ZLP Thesis

8/22/2019 ZLP Thesis

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COMPUTER-AIDED MOULD DESIGN MODIFICATION

AND TOOL PATH REGENERATION

ZHANG LIPING

(B. ENG.)

A THESIS SUBMITTED

FOR THE DEGREE OF PHILOSOPHY

DEPARTMENT OF MECHANICAL ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2004


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I

ACKNOWLEDGMENTS

First and foremost I would like to wholeheartedly thank my supervisors, Professor

Andrew Nee Yeh Ching and Associate Professor Jerry Fuh Ying Hsi for their support

(morally and academically) and for giving me invaluable guidance, suggestions,

encouragement and patience throughout the duration of my graduate study in National

University of Singapore. I appreciate very much all they have done for me and I will

gratefully remember all forever.

Sincere appreciation is expressed to Associate Professor Loh Han Tong and Associate

Professor Zhang Yun Feng for their kind words of advice during my research.

Thanks are conveyed to National University of Singapore for providing me with the

research scholarship and to Department of Mechanical Engineering and

CAD/CAM/CAE Center for the use of the facilities.

Finally, I wish to express my deepest thanks to some very special people in my life:

my husband, Dr. Ding Xiaoming, thank to his love, patience, understanding and great

support during my graduate study, for always encouraging me to do my best, for never

losing faith in my abilities; my son, Ding Changzhao, of his smiles, laughter and

understanding; my dear parents and in-laws, for their continuous concern, confidence

and moral support. This thesis is specially dedicated to them.


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There are many others who have indirectly contributed to my research and although I

am not mentioning any name here, I am grateful to all of them.


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TABLE OF CONTENTS

Acknowledgements.I

Table of ContentsIII

NomenclatureVIII

List of Figures..IX

Summary...XIII

Chapter 1 Introduction...1

1.1 Product development processes...31.2 Mould design and modification...6

1.2.1 Mould structure and subsystems..61.2.2 Mould design...81.2.3 Mould design modification10

1.3 Tool path generation and regeneration111.3.1 CNCmachines and cutters.111.3.2 Tool path generation..121.3.3

Tool path regeneration...13

1.4 Research objectives.141.5 Outline of the thesis....15

Chapter 2 Literature Review17

2.1 Mould design..182.1.1 Parting direction and parting line design.18


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2.1.2 Insert design.212.1.3 Mould system and subsystem design..23

2.2 Tool path generation.242.2.1 CC-point method.252.2.2 CL-point method.29

Chapter 3 Mathematical Background of Curves and Surfaces.34

3.1 Curve parameters..343.2 Surface parameters...363.3 Curves on surfaces.....403.4 Offset surface.41

Chapter 4 Mould Design Modification42

4.1 Basic concepts and principles of mould design modification...434.1.1 Concepts and assumptions of mould design modification444.1.2 Principles of the insert and pocket design.45

4.2 Architecture of the mould design modification system484.3 Identify the solid bodies of material to be added and removed...504.4

Identify the mould insert that material needs to be added to or

removed from51

4.5 Remove material from the mould...534.6 Add material to the mould...53

4.6.1 Create pocket and insert.534.6.2 Detect interference.60

4.7 Illustrative examples64


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Chapter 5 Tool Path Regeneration with the CL-point Method70

5.1 Terms and notations.715.2 Basic concepts of tool path regeneration735.3 Methodology for detecting affected CL-points..745.4 Tool path regeneration algorithms for CL-point method.78

5.4.1 Identifying and replacing affected CL-points805.4.2 Calculating scallop height values and adding new CL-points to

the modified region86

5.4.2.1Machining scallop height and step-over size.865.4.2.2Algorithm for checking the scallop height value and

adding new CL-points90

5.5 Illustrative examples.93

Chapter 6 Tool Path Regeneration with the CC-point Method.102

6.1 Terms and basic concepts..1036.2 Methodology of identifying the affected CL-points.1046.3 Tool path regeneration algorithms for the CC-point method108

6.3.1 Identifying and replacing the affected CL-points1096.3.2

Adding new CL-points for the modified region..116

6.3.2.1Calculating the CL-points with the given tolerance1166.3.2.2Calculating scallop height and adding new CL-points for

the modified region..119

6.3.2.3Detecting and removing gouging CL-points...1196.4 Illustrative examples...119


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Chapter 7 System Implementation and Case Studies..128

7.1 The computer-aided mould design modification and tool pathregeneration system..128

7.1.1 The platform.1287.1.2 The architecture of computer-aided mould design modification and

tool path regeneration system...130

7.1.3 The user interface.1337.1.4 The mould design modification module...1337.1.5 The tool path generation and regeneration module..134

7.2 Case studies...1367.2.1 Case 11367.2.2 Case 2142

Chapter 8 Conclusions and Recommendations149

8.1Conclusions.1498.1.1 Mould design modification...1508.1.2 Tool path regeneration..150

8.2Recommendations..1518.2.1

Mould design modification...151

8.2.2 Tool path generation.1528.2.3 Tool path regeneration..152

List of Publications from this Study.154


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References...155


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NOMENCLATURE

2D Two Dimensional

3D Three Dimensional

C The Boundary of Mould Modification Region

Co The Boundary of Affected CL-points

CAD Computer-Aided Design

CAE Computer-Aided Engineering

CAM Computer-Aided Manufacturing

CAD/CAM Computer-Aided Design and Manufacturing

CAD/CAM/CAE Computer-Aided Design/Manufacturing/Engineering

CC Cutter Contact

CC-point Cutter Contact point

CL-point Cutter Location point

CLSF Cutter Location Source File

CNC Computer Numerical Control

EDM Electrical Discharge Machining

EC Engineering Change

MRR Metal Removal Rate

UFUN User-Function

UG Unigraphics


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IX

List of Figures

Figure 1.1 Plastic part development processes..4

Figure 1.2 A typical injection mould structure..7

Figure 1.3 A general mould design process......9

Figure 2.1 Parting lines and parting surfaces..19

Figure 2.2 The iso-parametric method26

Figure 2.3 The inverse tool offset method...31

Figure 3.1 The Frenet frame....35

Figure 4.1 Different shapes of inserts and pockets..47

Figure 4.2 Framework of the mould design modification system...49

Figure 4.3 Material to be added to or removed from designed mould50

Figure 4.4 Cavity and core are affected by product design modification51

Figure 4.5 Designed insert and pocket....57

Figure 4.6 An ejector hole interferes with the pocket.58

Figure 4.7 Fix the insert with screw or welding process.59

Figure 4.8 Lifter and cooling holes.61

Figure 4.9 Minimum distance between pocket and other holes..63

Figure 4.10a Old product file..65

Figure 4.10b New product file....65

Figure 4.10c Old cavity...66

Figure 4.10d Modified cavity..67

Figure 4.10e Old core.....68

Figure 4.10f Modified core.69

Figure 5.1 Cutter contact (CC) and cutter location (CL) points..72


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Figure 5.2 Surfaces A and its offset Ao...75

Figure 5.3 Boundaries of A and TA.77

Figure 5.4 Surfaces A andA..78

Figure 5.5 Extreme points and affected points81

Figure 5.6 Difference between z and z...85

Figure 5.7 Overcut due to the wrong tool path direction86

Figure 5.8 Machining scallop height...87

Figure 5.9 Calculation of tool path interval....88

Figure 5.10 Circles interpreted from CL and CC-points..89

Figure 5.11 Changes of tool path direction due to an odd number of tool path

lines91

Figure 5.12a Part surface of a workpiece before modification...93

Figure 5.12b Tool paths of the workpiece before modification..94

Figure 5.12c Part surface of work-piece after modification94

Figure 5.12d Regenerated tool paths with replaced points and added lines after

modification...95

Figure 5.12e Tool paths before and after modification with replaced points and added

lines....96

Figure 5.13a Part surface of bezel mould before modification...98

Figure 5.13b Tool paths of bezel mould before modification.98

Figure 5.13c Part surface of bezel mould after modification..99

Figure 5.13d Regenerated tool paths with replaced points and added lines after

modification.100

Figure 5.13e Tool paths with replaced points and added lines before and after

modification.101


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Figure 6.1 CC-point, CL-point, section plane, CC-curve and tool path row104

Figure 6.2 Curves on surface r and offset surface ro.105

Figure 6.3 Removing undercut and interference from surface A..107

Figure 6.4 Identifying affected CL-points ....110

Figure 6.5 Step lengthL117

Figure 6.6 Convex gouging..118

Figure 6.7a Part surface of a workpiece before design modification..120

Figure 6.7b Tool paths of the workpiece before design modification.120

Figure 6.7c Part surface of work-piece after design modification.121

Figure 6.7d Regenerated tool paths with replaced points and added lines after design

modification.122

Figure 6.7e Tool paths with added lines before and after design modification..123

Figure 6.8a Part surface of T-cover mould before design modification.124

Figure 6.8b Tool paths of T-cover mould before design modification...124

Figure 6.8c Part surface of T-cover mould after design modification125

Figure 6.8d Regenerated tool paths with replaced points after design

modification.126

Figure 6.8e Tool paths of T-cover before and after design modification127

Figure 7.1 Framework of the mould modification and tool path regeneration

system...131

Figure 7.2 New product selection..133

Figure 7.3 Input mould machining status..134

Figure 7.4 Item selection..135

Figure 7.5 Input machining parameters.136


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Figure 7.6a The old plastic part of a dairy clear door.137

Figure 7.6b The new plastic part of a dairy clear door137

Figure 7.6c The original cavity of a dairy clear door..138

Figure 7.6d The modified cavity of a dairy clear door...138

Figure 7.6e The original core of a dairy clear door138

Figure 7.6f The modified core of a dairy clear door...139

Figure 7.7a Tool paths of the workpiece before modification140

Figure 7.7b Regenerated tool paths with replaced points and added lines after mould

modification.141

Figure 7.7c Tool paths before and after modification with replaced points and added

lines..142

Figure 7.8a The old plastic part of a riser...143

Figure 7.8b The new plastic part of a riser..143

Figure 7.8c The original cavity of a riser144

Figure 7.8d The modified cavity of a riser..144

Figure 7.8e The original core of a riser...144

Figure 7.8f The modified core of a riser.145

Figure 7.9a Tool paths of the workpiece before modification146

Figure 7.9b Regenerated tool paths with replaced points and added lines after mould

modification.147

Figure 7.9c Tool paths before and after modification with replaced points and added

lines..148


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SUMMARY

To shorten the product development time, a new plastic part is usually sent to the

mould manufacturing company before it is finalized. The design of the plastic part may

need to be changed many times during the mould manufacturing processes. It may be

necessary to modify the mould design and to regenerate the affected tool paths many

times. However, the existing CAD systems cannot automatically modify the mould

design for non-parametric moulds. In addition, the design of the plastic part may be

modified at different stages of mould manufacturing process, while the mould design

modification method is related to the mould machining status. Moreover, with the

existing CAM systems, no matter how small the portion of a mould is to be modified,

the entire tool path that covers this region will need to be recalculated, which could

take as much time as for generating a new tool path could increase the chance of NC

programming errors. Consequently, the process of mould design modification and tool

path regeneration is still very time-consuming. To solve these problems, this research

focuses on the following aspects:

Mould Design Modification. A new mould design modification algorithm that can

automatically modify the mould design for parametric and non-parametric parts

according to the mould machining status has been developed in this research. The

developed algorithm does not rely on the product parameters that increases with the

complexity of the product and the mould. Therefore, it is not sensitive to the


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complexity of the plastic part and the designed mould. Different methods have been

developed to modify the mould design according to the mould machining status. When

an insert needs to be designed to add extra material, the interference between the

pocket to be designed and the existing holes is detected automatically. Different

pockets, inserts and fasteners will be designed based on the result of interference

detection.

Tool path regeneration. Four propositions have been made and proven in this research

for tool path regeneration. The propositions indicate two important properties of a

gouge-free tool path: 1) the affected CL-points are enclosed by the boundary of CL-

points that is corresponding to the interference-free boundary of the modified region;

2) when projected onto the XY-plane, if one CL-point is before another one, their

corresponding CC-points follow the same topology. With these propositions, the

affected CL-points can be efficiently identified by only noting their x- and y-values.

New tool path regeneration algorithms have been developed to identify and replace the

affected CL-points for 3-axis NC machining. By utilizing the unaffected CL-points,

the tool path can be regenerated efficiently. Since the tool path regeneration method is

related to the tool path generation method, and the tool path methods can be

categorized into CC- and CL-point methods, two different tool path regeneration

algorithms are developed for them respectively.

From this research, a computer-aided Mould Design Modification and Tool Path

Regeneration System has been developed to modify the mould design and regenerate

tool paths automatically and efficiently.


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CHAPTER 1

INTRODUCTION

Thermoplastic parts, as they can provide properties of low density, superior corrosion

resistance, electrical insulation and suitability for volume production, are widely used

in engineering and consumer products. The most prevalent method for producing

thermoplastic parts in large quantities is injection moulding, which is a highly cost-

effective, efficient, and precise manufacturing method. The process can be highly

automated and produces almost no waste.

Facing the challenges of an increasingly more competitive market, time-to-market

plays a crucial role in new product development. Technology tools such as Computer-

Aided Design/Manufacturing/Engineering (CAD/CAM/CAE) have been developed to

help manufacturers achieve the goals of an ever-decreasing life cycle of a product from

concept to market. On the other hand, as they are required to accomplish more

functional and aesthetic requirements, plastic parts are becoming more complex. To

meet the tighter product development schedule, a plastic part may very often be passed

to the mould manufacturing company for manufacturing before it is finalized. The

design of a new plastic part may be changed many times during the mould design and

manufacturing processes. If the design of a plastic part has been changed, the mould

design would need to be modified and the affected mould inserts re-machined.


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Chapter 1 Introduction

2

Although some commercial CAD/CAM systems allow for automatic modification of

the design for parametric parts, they cannot automatically modify the mould design for

non-parametric moulds. Here, a parametric part means that geometric definitions of the

design, such as dimensions, can be varied at any time in the design process by

changing the parameters. In addition, it may be necessary to modify the design of the

plastic part at different stages of mould manufacturing process, while the method of

mould design modification is dictated by the mould machining status. However, this is

not taken into consideration in the existing CAD/CAM systems. Moreover, with the

existing CAM systems, no matter how small the portion of a mould is modified, the

entire tool path that covers the modified region will have to be recalculated. This could

take as much time as for generating a new tool path. Therefore, the process of mould

design modification and tool path regeneration in NC programming is still very tedious,

time-consuming and error-prone.

This research aims at developing a Computer-Aided Mould Design Modification and

Tool Path Regeneration System. With this system, when the design of the plastic part

is changed, the modified regions are identified and located by comparing the old and

the new plastic parts. The mould design is then modified automatically based on the

designed mould and the mould machining status. The affected tool path is regenerated

efficiently by identifying and replacing the affected Cutter-Location (CL) points. The

unaffected CL-points are reused directly to machine the modified mould, which would

greatly reduce the tool path regeneration time.

This chapter introduces the background and basic concepts of the proposed research.

The general process of plastic part development is summarized in the first section.


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Mould design and modification processes are analyzed in the second section. This is

followed by tool path generation and regeneration methods in the third section, and the

objectives of the research in the fourth section.

1.1 Product development processesAs shown in Figure 1.1, the processes of a product design and manufacturing include:

plastic part design, mould design, mould manufacturing, surface polishing, mould

assembly, mould try-out, design and manufacturing modifications if necessary,

moulding and product launch.

A plastic part is generally a component of a functional product. After the concept

design of a new product is created, the plastic part is designed based on the functional

and aesthetic requirements. The mould capability and manufacturability should be

considered when designing the plastic part. In addition, some rules for mould design

should be followed to avoid the common pitfalls, e.g., design optimal wall thickness

according to the function, the plastic material and the cost; keep the wall thickness of

the plastic part uniform; locate the gate so that the melt plastic enters the cavity in the

thickest area and flows to the thinner areas; design radius at all corners of the part; and

design optimal draft angles for removing the plastic part easily for the core and cavity.

Traditionally, plastic parts are designed with general CAD software based on the

designers experience, which is time consuming and error-prone. The development of

CAE systems has eliminated various trial-and-error practices and greatly streamlined

the product development cycle. However, as there are many parameters that affect the

quality of a moulded part, the design of the plastic part may not be optimal and the


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design may need to be modified many times before the product can be launched. For

example, the design of a space mouse was changed 9 times during the mould design

and manufacturing processes. Over the past decade, The Engineering Change (EC) is

becoming more and more frequent. The reasons can be summarized as follows: (1) The

new product design files are often passed to mould companies before it is finalized; (2)

The product design engineer is less experienced; (3) There are some changes from the

Figure 1.1. Plastic part development processes

Plastic part design

Mould design

Mould manufacturing

Surface polishing

Mould assembly

Satisfy?

Mould try-out

Moulding

Launch

De

signandmanufacturing

modificationprocess

N

Y

EC


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related parts; (4) The feedback from the market; (5) Many new products have only six

months to prove themselves in the marketplace.

After a three dimension (3D) solid model of the plastic part is designed, a prototype

may be created for checking and verification. If the prototype meets the requirements,

the mould can be designed and manufactured, which is generally done in another

company. Otherwise, the design of the plastic part will need to be modified and

verified again.

Since the plastic part and the mould are usually designed in different companies,

different CAD systems may be used. In this case, the designed plastic part file will be

transferred from one format to another, and the design parameters may be lost during

file transformation. When the mould designer receives the plastic part, he/she will

study and analyze the mould capability and then design the mould. If the design of a

plastic part is found to be not suitable for moulding, it will be returned to the product

designer for modification.

When the mould is designed, the material will be ordered and the mould can be

machined. Computer Numerical Control (CNC) milling and Electric Discharge

Machining (EDM) are the two common processes that are used to machine the mould

inserts with 3D profiles. Mould inserts are most commonly machined with CNC

milling machines. The EDM process is used when the part is difficult or impossible to

machine with milling cutters. This research focuses on the CNC milling process.

After the mould inserts are machined, the surfaces that form the profile of the plastic


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part will be polished. The mould is then assembled and tested. If the tested part

satisfies the requirements, the mould can be used for mass production and the product

can be launched. Otherwise, the design of the mould will be modified and the modified

portion will have to be machined again. If the failure is caused by the product design,

the design of the plastic part will be modified, which will in turn affect the design and

manufacturing of the mould.

Although the time and cost have been reduced dramatically in most areas of the

product development process, mould design and manufacturing is still the most time

consuming and costly phase for plastic parts. These aspects will be discussed in the

following two sections.

1.2 Mould design and modificationMould design is an important process for a successful plastic part. Proper design of an

injection mould is crucial to producing a functional plastic component. Mould design

has great impact on productivity and part quality, directly affecting the efficiency and

profitability of the moulding operation. About 70% of the mould manufacturing cost is

decided in the mould design process.

1.2.1 Mould structure and subsystemsInjection moulding is a process that softens the plastic material with heat and forces it

to flow into a closed mould. After the material cools and solidifies, a product with the

specific shape is formed. A mould is what determines the shape, and in most cases, the

final finish of the part. As shown in Figure 1.2, a typical injection mould system

usually includes mould base, guiding and alignment, sprue and runner system, cooling


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system, ejecting system and cavity system. Among them, the mould base is used to

securely retain all the inserts in the mould. The guiding and alignment system ensures

that the two mould halves (fixed half and moving half) remain in correct alignment and

the mould is accurately positioned on the machine. The sprue and runner system

Guiding & alignment

Cooling system

Sprue & runner system Cavity system

Ejection system

Figure 1.2 A typical injection mould structure

Mould base


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ensures that the impression can be filled properly and completely. It also positions and

orientates the various functional parts to ensure that the whole mould assembly works

properly. The cooling system makes sure that the hot material can be cooled down

rapidly to a temperature, at which it solidifies sufficiently to retain the shape of the

impression. When the plastic material cools down, it often shrinks onto the core insert,

which makes it difficult to remove. The ejecting system provides a means to eject the

moulded part from the core insert.

The cavity system forms the shape of the plastic part. It usually includes the cavity and

core inserts. When there is undercut in a plastic part, sliders and lifters will be

designed. Generally, a lifter is designed for internal undercut while a slider is designed

for external undercut. There are usually some cooling, ejecting, lifter and screw holes

in the inserts of the cavity system.

1.2.2 Mould designSince injection moulds are of multi-functionality and have various configurations, the

design of an injection mould is a complex task. In addition to satisfying the functional

requirements, many other aspects, such as geometric complexities, equipment and

tooling requirements, process capabilities, must also be taken into account in mould

design. In order to shorten the mould design lead-time, 3D CAD systems have

replaced the traditional drawing boards as a design tool in most mould manufacturing

companies. Several mould design systems have been developed to automate some of

the mould design processes and shorten the design time.

Figure 1.3 shows a general mould design process: Upon receiving the design of the


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plastic part, the mould designer studies the requirements and the geometries. The

plastic part is enlarged to compensate shrinkage. The shrinkage factor is the ratio of

the expected reduction of the plastic part dimension as the part solidifies in the mould

and cools to room temperature. The parting line and the parting surfaces are then

identified and designed. Based on the geometry and dimension of the part, the ordered

quantity and manufacturing cost, the injection machine and the mould type are

Shrinkage

Determine parting direction and parting line

Designed product model

Select the mould type and mould machine

Design the initial cavity layout

Design detailed layout, inserts and components

Create drawings

Order insert material and standard components

End

Figure 1.3 A general mould design process


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decided. The cavity layout and the feeding system including the runner and the gate

are designed.

After the initial mould layout design, the mould design engineer proceeds to the detail

design of mould inserts and components. The mould base, core, cavity, slider and lifter

are designed. The ejecting and cooling systems are also designed. The accessories such

as the fasteners, springs, heaters, etc. are added in last. When the mould is designed,

materials and standard components are ordered and the inserts with 3D profiles are

passed to the CAM department.

1.2.3 Mould design modificationWhen the design of a plastic part is changed, the mould design will need to be

modified. Since a mould has been designed and some mould inserts may have been

machined, the mould design modification method is different from the mould design

method. Besides the geometrical and functional constraints, the structure of the

designed mould also needs to be considered in modifying the mould design. In

addition, the product and the mould design may be modified in different mould

manufacturing stages. Different mould design modification methods should be applied

for different mould machining status.

Some parametric-based CAD systems can automatically modify the design of simple

moulds as they can preserve the design history. However, it may take very large

storage space to preserve the design history. Sometimes, this makes the file very large,

and the operation becomes very slow. This is a critical issue in designing complex

moulds. To solve this problem, some commercial CAD/CAM systems (e.g.,


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Unigraphics [Unigraphics 2000]) provide a function which allows the user to remove

the design parameters and history. In the mould manufacturing industry, many

CAD/CAM engineers do remove the design history to reduce the part file size and

improve the mould design and tool path generation speeds. Therefore, design

modification for complex mould parts is still time-consuming and tedious.

If the plastic part is designed with one CAD system while the mould is designed with

another one, the parameters of the plastic part many be lost when the part is

transferred, which makes it difficult to modify the mould design automatically.

In addition, the design of the plastic part may be changed in different mould

manufacturing stages, the existing mould design modification systems cannot modify

the mould design automatically according to the mould machining process status.

Therefore, when a complex or non-parametric mould design needs to be changed, it is

still done by the mould designer with the general CAD system based on his/her

experience, which is time-consuming and error-prone.

1.3 Tool path generation and regenerationCNC milling machines are widely used in mould manufacturing industry. Most mould

manufacturing companies use CAM software to generate tool paths for NC machining.

The CNC machine, the milling cutter and the tool path are three key factors that decide

the mould machining accuracy and efficiency.

1.3.1 CNC machines and cuttersAccording to the degree of the freedom of the tool relative to the workpiece, CNC


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milling machines can be classified into 3-, 4- and 5-axis machines. 3-axis and 5-axis

CNC machines are most commonly used in mould manufacturing. A 5-axis CNC

machine, with 2 additional rotating axes, can machine free-form surfaces with flat and

fillet end-mills instead of ball end-mills, which can drastically reduce the machining

time. However, this technology is being accepted only gradually in mould

manufacturing because the programming for 5-axis CNC machines is somewhat more

difficult and error-prone. Therefore, 3-axis milling machines are still most widely used

in the mould manufacturing industry, which is also the emphasis of this research.

Flat, fillet and ball end-mills are most commonly used in mould machining. Since in

sculpture surface machining with 3-axis milling machines, only a ball end-mill with

spherical face at its end can finish the machining task, ball end-mills are widely used in

the finish machining of moulds. This research will focus on ball end-mills.

1.3.2 Tool path generationThe CNC programming of a complex mould part typically consists of two general

sequences: rough and finish. Rough machining removes most of the unwanted raw

stock material while keeping the tool a safe distance from the parts finished surface. It

is during finish machining that the cutter contacts the part surface and removes the

remaining unwanted stock material.

Material Removal Rate (MRR) is the most important factor to be considered for rough

machining. Machining accuracy is not the critical issue in this process. For finish

machining, accuracy, surface finish and machining efficiency are the three most


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important parameters. Minimizing the machining time with required accuracy and

surface finish is the main objective in tool path generation for finish machining.

During the past decades, great improvement in tool path generation has been achieved,

and many tool path generation methods have been developed. Many commercial CAM

systems are available. Most CAM systems (e.g., CATIA, Unigraphics and

Pro/Engineer) can generate gouge-free tool paths automatically with the given cutting

tool and machining parameters. However, despite of rapid increase in computer speed,

the process of tool path generation is still time consuming. It may take more than two

hours to generate a finish machining tool path for a complex mould insert. Since the

NC codes for rough machining are generally much fewer than those for finish

machining, the time for generating rough machining tool path is also usually much less

than that for finish machining.

1.3.3 Tool path regenerationWhen the mould design is modified, the modified mould needs to be re-machined.

CNC and EDM are two common processes used to machine the modified mould. If the

modified mould is to be machined with a CNC machine, the tool paths need to be

regenerated.

With the existing CAM systems, no matter how small the portion of a mould insert is

to be modified, the entire tool path that covers this region will need to be recalculated.

As much time is needed to regenerate the tool path for the modified mould as that for

generating a new tool path, which is highly unproductive and very time consuming.

Sometimes, the mould needs to be modified when it is being machined. In this case,


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the tool path should be regenerated in a very short time. Otherwise, the NC machine

will be idle while waiting for the new tool path to be regenerated.

1.4 Research objectivesMany researchers have studied mould design and tool path generation in the past

decades, and improvements have been achieved in automating the design and

manufacturing process and increasing the efficiency. Some CAD systems can design

moulds automatically and most CAM systems can generate tool paths automatically

with given machining parameters. However, the following limitations are recognized

in the existing work:

(1) Some CAD systems can modify mould design automatically for parametric parts.However, it is very difficult to automatically modify mould design for complex

and non-parametric parts with existing CAD systems. Moreover, the mould

machining status is not considered in most CAD systems for modifying the

mould design.

(2) With the existing CAM systems, if the tool path needs to be regenerated, all CL-points of the tool path will be recalculated. It will take as much time to

regenerate an affected tool path as that for a new one.

The objective of this research is to develop a mould design modification and tool path

regeneration system that can solve the above two problems. This research will focus on

the following two issues:

(1) Mould design modification. Develop a mould design modification system that


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can automatically and efficiently modify a mould design based on the designed

mould and the mould machining status. The system should be applicable to both

parametric and non-parametric parts.

(2) Tool path regeneration. Develop new algorithms and methodologies that canregenerate tool paths efficiently. Since the time for generating a rough machining

tool path is generally short, this research will focus on finish machining. As the

tool path regeneration method is related to the tool path generation method, and

the tool path generation methods can be classified into CL-point method and

(Cutter Contact) CC-point method, two tool path regeneration methods will be

developed for them respectively.

It is assumed in this research that the product design, mould design and tool path

generation are all based on 3D solid models, while an original mould has been

designed and the corresponding tool paths have been generated. Since 3-axis CNC

machines with ball end-mills are widely used in mould machining, this research will

focus on regenerating tool paths for these configurations. In addition, the same size

cutters will be used to machine both the original and the modified moulds.

1.5 Outline of the thesisThe remaining chapters of this thesis are organized as follows. Chapter 2 presents a

review of the current research status in computer-aided injection mould design and tool

path generation. Chapter 3 introduces the mathematical background of curves and

surfaces for mould design modification and tool path regeneration. The mould design

modification system is introduced in Chapter 4. The tool path regeneration algorithms

for CL-point and CC-point tool path generation methods are introduced in Chapter 5


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and Chapter 6, respectively. Chapter 7 presents the computer-aided mould design

modification and tool path regeneration system. Some examples of mould design

modification and tool path regeneration are also implemented in this chapter.

Conclusions and future research recommendations are discussed in the last chapter.


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CHAPTER 2

LITERATURE REVIEW

Nowadays, product designers integrate more sculptured surfaces into their product

components to enhance product aesthetic and improve their designs. The increasing

complexity of manufactured parts requires more advanced CAD software and effective

NC programming capabilities to design moulds and generate tool paths efficiently.

Mould design and the mould manufacturing are two important factors that determine

the success of a mould.

During the past decades, many researchers have studied mould design and tool path

generation, and numerous papers have been published in these two areas. Most

reported research work on mould design has concentrated on one of the following

three topics: determining the optimal ejecting direction for a plastic product,

automatically generating side cores, and developing interactive CAD systems for

injection mould design; while research works on tool path generation have focused on

how to generate gouge-free tool paths efficiently. In this context, machining quality,

efficiency and accuracy are the three key issues studied by most researchers.

Although the reported literature can hardly be used directly for mould design

modification and tool path regeneration, these researchers work can provide useful

inputs in these two areas. A review on mould design and tool path generation is given


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Chapter 2 Literature Review

18

in this chapter.

2.1 Mould designIn general, an injection mould includes cavity system, guiding and alignment system,

runner system, ejection system and cooling system. Among them, the cavity system is

most important. Determining optimal parting direction and automatically generating

side cores are two of the most difficult tasks in designing a cavity system. Many

researchers have studied these two problems. In addition, as mould design is very

tedious and time-consuming, many researchers have tried to develop systems that

could design moulds automatically and efficiently. A brief literature review in these

three research areas is given in the following subsections.

2.1.1 Parting direction and parting line designParting direction and parting line are very important for a successful mould design as

they decide the number and the shape of side cores, and this decision will affect all the

subsequent steps in the design of a mould. Many researchers have studied how to

automatically identify the optimal parting direction and design the parting lines.

As shown in Figure 2.1, a parting direction is a direction along which a mould piece is

separated from the mould assembly. One of the principles of selecting the parting

direction is to minimize the undercut, where an undercut is the recess or protrusion

region on a plastic part that prevents its removal from a mould along the parting

direction. When the parting direction is determined, the parting line and the parting

surface can be designed. A parting line is a continuous closed curve on the surface of

the product part that defines the faces to be split into different mould pieces, and the


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parting surface is the contact surface of two mould pieces.

Chen et al. [Chen 1993] developed a method to determine the parting direction based

on the minimization of local external undercuts. Using the Gaussian and visibility

maps, they presented an algorithm to obtain a set of feasible parting directions. While

their approach was able to minimize the number of external undercuts, internal

undercuts were not considered. Based on two levels of visibility: complete and partial,

Chen et al. [Chen 1995] extended their work to parts with internal undercuts by

decomposing an internal undercut feature into two portions: the separable and the

internal undercuts.

Figure 2.1 Parting lines and parting surfaces

Core

Cavity

Parting surfaceParting lines

Parting direction

Parting direction

Plastic part


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Nee et al. [Nee 1997] classified the undercut features into two types, namely external

and internal undercuts. The external undercuts were further divided into outside

external undercuts and inside external undercuts, while internal undercuts were divided

into outside internal undercuts and inside internal undercuts. A group of recognition

criteria for undercut features were presented in their paper. After all the potential

undercuts were extracted, the optimal ejection direction was chosen based on the

number of possible undercuts and their corresponding undercut volumes.

Ye et al. [Ye 2001]developed a hybrid method to recognize undercut features from

moulded parts with planar, quadric and free-from surfaces. Their hybrid method took

advantage of graph-based and hint-based approaches, and various undercut features,

including interacting undercut features, could be recognized.

When the parting direction is determined, the parting line can be designed. Ravi and

Srinivasan [Ravi 1990] introduced sectioning and silhouette methods for parting line

generation. Chin and Wong [Chin 1996] presented a slicing strategy for generating the

parting line. Through a recursive uneven slicing method, several parting surfaces are

generated for further evaluation. Weinsten and Manoochehri [Weinsten 1997]

formulated the parting line determination problem as an optimization problem. Their

objective function is defined as a function of the flatness of the parting line, draw

depth, number of side cores required to form the undercuts, machining complexity, etc.

Majhi et al. [Majhi 1999] presented an algorithm for computing an undercut-free

parting line that is as flat as possible for a convex polyhedral object.

In summary, many researchers have studied how to identify the undercut, determine


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the parting direction and design parting lines. Generally, if the design of a plastic part

is changed, the parting direction should not be changed so as to minimize the

modification of the mould structure. With the given parting direction, the possible

undercut caused by the design modification can be identified with existing methods. If

the design change affects the existing parting line, the affected parting line can be

redesigned and the modified portion of the part can be split and united with the core

and cavity inserts automatically.

2.1.2 Insert design

Insert design includes the design of cavity, core, slider and lifter. These inserts form

the shape of the plastic part. The cavity and core form the profile without undercut,

while the slider and lifter are designed for the undercut profiles. Some researchers

studied how to generate inserts automatically.

Hui and Tan [Hui 1992] proposed a four-step sweeping method to create the cavity and

core: 1) Generate a solid by sweeping the plastic part in the parting direction; 2)

Subtract one end of the swept solid from the first mould block; 3) Subtract the other

end of the swept solid from the second mould block; and 4) Subtract the result of step

2 from that of step 3 with the mould plates in the closed position.

Shin and Lee [Shin1993] presented a procedure to recognise undercuts by checking the

interference faces between a product and its core/cavity. They also discussed the

generation of side cores by using the Eulers operations. For free-form surfaces

represented by u, v parameters, their algorithm determines an interference face by

checking the normal vectors at the points corresponding to the grid points in the


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parameter domain. Since it is difficult to determine the u, v parameters for trimmed

free-form surfaces, this method is not suitable for designing side cores that contain

trimmed surfaces.

Rosen [Rosen 1994] presented a procedure to design side cores based on the identified

undercuts. For external undercuts, accessibility directions were identified and used to

design side cores. For internal undercuts, form pins were constructed that accessed the

undercuts through the core of an injection mould. However, this approach is only

suitable for polyhedral solid models.

Zhang et al. [Zhang 2002] introduced an algorithm that could create complete lifter

subassemblies. With their algorithm, the virtual core and cavity were generated first

with the given parting direction without considering the undercuts. The undercuts were

then identified and grouped. For each group of undercuts, the releasing direction was

identified and a lifter head was designed. By attaching other standard components of

the lifter to the head, a complete subassembly of the lifter was designed.

In summary, most researchers have studied how to automatically generate inserts of

cavity, core, slider and lifter with the given parting direction and parting lines.

However, how to modify the design of the inserts accordingly based on the modified

plastic part was not considered in their research. More research is needed to

automatically modify the insert design based on the modified plastic part and the

mould machining process.


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2.1.3 Mould system and subsystem design

Even with the help of the general CAD systems, injection mould design is still a very

time-consuming and tedious process, and it is highly dependent on the experience of

the mould designer. To automate the mould design process and shorten the design

time, some researchers studied how to build up specific CAD systems for injection

mould design.

Yuan et al. [Yuan 1993] developed an integrated CAD/CAE system for injection

mould design and analysis. With their system, the drawings of a plastic product were

first transformed interactively into the drawings of mould impressions, the mould

design was then carried out by using a group of design tools for injection moulds. The

system could analyze the balance of the runner and simulate the flow process of the

plastic melt.

Kruth et al. [Kruth 1997] developed a design support system (IMES/DSS) for injection

mould design. The system supported the design of injection moulds through high-level

functional mould objects, e.g. basic assemblies, components and features. The system

managed the low-level CAD entities and allowed additional design information such

as process planning information to be incorporated. The user could create or modify

standard design objects and link them with a relational database.

The above two systems could only support 2D design of injection moulds. Thus, the

design facilities provided by the system were actually a group of tools for editing and

generating 2D drawings. To solve this problem, Lee et al [Lee 1997] developed a

knowledge-based injection mould design system, which supports 3D modeling. The


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system contains the design libraries for mould bases and standard parts. Mould design

tools such as parting line selection, parting surface generation, ejecting pin design,

cooling hole design, etc., are also provided by the system. Similar knowledge-based

systems were also introduced by Chan et al [Chan 2003] and Mok et al [Mok 2001].

Besides the entire mould design system, some mould design subsystems, such as the

feeding system [Ong 1995, Ravi 1997], the ejection system [Wang 1996] and the

cooling system [Lin 2001], have also been developed. Most of these researches

focused on how to optimally and automatically design the subsystems.

In summary, some CAD/CAE systems have been developed to automate mould design

processes and improve mould design quality. However, none of these systems could

automatically modify the mould design according to the changed plastic profile for

non-parametric parts. Research in this area is needed.

2.2 Tool path generationAfter the mould is designed, the CAM engineer generates tool paths for rough and

finish machining based on the designed mould parts. The purpose of rough machining

is to remove excess material from a stock, while finish machining aims to accurately

machine the part shape. This research focuses on tool path generation for finish

machining.

According to whether the topology of CC-points or CL-points is controlled, the tool

path generation can be classified into CC-point method and CL-point method. A brief

review of tool path generation in these two categories will be given in the following


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two sub-sections. Since 3-axis CNC machines with ball end-mills are widely used in

finish machining of sculptured surfaces, this review will emphasize on this

configuration.

2.2.1 The CC-point methodDuring the past few decades, many methods have been developed for tool path

generation of compound surfaces. Most of the available algorithms are based on the

CC-point method. With this method, a set of CC-points are planned on the compound

surface. CC-points are then offset along the surface normal vectors to compensate the

effect of the cutter size. The CL-points are thus obtained, and the final tool paths are

calculated by removing the interference CL-points. According to how the CC-points are

planned, the CC-point tool path generation methods can be further classified into the

iso-parametric method, the constant geodesic distance method, the constant scallop

height method, the principal direction method, the spiral tool path method and the

section curve method.

The iso-parametric method [Broomhead 1986, Loney 1987, Kuragano 1992, Yu 1996],

also known as the flow-line machining method, generates tool paths along the surface

constant parameter lines. With this method, the step-over size is first evaluated at each

cutter contact point along the CC-path such that the scallop height is within the

tolerance. The minimum step-over size within a single path will become the step-over

size. By keeping one of the two parameters constant, the iso-parametric curves are

formed and employed as the CC-paths. The method of iso-parametric machining takes

advantage of the parametric representation of the sculptured surface. It is very easy to

calculate tool paths for a parametric surface patch and can avoid the costly surface-to-


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surface intersection computation. Hence, it was widely used in the early CAM

systems. However, since each uniform tool path interval in the parametric space

between adjacent tool paths is constrained by the scallop-height requirements, the

generated iso-parametric tool paths are often much denser in one surface region than

others due to the non-uniform transformation between the parametric and Euclidean

spaces (see Figure 2.2). This results in varying scallop-height distribution on the

machined surface and non-optimal machining time [Elber 1994, Sarma 1997]. Another

shortcoming of this method is the difficulty in consistently generating tool paths for

the regions consisting of several trimmed surfaces on the part surface [Loney 1987,

Sarma 1997].

The constant geodesic distance method is also called the iso-distance method [Elber

1994]. With this method, the CC-points are planned on the surface curves such that the

geodesic distance between every two consecutive curves is constant. The tool path is

then calculated along these curves. The tool path length with this method is generally

shorter than the iso-parameter method. However, the machining scallop height is not

Figure 2.2 The iso-parametric method

Workpiece surface

Tool path


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only determined by the distance between two tool paths, it is also decided by the

surface curvature value. The tool path generated with this method may not be the

shortest.

The tool path generation method to achieve constant scallop height was first reported

by Suresh and Yang [Suresh 1994]. With this method, an initial curve, usually the edge

of the surface is selected first. The CC-curves are then planned on the surface to make

sure that the machining scallop height at every CC-point is constant. This method can

reduce the redundant machining in the iso-parametric and iso-planar methods since the

scallop height is kept constant, and the overall tool path length generated with this

method is generally shorter than with other methods. The disadvantage of this method

is that the selection of the initial curve has a direct impact on the total tool path length.

If the initial curve is not appropriately selected, the total tool path length can even be

longer than other methods in some special cases.

It was assumed in [Suresh 1994] that the corresponding swept sections on the adjacent

tool paths be coplanar. This assumption had caused inaccuracy in the calculation of

tool path intervals and compromised the generation of optimal tool paths. Sarma and

Dutta [Sarma 1997] improved the method of calculating the offset curve on the surface

by using swept sections along the tool paths to calculate the tool path intervals.

Nevertheless, the derivation by Sarma and Dutta [Sarma 1997] assumed that the

undetermined swept sections of the following tool path be in planes perpendicular to

the tangent vectors of the common scallop curve. This is in effect equivalent to the

assumption that the two corresponding swept sections on adjacent tool paths are in the

same plane, which also has its limitations.


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With the principal direction method [Marciniak 1991, Jensen 1993, Bedi 1997], the

shortest tool path can be obtained. With this method, the lines of curvature of the

surface are identified first. The tool path is planned along these lines of curvature. This

is because the step over size dcan be approximated as in [Marciniak 1991]:

d= 2

h2(2.1)

where =R

1-

1,R is the cutter radius andis the signed surface curvature radius in

the direction that is perpendicular to the tool path direction, > 0 for concave surface

and< 0 for convex surface.

It can be found from Eq. (2.1) that if the tool path is planned along the surface principal

direction that has the larger principal curvature radius, the step over size is maximum.

However, this method needs to calculate the lines of curvature which are very difficult

to compute. In addition, in some cases, the principal direction is not unique for some

surface shapes (e.g., a planar or a spherical surface). The lines of curvatures cannot be

identified for these areas.

The above two methods can only generate constant scallop height tool paths for single

surface machining. As there are usually many surfaces in a mould workpiece, it is

difficult to apply these methods in mould machining. To solve this problem, Lee [Lee

2003] proposed a spiral tool path generation method. With this method, a set of offset

curves of the workpiece boundaries are generated first. The distance of the offset is

determined to be the tool path interval such that the scallop height is maintained

constant. The tool paths are then planned on these offset curves. With this method, the


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possible intersection and self-intersection of the offset curves need to be removed

before calculating the CL-points. Another problem could be caused by the offset

curves in separating the surface into several machining areas, which may result in

machining marks along the boundaries of these areas.

The section curve method [Bobrow 1985, Choi 1988, Choi 1989, Suresh 1994 and

Huang 1994] calculates the tool path by intersecting the part surface with a series of

drive surfaces. The CC-points are then planned on the intersection curves. In general,

with the section curve method, the cutter follows planar cross-sections generated by

intersecting the designed surface with a set of parallel planes. It is characterized with a

uniform interval between adjacent tool paths in the Euclidean space. Each interval is

determined according to the scallop-height requirement. The main advantages with this

method include: the resulting tool paths are non-adaptive to the local surface geometry

and the CL-points of multiple adjoining surfaces are joined together into a single tool

path. Since there are usually many surfaces in a complex mould, to achieve

satisfactory surface quality, the tool paths for the entire workpiece should be as

continuous as possible. Therefore, the section curve method is widely used in

compound mould machining.

2.2.2 The CL-point methodWith the CL-point method, the x- and y-values of the CL-points are planned first, the

z-values are then calculated for each set of x- and y-values. According to how the CL-

points are planned, the CL-point method can be further classified into the surface

offset method, the highest point method, the inverse tool offset method and the Z-map

method.


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The surface offset method [Faux 1979, Tang 1995, Kim 1995, Maekawa 1997,

Lartigue 2001] is usually used in machining sculptured surfaces with ball-end cutters.

With this method, the offset surface is generated first by offsetting the original

workpiece surfaces. The intersection and self-intersection of the offset surfaces are

then trimmed off. The points on the trimmed offset surfaces are the gouge-free center

points of the cutter. The tool paths are generated directly on the offset surfaces. One

distinctive advantage of this method is that it allows flexibility in tool path planning. It

is therefore possible to generate constant scallop height tool paths with the offset

surface method [Lartigue 2001]. However, this method needs to calculate the offset

surfaces and remove the possible intersection and self-intersection of the offset

surfaces, which is computationally very intensive.

To solve this problem, Lai and Wang [Lai 1994] and Jun et al. [Jun 2002]

approximated the sculptured surfaces into triangles first. These triangles were then

offset. The CL-points were generated by slicing the offset triangles with a series of

drive planes. If two intersection curves overlapped, the lower one was removed. The

intersection curves were then sorted, trimmed and linked. Gouging is removed during

the trimming process. One disadvantage of this method is the need to convert the

original workpiece surfaces into triangles, which may lose the accuracy and the surface

properties information.

Hwang [Hwang 1992] and Yang and Han [Yang 1999] used the highest point method

to calculate the CL-points. With this method, the tool paths are planned in three steps:

1) the surfaces are converted into a set of facets; 2) the 2D tool paths are planned on

the xy-plane; and 3) for a given cutter center axis at point (x, y), the highest cutter


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position z is determined by lowing the cutter until it touched a triangular facet under

the cutter. With this method, the generated CL-points are gouge-free. This method can

also be applied to tool shapes other than ball end-mills.

Takeuchi et al. [Takeuchi 1989] introduced the inverse tool offset method that can be

used to calculate the tool paths. With this method, the offset surface is generated as an

envelope of a virtual tool transposed upside down moving along the workpieces

surface (see Figure 2.3). The gouge-free CL-points are then planned on the offset

surface. Besides the ball-end-cutters, this method is also applicable to other tool

shapes. When the tool path is generated with the z-map method, the inverse tool offset

method is usually used to calculate the CL-points.

The Z-map method [Choi 1988, You 1995, Huang 1996, Choi 1997, Lin 1998, Maeng

2003] is a common strategy used for machining compound surfaces. It is based on a

computer graphics z-buffer discretization of 3D objects which allows the

approximation of 3D objects by 2D arrays. A z-buffer is a collection of z coordinate

Offset surface

Workpiece surface

Figure 2.3 The inverse tool offset method


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values of the CL-points, computed at the sampled grid points. With the z-map method,

a set of grid points is first sampled on the xy-plane, in the domain of interest. It can be

obtained by the intersection of surfaces and vertical lines passing through the grip

points. Tool paths are generated from the z-map by the inverse offset method. The

step-over size between tool paths is determined by the sampled grid points and the

highest z value at each sampled point is accepted as the CL-point. With the z-map

method, the main advantages are that the final tool path is interference free and low

memory storage for the representation of complex surfaces is needed since the z

coordinates of the object are the only values stored. Another merit of this method is

that tools other than ball end-mills such as fillet end-mills can be used easily.

However, it has the weakness of providing only global control over the scallop height

and the chordal error, which may lead to low machining efficiency.

In summary, according to whether the CC-points or the CL-points are controlled, tool

path generation methods can be classified into the CC-point method and the CL-point

method. It is easy to control the scallop height with the CC-point method. The main

drawback of CC-point method is that it is prone to gouging, while the shortcoming of

CL-point method is that it is good only for preventing concave gouging [Choi 1997].

Generally, the CL-point method is better for satisfying the requirements of high-speed

machining, such as cutting-load smoothing, tool path smoothness and chip-load

leveling [Choi 1998].

Many researchers have studied tool path generation, and the research work focused on

how to efficiently generate gouge-free tool paths that can machine moulds in minimum

time while maintaining the required surface quality. There is no research work on how


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to regenerate tool path efficiently based on the original tool path and the modified

workpiece. More research studies in this area are needed.


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CHAPTER 3

MATHEMATICAL BACKGROUND OF

CURVES AND SURFACES

In order to obtain a better understanding of the mould design modification and tool path

regeneration methodologies and algorithms, the mathematical background of curves

and surfaces will be introduced in this chapter. The chapter is organized as follows. The

parameters of curves are discussed in the first section. The second section discusses the

parameters of surfaces. Some specific curves on surfaces are studied in the third

section. The offset surface is studied in the last section.

3.1 Curve parametersA space curve can be defined as the trajectory of a point moving in three-dimensional

space (3) with one degree of freedom. The Cartesian coordinates of a point on the

parametric curve r can be expressed as the function of parametertas follows:

r(t) =

)(

)(

)(

tz

ty

tx

(3.1)

where the Cartesian coordinates x, y andzare differentiable functions of parametert.

Any point on the space curve r can be obtained by specifying a value of the parameter

t. When a different parameter is used to represent the curve, the curve shape will not


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Chapter 3 Mathematical Background of Curves and Surfaces

35

change. The arc length of the curve is often used as the curve parameter. The arc

lengths can be calculated as follows:

s(t) =

1

0

t

t dt

drdt=

1

0

t

t

222

+

+

dt

dz

dt

dy

dt

dxdt (3.2)

The tangent (t), normal (m) and binormal (b) vectors of the curve form a local

Cartesian system with original at r(t) and three axes of t, m andb (see Figure 3.1).

They are given as follows:

=

=

=

rr

rrb

tbm

r

rt

DDD

DDD

D

D

(3.3)

Figure 3.1 The Frenet frame [Faux 1979]

m

bP

t

Osculating plane Normal plane

Rectifying plane


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where rC andrCC represent the first and second order derivatives ofr with respect to t.

The frame oft, m andb is called the Frenet frame. The planes through a given point

on the curve and contains the vectors t andm, m andb, andb andt are the osculating

plane, the normal plane and the rectifying plane, respectively (see Figure 3.1).

Using the arc length (s) as the curve parameter, the derivatives of t, m and b with

respect to arc length (s) yield the Frenet-Serret formulas:

=

=

=

mb

tbm

mt

(3.4)

where the prime () represents the differentiation with respect to arc length; andare

the curvature and torsion of the curve at the point of evaluation:

(s) = ''r (3.5)

(s) =)(

1

skdet [r, r, r] (3.6)

The reciprocal of curvature is the radius of curvature of the curve: = 1/.

3.2 Surface parametersA surface can be defined as the locus of a point moving in a three-dimensional space

(3), with two degrees of freedom. It can be given in parametric form

r(u, v)=

),(

),(

),(

vuz

vuy

vux

(3.7)


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where the Cartesian coordinates x, y andz are differentiable functions of the surface

parameters of u and v. The shape of the surface will not change when different

parameters are used to represent it. If the surface parameteru is related to v, r(u, v)

represents a curve on the surface. The unit normal vectorn of a point on the surface is

given by:

|vu

vu

|

rr

rrn

= (3.8)

where

ru =u

r

rv =

v

r

vu rr 0

The partial derivative r/u represents a tangent vector of the curve v = constant, and it

is denoted as ru, and so as that of the partial derivative rv.

The square of the infinitesimal distance between two points (u, v) and (u + du, v + dv)

on surface r defines the first fundamental form I of the surface:

I = dr dr = E du2 + 2F du dv + G dv2 (3.9)

where the fundamental magnitudes of the first order E, F and G are:

E = r2

u , F = rurv, G = r

2

v (3.10)

The inner product of the infinitesimal distance dr and the infinitesimal variation dn

defines the second fundamental form II of the surface:

II = dr dn = L du2 + 2M du dv + N dv2 (3.11)

where the second order fundamental magnitudes of L, M and N are:


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L = nruu , M = nru , N = nr (3.12)

The values of the first and second order fundamental magnitudes depend on the

location of the point on the surface but they do not depend on the direction of the

normal plane through that point.

At each point of a nonsingular parametric surface, a unique unit surface normal n is

defined by Eq. (3.8). The family of planes containing the normal n at point P on surface

r cut the surface in a family of normal section curves passing through that point. For

each normal section curve C, its tangent vectort defines the normal section direction.

The curvature n of the normal section curve C is defined as the surface normal

curvature in direction t. The surface normal curvature value n at point P can be

calculated from the first and second fundamental forms at this point:

n =I

II=

22

22

2

2

GdvFdudvEdu

NdvMdudvLdu

++

++ (3.13)

Although the first and second order fundamental magnitude values E, F, G, L, M and N

are fixed on a point of the surface, the value ofI

IIdepends on the ratio of

dv

du.

Therefore, the normal curvature n may have different values in different directions of

the normal section. The extreme normal curvature values 1 and2 are called principal

curvatures, and the corresponding directions t1 andt2 are the principal directions. In the

special case, where E:F:G = L:M:N, the normal curvature is independent of the normal

section direction t. The point with this property is called the umbilical point. For any

non-umbilical point on the surface, its principal directions are orthogonal, i.e. ( t1t2) =


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0. The principal curvatures 1 and2 can be calculated from Gaussian (K) and mean

(H) curvature values, and

K = 12 = 2

2

FEG

MLN

(3.14)

H =2

1(1 + 2) =

)(2

22FEG

MFLGEN

+(3.15)

The Gaussian and mean curvature values determine the surface shape around a point:

If K > 0, the surface shape is either concave or convex around the point.

If H > 0, it is a concave point; otherwise, it is a convex point.

If K = 0, at least one of1 and2 is zero.

If H = 0, it is a planar point. If H0, the surface is cylindrical or through-shaped around the point.

If H > 0, it is a concave point; Otherwise, it is a convex point.

If K < 0, it is a saddle point.

From Eqs. (3.14) and (3.15), the principal curvatures can be calculated as:

1,2 = H KH 2 (3.16)

In tool path generation, if the signed curvature value of the surface is greater than that

of the cutter, concave interference arises.


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The differential dn of a unit normal vector in the principal direction in terms of a

principal curvature i has the following relation:

dn + i dr = 0 (3.17)

where dr is the differential of r(u, v) at that point. Eq. (3.17) is called Rodrigues

formula.

3.3 Curves on surfacesA curve r(t) on the surface can be expressed as:

r(t) = r ( u(t), v(t)) (3.18)

The curve r(t) becomes an iso-parametric curve ifu(t) = constantorv(t) = constant.

If the tangents of curves on a surface coincide with the principal directions there, these

curves are called the lines of curvature. The lines of curvature form an orthonormal net

which is given by:

(GM - FN) dv2+ (GL EN)dudv + (FL - EM)du2 = 0 (3.19)

It is possible to generate the shortest tool path along the surfaces lines of curvature.

Let be an angle between the unit normal n of the surface r and the vertical direction

T. The angle can be expressed as:

cos= T n (3.20)

If = 90 o, the points given by Eq (3.20) form the silhouette curve with respect to

direction T. When there is no undercut, the parting lines are the silhouette curves with

respect to the parting direction.


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3.4 Offset surfaceAn offset surface can be defined as the locus of points, each of which has a constant

distance R from a corresponding point of surface r(u,v) in the direction of its normal

vectorn at that point:

ro(u, v) = r(u, v) +Rn(u, v) (3.21)

So long as ro(u, v) does not intersect with itself, a sphere of radiusR with its center on

the offset surface, touches the original surface at one point. If there are regions

bounded by the self-intersection curve of the offset surface, the sphere with its center

in this region will touch more than one point. In tool path generation, gouging occurs.

It was proven by Willmore [Willmore 1959] that the surface normal of the offset

surface ro(u, v) at point (u, v) is:

),()1)(1()1)(1(),(

21

21o vu

RRRRvu nn

= (3.22)

It can be seen from Eq. (3.22) that the normal vectors of surface r(u, v) and its offset

surface ro(u, v) is parallel. If (1 -R1)(1 -R2) > 0, the normal directions are the same.


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CHAPTER 4

MOULD DESIGN MODIFICATION

When the design of the plastic part is changed, the design of the affected mould inserts

need to be modified. The existing commercial CAD systems cannot automatically

modify mould design when the parameters of the mould and the plastic part are lost. In

addition, when the mould has been machined and material needs to be added due to

product design modifications, an insert may need to be designed to provide the extra

material for the machined mould. Existing commercial CAD systems cannot realize

this process automatically. In practice, when the design of a plastic product is modified

and passed to the mould manufacturing department, the mould designer studies and

identifies the modified region first. The mould design is then modified according to the

modified product and the mould manufacturing process status. The mould design

modification is based on the designers experience, which is time-consuming and

error-prone.

This chapter introduces a mould design modification system based on the designed

mould and the new plastic part. With this system, the old and the new plastic products

are compared. The mould is then modified automatically according to the designed

mould and the mould machining process. If material needs to be added to a machined

mould, inserts and pockets will be designed automatically. An algorithm of detecting

the interference between the pocket of the insert and the cooling, ejector, lifter and

screw holes of the mould insert is also introduced.


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Chapter 4 Mould Design Modification

43

This chapter is organized as follows. The basic concepts and principles of mould design

modification are discussed in the first section. Based on these principles, the mould

design modification system is developed, and the architecture of the system is

introduced in the second section. Section 3 introduces how to identify solid bodies of

material to be added or removed. Section 4 introduces how to identify the mould insert

that material needs to be added to or removed from. The methods of adding and

removing material from the designed mould are studied in Sections 5 and 6,

respectively. The algorithm of detecting interference between the pocket and the

cooling, ejector, lifter and screw holes of the mould insert is also introduced in Section

6. An example of modifying mould design with the developed algorithm is illustrated in

the last section.

4.1 Basic concepts and principles of mould design modificationSince the mould has been designed, the method of mould design modification is

different from that of designing a new mould. Besides the basic mould structure and

functional requirements, the designed mould and the mould machining status should

also be taken into account in modifying the mould design. The mould design may need

to be modified before or after the mould has been machined. If the mould has not been

machined, the mould design can be modified directly by uniting or subtracting metals

that need to be added to or removed from the mould. If the mould has been machined,

the mould needs to be modified with different methods according to whether metals

need to be added to the mould. This research emphasizes on the case that the mould

has been machined.Some basic concepts and principles of mould design modification

are introduced in this section.


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4.1.1 Concepts and assumptions of mould design modificationWhen the design of a plastic product is changed, the mould insert corresponding to the

modified region should also be modified. According to how the plastic part is changed,

material may need to be added to or removed from the designed mould. One or more

portions of the plastic part may be changed which may affect more than one mould

insert. To minimize the affected mould design and manufacturing processes, only the

mould inserts corresponding to the modified profile of the plastic product will be

modified. The other mould inserts and components should be kept unchanged as

possible.

After the mould design is modified, it is usually machined to the designed profile with

CNC or EDM machines. Since the machining process can only remove material from

the mould, the modification of the mould design should make sure that there is extra

material left for machining. If the mould has been machined and material needs to be

added to the designed mould, different methods may be used to modify the mould

design according to how the extra material will be added. In practice, depositing

material with a welding process and designing an insert are the two commonly used

methods to add material to a machined mould. With the welding process, the molten

metal is deposited directly to the portion that needs extra material. In this case, the

mould design can be modified through joining the solid body of the metal with the

designed mould and marking the area to be welded. The welded region will then be

machined to the design profile. However, only a limited amount of metal can be added

with the welding process, as this process may lead to internal stresses due to the high

welding temperature. Therefore, designing insert is widely used in practice to add extra


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material to the machined mould. This research will emphasize on this method for

adding material to the mould.

In order to shorten the mould design and manufacturing lead-time, many mould

manufacturing companies are using 3D CAD/CAM software. In practice, the plastic

part and mould inserts are usually managed in a way that they can easily be identified.

It is assumed in this research that the mould has been designed based on the old plastic

part with 3D CAD software and the same CAD system is used to modify the designed

mould and unique names have been assigned to the old plastic part and the designed

mould inserts. The system can thus automatically identify these parts. In addition, it is

assumed that the new plastic part has been enlarged with the same scale factor as for

the old one, and it has been oriented and positioned to the same orientation as the old

plastic part.

4.1.2 Principles of insert and pocket designIf the mould design modification needs to remove material from the machined mould,

the mould design can be modified by subtracting the material from the affected mould

insert directly. If material is to be added to the machined mould, an insert needs to be

designed for the added material.

If an insert needs to be designed for the added material, a pocket should be created in

the mould insert to hold and fix the insert. There are some principles in designing the

insert and the pocket:

1) Since the insert will form the profile of the plastic part, the gap between the insert


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and the pocket should be small enough to prevent the molten plastic from escaping.

The pocket and the insert body should be designed with the same dimension.

2) The designed insert and the pocket should be easy to machine and assemble. Theinsert body is usually designed with a cylindrical or a rectangular shape. To make

it easier to fix the insert in the mould, a through pocket should be designed as

much as possible. In practice, a shoulder is usually designed at the bottom of the

insert and the pocket to fix the insert (see Figure 4.1 a).

3) If a rectangular shape insert is designed, since only the z dimension of the shoulderneeds to be controlled, to make it easier to machine and assemble, the size of the

pockets shoulder is usually designed to be bigger than that of the insert in x- and

y-directions with two semi-cylinders created at the two sides (see Figure 4.1a). The

radius of the cylinder usually equals to the cutter radius that will be used to

machine the block.

4) When a cylindrical shape of insert is designed, a planar face that is parallel to theZX-plane or ZY-plane is usually designed to prevent the insert from rotating about

its axis (see Figure 4.1b).

5) There are usually some cooling channels, screw and lifter holes in a mould insert.When a pocket is designed, it should not interfere with these holes. The minimum

distance between the pocket and these holes should be greater than a given value,

which is the minimum thickness value for enough strength and machining

tolerance. This value is decided by the mould size and is usually in the range of 3


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c

Cooling system

Blind insert

a

b

Designed mould

Rectangular insertand its shoulder

Cylindrical insert andits shoulder

Figure 4.1 Different shapes of inserts and pockets


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to 8 mm. If a through pocket interferes with other holes, a blind pocket should be

designed (see Figure 4.1c).

Based on these concepts and pr

Documents

ZLP Thesis