tool orientation is the reverse direction of the average

normal. Thus the tool orientation is determined by the local gemnetry Of a free-form

42

surface.

3.5.3 Tool Trajectory Generation

The generated tool trajectory is on a free-form surface. In surface manufacturing, the
tool trajectory has to be offset a distance of the tool standoff along the opposite tool

direction to form a tool trajectory. Figure 3.16 is an illustration of the process.

Tool
i

h Free-form surface

 

 

 

 

 

Sample point Tool path

 

Figure 3.16: A tool trajectory on a free—form surface is projected to form an Offset
tool trajectory.
After all points on the tool trajectory are offset, an offset tool trajectory is gen-

erated.

3.6 Trajectory Verification Model

Trajectory verification is an important process because it checks if the generated tra-
jectories satisfy the given constraints. A trajectory verification model is developed
to compute the material thickness on a free-form surface using the generated trajec-
tories. A typical tool model [8, 9, 38, 39] is adopted here to calculate the material
thickness of a point on a free-form surface. Figure 3.17 shows the material deposition

on a free-form surface. The plane is generated using the tool direction and the desired

43

 

 

 

 

 

 

Projected [T—
point
6i
Plane h
Free-form hi
surface X I
iii
7:
s .

Figure 3.17: Material deposition on a free-form surface. ii,- is the normal of a triangle;
7,1 the deviation angle from the gun direction; h the desired tool standoff; h,- the actual
tool standoff.

tool standoff.

The development Of the trajectory verification model is based on an assumption
that the amount of material from the tool is the same as that sprayed on a free-
form surface, which is independent of the geometry of the free-form surface and the
distance between the tool and the free-form surface [8, 32, 39, 40]. Suppose the
material sprayed on a small area C1 is projected to the area C2, as shown in Figure
3.18. The relationship between the two areas is:

h.-

502 = (XVSC. (3-27)

where SC, and So, are the areas of C1 and C2 respectively.
Suppose the material on C1 is projected to 02. Based on the assumption, the

material thickness on C2 can be expressed as:

ch = 611;?!)2 (3.28)

44

 

 

 

 

 

 

Figure 3.18: The trajectory verification model: material projection.

where g and (12 are the material thicknesses on the planes C1 and 02, respectively.

Free-form surface

£31 ,,

 

 

 

(a) (b)
Figure 3.19: Material projection: (a) from C2 to C3; (b) from 03 to a small area on
a free-form surface.

Figure 3.19(a) shows a circle C3, which is perpendicular to the material emission

45

direction. The material thickness on C3 can be expressed as:

(12
cosH,°

 

G3 = (3.29)

The material on C3 is projected to the free-form surface with a deviation angle

7,, as shown in Figure 3.19(b). The material thickness on the free-form surface is:

q. = 11360875. (3.30)

Therefore, based on equations (3.28), (3.29) and (3.30), the material thickness on

the free-form surface can be obtained:

 

_ h 2cosry,
qs = 71' (331)

c036,.

If the distance from the tool to the point 8 is l,-, then
hi '1 liCOSgi. (3.32)

Then equation (3.31) can be expressed as:

 

_ h 2 C087,‘
q.=q I (3.33)

cos3di'

When the deviation angle '7.- > 90°, there is no material sprayed on a surface. Hence,

the material thickness on a free-form surface can be modeled as:

 

2
- h cosy, , o
q (—) . 1.- : 90
q, = ’1 91 . (3.34)
0 7,- > 900

Using this trajectory verification model, the material thickness on a free—form surface

can be calculated.

46

3.7 Suboptimal Tool Velocity

To obtain an optimal tool trajectory for a free-form surface, an optimal tool planning
algorithm has to be developed. Optimal tool planning may make the computational
load high. To reduce the computational load, a suboptimal tool velocity planning

algorithm is developed. The lower and upper bounds of the material distribution are

defined as:

Agrnar : qmaI — (Id (335)

Aqmin = Qd _ (1min

where qmax and qmin are the maximum and the minimum material thicknesses on
a free-form surface, respectively; Aqmar and Aqmin the upper and lower bounds,
respectively. According to equation (3.19), the upper bound of the material thickness
is dependent on the maximum material thickness on a plane. However, the lower
bound is dependent on both the minimum material thickness on a plane and the
maximum deviation angle of a free-form surface. A larger the maximum deviation
angle gives a bigger material thickness deviation. This means the lower bound is
larger than the upper bound. To minimize the material thickness deviation from
the desired material thickness, the lower bound has to be decreased. A method is
deveIOped here to decrease the lower bound by approximately optimizing the tool
velocity. Figure 3.20 shows the material thickness projected from a plane to a free-
form surface. Because the material of an area S on a plane is projected to an area S’
on a free-form surface, the material thickness on the free-form surface is decreased.
According to Theorem (3.2.1), the material thickness is inversely proportional to the

tool velocity. Therefore, the tool velocity can be modified to increase the material

47

 

so /
"CD

A free-form surface

 

 

 

 

v

Figure 3.20: The material thickness projected from a plane to a free-form surface.

thickness on the free—form surface, i.e.,

, S

where v’ is the approximately optimized tool velocity. Thus, we have,

q3' = q. (3.37)

Hence, the material thickness deviation from the desired material thickness is de-

creased using the suboptimal velocity algorithm.

48

CHAPTER 4
TOOL TRAJECTORY INTEGRATION

A free-form surface may consist of several patches. After the trajectory for each
patch is generated, the trajectories of the patches have to be integrated to obtain a

trajectory for the free—form surface. In this chapter, a trajectory integration algorithm

for a surface with multiple patches is developed.

4.1 Material Distribution in the Intersecting Area of Two

Patches

The material thickness optimization of a surface with two patches is much more
complex than that of a surface with one patch. The overlapping distance and the
tool velocity should be kept the same as those of a surface with one patch except at
the intersecting areas among patches. In the intersecting area, the path in one patch
contributes to the material thickness on the other. Figure 4.1 shows two patches with
an angle a.

In Figure 4.1, O is the spray tool center; 01, 02, 03, 31 and 32 are points on the
two patches; hl is the distance from 01 to 03; hg the distance from 02 to 03; l, the

distance from O to .92; :r the distance from 01 to 31; y the distance from 52 to 02.

The distance I from 03 to .92 can be expressed as:

 

(a: — h1)0086
z =
608(6 + (1)

Using the trajectory verification model (3.33), the material thickness on Patch 2

49

 

 

 

Patch 1

 

 

 

 

Patch 2

Figure 4.1: The material distribution on the intersecting area of two patches.

can be expressed as:

h2003(0 + a)

 

 

(132013.31) = (12(31) + (11(23) 13c0330 (42)
Equations (4.1) and (4.2) lead to:
h — cos 6+0 h2cos 6+a
932(18): q2(y) + (11(h1'l' ( 2 y) ( l) l l (4.3)

0036 [$00339

Equation (4.3) is quite complicated if it is used to calculate the material thickness at
the intersecting area of two patches. Since the tool standoff h, is much larger than
the spray radius, i.e.,

R << h. (4.4)

50

Therefore, the angle 6 is a small angle. Then the following approximations are. valid:

tan6 % 0, h, z 1,0030. (4.5)
Equation (4.3) can be simplified as:
(132(31) = (12(31) + (11011 + (’12 - ylcosalcosa- (4-6)

a > 90" is not considered here because the material thickness on one patch is not

affected when spraying the other patch.

Similarly, the material thickness on Patch 1 is computed:

q,l (11:) = q1(;2:) + q2(h2 + (hl — :r)cosa)cosa. (4.7)

4.2 Optimization Process for a Surface with Two Patches

According to the criteria that the main part of a tool path is parallel or perpen-
dicular to the intersecting line, different cases are studied: parallel-parallel (PA-

PA) case; parallel-perpendicular (PA-PE) case; perpendicular-perpendicular (PE—PE)

case. Figure 4.2 shows the three cases.

4.2.1 Case I: Parallel-parallel (PA-PA) Case

Figure 4.3 shows the PA-PA case.

In this case, we need to optimize the distance h between the two paths. Because
the two paths are symmetric, the distances of the two paths to the intersecting line
are the same. Since the material distribution on any line which is parallel to the
intersecting line is the same, we only need to consider the material thickness on CA

as shown in Figure 4.3. Suppose the angle l‘)etwcen the two patches is a. The material

51

 

Patch1-'. E /
///Path // o . . at . . Patchl

 

 

 

 

 

 

 

 

 

 

 

 

 

PatchZ E Patch2 5
(a) (b)
. . . fab /. Patch]
Patch2 Path

 

 

(C)

Figure 4.2: (a) Case 1: parallel-parallel case; (b) Case 2: parallel-perpendicular case;
(c) Case 3: perpendicular-perpendicular case.

X

/ ll Patch 2

h A Intersecting line

do 0 Patch 1/

Figure 4.3: Parallel—parallel (PA-PA) case.

 

 

 

thickness on DA can be expressed as:

q(gr) = (11(|;r — doll + (12(h + ((10 + h, — :r)cosa)cosa (4.8)

52

where q1(.1:) and q2(:1:) are the material thicknesses due to the paths in Patch 1 and

Patch 2, respectively, which can be expressed as:

vRfivyi

(11(9) = 2]; v f(\/(vt)2+y2)dt

q2<y>= / ” f(x/(vt)2+y2)dt- (4.9)

Then, the error function can be formulated as:

h+do
19.02) = f (q. — q(cc))2dx. (4.10)

Since the maximum and the minimum material thicknesses determine the maxi-
mum material thickness deviation from the average material thickness, they have to
be minimized, i.e.,

E201) = (me1 — (1.02 + (qd - qmm)2 (4-11)

where qmar and qmm are the maximum and the minimum material thicknesses, re-
spectively.
Finally, a multi-objective optimization problem is formulated using equations
(4.10) and (4.11),
min {E 2 (E1, E2)T}. (4.12)

The optimization problem can be solved using the method in Appendix A.

4.2.2 Case 2: Parallel-perpendicular {PA-PE) Case

Figure 4.4 shows the PA-PE case.
The highlighted area can represent the intersecting area due to the symmetry of
the material distribution in the intersecting area. To obtain the Optimal material

distribution, the paths are divided into small segments to optimize the tool velocity.

53

 

 

 

 

 

 

 

 

Patch 2
Path 11
h;
Intersecting line A P ( x, y )
’11
P1 ___’____q __________ Vi”: ; via
":0 P6 P7
P2 Path 1
Patch 1 P5 , P3
0 V0 ’ X
P3 P4 V P9

 

 

 

Figure 4.4: Parallel-perpendicular(PA-PE) case.

The material thickness on point P in the highlighted area due to Path I can be

calculated using the path segments P,- (z = 1, ..., 9) shown in Figure 4.4.

P1, P6 and P7:

2R—d ~ .
. 1 2k (1“)
qpl.6,7($ay7]) = _L f(7)dz,

”j {3304—1)

7= \/(Z+zo)2+(do—y)2,

2R—d
2

QR—d
2 _

 

 

 

 

P1, 20 =

+27,

 

(‘Q

P6, :r,
2 —d
.r— __3( R2 ).

0

P7,

1‘»)

0

54

P2, P5 and P8:

.I'_‘.d0

 

 

 

. 1 z+1
qP2,5,8(‘Irvy7]) : — / f(7)(1Z,
’7: \/($+$0)2+(Z—y)2.
2R — d
P2, $0 = 2 ,
2R — d
P5, (130 = — 2 ,
P8, $0 = _3(2R — d)
2
P3, P4 and P9:

(1103.,49($ay)= %/0R( f(V

'y=\/(;r+:r0)2 +(z—y— R)2,

 

 

 

2R — d
P37 1‘0 : 2 a
2R — d
P4) IEO : _ 2 a
P9, $0 = 3952112. (4.13)

where qu represents the material thickness due to the path segments. Then the

material thickness q, on point P due to the path in Patch 1 is:

i+k
q1(:vy)-=qu167ivyj)+ quzfiss xyj)+qp3.9(ar .71) (4-14)
j=0 j=i+1

Since the path in Patch 2 is parallel to the intersecting line, the material thickness

411 on point P due to the path in Patch 2 is:

(1110/1): ‘2'oRf yl f( \/ 22 + 31$le (4-15)

where yl is the distance from a. point to the path in Patch 2. Then the material

55

thickness on point P can be calculated using equations (4.6) and (4.7):

l (1103,?!) + (111(h2 +(h1+ do —— y)cosa)cosa 0 g y S (h1+ do)
q(I,y) : l (11(55,h1+ do + (y — h] — d0)cosa)cosa'+

q11(h2+y—h1—d0) h1+d0<$ghl+h2+do
(4.16)

 

Then an error function can be formulated:
E1 = 5’24 0d°+’“+":<qd — q(x.y))2dydx. (4.17)

Similar to the PA-PA case, the maximum and minimal material thickness devia-

tions from the average material thickness have to be minimized, i.e.,

E2 = (Qmax _ qd)2 + (Qd - (1mm)2 (4.18)

where qmax and qmm are the maximum and the minimum material thicknesses, re-
spectively.

Finally, a multi-objective optimization problem is formulated using equations
(4.17) and (4.18),

- _ T
hTIizriv {E — (E1, E2) }. (4.19)

This problem can be solved using the method in Appendix A.

4.2.3 Case 3: Perpendicular-perpendicalar {PE-PE) Case

Figure 4.5 shows the PE-PE case.
The highlighted area can represent the intersecting area due to the symmetry of
the material distribution in the intersecting area. The material thickness on point
P in the highlighted area due to the path in Patch 1 is the same as that in PA-PE

case, which can be calculated using equation (4.14). The material thickness due to

56

 

 

 

 

 

 

 

 

 

 

 

t Y
Patch 2
P15 P12 P13
AP"). P11
- -, v
Pl4
h P( X. Y) Intersecting line
Vi+k VH1“- O = :
vi I
0
V0 ’
0 X
Patch 1

 

 

 

Figure 4.5: Perpendicular-perpendicular (PE—PE) case.

the path segments P,- (z' = 10, ...15) in Patch 2 can be formulated as:

P10, P11 and P14:

2R—d .-
. 1 2k (.7—1')
qP10,11,14($aya.7) = _ LR f(7)dz,

 

 

 

 

'Uj —,;—“o—i—1)
7 = x/(z + Zo)2 + (h + (do + h — ”may:
P10, zo = ‘2R2— d — at,
P11, 20 = —2R2_ d + :17,
P14, zo = w “ 33~

P12, P13 and P15:

1 4%‘10
qP12.13,15($aya]) : — / 11(7le,

1).
] :i-ldo

7 = \/(:r,+ 170)2 + (do + h+ (do + h -— y)cosa -- z)2,

 

 

2R — d
P2, L130 2 — 2 ,
2 — d
P5) T0 _3( R2 )v
P8, x0 = 2R; d. (4.20)

Then the material thickness on the point P can be calculated:

q(r, y) = q1(;I:, y) + (111(13, y)cosa (4.21)
where
i i+k
q11($3 y) : Z qP12.13,15($’ y? j) + Z QP10,11.14 (It? y’j)' (422)
j=0 j=i+l
Then an error function can be formulated:
(4.23)

E1 = fem—d 0d0+h((1d — q(r,y))2dydx-

Similar to the PA—PA case, the maximum and minimal material thickness devia-
tions from the average material thickness have to be minimized, i.e.,

(4.24)

E2 = ((Imax — le2 + (9d _ Qmin)2

where qmax and qmm are the maximum and the minimum material thicknesses, re-

spectively.
Finally, a multi-objective optimization problem is formulated using equations

(4.23) and (4.24),
min {E = (E, E2)T}. (4.25)

This problem can be solved using the method in Appendix A.

4.3 Optimization Process for a Surface with Multiple Patches

According to the types of intersecting areas, a surface with multiple patches can be
categorized into two cases: Point and Line. If the patches intersect in a point, it is

called Point case. If the patches intersect in lines, it is called Line case. The two

cases are discussed individually. Some surfaces may have. both cases.

58

4.3.1 Point Case of a Surface with Multiple Patches

Figure 4.6 shows the Point case of a surface with three patches.

 

 

 

 

Figure 4.6: The Point case.

The material distribution between Patch 1 and Patch 2, Patch 2 and Patch 3,
Patch 1 and Patch 3 is optimized. The only part we need to consider is the thickness
on the area around the intersecting point P. Since the material thickness between
Patch 2 and Patch 3 is optimized, we can merge them into one patch: Patch 1. The
material thickness on Patch I is optimized. Since the material thickness between Patch
1 and Patch 3, Patch 1 and Patch 2 is Optimized, the material thickness between Patch

I and Patch 1 is optimized too. Hence, the material thickness on the area around the
intersecting point P is optimized.

This method can be applied to a surface with more than three patches which
intersect at one point. Therefore, if the material thickness between any two patches

is optimized, the material thickness on a surface that consists of multiple patches

must be optimized.

4.3.2 Line Case of a Surface with Multiple Patches

If one patch is between the other two patches, as shown in Figure 4.7, there are

different cases depending on the patterns of the paths.

In Figure 4.7(a), because the path in Patch 2 is perpendicular to the intersecting

lines, the PA—PE or PEI-PE cases can be applied to determine the parameters. How-

59

   
 
    

Patch 3

Patch 2

 

(a) (b)

Figure 4.7: A surface with three patches: (a) perpendicular path for patch 2; (b)
parallel path for patch 2.

ever, for the case in Figure 4.7(b), the path in Patch 2 is parallel to the intersecting
lines. If the Optimal h is applied, the actual spray width for the rest area of Patch 2
may not be the Optimal spray width. Since the material distribution in the intersect-
ing area is more sensitive to h, the spray width has to be modified. Here two methods

are developed to change the spray width for Patch 2.

Method 1:

The spray width can be changed in a certain range without affecting the maxi-
mum and minimum material distribution too much. Table 4.1 shows the relationship
between the spray width, the maximum and the minimum material thicknesses. The
velocity is Obtained by optimizing a spray process on a plane when the spray width is
given. Spray painting is used as an example. The conditions are the average material
thickness qd = 50 pm, the spray radius R = 50 mm. and the paint deposition rate
f(r) = .1502“: — r2) Inn/8-

When the spray width is increased / decreased about 5 mm, the maximum material
thickness deviation from the average increases about 5 am. Figure 4.8(a) shows the
relationship between the spray width and the tool velocity. The relationship between

the spray width and the maximum and the minimum material thicknesses is shown

60

Table 4.1: The relationship between the spray width and the maximum and the
minimum material thicknesses

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Spray Width (mm) Velocity (mm/s) (1mm (um) gm," (,um)
66.0 310.0 54.1 45.0
65.0 312.9 53.6 45.7
64.0 315.9 53.1 46.3
62.0 320.9 52.3 47.4
60.8 323.3 52.0 48.0
59.5 333.4 52.3 47.5
58.0 344.0 52.8 46.8
55.0 363.5 53.8 45.5

 

in Figure 4.8(b).

Method 2:

From Method 1, the spray width cannot be changed tOO much since the maximum
material thickness deviation increases as the the spray width deviation from the de-
sired spray width increases. The tOOl height can also be adjusted to change the spray
width. Figure 4.9 shows the tool height is increased from the desired tOOl height.

In Figure 4.9,

a,- = 7,. (4.26)

Therefore, equation (3.31) can be written as:

h 2
(13 = (I (7) (4-27)
1i

where q,2 is the material thickness on point. S. From Theorem (3.2.1), the material

61

 

380 I T I I l T

370 _ » ~

360 -

350 -

Velocity (mm/s)

 

 

 

 

 

330 ~ 4
320 ~ -
31 0 ~ 4
30054 52. 5; go 6:. a. .8
Spray Width (mm)
(a)

58 I . I . y 3

56 .. , 7, , , . , . , 1 t -
54 ~ .

Thickness (um)
8

 

 

 

 

46 — ~
44 - 4
42 l l l l 1 l

54 56 58 60 62 64 66 68

Spray Width (mm)
(b)

Figure 4.8: The relationship between the spray width and (a) velocity; (b) the maxi-
mum and minimum material thicknesses.

thickness is inversely proportional to the tool velocity. Thus, the material thickness

on point S can be increased. If

(4.28)

{9 I

(13:

62

   

Actual Surface

 

Virtual Plane

 

 

 

Figure 4.9: The tool height is increased from the desired tool standoff.

then

v’=v (h)2 (4.29)

h—.-
where v’ is the modified velocity. This means the maximum material thickness de-
viation is the same as before. However, since the tool height is changed, the spray

radius becomes

R’ = R—' (4.30)

w = w—'-. (4.31)

From equations (4.28) and (4.31), the spray width can be modified without sacri-
ficing the maximum material thickness deviation. However, since the spray radius
is changed, the optimization process for the intersecting area has to be performed
again to obtain the optimal distance(s). This makes the integration problem more

complicated.

63

CHAPTER 5
IMPLEMENTATION OF AUTOMATED TOOL
PLANNING

In this chapter, the automated tool planning is implemented to generate trajecto—
ries for different processes, such as spray painting, spray forming and indirect rapid
tooling. The generated trajectories are also verified using the trajectory verification
model. The trajectory integration algorithm is also implemented. Since coverage is
a special case of material uniformity, implementation for coverage is not discussed
here. The algorithm was implemented in C++. The triangular approximation was

exported from GID (http://gid.cimne.upc.es/) with an error tolerance of 2 mm.

5.1 Optimization Process

The material thickness optimization process is performed for spray painting because

the Optimization for other applications is similar.

5.1.1 Determination of Tool Trajectory Parameters

Suppose the desired paint thickness is qd = 50 pm, the required paint thickness

deviation 15pm and the spray radius R = 50 mm. The paint deposition rate is:

1
f(r) = E(R2 — r2) um/s. (5.1)
The paint gun velocity and overlapping distance are calculated by optimizing equation

(3.12):
v = 323.3 mm/s, d = 39.2 mm. (5.2)

64

The maximum and minimum thicknesses are:

(Imar = 52.02 pm, (2mm 2 48.05 pm. (5.3)

The optimized paint thickness on a plane is shown in Figure 5.1.

 

70 T MM I I I I I I

65*

O)
C
r

l

01
01
r

 

Thickness (um)
a 8

$

(A)
U"
I

l

 

 

 

20 40 60 80 100 120 140 160 180 200
Points

Figure 5.1: The Optimized paint thickness on a plane.

Using the maximum and minimum thicknesses and equation (3.22), the threshold

angle is calculated:

fith = 43-20- (5.4)

5.1.2 Paint Thickness Optimization for a Surface with Two Patches

Case 1: Parallel—parallel (PA-PA) Case

In this case, do = R. After performing the optimization process using equation

(4.12), the optimized paint thickness for a = 30° is shown in Figure 5.2.

Case 2: Parallel-perpendicular (PA-PE) Case

For this case, i = 3, do = 2R and k = 4 are chosen. The optimization process is

performed using equation (4.19). The optimized paint gun velocities when a = 30°

65

 

70 Y I M I I

65» ~ +
60b q
55“ '*
A ”....... ..
€50“ ."Oeoeoe‘0000"""".” """'*000000.‘
tn
«0
“st . . w . , . .
C
x
.9
.C i- .4
P40

w
01
r

3?

 

 

 

20 l l l l l
0 5 10 15 20 25 30

Points
Figure 5.2: The optimized paint thickness for the PA-PA case when a = 30°.
are:
120 = 272.2mm/s, v1 = 333.1mm/s, v2 = 459.2mm/s, v3 = 336.4mm/s,

v4 = 226.7mm/s, v5 = 355.3mm/s, v6 = 547.2mm/s, v7 = 690.8mm/s.

The optimized paint thickness for a = 30° is shown in Figure 5.3.

 
   
  
 

 

 

70‘
. ‘ . 0.0u":'e
60~ ' ' 0".'0 .. . .0 . . .€..
... . . . . .. .
... . . . ‘ _. O .. . O
o "a 1 o . o ' . 3". I." o ' .
E O. .0 0 o : . fi '.' C 00:..M:o ..
: 50~ 0. o . ‘ .3 0(W"ooooeo.
‘8’ . . . 0.... Dingoo 0.
g . ' ..:. 3‘ O.
O. C

i) 40" . no " o
5 '0...- 5.:.

30~

20-

150 , 60

100 40
50 20
0 0
Y(mm) X(mm)

Figure 5.3: The optimized paint thickness for the PA—PE case when a = 30°.

66

Case 3: Perpendicular-perpendicular (PE-PE) Case

For this case, i = 3, do = 2H and k = 4 are chosen. The optimization process is
performed using equation (4.25). The optimized paint gun velocities when a = 30°

are:

to = 252.0mm/s, v1 = 308.4.1mm/s, v2 = 425.2, to = 311.5mm/s, mm/s

v4 = 209.9mm/s, v5 = 329.0mm/s, v6 = 506.7mm/s, v7 = 639.6mm/s.

The optimized paint thickness for 0: = 30° is shown in Figure 5.4.

70‘ ' " .00. :

 

.TOOOO

. ...
N ...OO.

E O . - .0

d.‘

3 ."e

m ”'e

8

x

£240~

L

.—

 

 

0 0 X (mm)

Y (mm)

Figure 5.4: The optimized paint thickness for the PE—PE case when a = 30°.

The maximum and the minimum thicknesses for the three cases with a = 30° are

summarized and shown in Table 5.1.

The results in Table 5.1 show that the PA-PA case achieves satisfactory results.
The paint thickness deviation is about 1.5,um. The paint thickness deviation for the
PE-PE case is about 5.4mm However, for the PA-PE case, the paint thickness devi-

ation is about 10pm. Therefore, the PA-PE case should be avoided in tool trajectory

planning.

67

Table 5.1: The maximum and minimum thicknesses for the three cases when a = 30°

 

Thickness qmm (pm) qnm (pm)

 

 

 

 

PA-PA 48.8 51.5
PA-PE 40.7 59.4
PE—PE 44.6 55.8

 

 

 

 

5.2 Spray Painting

5.2.1 Trajectory Generation and Verification

Three parts, portion of a car hood, fender and door, shown in Figures 2.3, 5.5(a) and
5.5(b), respectively, are used to test the algorithm. The car hood, fender, and door
have 3320 , 9355 and 4853 triangles, respectively.

Using the patch forming method, the car hood, fender and door form only one
patch each.

The tool paths are generated using the improved bounding box method in Section
3.5.1. The generated tool paths are shown in Figures 5.6(a), 5.6(b) and 5.6(c) for
the car hood, fender and door, respectively.

The gun direction is computed for each sample point and the maximum deviation
angle is calculated for each part, respectively. The number of triangles and the
maximum deviation angle for each part are shown in Table 5.2.

The maximum deviation angles 3 in Table 5.2 are less than the threshold angle
flu, for the three parts. This means the generated gun trajectories can satisfy the
thickness requirements.

When simulating the paint thickness on a free-form surface, the paint thickness of
randomly chosen points on the car hood, fender and door are computed and shown in

Fi ures 5.7 a , 5.7 b and 5.7 c . res ectivelv. The averaO‘e, maximum. and minimum
. . 9 O .

68

0.94 y
0.8\

0.7\

Height (m)

0.6\

 

 

0.5A
1.4

4.5

  

. 3 3.5
Width (m) 0.6 25

Length (m)

0.9\-

Height (m)

 

 

Length (m)

Figure 5.5: The triangular approximation of (a) a car fender; (b) a car door.

paint thicknesses are calculated and summarized in Table 5.3. The simulation results
show that the average, maximum and minimum thicknesses for the car hood, fender
and door satisfy the thickness requirements. The trajectories generated using the
automated tool planning algorithm can achieve required paint thickness. The big

jump in Figure 5.7(c) is due to the curvature of the car door.

69

..

Helght (m)

0.95

 

    

- 3
Width (m) 2 Law", (m)

(b)

Helm (m)

 

main (m) 0-8 2.5

(C)
Figure 5.6: The generated paths for (a) a car hood; (b) a car fender; (c) a car door.

70

Table 5.2: The calculated parameters

 

 

 

 

 

 

Part Triangles ,6
hood 3320 13.1°
fender 9355 29.7°
door 4853 426°

 

 

 

Table 5.3: The simulation results

 

 

 

 

 

 

 

 

Average Maximum Minimum

Part thickness thickness thickness

(i (W) qmax (um) (1m (1m)
hood 50.1 54.8 46.0
fender 49.1 55.0 42.6
door 49.1 55.0 35.1

 

 

The generated spray gun trajectories are also exported to ROBCADTM / Paint
to simulate the painting process. An ABB irb6K30—75 robot is used. The work-cell
setup is shown in Figure 5.8 for painting a car hood. A part of the gun path is shown
in Figure 5.9. A part after painting is shown in Figure 5.10. The simulation results

show that the generated trajectories can be applied to paint free-form surfaces.

71

Thickness (um)
8 8:

G

 

 

 

Thickness (um)

Thickness(um)
a 8 8: 8 a E;

8

Figure 5.7: The simulation result of paint thickness for (a) a car hood; (b) a car

fender; (c) a car door.

 

 

A

50100150200250300350400450500
Points

 

(b)

 

50100150200250300350400‘50500
Points

(C)

72

 

Figure 5.10: A painted part (part of a car hood).

73

5.2.2 Suboptimal Velocity Verification

After the trajectories are generated, the suboptimal velocity algorithm developed in
Section 3.7 is applied to optimize the paint thickness. Simulations are performed only
for the car fender and door since the upper and lower bounds of the car hood are quite
close. Figures 5.11(a) and 5.11(b) show the simulation results for the car fender and
door, respectively. Table 5.4 shows the maximum, minimum and average thicknesses
for the three parts using the suboptimal velocity method. The results show that the
lower bounds of the suboptimal velocity method are decreased for the car fender and
door. The lower bound of the car door is 10pm, instead of 15am for the original
method. That of the car fender is 4.9jam, instead of 7.6pm for the original method.
The thickness deviation is decreased from 30% to 20% for the car door, and 15% to
10% for the car fender, respectively. Therefore, the developed suboptimal velocity

method can improve the paint thickness deviation from the required paint thickness.

Table 5.4: The simulation results using the suboptimal velocity method

 

 

 

 

 

 

 

Average Maximum Minimum
Part thickness thickness thickness

6 ([1771) gmax (,um) qmin (Hm)
fender 50.8 56.0 45.1
door 51.5 59.4 40.1

 

 

5.2.3 Comparison with Other Methods

Simulations with fixed gun direction (Case 2) are also performed to show the advan-
tages of the developed gun direction generation method in Section 3.5.2 (Case 1).
The fixed gun direction is determined using the average normals for the car hood,

fender and door, respectively. The results are shown in Table 5.5.

74

 

70 I M T I I TI

Thickness (um)
25‘

 

 

 

50 100 150 200 250 300 350 400 450 500
Points

(3)

 

7G I I I 1M T I I I I

Thickness (um)

40-

 

 

 

50100150200250300350400450500
Points

0))

Figure 5.11: The simulation results of paint thickness using the suboptimal velocity
method for (a) a car fender; (b) a car door.

The maximum deviation angle for each part in Case 1 is much smaller than that
in Case 2. The deviations of the average thicknesses to the required thickness are 0.0,
0.9 and 0.6 pm for the car hood, fender and door, respectively in Case 1. However,

they are 1.1, 1.8 and 2.4 pm in Case 2. The minimum thicknesses are 46.0, 42.6

and 35.6 pm for the car hood, fender and door respectively in Case 1, while 40.3,

75

Table 5.5: The simulation results for fixed gun directions

 

 

 

 

 

 

 

 

 

Average Maximum Minimum
Part thickness thickness thickness 6’
61" (Hm) (117...; (#m) aim-n (um)
hood 48.9 54.3 40.3 328°
fender 48.2 54.6 35.5 420°
door 47.6 54.6 24.3 642°

 

 

35.5 and 24.3 pm for the car hood, fender and door, respectively in Case 2. As you
can see, by using the suboptimal velocity method, much better results are achieved.
The results show that the developed gun direction generation method achieves better
paint distribution.

The thickness deviation percentage presented by Asakawa et al. [7] is more than
58%. For our results, the thickness deviation percentage is less than 20% using the
suboptimal velocity method. For the car hood, much better result (8%) is achieved.
Although the result presented by Suk et al. [41] is 20%, the over and under-painted
areas are not included. Also the paint deposition rate is a constant instead of a

parabolic curve.

5.3 Spray Forming

5.3.1 Trajectory Generation and Verification

Because glass fiber is sprayed on a surface in the spray forming process, area density
[14] is considered instead of thickness in spray painting process. The area density is
defined as the material weight on a unit area (g/m2). If the glass fiber deposition
rate is the same as the paint deposition rate in equation (5.1) with exception to the

unit used, the optimized parameters are the same with exception to the unit used.

76

Part of a car frame is used to test the algorithm. Figure 5.12(a) shows the part;
Figure 5.12(b) the generated path and Figure 5.13(a) the area density. The average,
maximum and minimum area densities are 40.8, 44.5 and 36.0 g/m2, respectively. The

average area density is smaller than the required density due to the surface curvature.

Height (m)
.<'=
7

—o.2., 7

3491-3115???

r"

» .- - 'Ia'n'e'efi
—0.3 . . , "zifimzerrc‘
T , nix” 1'

 

 

   
 
   

-0.5

Width (m) 1 .8

1 .2
Length (m)

0.8 ‘

 

    

,4
Width (m) '1 0.8 1 1-2 ‘

Length (m)
(b)

Figure 5.12: A car frame (a) CAD model; (b) The generated path.

77

 

70- .. , . . ,. . . ..l

60"

 

Areal Density (g/m’)
8

40_ . .. ‘ A : .. . ,l

30*

 

 

 

 

 

 

 

2 l 1 L 1 M L 1 l l
G50100150200250300350400450500
Points
(a)
80 f ,
70L
«7‘60”
E
a
E
850
8
E
240_ ........
30- J
20 1 1 l l 1 l 1 1 1
50100150200250300350400450500
Points
(b)

Figure 5.13: The calculated thickness of a car frame (a) without velocity optimization;
(b) with suboptimal velocity.

5.3.2 Suboptimal Velocity Verification

Due to the high curvature of the surface, the average area density is smaller than the
required area density. Velocity has to be optimized to increase the area density. The

spray gun velocity is optimized using equation (3.36). Figure 5.13(b) shows the areal

78

density after applying the suboptimal velocity method.

For the spray forming process using the suboptimal velocity algorithm, the aver-
age, maximum and minimum area densities are 49.9, 60.3 and 41.6 g/m2, respectively.
The average area density is 49.9 g/m2 instead of 45.4 g/m2 without the velocity op-
timization. The area density deviation decreases from 14.9 g/m2 to 10.3 g/mz. The
results Show that the suboptimal velocity algorithm indeed improves the area density

deviation.

5.4 Rapid Tooling

5.4.1 Trajectory Generation and Verification

In indirect rapid tooling, a part is sprayed many times using the same trajectories.
Typically, two perpendicular trajectories are used and repeated to spray a mold.
Because two trajectories are used, suppose the desired metal thickness is 100 mm and
the thickness deviation 30 mm. Figure 5.14 shows a mold rendered into triangles.

Figures 5.15(a) and 5.15(b) show two perpendicular paths.

0.6\
0.4».

02‘

.‘ " . )‘r’. ;1.
. V r- '4'"
. i4 ‘
o - " "v 31M
‘ ' 5min was.
‘ ”:7; 9351;335:6313

  

Height (rn)

    

“O F... _ :

 

0.8 0.5

 
  

—0.5

0.6 -1

Width (rn) Length (m)

Figure 5.14: The mold for indirect rapid tooling.

79

 

 

Height (m)

 

 

 

 

 

Height (m)
1°
j
j

 

-0.4_>j

 

 

 

 

L7.

\ l\ 7\ . \ '\ "\
\-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

. 0.6 (_1
Width (m) Length (m)

(b)

Figure 5.15: The two perpendicular paths of a mold for indirect rapid tooling.

Simulations are performed to calculate the metal distribution. The parameters
used are the same as those used in spray painting with exception to the unit used.
Figure 5.16(a) shows the metal thickness on the mold. The average, maximum, and
minimum metal thicknesses are 93.4, 114.3 and 70.2 mm. The average metal thickness
is smaller than the required metal thickness (100 mm) due to the curvature of the

mold.

80

 

Thickness (mm)
8

 

   

 

 

 

 

20 4O 60 80 100 120 140 160 180 200

 

150 I I I I I I I I I
140L . ............... i . ...... -
130i ~~~~~~~~ 3 ----- , ' . : .. ....... . ........ 1

120» J .1 ,,,,,,,,

.5
d
0

Thickness (mm)
8 8

 

 

 

20 4O 60 80 100 120 140 160 180 200

Figure 5.16: The calculated thickness for indirect rapid tooling (a) without velocity
optimization; (b) with velocity optimization.

5.4.2 Suboptimal Velocity Verification

To increase the average metal thickness and decrease the metal thickness deviation,
the spray gun velocity is optimized using equation (3.36). Simulations are performed

using the optimized spray gun velocity. Figure 5.16(b) shows the simulation results

81

for the indirect rapid tooling process. The average, the maximum and minimum
metal thicknesses are 102.7, 80.1 and 120.4 mm, respectively. The average metal
thickness is increased from 93.4 mm to 102.7 mm, which is closer to the required
metal thickness (100 mm). The deviation of the metal thickness is decreased from
30% to 20%. The simulation results show the suboptimal velocity algorithm improves

the material distribution on a surface for the indirect rapid tooling process.

5.5 Verification of Tool Trajectory Integration

5. 5. 1 Spray Painting

A part with two flat patches is generated and rendered into triangles. The angle be-

tween the two patches is 30°. The part rendered into triangles is shown in Figure 5.17.

0.5

Height (m)

  

-0.5

 
 
 

Length (rn)
Width (m)

Figure 5.17: The part with two flat patches when a = 30°.

The paths of the part are generated for the PA-PA, PA-PE and PE—PE cases.
The optimized parameters are applied to calculate the paint thickness using equation

(3.34). Figure 5.18 shows the path and paint thickness for the PA-PA case; Figure

82

5.19 for the PA-PE case; and Figure 5.20 for the PE-PE case.

Height (m)

    

. vam ("1)
Width (m) -1 -1

 

882$
..

0|
()1
f

2:

Thickness (um)
u:
0
i i

35' i

 

 

 

50 100 150 200 250 300 350 400 450 500
Points
0))

Figure 5.18: Verification results for the PA-PA case: (a) the path; (b) the paint
thickness.

The maximum and minimum paint thicknesses for the three cases when a = 30°
are shown in Table 5.6.

The results shown in Tables 5.1 and 5.6 are quite close. This means the developed

trajectory integration algorithm can optimize the paint thicknesses. The optimization

83

Height (in)

 

 

Thickness (urn)

 

 

50100150200250300350400450500
Points

0))

Figure 5.19: Verification results for the PA—PE case: (a) the path; (b) the paint
thickness.

and verification results show that the optimized paint thickness for the PA-PA case
is quite uniform; the paint thickness for the PE—PE case is uniform too. The paint
thickness deviation from the required thickness is about 5pm. However, the paint
thickness for the PA-PE case is about 10pm. Thus, the PA-PE case should be avoided

in the tool trajectory planning.

84

Height (m)

-O.8 Length (m)

 

Width (m) I -1 -1

 

Thickness (um)

 

 

 

W50100150200250300350400450500
Points
(b)

Figure 5.20: Verification results for the PE—PE case: (a) the path; (b) the paint
thickness.

5. 5.2 Spray Forming

Since area density, instead of paint thickness, is considered for spray forming, the area
densities for the three paths shown in Figures 5.18, 5.19 and 5.20 are computed and
shown in Figures 5.21(a), 5.21(b) and 5.21(c), respectively. The maximum, minimum

and average densities are shown in Table 5.7. The area density deviations from the

85

Table 5.6: The simulation results

 

 

 

 

 

 

 

Case Minimum Maximum
thickness (pm) thickness (um)
PA-PA 47.6 51.6
PA-PE 41,6 59.5
PE—PE 47.5 53.0

 

 

required area density are quite small for the three cases. This means the three cases

can be used in the trajectory generation for spray forming without big difference.

Table 5.7: The simulation results

 

 

 

 

 

 

 

 

Case Average Minimum Maximum
area density (g/m2) area density (g/m2) area density (g/m2)
PA-PA 50.0 49.6 50.7
PA-PE 49.9 48.5 50.9
PE—PE 50.1 49.7 50.8

 

 

86

 

70 If I I I I’ I T I M

is?

Area Density (g/mz)
8

 

 

 

45 ’- ~
40 .
3G

50100150200250300350400450500
Points

(3)

7G I I I I I I I I I

 

a 8

Area denxity (W)
8

 

 

 

 

45L .
40’

35i-

w l l 1 L l A l 1 1

50 100 150 200 250 300 350 400 450 500
Points
0))

7c M I II I I I IT I W

65..- q
60* .

8

Area denxxty (g/m’)
8

 

 

 

45 .
40 - .
35 ~ , l
m 1 l 1 1 LL 1 L L 1
50 100 150 200 250 300 350 400 450 500
Points

(C)
Figure 5.21: The computed area densities for (a) the PA-PA case; (b) the PA-PE
case; (0) the PE—PE case.

87

CHAPTER 6
OPTIMAL TOOL PLANNING AND IMPLEMENTATION

This chapter discusses the Optimal tool planning for constant material distribution.
The algorithm for Optimal tool planning is developed. A preference articulation
method is discussed to control the preference Of the Objective functions. Simulations
are performed. The simulation results of four cases are presented: Optimal time,

Optimal material distribution, no preference articulation and preference articulation.

6.1 Optimal Tool Planning

The proposed technique for solving the optimal tool planning problem is based on
approximating the Optimization parameters as piecewise constants. The tool trajec-
tories are divided into segments. Figure 6.1 shows a path with P segments. Each
segment is further divided into smaller segments. It is assumed that the parameters

in the smaller segments are nearly constants.

 

Figure 6.1: A path is divided into segments.

In the derivative Of equation(3.34),

dq, d(] h 2 cosy, h. 2 cosy,
i Z _ — —“ = i — . 6.1
(It fit (li) 00539: f(r) (la) 608°92’ ( )

88

 

 

with
r,- = htandi. (6.2)
Suppose for each smaller segment, the spray angle 6, and deviation angle 7,- are nearly

constants. Then for the jth triangle on a free-form surface, its material thickness due

to the kth segment, which is divided into Mk smaller segments, can be written as:

2
COS’Yi

All: ‘
h
qjk : i=1 f(htan6,) (E) (308361- Atk. (0.3)

 

Therefore, the material thickness for the jth triangle is:

 

P M" h 2 cos'y- t
- = ht 6, — ' -——’“—. 6.4
q] 2:31;“ an )(li) cos3i9,-.M;C ( )

This equation can be written as:

 

 

(1,, h 2 cosy,-
qJ‘ — Z Mk’Uk Z f(htan0,) (l7) C0836i. (6.5)

P P d
r: it. = 2i. (6.6)

Then the Optimal time and material thickness tool planning is formulated as:
Given the CAD model of a free-form surface and a tool model, find the minimum
time to spray the surface such that the given constraints are satisfied, material thick-

ness deviation from the desired material thickness is minimized and the maximum

89

material thickness deviation is minimized, i.e.,

minJ = (Jl, J2, Js)

subject to: It], — dqd| _<_ Aqd

 

 

Mk
. cosvi
with qj= 2 Mi; Zfl htan6) (1h )2 00336 (6.7)
where
P
d
J1 = —"
k=1 1”“
N
J2 = 2013' ‘ CId)2
j=1
J3 : (Qmax — qd)2 + (qd _ Qmin)2 (68)

where N is the number Of triangles in a part. This is a constrained multi—objective

optimization problem. The Objective functions J1, J2 and J3 are conflicting with each
other. According to Appendix A, e,(:r) can be formulated using the given constraints,
i.e.,

edit) = Aqd — IQj - (Idl (6.9)

where a:=(v1, v2, ..., UP)T since the velocities are the Optimization parameters. Then

the method in Appendix A can be applied to solve the problem.

6.2 Preference Articulation

The method to solve the Optimization problem in Appendix A is a nO preference artic-
ulation method. The no preference articulation method does not use any preference
information. It is based on minimization Of the relative distance from a candidate
solution tO the utopian solution. Therefore, there is no control tO the preference Of

the Objective functions. TO control the preference Of the Objective functions, prefer-

90

ence articulation should be used. From equation (A3), the preference articulation is

developed,

W.) - i; (21);” '1”

i=1 3
subject to: 8(a)) = (el(:1:),e2(m), ...,e.,,,(:r:))T with e,(:1:) Z 0, i = ,...,m
a: = ($1,232, ...,:r,,)T (6.10)

Where wj is the weight,

k
ij = 1 (6.11)
j=1

6.3 Implementation and Results

Two parts, part of a car hood and a car door, shown in Figures 2.3 and 5.5(b),
respectively, are used to test the algorithm. The gun paths are shown in Figures 5.6(a)
and 5.6(c) for the car hood and door, respectively. The generated tool paths have
270 and 293 sampling points for the car hood and door, respectively. Thus, there
are 270 and 293 segments, respectively. Suppose the velocity in each segment is a
constant, there are 270 parameters (velocities) to be Optimized for the hood and 293
parameters for the door. Each segment is further divided into 10 smaller segments.
The optimization processes are performed to generate Optimal tool trajectories. In

the implementation, the maximum velocity is set to 800 mm/s.

91

6'- 3.] Optimal Tool Planning with Optimal Time

The Optimal tOOl planning with Optimal time is formulated as,

minJ 2 J1
subject to: Iqj — qdl S Aqd

P d Mk ’7, 2
k=l i=1 '

cosy,-

 

 

.12
60336,- (6 )

The optimization for the Optimal tool planning with Optimal time is performed.
Using the trajectory verification model (equation (3.34)), the material thicknesses on
the two parts are computed and shown in Figures 6.2(a) and 6.2(b), respectively. The
Optimized velocities are shown in Figures 6.3(a) and 6.3(b), respectively for the two
parts. The simulation results are summarized in Table 6.1. The maximum thickness

errors are within the given constraints.

Table 6.1: The results for optimal tool planning with Optimal time

 

 

 

 

 

 

 

 

Part Average Minimum Maximum Spray
thickness (um) thickness (um) thickness (um) time (8)

Hood 42.0 40.0 55.4 36.0

Door 42.1 40.0 50.1 42.1

 

92

 

Thickness (um)

Thickness (um)

Figure 6.2: The Optimized material thicknesses for the
Optimal time: (a) the car hood; (b) the car door.

 

80

 

 

 

 

 

30 .-
20 1 1 L L 1 l
0 200 400 800 1000 1200 1400
Points
(a)

80 I I I I I I

70 ~ «

60 ~ _

30-

 

 

 

 

20

200

400

93

600

800

Points

(13)

1000

1200 1400

Optimal tool planning with

 

1000 T

800*

700*

mMWwwaW

 

 

 

 

 

 

Velocity (mm/s)
§

 

 

 

 

 

 

 

 

 

50 100 1 50 200 250
Points

(80

1000

 

800'-

700*

 

 

Velocity (mm/s)
§

 

 

 

 

 

 

 

 

 

 

“WWWWWWW

200t-

 

 

100

 

50 100 150 200 250
Points

0))

Figure 6.3: The Optimized velocities for the Optimal tool planning with Optimal time:
(a) the car hood; (b) the car door.

94

5’- 3.2 Optimal Tool Planning with Optimal Material Distribution

The Optimal tool planning with Optimal material distribution is formulated as,

minJ 2 (J2, J3)

subject to: lqj — qd| g Aqd

 

P d M" h 2 cos)
. Z I: Z ’1'
With 43' = levk f(htan6,) (E) m (6.13)

The Optimization for the optimal tool planning with Optimal material distribution
is performed. Using the trajectory verification model (equation (3.34)), the material
thicknesses on the two parts are computed and shown in Figures 6.4(a) and 6.4(b),

respectively. The Optimized velocities are shown in Figures 6.5(a) and 6.5(b), respec-
tively for the two parts. The simulation results are summarized in Table 6.2. The

maximum thickness errors are within the given constraints.

Table 6.2: The results for the Optimal tool planning with Optimal material distribution

 

 

 

 

 

 

 

 

Part Average Minimum Maximum Spray
thickness (um) thickness (um) thickness (jam) time (8)

Hood 50.0 41.7 57.9 45.9

Door 50.0 46.3 55.4 48.4

 

95

 

 

 

 

 

 

 

80 I If I I I
60": ‘i
’E‘
3
is ‘
.9
if
40 ..
30* s
20 l l 1 1 I l
0 200 400 600 800 1000 1200 1400
Points
(8)
80 f I I I I I
70*
60" .................. .1

Thickness (um)

 

 

 

 

30 - -
20 1 L 1 1 M A
0 200 400 600 800 1000 1200 1400
Points
0))

Figure 6.4: The Optimized material thicknesses for the Optimal tool planning with
Optimal material distribution: (a) the car hood; (b) the car door.

96

 

10% I r I M I

 

   

 

 

 

 

 

 

 

 

 

900- .
8m- . . i. .1
A 700» . ~
E
E 500» .
.3
3 500- -
‘76
>
100 4
o l 1 1 l 1
50 100 150 200 250
Points
(3)
1000 I v I r y
gmL... . ..... .. '. ...... ..,
800~ . .
700 ~
1:?
E 600- .
.B‘
Q 500- ~
§
400* 1 I
200- 4
1m 1 I. I J I
50 100 150 200 250
Points
0))

Figure 6.5: The Optimized velocities for the Optimal tool planning with Optimal ma-
terial distribution: (a) the car hood; (b) the car door.

97

6'- 3.3 Optimal Tool Planning with No Preference Articulation

The no preference articulation Of Optimal tOOl planning can be formulated using equa-
tions (6.7) and (A4). The Optimization for the Optimal tOOl planning with no pref-
erence articulate is performed. Using the trajectory verification model (equation
(3 - 34)), the material thicknesses on the two parts are computed and shown in Figures
6 - 6(a) and 6.6(b), respectively. The optimized velocities are shown in Figures 6.7(a)

and 6.7(b), respectively for the two parts. The simulation results are summarized in

Table 6.3. The maximum thickness errors are within the given constraints.

Table 6.3: The results for Optimal tool planning with nO preference articulation

 

 

 

 

 

 

 

 

Part Average Minimum Maximum Spray
thickness (,um) thickness (um) thickness (um) time (5)

Hood 49.8 41.5 58.1 41.0

Door 49.8 45.8 55.3 46.4

 

98

 

 

70r * . , d

 

Thickness (urn)

 

 

 

 

 

30 ,. q
20 1 1 1 1 1 1
0 200 400 600 800 1000 1200 1400
Points
(a)
80 I I I I I
70 ~ - ~
60 h -4

Thickness (um)
2;

 

 

 

40 r -
30 r .
20 1 L 1 l 1 1
0 200 400 600 800 1000 1200 1400
Points
(*3)

Figure 6.6: The Optimized material thicknesses for the Optimal tool planning with no
preference articulation: (a) the car hood; (b) the car door.

99

 

1000

8CD“ r—

700-

Velocity (mm/s)
§

 

 

 

 

 

 

 

 

 

 

 

 

200~

 

 

 

50 100 150 200 250
Points

(3)

 

Velocity (mm/s)

 

 

 

 

 

 

 

 

 

 

 

 

:Qmwwwdqwmwixlp

200*-

 

 

 

1 m 1 1 J 1 1
50 1 00 1 50 200 250
Points

0))

Figure 6.7: The Optimized velocities for the Optimal tOOl planning with no preference
articulation: (a) the car hood; (b) the car door.

100

6. 3.4 Optimal Tool Planning with Preference Articulation

The preference articulation Of Optimal tool planning can be formulated using equa-
tions (6.7) and (6.10). The Optimization for the Optimal tOOl planning with preference

articulate is performed. The weights are set to:

101 = 0.8, 102 = 0.1, 103 = 0.1 (6.14)

Using the trajectory verification model (equation (3.34)), the material thicknesses
on the two free-form surfaces are computed and shown in Figures 6.8(a) and 6.8(b),
respectively. The Optimized velocities are shown in Figures 6.9(a) and 6.9(b), respec-
tively. The simulation results are summarized in Table 6.4. The maximum thickness

errors are within the given constraints.

Table 6.4: The results for Optimal tool planning with preference articulation

 

 

 

 

 

 

 

 

Part Average Minimum Maximum Spray
thickness (,um) thickness (,um) thickness (,um) time (3)

Hood 49.2 40.0 58.4 40.1

Door 49.3 41.1 55.4 44.9

 

101

 

 

 

 

Thickness (um)
53

 

 

 

20 l l l l 1
0 200 400 600 800 1000 1200 1400

 

Thickness (um)
83

40» . .. .

 

l l

 

 

2 l L L 1
00 200 400 600 800 1000 1200 1400

Points
0))

Figure 6.8: The optimized material thicknesses for the Optimal tool planning with
preference articulation: (a) the car hood; (b) the car door.

102

 

Velocity (mm/s)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 1 00 150 200 250
Points

 

Velocity (mm/s)

 

 

 

 

 

 

 

 

 

 

 

 

 

:wwwwwwup

 

 

 

50 100 150 200 250
Points

0))

Figure 6.9: The Optimized velocities for the Optimal tOOl planning with preference
articulation: (a) the car hood; (b) the car door.

103

6.3.5 Comparison among the Methods

The implementation results summarized in Tables 6.1, 6.2, 6.3 and 6.4 Show that
the maximum material thickness deviation is less than or equal to 10am for both
parts. The material distribution constraints are satisfied. The Optimal tool plan-
ning with Optimal time takes less time tO spray a part, 36 s and 42.1 s for the car
hood and door, respectively. However, the maximum material thickness deviation is
about 10 pm. The Optimal tOOl planning with Optimal material distribution has the
smallest material thickness deviation. However, it takes the longest time to spray
the parts, 45.9 s and 48.4 s for the car hood and door respectively. For the Optimal
tOOl planning with no preference articulation and preference articulation, the average
material thickness is quite close to the desired material thickness and also takes less
time to spray the parts compared to the Optimal tool planning with optimal material
thickness and has better material distribution compared tO the Optimal tool planning
with Optimal time. With the preference set to time, the Optimal tool planning with
preference articulation takes less time to spray the parts compared to the Optimal
tool planning with no preference articulation. Therefore, the weight can be set to
adjust the preference in the Optimal tool planning. These results are consistent with

theoretical analysis.

104

CHAPTER 7
OPTIMAL TOOL PLANNING FOR NON-UNIFORM
MATERIAL DISTRIBUTION

This chapter discusses the Optimal tOOl planning with non-uniform material distribu-
tion. The algorithm for Optimal tool planning with non-uniform material distribution
is developed. Simulations are presented. The results of Optimal tool planning for four
cases are presented and compared: optimal time, Optimal material distribution, no

preference articulation and preference articulation.

7 .1 Optimal Tool Planning for Non-uniform Material Distri-
bution

TO generate a tOOl path for a free-form surface, the spray width has tO be deter—

mined. For a non—uniform material distribution, it is challenging to Obtain the spray

width. Since the desired non-uniform material thickness is given, the average material

thickness on a surface can be calculated:

N
_ Ejzlqdj(xj7yjtzj($jayj))

 

7d — N , (7.1)
or the area-weighted average material thickness can be computed:
N
_ _ 2,21qdj(a:j,yj,zj(:rj.yj))sj (7 2)

 

V
2;.21 8]”

where gab-(:9, yj, zj($j, y,)) is the material thickness at a point (x), y,-, zj(.rj, yj)) on a
free-form surface and 83- is the area with the material thickness.
Once the average material thickness or area-weighted average material thickness

is Obtained, an Optimization process for spraying a plane in Section 3.2 is applied to

105

determine the spray width. After the spray width is found, an improved bounding
box method in Section 3.5.1 is applied to generate a tOOl path for a free-form surface.

Similar to the algorithm in Chapter 6, the Optimal time and material distribution
deviation tOOl planning with non-uniform material distribution can be formulated as:

Given the CAD model of a free-form surface, a tool model, find the minimum time
to spray the surface such that the given constraints are satisfied, material deviation
from the desired material thickness is minimized and the maximum material thickness

deviation is minimized, i.e.,

min] = (J1,J2,JB)

subject to: lg, - qd(:z:, y,z z,(:i: y))l < A0101? 9,205.30)
P Mk

(1 . ,-
with qJ-z 2M 160;:sz (htan6,) )G )2 66:93,; (7.3)
1i 8 i

 

 

where

1:
=20 q-—qd(rvy,z zrv( ,y)))2,

(AIM . (7.4)

Aqmar is the maximum material deviation.
This is a constrained multi-Objective Optimization problem. The Objective func-
tions J1, J2 and J3 are conflicting with each other. According to Appendix A, e,(:r)

can be formulated using the given constraints, i.e.

81(1) = Antes 2(17. 31)) - lqj - (1.10: y. z(.r,y))l (7-5)

where :l:==(vl, vg, v19)T since the velocities are the Optimization parameters. Then

106

the method in Appendix A can be applied to solve the problem.

7 .2 Implementation and Results

Two parts, part Of a car hood and a car door, shown in Figures 2.3 and 5.5(b),
respectively, are used to test the algorithm. The gun paths are shown in Figures 5.6(a)
and 5.6(c) for the car hood and door, respectively. The generated tool paths have
270 and 293 sampling points for the car hood and door, respectively. Therefore, there
are 270 and 293 segments, respectively. Suppose the velocity in each segment is a
constant, there are 270 parameters (velocities) to be Optimized for the hood and 293
parameters for the door. Each segment is further divided into 10 smaller segments.
Then the Optimization processes are performed to generate Optimal tool trajectories.

The desired material thickness could be any values on a free-form surface. TO
implement the developed algorithm, a desired material thickness is computed based
on the bounding box Of a part. The points on the part are projected to the bottom
plane Of the bounding box in Figure 3.12. The center point PC is found. Then a

non-uniform material distribution is formulated:

qd(d) = 10(1 —12) + (IdO (7.6)

where l is the distance Of the projected points to PC and qdo a constant. Here, qdo is
set to 41.5 pm for the car hOOd and 42.5 pm for the door to get the average material
thickness 50 ,um. Figure 7.1 shows the material thicknesses on the X-Y plane for the
car door and hood, respectively.

Once the desired non-uniform material thickness is determined, the average ma-
terial thickness can be calculated using equation (7.1) or (7.2). Here equation (7.1)
is used. The parameters used in the implementation are the same as those in Section

5.1.1. In the implementation, the maximum velocity is set to 800 mm/s.

107

Desired Thickness (urn)

 

 

Y (m) o 0.5 x (m)

Desired Thickness (urn)
6:
1

 

 

 

Figure 7.1: Desired non—uniform material thicknesses for: (a) a car hood; (b) a car
dOOL

108

7.2.1 Optimal Tool Planning with Optimal Time

The Optimal tOOl planning with Optimal time is formulated as,

mth = .11

subject to: Iqj — dqd(:r, y,z($ y))l < AleT yazlxvyll
Mk
‘ 60.37%
With qj= ICE: 1”:ka ,1: f( htan6) )(Z)2 c0536i' (7.7)

 

 

The Optimization for the Optimal tool planning with Optimal time is performed.
Using the trajectory verification model (equation (3.34)), the material thickness on
the two free—form surfaces are computed and shown in Figures 7.2(a) and 7.2(b),
respectively. The Optimized velocities are shown in Figures 7.3(a) and 7.3(b), respec-
tively. The simulation results are summarized in Table 7.1. The maximum thickness

errors are within the given constraints.

Table 7.1: The results for Optimal tOOl planning with optimal time

 

 

 

Part Average Maximum thickness Spray
thickness (um) error (um) time (5)

Hood 42.3 10.0 35.8

Door 42.1 10.0 39.5

 

 

 

 

 

 

109

Thickness (um)
8 81 8 a 8 8: 8 8

.0
a:

 

y (m) 0 0.5 X (m)

8%

Thickness (urn)
a

b
O

‘88

 

(b)

Figure 7.2: The Optimized material thicknesses for the Optimal tOOl planning with
Optimal time: (a) the car hood; (b) the car door.

110

 

 

 

 

Velocity (mm/s)

 

 

 

 

 

 

 

 

 

200-... . .. ., . .. ............. _.

 

 

 

1 1 1 1 1 1
00 50 100 150 200 250
Points

(3)

 

1000

800*
700*

600" . , ..... . _ ..... ....,

izwlhllnhwt

3mg j .. ....... .' .......... . ; .......

 

 

Velocity (mm/s)

 

 

 

 

 

 

 

 

 

200*

 

 

 

1 m 1 1 1 1 M
50 100 150 200 250
Points

0))

Figure 7.3: The Optimized velocities for the Optimal tool planning with optimal time:
(a) the car hood; (b) the car door.

111

7.2.2 Optimal Tool Planning with Optimal Material Distribution

The Optimal tool planning with Optimal material distribution is formulated as,

minJ 2 (J2, J3)

subject to: |qj — d,qd(:r y,z(:z:, y))| < ACMCF 31,413,?!»

Mk
, C0873
t . .
With qj= E: INIkkUk :1 f( (h an6) )(— f)2 c0336,- (7 8)

 

 

The Optimization for the Optimal tOOl planning with Optimal material distribution
is performed. Using the trajectory verification model (equation (3.34)), the material
thicknesses on the two parts are computed and shown in Figures 7.4(a) and 7.4(b),
respectively. The Optimized velocities are shown in Figures 7.5(a) and 7.5(b), respec-
tively for the two parts. The simulation results are summarized in Table 7.2. The

maximum thickness errors are within the given constraints.

Table 7.2: The results for the Optimal tool planning with Optimal material distribution

 

 

 

 

Part Average Maximum thickness Spray
thickness (um) error (um) time (8)

Hood 50.0 8.1 45.6

Door 49.8 5.1 46.6

 

 

 

 

 

112

Thickness (um)
8 8i 8 a 8 8: 8 8%

.0
a:

 

Thickness (um)

 

Figure 7 .4: The optimized material thicknesses for the optimal tool planning with
optimal material distribution: (a) the car hood; (b) the car door.

113

 

 

 

 

 

 

 

 

 

 

 

 

1% j I 7 Y I
900" .
800* w <
7m” , -4
’0? ‘.
E 600» ,
g l
3
o
> I!
g i
G l 1 l 1 l
50 100 150 200 250
Points
(3)
1000 T 7 I Y I
9m,_ ...... .4
amp , rrrrrr ,, "f' , . .. .‘
A 700,. ‘ : . .
«n :
E
g 600r
.3”
m V ,
> » g
400- 1
200,. ,,,,,,,,,, 1 V ..... ..z
1w 1 l l 1 L
50 100 150 200 250
Points
(1))

Figure 7.5: The optimized velocities for the optimal tool planning with optimal ma-
terial distribution: (a) the car hood; (b) the car door.

114

7.2.3 Optimal Tool Planning with No Preference Articulation

The no preference articulation of optimal tool planning can be formulated using equa—
tions (7.3) and (A4). The optimization for the optimal tool planning with no pref-
erence articulation is performed. Using the trajectory verification model (equation
(3.34)), the material thicknesses on the two parts are computed and shown in Figures
7.6(a) and 7.6(b), respectively. The optimized velocities are shown in Figures 7.7(a)
and 7.7(b), respectively. The simulation results are summarized in Table 7.3. The

maximum and the minimum thickness errors are within the given constraints.

Table 7.3: The results for the optimal tool planning with no preference articulation

 

 

 

Part Average Maximum thickness Spray
thickness (,am) error (pm) time (5)

Hood 49.9 8.2 41.7

Door 49.3 . 8.9 44.9

 

 

 

 

 

 

115

Thicknessmm)
8 8’- 8 is 8 a 8 8:

.0
a

Thickness (um)
8 g 8 8!

.8833

 

Figure 7.6: The optimized material thicknesses for the optimal tool planning with no
preference articulation: (a) the car hood; (b) the car door.

116

 

1“” r fi fi f
900"

7m. 7 .1, ,,,,,, . . ,. .:, 1

 

 

 

 

 

 

 

 

 

 

Velocity (mm/s)
§

 

 

:uttuuuuatuti;

200- : ,

 

 

 

50 100 150 200 250
Points

 

1000
9“)... .........
800» l

:LJwWUwaquUU

200*

Velocity (mm/s)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 100 150 200 250
Points

(b)

Figure 7.7: The optimized velocities for the Optimal tool planning with no preference
articulation: (a) the car hood; (b) the car door.

117

7. 2.4 Optimal Tool Planning with Preference Articulation

The preference articulation of optimal tool planning can be formulated using equa-
tions (7.3) and (6.10). The optimization for the optimal tool planning with preference

articulate is performed. The weights are set to:

w1 = 0.8, mg = 0.1, w3 = 0.1. (7.9)

Using the trajectory verification model (equation (3.34)), the material thicknesses on
the two parts are computed and shown in Figures 7.8(a) and 7.8(b), respectively.
The optimized velocities are shown in Figures 7.9(a) and 7 .9(b), respectively. The
simulation results are summarized in Table 7.4. The maximum and the minimum

thickness errors are within the given constraints.

Table 7.4: The results for the optimal tool planning with preference articulation

 

 

 

 

 

 

 

 

Part Average Maximum thickness Spray
thickness (um) error (um) time (3)

Hood 49.2 10.0 40.0

Door 49.0 10.0 44.5

 

118

 

 

v (m) o 0.5 x (m)

(a)

 

 

Y (m) 0.8 2 X (m)

Figure 7.8: The optimized material thicknesses for the optimal tool planning with
preference articulation: (a) the car hood; (b) the car door.

119

 

900* .4
m n W‘
700-

Velocity (mm/s)
§

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200*
100%
G l 1 l l l
50 100 150 200 250
Points
(a)

1m 7 1 T T T

9w... ..................................

800-

ml , «
73‘
E SW.— . .................................. .1
_8 5m . . . . .. . ..
o .
> : E

4w» ...... _ ....... . j ..... . - ..... U .7 .4

WNMWULMh4613kJ

200~ , - , _

1m 1 1 1 1 l

50 100 150 200 250
Points
(b)

Figure 7.9: The optimized velocities for the optimal tool planning with preference
articulation: (a) the car hood; (b) the car door.

120

 

7.2.5 Comparison among the Methods

The implementation results summarized in Tables 7.1, 7.2, 7.3 and 7.4 show that
the maximum material thickness deviation is less than or equal to 10pm for both
parts. The material distribution constraints are satisfied. The Optimal tool planning
with optimal time takes less time to spray a part, 35.8 s and 39.5 s for the car hood
and door, respectively. However, the average material thickness deviation is about
10 um. The optimal tOOl planning with optimal material distribution has the smallest
material thickness deviation. But it takes the longest time to spray the parts, 45.6 s
and 46.6 s for the car hood and door, respectively. For the optimal tool planning with
no preference articulation and preference articulation, the average material thickness
is close to the desired material thickness and also takes less time to spray the parts
compared to the optimal tool planning with optimal material distribution and has
better material distribution compared to the optimal tool planning with optimal
time. With the preference set to time, the optimal tOOl planning with preference
articulation takes less time to spray a part compared to the optimal tOOl planning
with no preference articulation. Therefore, the weights can be set to satisfy the needs

in Optimal tool planning. These results are consistent with theoretical analysis.

121

 

CHAPTER 8
EXTENSIONS OF THE GENERAL FRAMEWORK

The developed general framework can also be extended to other applications. This
chapter presents the extensions Of the general framework to dimensional inspection

and nanomanufacturing.

8.1 Extension to Dimensional Inspection in Manufacturing

Dimensional inspection is an important process in manufacturing industry. Quality
and process control activities require that parts be measured, or dimensionally in-
spected [42]. Inspection generally is time—consuming, which has been creating serious
bottlenecks in production lines [43]. Active Optical inspection techniques have been
developed and greatly reduces the time in dimensional inspection. Structured light,
which Obtains 3D coordinates by projecting specific light patterns on the surface of an
object, is one Of the active methods and it has been successfully implemented in vari-
ous applications [44]. However, to achieve full automation and improve the efficiency
of the inspection system, sensor planning, or finding the suitable configurations of
sensors is very important so that the inspection task can be carried out satisfactorily.
It is, therefore, highly desirable to develop a camera positioning system that is able to
plan and realize the camera configurations in a fully-automated, accurate and efficient
way. The general framework (Section 2.1) can be applied to generate a camera path
for the dimensional inspection Of a part. Sheng [28] developed a CAD-guided robot
motion planning system for dimensional inspection in manufacturing. The system is

one Of the extensions Of the general framework.

122

 

8.2 Extension to N anomanufacturing

8. 2. 1 Introduction

Nanotechnology, a promising advanced technology for the forthcoming century, has
been a recent hot research topic. The deveIOpment Of nanomanufacturing technolo-
gies will lead to potential breakthroughs in manufacturing Of new industrial products.
Nanoscale products with unique mechanical, electronic, magnetic, Optical and/or
chemical prOperties, Open the door to an enormous new domain of nanostructures
and integrated nanodevices. They have a variety Of potential applications such as na-
noelectromechanical systems (NEMS) and DNA computers etc. Nanomanufacturing
requires positioning Of nanoparticles in complex 2D or 3D structures. The techniques
for nanomanufacturing can be classified into “bottom-up” and “top-down” methods.

Self-assembly in nanoscale is a promising “bottom-up” technique which is applied
to make regular, symmetric patterns of nanoparticles [45]. However, many potential
nanostructures and nanodevices are asymmetric patterns, which cannot be manufac-
tured using self-assembly.

A “top-down” method is desirable to fabricate complex nanostructures. Atomic
force microscopy [46] has been proven to be a powerful technique to study sample
surfaces down to the nanometer scale. Not only can it characterize sample surfaces,
but it can also change the sample surface through manipulation [47, 48], which is
a promising “top-down” nanofabrication technique. In recent years, many kinds of
nanomanipulation schemes have been developed [49, 50, 51] to position and manip-
ulate nanostructures. The main problem Of these manipulation schemes is that they
go through the scan-design-manipulation-scan cycle manually, which is time consum-
ing and makes mass production impossible. Recently, some researchers have been
trying to combine an atomic force microscope (AF M) with haptic techniques and

a virtual reality interface to facilitate nanomanipulation [52, 53]. Although virtual

123

 

reality, which can display a static virtual environment and a dynamic tip position,
has been constructed, it does not display any environment changing due tO manipu-
lation. Therefore Operators are still blind because they cannot see the environment
changing in real-time. The manual manipulation of nanoparticles also reduces the
manipulation speed.

The complexity of nanomanufacturing requires positioning, manipulating and as-
sembling nanoparticles to form a given pattern. Typical manual nanomanipulation
is complex and time-consuming. Also, the paths are Obtained in an interactive way
between the users and the AF M images, which is inefficient. In order to increase
efficiency in nanomanufacturing, automated manipulation using collision-free paths
is necessary because particles are randomly distributed on a surface. Automated path
planning is crucial to manufacture nanostructures and nanodevices. However, auto—
mated tool path planning for nanomanufacturing does not receive much attention.
Makaliwe [54] developed a path planning algorithm for nanoparticle assembly. Ob—
ject assignment, Obstacle detection and avoidance, path finding and sequencing are
addressed. The obstacles discussed in the paper are polygons, which do not occur Of-
ten in nanoworld. Also the collision Of nanoparticles during nanomanipulation is not
discussed. In AFM manipulation, indirect path around obstacles should be avoided
since manipulation using indirect path may lose nanoparticles. Therefore, direct path
is desirable for nanomanipulation. TO generate a path for nanomanufacturing, Obsta-
cle avoidance has to be considered. A combination Of both theoretical (analytical and
computational) and experimental methodologies is appropriate to address the under-
lying necessities for nanomanufacturing. The developed general framework (Section

2.1) can be applied for the tool path generation in nanomanufacturing.

124

 

8.2.2 Automated Nanomanipulation System

An automated nanomanipulation system has been developed to manipulate nanopar-
ticles to manufacture nanodevices and nanostructures automatically. Figure 8.1 shows

the automated nanomanipulation sytem.

 

 

AFM Image .

CAD Model

4—[\..\

r‘_ ______~v
|

ToOl—tha
l Planner [

   

 

 

 

 

 

 

 

 

 

 

Control 8' 1 ti Real-time
mu 3 on dis 1a

Real-time

Operation

   

Force

 

 

 

 

 

 

 

 

 

Figure 8.1: A general framework for nanomanufacturing.

Based on the CAD model of a nanopart and an AFM image of a surface with
nanoparticles, a collision-free path is generated to manufacture the nanopart. After
the path is generated, it is input to a nanomanipulation system assisted by augmented
reality tO perform the actual manufacturing process.

During nanomanipulation, it is desirable for the Operator to Observe the real-time
changes Of the nanO-environment. Previous nanomanipulation using AFM has been
blind work. Each operation is designed Off-line based on a static AFM image and then
downloaded to the AFM system to visualize the Operation in Open loop. Whether
the Operation is successful or not has to be verified by a new image scan. Obviously,
this scan-design-manipulation-scan cycle is very time-consuming because it usually
takes several minutes to Obtain a new AFM image. Therefore, an augmented reality
system [55] has been developed to provide Operators with real-time visual display.
The real-time visual display is a dynamic AFM image of the Operating environment

which is locally updated based on real-time force information. Here the augmented

125

reality system is adopted to perform the nanomanufacturing process.

8.2.3 A General Framework

A general framework for the path planning is tO find a path based on the CAD
model of a 2D part and an AFM image Of particles. Path planning is to plan the tip
position and orientation of an AFM. A general framework of automated CAD-guided
path planning for nanomanufacturing can be formulated as follows:

Given the CAD model of a 2D nanopart M and an AFM image of a surface Q,

find a path P such that the nanopart can be manufactured using an AFM, i.e.,

F(M,Q) = r. (8.1)

 

 

 

 

 

 

 

CAD Model
a. Tool
AFM Ima e Path
g Path Simulation
W Planner

  

 

 

 

 

 

 

 

l l..—

 

 

Figure 8.2: A general framework for the automated CAD-guided path planning sys-
tem.

Figure 8.2 is the illustration of the general framework. Based on the CAD model
of a 2D part and the AFM image, the path planner generates a path automatically to
manufacture the part. The path is input to a simulation software to verify if the path

can manufacture the part without any collisions. Finally, the path is implemented to

126

 

manufacture a nanodevice or nanostructure.
The tool path planner is the core of the general framework. Figure 8.3 shows the

steps for the tip path planner. Based on the CAD model Of a nanopart and an AF M

 

CAD model and a surface with nanoparticles

3
Identify objects and obstacles

3

Generate direct paths

I

Generate virtual objects and destinations

I
Connect paths

5
Tool path

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 8.3: Tip path planner.

image of a surface with particles, Objects and obstacles are identified. After that,
direct paths are generated. Then, virtual Objects and destinations are generated to

avoid Obstacles. Paths are connected to form an AF M tip path.

CAD Model

Since nanoparticles are manipulated to manufacture nanostructures or nanodevices,
a part has to be designed using the nanoparticles. Based on the average size Of
nanOparticles, nanostructures and nanodevices are designed. Figure 8.4 shows a de-

signed nanostructure.

127

 

 

Vx

 

 

Figure 8.4: A designed nanopart.
Object and Obstacle Identification

An image of a surface with nanoparticles can be Obtained using an AFM in the
tapping mode. The data of the X Y coordinates and height Of each pixel are saved to

a data file. Figure 8.5 shows the raw data from an AFM.

 

Figure 8.5: The raw data from an AFM.

Since the surface is not completely fiat, a threshold height value is set for particle
identification. If the height of a pixel is larger than the threshold, it is considered
as an element of a particle. The particles can then be identified and the size Of each

particle can be determined. If the size Of a particle is too large, it is difficult for the

128

 

AF M tip to manipulate it. If the size Of a particle is too small, it is better not to be
used as a component of a nanostructure since it may cause gaps between components.
Therefore, the size of a particle must be in a certain range to be considered as an
Object, which is good for manufacturing nanodevices or nanostructures; otherwise, it

is an Obstacle, i.e.,

Obstacle 3,, S (11 or 5,, 2 a2
Particle = . (8.2)

Object 01 < 5,, < 012

8.2.4 Automated Tool Path Planning

Once the destinations, Objects and Obstacles are determined, a collision-free path can

be generated to manufacture a nanostructure or nanodevice.

Direct Path

A direct path is a connection between an Object and an Obstacle using a straight line.
After the Objects and obstacles are identified, each Object is connected with each
destination using a straight line. Figure 8.6 shows the connection. The path between
O2 and D2 is a direct path; the path between 01 and D1 is not a direct path due to

collision.

 

 

 

 

Figure 8.6: The straight line connection between an object and an destination. 01
and 02 are Objects; D1 and D2 destinations; S1 is an Obstacle.

129

 

Due to the van der Waals force between an Object and an obstacle, the object
maybe attracted to the Obstacle if the distance between the Object and the Obstacle
is tOO small. Therefore, the minimum distance has to be determined first to avoid

the attraction. Figure 8.7 shows an object and an Obstacle.

Object fbstacle

   

Fc
‘

 

A
W

 

Figure 8.7: The van der Waals force between an Object and an Obstacle. R1 and R2
are the radius Of the two spheres, respectively; D is the distance between the two
spheres; Fw van der Waals force; E; the friction force.

Suppose all Objects and Obstacles are spheres, then the van der Waals force can

be expressed as [56]:
_ —A 12le
_ GU a1 + R2

 

Fw (8.3)

where Fw is the van der Waals force; A the Hamaker constant; D the distance between
the two spheres; R1 and R2 are the radius of the two spheres. Different materials
have different Hamaker constants. Nevertheless, the hamaker constants are found to
lie in the range (0.4 — 4)10‘19 J. If an Object is not attracted to an Obstacle, the van
der Waals force has to be balanced by the friction force as shown in Figure 8.7. The
friction force is caused by the repulsive and adhesive forces and can be formulated as
[57]:

FC = #03ng + VFSS (8.4)

where Fe is the friction force; has the sliding friction coefficient between an Object
and the substrate surface; 1/ the shear coefficient; F; the repulsive force and F;

the adhesive force. When pushing an Object, the repulsive force equals to 0. Then

130

 

equation (8.4) becomes

F, = urgs. (8.5)

The adhesive force F :5 can be Obtained using the tip adhesive force F a which can be

ts?

measured [57] :

A
F“ = —°—s-F“‘ .6
03 Ats ts (8 )

where A0, is the nominal contact area between an Object and a substrate surface; At,
the nominal contact area between the AFM tip and the substrate surface.

Since the van der Waals force has to be balanced by the friction force during
manipulation, the minimum distance Dmin can be calculated using equations (8.3,

8.5, 8.6):
A R1R2 Ats

Dmin : _ -
6 R1 + R2 111403th

 

(8.7)

The distance between an Object and an obstacle must be larger than Dmin during
manipulation. If there is an Obstacle which is close or on the straight line, the path
formed by the straight line is not considered as a straight path. For example, the
path between O2 and D1 in Figure 8.6 is not a direct path due to attraction. This
means any obstacle cannot block the connection between an object and a destination

if there is a direct path.

Virtual Objects and Destinations

After the direct paths are generated, Objects are assigned to the destinations one by
one. One Object is assigned to one destination and vice verse. After the Objects are
assigned to the destinations, there are some destinations which may not have any
Objects assigned to them. Thus, paths that avoid the Obstacles have to be generated.
In nanO—manipulation, the scanning time is much longer than the manipulation time.
A surface has to be scanned again if an Object is lost during manipulation. Therefore,

the planned path should avoid losing Objects during manipulation. A path with turns

131

L

as shown in Figure 8.8 with much higher possibility of losing Objects than a direct

path. Therefore turns should be avoided during nanomanipulation.

 

 

 

 

 

 

Figure 8.8: An object may be lost during turns. 01 is an object; D1 a destination
and S1 an Obstacle

A virtual object and destination algorithm is developed to solve the problem.

Figure 8.9 shows a virtual Object and destination (VOD).

 

    

. SI
‘5' ‘.
1
4‘ ".
.

01 ”1

 

 

U

Figure 8.9: A virtual Object and destination (VOD) connects an Object and a desti-
nation. Ol is an Object; D1 a destination; 81 an Obstacle and V1 a VOD.

 

The Object and the destination are connected using direct paths through the VOD.
Since there are many possible VODs to connect an object and a destination, minimum
distance criterion is applied to find the minimum distance VOD. The total distance

to connect an Object and a destination is,

 

 

‘1 = \/(-’32 — 4730)? + (U2 — 310):2 + \/(-F2 — $02 + (312 — 91)2 (88)

where 1:;, yg are the coordinates of the center of a VOD; 170,310 the coordinates of the

center of an Object; .171, yl the coordinates Of the center Of a destination.

132

The connections between the VOD, Object and destination have to avoid the

Obstacles, i.e.,

 

\/(.’II - $3)2 + (y —‘ ys)2 2 Dmm + R1+ R2 (8.9)

where :13, y are the coordinates Of the object center along the path; 233,318 the coor-
dinates of the center Of the Obstacle. Then a constrained optimization problem is

formulated:

 

gig/r; d = \/($2 - $0)2 + (312 - yo)2 +
\/(.'132 — $1)2 + (92 — 311)2

subject to: \/(;r: — 93,)2 + (y — us)2 2 Dmin + R1+ R2 . (8.10)

 

 

This is a constrained optimization problem. A quadratic loss penalty function method
[58] is adopted tO deal with the constrained Optimization problem. This method

formulates a new function C(m):

min G = min d + 6 (min[0,g])2 (8.11)

12,312 172,112

where 6 is a big scalar and g is formulated using the given constraints, i.e.,

 

g = \/(.’E — $3)2 + (y — y3)2 — (Dmin + R1+ R2). (8.12)

Then the constrained optimization problem is transferred into an unconstrained one
using the quadratic loss penalty function method. The pattern search method [59]
is adopted here to Optimize the unconstrained Optimization problem to Obtain the
VOD.

If one VOD cannot reach an unassigned destination, two or more Vods can be

found to connect the Object and destination. Figure 8.10 illustrates the process.

133

 

Similarly, a constrained Optimization problem can be formulated to compute the

 

 

 

 

 

Figure 8.10: Two VODs connect an Object with a destination. 01 is an object; D1
the destination; SI and S2 are Obstacles.

VODs

Path Connection

When an Object is manipulated to a destination, the destination becomes an Obstacle
(Destination Obstacle). Before an object is pushed to a destination, it could be an
Obstacle for other objects (Object Obstacle). The following definitions are used to

find a collision—free path for nanomanufacturing.

Definition 8.2.1 Object Priority Index (OPI) of an object is the number of

objects, which are obstacles along the path between the object and a destination.
The minimum OPI (MOPI) is 0.

Definition 8.2.2 Destination Priority Index (DPI) of a destination is the num-
ber of destinations, which are obstacles along the path between the destination and an

object.

For a destination, minimum destination priority index (MDPI) can be defined.

Definition 8.2.3 The MDPI ofa destination is the minimum DPI among all DPIs.

134

For all destinations, the maximum MDPI (MMDPI) can be found.
Definition 8.2.4 The MMDPI is the maximum value of all MDPIs.

Criterion: The destination with the MMDPI is filled with an object with the
highest priority.

The following theorem can then be formulated:

Theorem 8.2.1 There is no obstacle between an object with M OPI and a destination
with MMDPI.

Proof. According to the direct path, there is no actual Obstacle between them.
If there is an object Obstacle 0 between the Object A and destination V as shown
i I). Figure 8.11(a), then the OPI Of 0 must be less than that Of A. This is contrary to
t hat the OPI Of A is the minimum.
If there is an destination obstacle D between them as shown in Figure 8.11(b), D
must be filled before V. According to the Criterion, the MDPI Of D must be larger

than that Of V. This is contrary to that the MDPI Of V is the maximum. <1

 

 

01
(a)
D1 D2
0 -------------- a: ----------- *
01

(b)

Figure 8.11: (a) Object Obstacle; (b) Destination obstacle.

In path generation, the Objects are assigned to the destinations using the minimum

distance temporarily. Assume the number Of objects is larger than or equal to that

135

Of destinations. One Object is assigned only to one destination and vice versa. After
that, destinations with MMDPI are found first. Then one Of the destinations is chosen
and one object with MOPI to the destination is assigned to it. Figure 8.12 shows the
process to assign an Object to a destination.
D1
03 *
0 D3

0
02 *DZ

01

Figure 8.12: The assignment of an object to a destination.

After an Object is assigned to a destination, a path is generated. Then all Of the
indices are updated and the path generation algorithm is applied again to generate
another path. The process continues until all destinations are assigned. The path
generation process Of planning an AFM tip path is summarized in Figure 8.13.

All direct paths from Objects to destinations are generated first. Then the Objects
are assigned to the destinations. If there are some destinations that are not assigned,
VODs are generated. After that, a collision-free path is generated. Then the path
is checked if there are any destination Obstacles. If there are, the destination should
be inserted before the Obstacle destinations. Then the process continues until all

destinations are assigned.

8.2.5 Implementation and Testing

The developed algorithm is implemented to generate paths to manipulate nanopar-
ticles to manufacture nanostructures. The CAD models of two nanostructures are
shown in Figures 8.14(a) and 8.14(b).

Two samples with 100 nm latex particles are prepared to perform the nanoman-

ufacturing. Figure 8.15 shows two images taken by an AFM.

136

 

 

 

Objects, obstacles and destinations

l

Find all direct paths

 

 

 

 

 

 

 

Assign Objects to destinations

 

 

 

 

   
   
  

Find virtual destinations
and Objects

 

 

 

 

 

 

 

More destination?

 

Find MDPI destination Dm,
Assign an MOPI Obiect to Dm

 

 

 

 
 

 

  
   

NO

  

Destination
Obstacle Do"

 

 

Insert Dm before Do

J

Figure 8.13: Path generation algorithm.

 

 

 

 

After applying the algorithms, Objects and Obstacles are identified. Two collision-
free paths are generated. The simulation results show that there is no collision.
Then the generated paths are implemented to control the AFM tip to perform the
nanomanufacturing. The real-time images are shown in Figures 8.16(a) and 8.16(b),
respectively.

After the processes are complete, the surfaces are re-scanned to check the actual

results. Figures 8.17(a) and 8.17(b) show the actual manufactured nanostructures.

137

 

 

 

 

 

 

(a)

 

were
. e
ciao:

 

 

 

 

(b)

Figure 8.14: The CAD models Of two nanostructures: (a) a line; (b) a rectangular.

The results are consistent with the real—time image shown in 8.16(a) and 8.16(b), re-
spectively. In Figure 8.17(b), the objects are attracted together because the distances

between the objects are smaller than the minimum distance D,,,,,,. The van der Waals

138

 

(b)

Figure 8.15: The AFM images with nanoparticles to manufacture: (a) a line; (b) a
rectangular.

force attracts the particles closer.

139

 

(b)

Figure 8.16: The real-time AFM images in the augmented reality system with man-
ufactured nanostructures: (a) a line; (b) a rectangular.

8.3 Conclusion

The developed general framework of automated tool path planning has been im-

plemented successfully to manufacture nanostructures in nanomanufacturing. The

140

 

(b)

Figure 8.17: The manufactured nanostructures: (a) a line; (b) a rectangular.

collision-free paths have been generated using the CAD-guided automated path plan-
ning algorithm. Simulations have been performed to verify the generated paths.

Experiments tO manufacturing nanostructures have been implemented successfully

141

and achieved satisfactory results. The simulation and experimental results show that
the developed CAD—guided tOOl path planning system can be applied to manufacture

nanostructures and nanodevices.

142

 

CHAPTER 9
CONCLUSIONS

A general framework for CAD-guided optimal tool planning in surface manufacturing
has been developed and implemented successfully. In this chapter, the conclusions

and the extensions Of this framework are discussed.

9. 1 Conclusions

Tool planning builds communication between the CAD model of a part and the
product manufactured based on the CAD design. Automated tool planning process
is highly desirable in today’s manufacturing. A general framework of automated tool
planning for surface manufacturing is develOped based on the CAD model Of a free-
form surface, a tool model and constraints. Both material uniformity and coverage are
considered in one constraint. Since different material deposition patterns are used in
tool planning, a comparison between the raster and spiral material deposition patterns
is made. The implementation results show that the raster material deposition pattern
is better than the spiral one for continuous material deposition. A free-form surface
is divided into one or several patches using the patch forming algorithm such that
the given constraints are satisfied. The improved bounding box method has been
implemented to generate a tool trajectory for a patch. To integrate the trajectories
of the patches in a free—form surface, a trajectory integration algorithm has been
developed. The tool orientation is determined based on the local geometry Of a free-
form surface. The automated tOOl planning algorithm is implemented to generate
trajectories for different parts in different applications. Simulations are performed to
compute the material deposition on free-form surfaces, and the results show that the
generated trajectories satisfy the given constraints. A suboptimal velocity algorithm

is developed to minimize the material thickness deviation from the required material

143

constraints. Simulation results show that the automated tool planning algorithm
can be applied to generate a trajectory for a free-form surface to satisfy the given
constraints.

A general framework for optimal tool planning in surface manufacturing has also
been developed based on the CAD model of a free-form surface, a tool model, con-
straints and Optimization criteria. Multi-Objective constraint Optimization problems
have been formulated. After the optimal tool planning algorithm is developed, simu-
lations have been performed for the Optimal tOOl planning with Optimal time, Optimal
material distribution, no preference articulation and preference articulation. Simu-
lation results for the four cases are presented and compared. The simulation results
are consistent with theoretical analysis.

The developed general framework of automated CAD-guided tOOl planning and
Optimal tOOl planning has been implemented successfully. The developed tool trajec-
tory planning algorithm has been tested in the Ford Motor Company and can greatly

decrease the cost and increase the efficiency.

9.2 Extensions to Other Applications

The developed general framework has been extended to other applications such as
dimensional inspection and nanomanufacturing.

Dimensional inspection is an important process in the manufacturing industry. It
is highly desirable to develop a camera positioning system that is able to plan and
realize the camera configurations in a fully-automated, accurate and efficient way.
The general framework Of automated tool planning and Optimal tool planning has
been applied to generate a camera path for the dimensional inspection Of a part.

Nanotechnology, a promising, advanced technology for the forthcoming century,
has been a recent hot research topic. The complexity of nanomanufacturing requires

to position, manipulate, assemble nanoparticles to manufacture nanostructures, nan-

144

 

odevices and nanosensors. The general framework of automated tool planning has
been applied to generate paths to manufacture nanostructures and nanodevices. Ex-
perimental results show satisfactory results.

The general framework can also be extended to other similar applications, such

as demining [43, 60].

145

 

APPENDIX A
MULTI-OBJECTIVE CONSTRAINED OPTIMIZATION

In this appendix, a multi-objective constrained Optimization problem is presented and
the algorithm to solve the problem is discussed.
A.1 A Multi-objective Constrained Optimization Problem

A general multi-Objective constrained optimization problem can be formulated using
the Objective functions, constraints and Optimization parameters (decision variables),

i.e.,

minF(:c) : (f1($),f2($), "'ifk(m))T
subject to: e(a:) =(e1(:1:),e2(:r:),...,em(:1:))T with e,(:c) Z 0, i = ,...,m

a: = (r1,r2,...,:r,,)T (A.1)

where f1(:z:), f2(a:), ..., fk(a:) are k objective functions; (231,12, ...,:r,,) n Optimization
parameters and e1(:1:), e2(a:), ..., e,,,(a:) m constraints.
The utopian solution is a set of minima Of each respective objective function

subject to the given constraints, i.e.,

F: = (f;,f;....,f,:)T (A2)

where ff, fg, f; are the individual minima of the Objective functions.

A.2 Optimization Method

There are different methods to perform the multi-objective optimization [61, 62, 63],

such as weighted-sum approach, no preference articulation, nonlinear approach, utility

146

theory, goal programming and STEM method [64]. N O preference articulation method
does not use any preference information. It is based on minimization of the relative

distance from a candidate solution to the utopian solution, i.e.,

minF(:c) = [i (fl-(w): f;)”]’l’

3'21 .7

subject to: 6(3) = (e1(:1:),e2(:1:),...,em(:1:))T with e,(:c) 2 0, i = 1, ...,m

a: = ($1,132, ...,:rn)T (A3)

The most frequently used value for p is 1 [64]. Equation (A.3) can be transferred to:

k
mime) = Z we)
j=1
subject to: e(:c)=(e1(:1:),e2(:1:),...,e,,,(:r:))T with e,-(a:) 2 0, i = 1, ...,m

a: = ($1,233, ...,xn)T (A.4)

where A,- is defined as:

X = __ A5
.7 f; ( )

After applying the no preference articulation approach, the multi-objective con-
strained problem is transferred into a single Objective constrained problem. A quadratic
loss penalty function method [58] is adopted to deal with the constrained problem.

A new function G (:13) is formulated as:

minG(m) = F1(a:) + e Z (min[0, act-)1)? (A.6)

i=1

where 6 is a big scalar. Thus a constrained Optimization problem is transferred into
an unconstrained one using the quadratic loss penalty function method. Finally, a
single objective unconstrained problem is formulated. The simplex method [59] is

adopted to solve the single Objective unconstrained problem.

147

1

AUTHOR’S PUBLICATION

H. Chen, N. Xi, W. Sheng, M. Song, Y. Chen. CAD-Based Automated Robot
Trajectory Planning for Spray Painting Of Free-Form Surfaces. An International
Journal of Industrial Robot, 29(5):426—433, 2002.

H. Chen, N. Xi, Y. Chen, J. Dahl. CAD-Guided Spray Gun Trajectory Planning
Of Free-Form Surfaces in Manufacturing. Journal of Advanced Manufacturing
Systems, 2(1):47—69, June 2003.

H. Chen, N. Xi, W. Sheng, Y. Chen. A General Framework Of CAD-Guided
Optimal Tool Planning for Free-form Surfaces in Surface Manufacturin. The
ASME Journal of Manufacturing Science and Engineering.

H. Chen, N. Xi, S. K. Masood, Y. Chen. Software Development of Automated
Chopper Gun Trajectory Planning for Spray Forming. An International Journal
of Industrial Robot.

H. Chen, W. Sheng, N. Xi, M. Song, Y. Chen. CAD-Guided Uniformity Guar-
anteed Robot Trajectory Planning for Spray Painting of Pfee Form Surfaces .
IEEE International Conference on Mechatronics and Machine Vision in Prac-
tice 2001, HongKong.

H. Chen, W. Sheng, N. Xi, M. Song, Y. Chen. Automated Robot Trajectory
Planning for Spray Painting of Free-Form Surfaces in Automotive Manufactur-
ing. the International Conference on Robotics and Automation, 2002, Washing-
ton DC.

7 H. Chen, N. Xi, W. Sheng, Y. Chen, A. Roche, J. Dahl. A General Framework

8

9

10

11

for Automatic CAD-Guided Tool Planning for Surface Manufacturing. The
International Conference on Robotics and Automation, 2003.

H. Chen, N. Xi, Z. Wei, Y. Chen, J. Dahl. Robot Trajectory Integration for
Painting Automotive Parts with Multiple Patches. The International Confer-
ence on Robotics and Automation, 2003.

H. Chen, N. Xi, Y. Chen. Multi-objective Optimal Robot Path Planning in
Manufacturing, IEEE/RSJ International Conference on Intelligent Robots and
Systems, 2003.

W. Sheng, N. Xi, H. Chen, M. Song and Y. Chen. Surface Partitioning in Au-
tomated CAD-Guided Tool Planning for Additive Manufacturing. IEEE/RSJ

International Conference on Intelligent Robots and Systems, 2003.

W. Sheng, N. Xi, H. Chen, M. Song and Y. Chen. Part Geometric Understand-
ing for Tool Path Planning in Additive Manufacturing. IEEE International
Symposium on Computational Intelligence in Robotics and Automation, 2003.

148

l2

13

14

15

16

17

18

19

20

H. Chen, N. Xi, W. Sheng, Y. Chen and J. Dahl. Chopper Gun 'Iiajectory
Integration for Spray Forming in Automotive Manufacturing. The 8th Interna-
tional Conference on Numerical Methods in Industrial Forming Processes ( N U-

MIFORM), 2004.

W. Sheng, H. Chen, N. Xi, M. Song and Y. Chen. Optimal tool path planning
for compound surfaces in spray forming processes. The International Confer-
ence on Robotics and Automation, 2004.

H. Chen, N. Xi, W. Shen, Y. Chen. Automated Chopper Gun Trajectory Plan-
ning for Variational Distribution in Spray Forming. The International Confer-
ence on Robotics and Automation, 2004.

G. Li, N. Xi, H. Chen. A. Saeed, M. Yu. Assembly of Nanostructure Using
AFM Based Nanomanipulation. The International Conference on Robotics and
Automation, 2004.

Q. Shi, N. Xi, H. Chen,Y. Chen. Automated Dimensional Inspection of Auto-
motive Parts by An Area Sensor. The 2004 Japan USA Symposium on Flexible
Automation (JUSFA), 2004.

H. Chen, N. Xi and Y. Chen. Theoretical Comparison Of Raster and Spiral
Tool Patterns for Material Deposition in Surface Manufacturing. The 2004
Japan USA Symposium on Flexible Automation ( J USFA ), 2004.

H. Chen, N. Xi, G. Li, A. Saeed and J. Zhang. Automated Assembly Of Compli-
cated N anodevices Using Atomic Force Microscopy. The 4th IEEE Conference
on Nanotechnology, 2004.

G.Y. Li, N. Xi, H. Chen, A. Saeed, W.J. Li, C.K.M. Fung, R.H.M. Chan,
M. Zhang and T.-J. Tarn. Nano—assembly Of DNA Based Electronic Devices
Using Atomic Force Microscopy. The IEEE/RSJ International Conference on
Intelligent Robotics and Systems,2004.

G.Y. Li, N. Xi, H. Chen, A. Saeed, J. B. Zhang, W.J. Li, C.K.M. Fung, R.H.M.
Chan, M. Zhang and T.-J. Tarn. Experimental Studies of DNA Electrical Prop—
erties Using AFM Based N ano—Manipulator. The 4th IEEE Conference on Nan-
otechnology, 2004.

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