The determination of undercut regions and their releasing directions plays an important role in injection mold design. Most of the approaches in the literature face difficulties in recognizing the undercut regions of real-life parts. This thesis proposes an approach to automating the determination of undercut regions and their releasing directions for complex parts with free-form surfaces. In order to delineate the border of undercut regions, orthogonal cutting planes are firstly employed to automatically find the inner loops of a part model using the concept of “shared vertices” and “adjacent points”. The inner loops are classified into two groups: closed inner loops and open inner loops. In order to determine undercut regions, open loops are further converted to closed ones through the introduction of additional line segments. To discover the surfaces belonging to undercut regions, attributes are then assigned to the surfaces of the part model based on the topological relationship of adjacent surfaces of each inner loop. After that, the concept of “target facets” is proposed to separate the undercut regions from other surfaces in the model. Through the recognized surfaces of the undercut regions, the concept of “visibility map” is further applied to determine feasible releasing directions for each of the undercut regions. Delaunay triangulation is adopted here to represent a set of releasing directions. The undercut regions having the same releasing direction are finally grouped to form a slider in the injection mold.
In addition to proposing the methodologies to find undercut regions and their releasing directions for free-form surfaces, this thesis also uses commercial software packages Pro/Engineer Wildfire 5.0 and Matlab 9.0 to implement the algorithms developed for the proposed methodologies. Several real-life parts, such as cell phone cover and bike helmet, are used as testing examples to demonstrate the applicability of the implemented system. While these example parts contain a large number of complicated free-form surfaces, the implementation results show that undercut regions and their releasing directions can be found within acceptable range of time.

The determination of undercut regions and their releasing directions plays an important role in injection mold design. Most of the approaches in the literature face difficulties in recognizing the undercut regions of real-life parts. This thesis proposes an approach to automating the determination of undercut regions and their releasing directions for complex parts with free-form surfaces. In order to delineate the border of undercut regions, orthogonal cutting planes are firstly employed to automatically find the inner loops of a part model using the concept of “shared vertices” and “adjacent points”. The inner loops are classified into two groups: closed inner loops and open inner loops. In order to determine undercut regions, open loops are further converted to closed ones through the introduction of additional line segments. To discover the surfaces belonging to undercut regions, attributes are then assigned to the surfaces of the part model based on the topological relationship of adjacent surfaces of each inner loop. After that, the concept of “target facets” is proposed to separate the undercut regions from other surfaces in the model. Through the recognized surfaces of the undercut regions, the concept of “visibility map” is further applied to determine feasible releasing directions for each of the undercut regions. Delaunay triangulation is adopted here to represent a set of releasing directions. The undercut regions having the same releasing direction are finally grouped to form a slider in the injection mold.
In addition to proposing the methodologies to find undercut regions and their releasing directions for free-form surfaces, this thesis also uses commercial software packages Pro/Engineer Wildfire 5.0 and Matlab 9.0 to implement the algorithms developed for the proposed methodologies. Several real-life parts, such as cell phone cover and bike helmet, are used as testing examples to demonstrate the applicability of the implemented system. While these example parts contain a large number of complicated free-form surfaces, the implementation results show that undercut regions and their releasing directions can be found within acceptable range of time.

ABSTRACT vi
ACKNOWLEDGEMENTS viii
TABLE OF CONTENTS ix
LIST OF FIGURES xii
LIST OF TABLES xviii
NOTATIONS xix
Chapter One INTRODUCTION 1
1.1 Research background and motivation 1
1.2 Research objectives 4
1.3 Thesis structure 4
Chapter Two LITERATURE REVIEW 6
2.1 Definition and classification of undercut regions 6
2.1.1 Definition of undercut regions 7
2.1.2 Classification of undercut regions 7
2.1.3 Geometric factors of an undercut region 10
2.1.3.1 Surfaces of undercut regions 10
2.1.3.2 Releasing directions of undercut regions 11
2.2 Recognition of undercut regions 12
2.3 Determination of parting directions 27
2.4 Slicing methods for mold design 30
2.5 Concept of visibility map 32
2.6 Delaunay triangulation representation 36
2.7 Comments on the past literatures 38
Chapter Three AUTOMATIC DETERMINATION OF INNER LOOPS OF UNDERCUT REGIONS 44
3.1 Classification of inner loops 44
3.2 Workflow of finding inner loops 46
3.3 Selection of parting directions 48
3.4 Formation of 3 sets of orthogonal cutting planes 48
3.5 Extraction of intersection points 50
3.6 Collection of candidate points belonging to inner loops 51
3.7 Formulation of inner loops 58
3.8 Conversion of open inner loops to closed loops 61
3.9 Discussions 64
Chapter Four AUTOMATIC DETERMINATION OF SURFACES OF UNDERCUT REGIONS 66
4.1 Determination of surfaces of undercut regions using B-rep data 66
4.1.1 Formation of three sets of cutting planes 68
4.1.2 Generation of intersection curves of cutting planes and part surfaces 69
4.1.3 Generation of projected curve of inner loops onto the current cutting plane 70
4.1.4 Analysis of loops in the current cutting plane 70
4.1.5 Assignment of surface attributes 71
4.2 Determination of undercut surfaces using STL file 74
4.2.1 Formation of three sets of cutting planes 75
4.2.2 Determination of intersection line-segments between cutting planes and STL model 76
4.2.3 Projection of inner loops 80
4.2.4 Assignment of facet attributes 85
4.3 Discussions 87
Chapter Five AUTOMATIC DETERMINATION OF RELEASING DIRECTIONS OF UNDERCUT REGIONS 88
5.1 Calculation of releasing directions of undercut regions 88
5.2 Grouping of undercut regions 94
5.2.1 Grouping of undercut regions into a side-core region 94
5.2.2 Grouping of undercut regions into core or cavity 98
5.3 Discussions 100
Chapter Six SYSTEM IMPLEMENTATIONS 101
6.1 Implementation Example 1－Lamp cover 101
6.2 Implementation Example 2 – Plastic cover of a hair dryer 114
6.3 Implementation Example 3 – Component of cell phone 117
6.4 Implementation Example 4 – Bike helmet model 121
Chapter Seven CONCLUSIONS AND DISCUSSIONS 146
7.1 Conclusions 146
7.2 Future works 147
REFERENCES 150
AUTHORIZATION 155
BRIEF INTRODUTION OF THE AUTHOR 156

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