UNIVERSITY OF CINCINNATI

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I,______________________________________________,hereby submit this as part of the requirements for thedegree of:

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in:________________________________________________

It is entitled:________________________________________________

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Approved by:________________________

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A SHEET METAL DESIGN ADVISOR: DESIGN RULES AND INTER-FEATURE DESIGN CHECKING

A thesis submitted to the

Division of Research and Advanced Studies of the University of Cincinnati

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in the Department of Mechanical, Industrial and Nuclear Engineering of the College of Engineering

2003

by

Shashikiran R. Hegde Bachelor of Engineering (B.E.)

University of Pune, Pune, India, 2000 Committee Chair: Dr. Sam Anand

ABSTRACT

Sheet metal part design relies heavily on manufacturing experience, which is not

very easily available to the designer. The manufacturing experience has to be

documented and incorporated in the design process. This would eliminate frequent

redesign of parts, after being assessed as infeasible or costly for manufacture in the

design stage. Such a DFM analysis would reduce product time to market and reduce

overall product costs.

The present work aims at compiling a comprehensive set of design rules for sheet

metal part design and a methodology for implementing inter-feature design rule checking

for reducing infeasible designs, costs and production cycle times. The inter-feature

module is part of a Design Advisory and Feature Extraction system that aims at checking

the CAD model for various design rules. These rules are incorporated here and

implemented for SolidWorks 2000, which has a separate sheet metal modeling module.

The implementation has been done in Visual Basic using the OLE Interface provided by

SolidWorks API.

i

ii

ACKNOWLEDGEMENTS

I thank my advisor Dr. Sam Anand for his invaluable guidance and advice

throughout my graduate studies. This research has been a learning experience and Dr

Anand has been a constant source of inspiration, throughout this process. I also wish to

thank him for allowing me to work in a healthy research environment that has given me a

well-rounded educational experience

I also thank my friends at the CAM lab and my project partner Sushilendra

Deshpande, who has been a great help with his interesting and rewarding suggestions

during the development of the algorithm and its implementation. I am indebted to all my

friends at UC, who have been a constant source of encouragement and for making this

stay very memorable.

I am thankful to Dr. Ernie Hall and Dr. Richard Shell for being on the defense

committee and for their cooperation.

I finally thank the University of Cincinnati for providing me the opportunity to

pursue my dreams, do research and for providing financial assistance.

iii

CONTENTS

Abstract

Acknowledgments

Contents

List of Figures and Tables.vi

1. Introduction........................................................................................................... 1

1.1 Background and Need for Research ................................................................... 1

1.2 Objectives of Research ....................................................................................... 2

1.3 Outline of Thesis................................................................................................. 2

2. Literature Review ................................................................................................. 4

2.1 Design And Manufacturability Analysis ............................................................ 4

2.2 Feature Extraction............................................................................................... 6

2.3 Process Planning................................................................................................. 7

3. Manufacturability Rules ...................................................................................... 9

3.1 Intrafeature Vs. Interfeature................................................................................ 9

3.2 Intrafeature rules ............................................................................................... 10

3.3 Inter-feature Rules ............................................................................................ 14

3.4 Part Nesting Considerations ............................................................................. 18

3.5 Shearing Operations.......................................................................................... 23

3.6 Forming Operations .......................................................................................... 26

3.7 Drawing Operations.......................................................................................... 28

iv

4. Design Advisory System ..................................................................................... 33

4.1 Feature Extraction............................................................................................. 34

4.1.1 Internal feature extraction .......................................................................... 35

4.1.2 External feature extraction ......................................................................... 36

4.1.3 Bend feature extraction .............................................................................. 38

4.2 Intra-Feature Design Checking......................................................................... 39

4.3 Inter-Feature Rule Checking............................................................................. 39

4.3.1 Profile Offsetting........................................................................................ 43

4.3.2 Intersection Checking................................................................................. 50

5. SolidWorks API Description.............................................................................. 57

5.1 Class Modules................................................................................................... 57

5.1.1 CofVertex................................................................................................... 57

5.1.2 CofFace ...................................................................................................... 57

5.1.3 CofLoop ..................................................................................................... 57

5.1.4 IofEdge....................................................................................................... 57

5.1.5 CofStraightLine.......................................................................................... 58

5.1.6 CofCircle .................................................................................................... 58

5.1.7 CofArc........................................................................................................ 58

5.2 Main Code Modules ......................................................................................... 58

5.2.1 Main Module.............................................................................................. 58

v

5.2.2 Preliminary Offsetting Module .................................................................. 59

5.2.3 Pair-wise Processing Module..................................................................... 59

5.2.4 swConst ...................................................................................................... 60

6. Conclusions.......................................................................................................... 61

6.1 Conclusions....................................................................................................... 61

6.2 Directions for Future Research......................................................................... 62

References.67

vi

LIST OF FIGURES AND TABLES

Fig. 2.1: ProMod-S Environment........................................................................................ 4

Fig. 2.2: Medial Axis Transform ........................................................................................ 5

Fig. 2.3: BendCad System .................................................................................................. 8

Fig. 3.1: Consideration for hole diameter ......................................................................... 10

Fig. 3.2: Rules for notches ................................................................................................ 11

Fig 3.3: Lanced lug ........................................................................................................... 11

Fig 3.4: Rules for blanks and recesses .............................................................................. 12

Fig 3.5: Rule for components with round ends................................................................. 12

Fig 3.6: Rule for components with round ends and radius less than 0.5 w ...................... 12

Fig. 3.7: Rules related to bends and grain direction ......................................................... 14

Fig. 3.8: Rules for tapped holes ........................................................................................ 14

Fig. 3.9: Rule for distance between holes ......................................................................... 14

Fig. 3.10: Rule for distance between hole and outer edge ................................................ 15

Fig. 3.11:Rule between bends and holes........................................................................... 15

Fig. 3.12: Slot parallel to bend.......................................................................................... 15

Fig. 3.13: Spacing between adjacent tabs and slots .......................................................... 16

Fig. 3.14: Rule for spacing between internal slot and external edge ................................ 16

Fig. 3.15: Spacing between extruded holes ...................................................................... 17

Fig. 3.16: Spacing considerations for tapped holes .......................................................... 17

Fig 3.17: Rule for aligned holes on opposite faces........................................................... 18

Fig. 3.18: Cut off operation without any loss of material................................................. 18

Fig. 3.19: Circular blanks are suited for staggered layout ................................................ 19

vii

Fig. 3.20: Blanks can be redesigned for nesting to eliminate scrap.................................. 19

Fig. 3.21: Double-row layout............................................................................................ 19

Fig. 3.22: Blanks may be interlocked for more utilization of the material....................... 20

Fig. 3.23: Short center distances permit faster stock feed ................................................ 20

Fig. 3.24: Scrap left between parallel edges will avoid necessity for precision alignment

................................................................................................................................... 21

Fig. 3.25: Blanking part (A) utilizes scrap necessitated by difficult design (B)............... 21

Fig. 3.26: Stock strip allowances ...................................................................................... 22

Fig. 3.27: Recommendation for large irregular shaped blanks......................................... 22

Fig. 3.28: Direction of grain is a characteristic of rolled stock......................................... 23

Fig. 3.29: Design should consider burrs ........................................................................... 24

Fig. 3.30: Design recommendation for relief slots for tabs .............................................. 24

Fig. 3.31: Standard punch shapes - Round most preferred ............................................... 24

Table 3.1 Shaving allowance ............................................................................................ 25

Fig. 3.32: Use of ribs for extra strength in a right angle bend .......................................... 25

Fig. 3.33: Rules for setouts ............................................................................................... 26

Fig. 3.34: Grain direction for bends.................................................................................. 26

Fig. 3.35: Recommended bend allowance for a square corner ......................................... 27

Fig. 3.36: Design recommendation for flanges................................................................. 28

Fig. 3.37: Design recommendations for channel bends.................................................... 28

Fig 3.38: Design guideline for draw height using short-run tooling................................. 29

Fig. 3.39: Minimum radius design rule for drawn parts ................................................... 29

Fig 3.40: Minimum radius for rectangular box-type parts................................................ 29

viii

Table 3.2 Average number of reductions.......................................................................... 31

Table 3.3 Average permissible reduction ......................................................................... 32

Fig. 4.1: Design Advisory System .................................................................................... 33

Fig. 4.2: Internal Stamped Feature Library....................................................................... 34

Fig. 4.3: External Stamped Feature Library...................................................................... 34

Fig. 4.4: Internal Stamped Single D Feature..................................................................... 35

Fig. 4.5: Feature String Pattern formation-1..................................................................... 36

Fig. 4.6: Explanation of Feature String Pattern formation-2 ............................................ 37

Fig. 4.7: Explanation of Feature String Pattern formation-3 ............................................ 37

Fig. 4.8: Explanation of Feature String Pattern formation-4 ............................................ 38

Fig 4.9: Example Sheet Metal Part ................................................................................... 41

Fig 4.10: Offset directions for individual edges ............................................................... 41

Table 4.1: Distances between features.............................................................................. 42

Fig. 4.11: Offset of tangential edges................................................................................. 44

Fig. 4.12: Offset of convex edges ..................................................................................... 45

Fig. 4.13: Offset of non-convex edges.............................................................................. 45

Fig. 4.14: Offset Direction for Outer Edges ..................................................................... 46

Fig 4.14: Output of preliminary offsetting module........................................................... 48

Fig. 4.15: Output pair wise processing of edges............................................................... 49

Fig. 4.16: Edge Quadtree .................................................................................................. 51

Fig. 4.17: PR quadtree ...................................................................................................... 52

Fig. 4.18: PM2 Quadtree ................................................................................................... 53

Fig. 4.19: Example of decomposition of offset profiles ................................................... 56

ix

CHAPTER 1

INTRODUCTION

Design is the most important and an expensive stage in the product development

process. This stage heavily influences the final product cost. In typical industrial

situations there is a lack of interaction between the design and manufacturing

departments. The design process must also incorporate the manufacturing knowledge in

the industry for a seamless transition of the product development process from design to

manufacturing. Systems that aim at storing and using the manufacturing knowledge to

influence the product design during design are successful in reducing the product cost.

This chapter discusses the need for the current research and the outline of the thesis.

1.1 Background and Need for Research

The product design has to conform to the specifications and also it has to be

suited to the manufacturing environment. The design stage is the key, and reverting back

to the design stage, to modify the product design, after encountering a problem in

manufacturing will only add to the cost.

Design for manufacture is a step towards integrating manufacturing and the

design processes. An attempt at doing this is nothing new. Design for manufacture

(DFM) is a proven design methodology that works for any company. For DFM to work,

designers must know how to actually design products that are manufacturable.

Experience in manufacturing is a necessity for optimal design, but designers who dont

have this experience are at a loss while designing new components. A good DFM

program will aid designers through the design process.

A DFM program accomplishes the following objectives.

1

Experience is documented. New DFM knowledge is introduced. Everyone follows the same policy.

Design of sheet-metal products is heavily dependent on manufacturing

constraints. This makes this industry very conducive to DFM analysis. The design

process for sheet metal products is based on empirical and experience based rules. There

have been a few attempts at incorporating the manufacturing rules into the design domain

for sheet metal parts.

1.2 Objectives of Research

This works aims at collecting all the design rules for sheet metal parts, compiling a

comprehensive set and using these for DFM analysis of the product. The design rules are

based on the failure of metal during metalworking. The comprehensive approach should

successfully encompass the design rules, standard manufacturing practices and design

recommendations across all sheet metal processes and also investigate the interaction

between these elements in the creation of a final sheet metal part.

The rules have been classified into intrafeature and interfeature design rules. An

algorithm is presented for checking the inter-feature design rules. The feature extraction

and intra-feature rule checking module, which is a part of the system, has been developed

by Deshpande S. [23]. This system is implemented in Solidworks using the Solidworks

VB API.

1.3 Outline of Thesis

The introduction is followed in chapter 2 by a literature review on other systems for

sheet metal parts and associated sub-systems in the new framework proposed. The

2

comprehensive set of design rules for sheet metal part design are presented in chapter 3.

Chapter 4 describes the methodology used for implementing the design rule checking for

sheet metal parts. Techniques for applying these design rules in a solid modeling system

are presented. This is followed by the methodology and implementation of Feature

Extractor and Design Advisor for SolidWorks. Chapter 5 describes the implementation

details and explains the various VB modules used for implementing the design checking

method. Finally, the conclusions and directions for future work are described in Chapter

6.

3

CHAPTER 2

LITERATURE REVIEW

There have been various attempts at automating sheet metal design and

manufacturing processes. Various CAD/CAM systems have been developed that aid the

production and design of sheet metal parts. Most of the CAD packages used in the

industry come equipped with a separate sheet metal design module that aids specifically

in designing sheet metal parts. The following section describes the existing research in

sheet metal design and manufacturability analysis of parts.

2.1 Design And Manufacturability Analysis

Yeh. et. al. [6] describe a feature based product modeler, ProMod-S, which includes a

rule-based design advisor among several other modules. The schematic is shown in the

Figure 2.1

1

Fig. 2.1: ProMod-S Environment [6]

Methodologies for both the identification and correction of design violations are

presented. The ProMod-S system considers only one side of the sheet metal part and

4

reduces many three-dimensional problems to two-dimensional ones by assuming constant

thickness across the part. Inter-feature violations are also addressed in this work. Voronoi

diagrams, shown in Figure 2.2, are used to solve proximity problems are used in this

system. The Voronoi diagrams for the feature and the surface that encloses it are

generated and blended to obtain a medial axis transform (MAT). MAT greatly reduces

the complexity of the search for design rule violations and avoids a combinatorial

explosion.

Fig. 2.2: Medial Axis Transform [6]

Radhakrishnan, et al. [1] further advances the medial axis transform technique by

analyzing the design rules and derives the common characteristics of these rules shown in

Figure 2.2. This aids in checking for violation of design rules for user-defined features as

well. The rule-checking problem is modeled as a proximity problem of a multiply

connected polygon and proceeds one face at a time. Each face is modeled as a multiply

connected polygon. The medial axis approach reduces the search space considerably

while checking for design violations in complex sheet metal parts. It also reveals

plausible displacing directions for features that violate design rules to correct these

violations. However, they do not consider rules for formed features and deep drawn parts.

5

2.2 Feature Extraction

Feature extraction for cad models has been extensively studied and a vast amount of

literature is available. A few attempts at feature extraction, specifically for sheet metal

parts are described below.

Nnaji B. O. [29] et al has developed a feature extraction module for identifying

various sheet metal features. The module has been developed for the ProMOD-S solid

modeler. The feature extractor uses a neutral cad file format (IGES) as the input. A

graph-based approach is used to identify the features. In this paper, a strategy using a

combination of geometric reasoning and feature pattern recognition is employed for

feature recognition purpose. There are two levels of recognition process, the first level is

geometric reasoning between feature classifications, and while the second level is pattern

matching based on feature patterns. In this research, the features on the outer loop, such

as various types of notches are not extracted; the internal features, bends and holes are

recognized.

Lentz D. H. and Sowerby R, [24] have developed a method for hole-extraction for

sheet metal parts. Holes are grouped into types on the basis of the number of faces they

emanate from. Topological and geometric properties of holes are developed. The

algorithm uses a modified face adjacency graph (MFAH) that provides all the necessary

information for feature recognition and extraction. The algorithm can identify all types of

holes in stretch drawn parts forming an enclosure.

Jagirdar R. [25] et. al. describe a feature recognition methodology for shearing

operations for sheet metal components. This paper attempts to identify manufacturing

features based on the proposed classification system using feature sets. The methodology

6

initially identifies geometric data for various entity groups. The entity groups are

classified into raw material feature set, a boundary feature set and an inside feature set.

Components are then arranged lexicographically and the various feature patterns are

matched.

2.3 Process Planning

Wang C.[8] et. al. have developed a system for design and production of sheet metal

parts. The system consists of two sub-systems, the design system and the planning

system. The design system called BendCad, which is a design-with features system,

manages the relationships among the multiple representations of sheet-metal parts. The

system uses multiple representations of the part during different manufacturing stages.

The final assembly of the sheet metal product is represented as the connectivity

relationship between 3-d parts.

The planning system consists of an operations planner, a tooling system, a grasping

system, a robot motion planner and an open architecture controller. The planner generates

the possible bend sequences and asks the sub-systems to evaluate the manufacturability

costs. The planner uses a heuristic search method that uses the heuristic estimate of the

cost between the current state and the goal state.

The BendCad system has various pre-defined features and these can either be directly

generated using this system or are reasoned using the BendCad geometric kernel.

The features in this system suggest precedence rules or the tool selection, grasping and

motion strategies. These precedence rules form the knowledge base of the system and can

be used as precedence heuristics or precedence constraints based on the certainty factors

7

of these rules. Features also suggest special tools, workpiece grasping and fine motion

strategies. These are used as constraints, which are related to the bending sequence.

Fig. 2.3: BendCad System [8]

Duflou J. R. [15] has developed a directed graph based approach for the problem size

reduction for bend sequence verification of sheet metal parts. The basic problem is to

identify a feasible bending sequence, according to geometric constraints, and to select the

optimum solution based on ergonomical considerations. The process of evaluating

feasible bending sequences for a part is computationally intensive and would require a

study of 2nn * n! operations. Bending verification implies identification of a suitable

gauging edge, interference checking for positioning and collision checking between

machine and workpiece. The author suggests a redundancy elimination check. Also the

use of a directed graph eliminates the number of cases to be considered. Pre-processing

of the part geometry further reduces the problem size. This includes a backwards-

unfolding check that identifies the bends that can be performed last. These and a few

other set of heuristics described reduces the problem size.

8

CHAPTER 3

MANUFACTURABILITY RULES

This section describes the rules for sheet metal component design. This is an

attempt to compile a comprehensive design rule database across all operations for the

domain of sheet metal parts. Most companies have their best practice knowledge base for

manufacturing to reduce infeasible designs, costs and production cycle times. However,

this knowledge is treated as a trade secret and is not readily available. As a result, as

Radhakrishnan, et al. [1] rightly point out, compiling comprehensive design rules for

manufacture rules is a challenging task involving scavenging literature extensively,

synthesizing the knowledge base in bits and pieces.

Research carried out by S. Mallikarjun[18] identifies quite a few of the design rules.

The rules presented here are a superset of the rules collected by S. Mallikarjun. This

research helps in detecting violations leading to material failures across processes

involved in sheet metal manufacture. This is a very important precursor to costing of the

part since a rule violation may imply that special tooling is required and the costs tend to

accelerate. This means that two similar looking parts can widely vary in cost if any

design rule is violated. If the designer costs the part with a design rule violation, only to

find it very high, he/she might not know how to correct the wrong design unless suitable

design recommendation is suggested.

3.1 Intrafeature Vs. Interfeature

The design recommendations may be broadly classified as intrafeature rules and

interfeature rules. Intrafeature rules are those rules that are applied to the set of geometric

elements that constitute a single feature.

9

Interfeature rules are those rules that involve relationships between elements of more

than one feature, which may be of the same kind or different kind. These rules need

search algorithms to identify the conditions under which the rule applies in their

topology. Techniques have to be developed specific to each interfeature design guideline

that are easy to implement and also very efficient. Since this involves a combination of

two or more features, it can soon lead to a combinatorial explosion if not searched for

every possible combination. Ways to reduce the possible search space have to be devised.

The design advisory system developed in the current research has incorporated both

intra- and inter-feature type of rules.

3.2 Intrafeature rules

1. Holes

1. The diameter of punched holes should be greater than the thickness of the work

piece and not less than 2.4892 mm (0.098 in) as shown in Figure 3.1. This is

because the punch diameter becomes too small to bear the shear force required to

punch the hole over a small area, often leading to failure. These small diameter

holes are punched using the fine-blanking process.

Fig. 3.1: Consideration for hole diameter [13]

10

2. Oblong Holes

Oblong holes are generally incorporated as adjustment slots. As a general rule,

the length to width ratio of an adjustment slot should be no more than a 5 to 1

ratio, with a maximum of 2 to 1 permissible.

3. Holes on faces having surface angles greater than 30o should be avoided as far as

possible.

Fig. 3.2: Rules for notches [13]

2. Notches

1. Notches should extend inside the stock edge at least 1.5 times the thickness but

not less than 0.508 mm.

2. The minimum widths of tabs and slots should be 1.5T or 0.5 mm (0.020 in). Their

length should be a maximum of 5 times their width.

3. For long narrow projections the minimum width of narrow sections should be 1.5

times the thickness. The rules are shown in the following figure 3.2.

3. Lanced lugs

1. Lanced lugs should have tapered sides if no clearance is provided.

Fig 3.3: Lanced lug [13]

11

4. Triangular tabs or slots

1. Triangular tabs or slots should have minimum end radii of one thickness and

should form included angles of 60 or more as shown in Figure 3.4. 2. Tapers for blanks should be recessed at least one thickness from the edge of the

part.

Fig 3.4: Rules for blanks and recesses [13]

3. Components requiring round ends should have a radius greater than or equal to

0.75W unless otherwise stated as shown in Figure 3.5. The radius is arrived at

here based on the minimum angle that is recommended as acceptable.

Fig 3.5: Rule for components with round ends [13]

4. 0.5W may be used if a relief angle 10 or greater at the point of tangency with the part edge is also used as shown in Figure 3.6.

Fig 3.6: Rule for components with round ends and radius less than 0.5 w [13]

12

5. Beads

1. The maximum height for beads is 2 times the thickness.

2. The minimum inner radius for beads is equal to the thickness of the piece

6. Bridges

1. The maximum ratio of lance length to bridge height is 4:1.

7. Curls

1. The inner diameter for curls should be 2.5 times to 8 times the metal thickness.

8. Bends

1. The width along the bend axis should be greater than or equal to 3 times the

thickness.

2. The bend radius (rb)

rb >= 1.6mm

or rb >= t (thickness of workpiece)

, whichever is greater.

3. Metal that is rolled shows a grain along the direction in which the stock was

drawn though the mill rolls. Bends should be at right angles to the grain or as

close thereto as possible, in order to avoid breakage of the blank as shown in

Figure 3.7. These factors must be considered while producing the blank and

sometimes the most economical layout of the strip will have to be abandoned in

order to avoid trouble in later forming operations. If the bends are at right angles,

the blank should be made at a diagonal to the grain.

13

Fig. 3.7: Rules related to bends and grain direction [30]

9. Tapped Holes

1. A design guideline for the minor thread diameter (tap-drill size) as shown in

Figure 3.8, is that it should not exceed twice the stock thickness for steel and

brass and 1.5 times the stock thickness for Aluminum, copper and zinc.

Fig. 3.8: Rules for tapped holes [13]

3.3 Inter-feature Rules

1. The spacing between the holes should be at least 2 times the stock thickness but not

less than 1.5 mm (0.060 in) and preferably 3 times to provide additional strength to

the die, by allowing a greater wall thickness as shown in Figure 3.9.

Fig. 3.9: Rule for distance between holes [13]

14

2. The minimum distance from the edge of the hole to the edge of any other feature

should be greater than the stock thickness and not less than 0.8 mm (0.030 in). It is

recommended that this space be at least 1.5 to 2 times the thickness of the work-piece

to the hole.

Fig. 3.10: Rule for distance between hole and outer edge [14]

3. The lowest edge of the hole should be at least 1.5 times stock thickness plus radii of

the bend. Distortion of the hole will occur if the two features are any closer. If this

placement is absolutely necessary, then a stress discontinuity should be provided

during forming to prevent the distortion of the hole by a non-functional hole, slot or

tab as shown in Figure 3.11.

Fig. 3.11:Rule between bends and holes [13]

4. Slots that are parallel to the bend should be a minimum of 4 times the stock thickness

(T) from the bend tangent line as shown in Figure 3.12.

Fig. 3.12: Slot parallel to bend [13]

15

5. Sharp corners, which are stress concentration points, should be avoided wherever

possible. Sharp external corners of punches and dies tend to break down prematurely,

causing more pull-down, larger burrs, or rougher edges of the blanked part in the area

of the corner. Similarly, sharp interior corners of punches and dies are a stress-

concentration point. A design guideline is to allow a minimum corner radius of two

times the stock thickness and never less than 0.16 in. Sharp corners produced by

shearing, slotting or blanking operations intersect at approximately 90 or less may have to be rounded by some secondary operation to achieve corners.

6. Adjacent tabs or slots should be spaced a minimum of 2T or 0.8 mm (0.030 in) apart

as shown in Figure 3.13.

Fig. 3.13: Spacing between adjacent tabs and slots [13]

7. Internal slots should be at least 1.5T or 0.8 mm (0.030 in) from the edge of the stock

as illustrated in Figure 3.14.

Fig. 3.14: Rule for spacing between internal slot and external edge [13]

8. Extruded holes should have a minimum spacing of 6T between their edges and should

be at a minimum of 4T from the blank edge. Depth of the extrusion should be a

maximum of 30 percent of its outer diameter as shown in Figure 3.15.

16

Fig. 3.15: Spacing between extruded holes [13]

9. Threaded screw or bolt holes should be at least 1.5 times the screw diameter from the

centerline of the hole to the edge of the part as shown in Figure 3.16.

Fig. 3.16: Spacing considerations for tapped holes [13]

10. Aligned hole in opposite bends - It is often required to include two aligned holes in

opposite legs of a U-bent part for holding a shaft or for some other purpose. It is

difficult to form such a part from a pre-pierced blank and have the holes aligned

precisely. Several alternatives can be considered as shown in Figure 3.17: (1) Pierce

or drill holes after forming, this provides excellent alignment though more expensive.

(2) Use broad tolerances on the holes, or make one a slot, allowing for misalignment

if the part function permits. (3) Include a pilot hole in the bottom of the U bend. This

hole is located over a pin in the pad of the forming die that will position the blank

consistently. (4) Stock of close thickness can be used for true alignment. Though the

material is more costly, savings resulting from not having to perform a second

operation may offset the extra cost.

17

Fig 3.17: Rule for aligned holes on opposite faces [13]

The following rules cannot be classified as inter-feature or intra-feature rules, but are

classified according to the sheet-metal process that they apply to. These rules were

collected by S. Mallikarjun [18] and have been added for completeness.

3.4 Part Nesting Considerations

1. Rectangular blanks permit nearly 100 percent utilization of the stock strip as shown in

Figure 3.18. Sheet metal operations are high volume, rapid production operations and

material alone can typically account from 50 to 90 percent of the total part cost.

Hence it is important to try and use these recommendations for nesting in stock strip.

Fig. 3.18: Cut off operation without any loss of material [12]

18

2. Circular blanks lend themselves well to double-row staggered layout as shown in

Figure 3.19.

Fig. 3.19: Circular blanks are suited for staggered layout [12]

3. The ideal blank nests into each other and has a width corresponding to that of

4. When possi layout of

5. ve a cumbersome web, consider a preliminary

6. ped blanks that cannot be positioned in a single row for maximum

commercially available strip stock as shown in Figure 3.20.

Fig. 3.20: Blanks can be redesigned for nesting to eliminate scrap [12]

ble, eliminate passing a scrap web or skeleton from the press. If

stock strip does not permit utilizing full width of strip, consider incorporating a scrap

cutter on the end of the press bed.

On large blanks that would lea

production of unit stock. The blanking operation will then leave an easily handled

scrap form.

Irregular-sha

utilization of stock may be more adaptable to a double-row layout. In Figure 3.21, the

blanks shown at positions 1 and 2 are cut simultaneously

Fig. 3.21: Double-row layout [12]

19

7. Irregular shaped parts can of as illustrated in Figure

Fig. 3.22: Blanks ma n of the material [12]

8. Double r lanking

9. widely used for nesting large blanks, costly materials and

10. two blanking centers constitutes the feed length and should

ten be interlocked for blanking

3.22.

y be interlocked for more utilizatio

ows that require two passes can be difficult to handle, since when b

the second row the blanked openings in the first row have a tendency to creep until

two openings overlap.

Double rows are most

production not high enough for a multiple operation die but too high to throw away

any scrap unnecessarily.

The distance between the

be kept as short as possible as shown in Figure 3.23 in order to speed up the

operation. In some instances, it would be wise to sacrifice a small amount of scrap in

order to gain on this point.

Fig. 3.23: Short center distances permit faster stock feed [12]

20

11. It is usually desirable to leave some scrap between parallel edges of irregular-shaped

pieces as shown in Figure 3.24 since the alignment of two overlapping lines on

successive strikes may be troublesome and costly.

Fig. 3.24: Scrap left between parallel edges will avoid necessity for precision alignment [12]

12. If a substantial area must be left in the scrap web, consider using this portion for

blanking another part that requires comparable production. An example of using this

guideline is shown in Figure 3.25.

Fig. 3.25: Blanking part (A) utilizes scrap necessitated by difficult design (B) [12]

13. The allowance shown in the Figure 3.26 should be used for mild steels as general

guidelines in the layout of the scrap strip. They will assure the web being strong

enough to resist breaking while in the tooling area and stiff enough to facilitate

handling when leaving the press. However, when a scrap cutter is employed on the

press, experience may show where allowances can be decreased but not beyond the

point where web will break while in the tooling area of the press.

21

Fig. 3.26: Stock strip allowances[12]

14. Irregular-shaped blanks with overlapping details cannot always be readily produced

in a single stage and the alternative is to blank at two stations or to make two passes

of the strip through the die. The latter procedure is often the most economical way to

produce medium or large blanks in small quantities. This technique for a sample part

is shown in Figure 3.27.

Fig. 3.27: Recommendation for large irregular shaped blanks [12]

15. A rectangular outline is preferred to a curved outline.

16. A symmetrical design is preferred, particularly on complicated high-production dies

where segmented carbide construction is preferred.

22

17. On strip stock, the grain will be parallel with the edges of the strip as shown in Figure

3.28 and the stock strip layout must be planned accordingly. The designer, especially

if important for assembly purposes should specify the direction of grain desired.

Fig. 3.28: Direction of grain is a characteristic of rolled stock [12]

18. If other operations can be handled in the same press setup with the blanking

operation, the layout of the stock strip must be appropriately determined.

19. The amount of shrinkage or stretching must be considered while developing the blank

from a part drawing if the part requires bending or drawing.

3.5 Shearing Operations

1. Flat surfaces are better than formed surfaces since they allow easier handling and

formed surfaces would require fixtures to properly position the part on the press.

Thus, punching a hole before forming is better than punching or drilling as a separate

operation.

2. The characteristic edges of stamped parts should be kept in mind if smooth edges are

required for bearing surfaces or for other reasons such as appearance and indicated as

shown in Figure 3.29. The design should take into account and also mention the burrs

on one side and should permit their easy removal or ensure that they do not interfere

with subsequent operations or functions.

23

Fig. 3.29: Design should consider burrs [13]

3. Relief slots for tabs and short flanges that have their edges flush with the external

blank outline should have a depth of at least thickness T plus the bend radius as

shown in Figure 3.30.

Fig. 3.30: Design recommendation for relief slots for tabs [13]

4. Round holes are most preferred when compared to all other punch shapes - square,

rectangular, etc shown in Figure 3.31. The tooling costs of round-hole punches and

dies are far below those for holes of other than round shapes. Further, round punches

are readily available in standard diameters and these standard diameters should be

selected as far as possible.

Fig. 3.31: Standard punch shapes - Round most preferred [35]

5. For parts shaved to provide a smooth edge after blanking, the recommended stock

allowance for this shaving operation is shown in table 3.1.

24

Table 3.1 Shaving allowance [4]

6. The formed part or section must be designed with stiffening ribs as shown in Figure

3.32 when extra resistance to flexing greater than that afforded by strength, thickness

or temper of the material is required.

Fig. 3.32: Use of ribs for extra strength in a right angle bend [13]

7. Setouts can serve as locators, rivets, cam followers, pins etc. and are economical

since separate components need not be purchased, handled and assembled. To avoid

fracture, setouts should not exceed one-half of the stock thickness in height. If the

setout is made hollow, a height of 1.5 times stock thickness may be obtained. These

rules are captured in Figure 3.33.

25

Fig. 3.33: Rules for setouts [13]

3.6 Forming Operations

1. Bends should be at right angles to the grain as shown in Figure 3.34 or as close as

possible to this relationship, in order to avoid breakage of the blank.

Fig. 3.34: Grain direction for bends [13]

2. Mutually perpendicular bends should be made at 45 to the grain orientation as shown in Figure 3.34.

3. Bends made parallel to the grain are likely to fracture, this likelihood becoming

greater the sharper the corner, the heavier the stock gauge, the less ductile the

material.

4. Any forms should, if possible be straight bends; and, there should be two parallel

forms whenever possible to promote proper balance in the dies.

5. Where possible on formed surfaces, tolerances on dimensions affected by thickness of

the stock should not be closer than expected variations in the thickness, since more

26

exacting tolerances may require additional coining, grinding, trimming or shaving

operations.

6. Bend axes should not be scattered in all directions to avoid being parallel to the

direction of grain of the blank.

7. Forming operations should never be performed too close to the edge of any opening

without proper support along the edge.

8. The minimum bend allowance used to form a square corner should be 1.5T or R+0.5T

if the corner is on a tapered end and 2T or R+T if on a square end as shown in Figure

3.35.

Fig. 3.35: Recommended bend allowance for a square corner [13]

9. The design should specify shapes that can be produced with standard existing,

universal bending dies. The inside bend angle should preferably be 90. 10. If the flanges extend over a portion of the part, a notch or circular hole should be used

to eliminate tearing. Notch depth should be equal to the thickness plus bend radius. A

hole should have a diameter of three times the thickness of the sheet. This is shown in

Figure 3.36.

27

Fig. 3.36: Design recommendation for flanges [13]

11. To avoid twisting and distortion, the width of the part along the bend axis should be

at least 3 times the stock thickness.

12. In forming channels, the relationship between the leg height and width should allow

the use of a single standard 90 bending tool whenever possible. A design recommendation is that the width of the channel should be at least twice that of the

leg height, though the minimum ratio depends on the width of the forming punch.

This recommendation is shown in Figure 3.37.

Fig. 3.37: Design recommendations for channel bends [13]

3.7 Drawing Operations

1. On drawn forms, a round or circular shell is preferable to a rectangular one.

2. Annealing may be necessary to restore the original properties of the material between

multiple drawings.

3. Tapered wall shells and flanged shells must be avoided. These are more costly than

straight cylindrical shells.

28

4. Without special tooling, for short-run purposes, the height of a draw should not

exceed 10 percent of the diameter as shown in Figure 3.38.

Fig 3.38: Design guideline for draw height using short-run tooling [13]

5. A good average draw radius is four times the thickness of the stock as shown in

Figure 3.39.

Fig. 3.39: Minimum radius design rule for drawn parts [13]

6. For rectangular boxes, specify corner radii at least 0.25 times the depth of draw as

shown in 3.40.

Fig 3.40: Minimum radius for rectangular box-type parts [13]

7. On a cupping or first draw operation, it is good practice to allow from 25 percent to

50 percent of the stock thickness as a clearance. A clearance gives such advantages as

lower stresses; longer die life, less tendency to scratch and easier ejection.

8. The number of drawing or cupping and redrawing operations should be kept at a

minimum. There are several methods for determining the correct number of draws. A

fast estimate of the number of redraws necessary can be made on the basis of height-

29

to-diameter ratio of the finished shell as shown in table 3.2. The usual method is to

work from the required blank size, designing each successive die to the generally

accepted safe maximum percentage of reduction in diameter of the piece. When using

the shell diameter in calculations, it is customary to use the mean diameter (or the

inside diameter plus one side wall thickness). The average permissible reductions for

each material are shown in table 3.3.

30

Table 3.2 Average number of reductions [12]

31

Table 3.3 Average permissible reduction [12]

32

CHAPTER 4

DESIGN ADVISORY SYSTEM

This chapter describes the design advisory system and the various modules and sub-

modules. This research aimed primarily at collecting a comprehensive set of design rules

(described in chapter 3) and development of the inter-feature rule-checking module. The

other modules, developed by Deshpande S [23], have been described briefly for

completeness.

The figure 4.1 below describes the advisory system.

Design Advisor

Feature Extractor

Solid Modeler

Design RulesDatabase

Internal FeatureExtractor

External FeatureExtractor

Intra-Feature DesignChecker And Advisor

Inter-Feature DesignChecker And Advisor

Online Design Advice

Interpretation ofDesign Rules

Bend FeatureExtractor

UserFeature File

Fig. 4.1: Design Advisory System

33

4.1 Feature Extraction

As mentioned in the earlier chapter, all the design rules are specified with reference to

different types of features, hence feature extraction is the preliminary and an important

part of the advisory system.

The feature extraction and the intra-feature checking modules have been developed

by Deshpande S. [23]. The feature extraction module identifies various features and gets

the feature information for each feature. The external feature extraction module identifies

features that lie on the outer boundary of the part (notches) and the internal feature

extractor identifies internal features such as various different types of holes (round, single

D, double D). The bend feature extraction module identifies the bends in the model and

outputs the total bend length and type of bend.

The Feature library for external and internal features is shown below.

Internal Stamped Features:

(a) Circular Feature

(b) Single-D Feature

(c) Rectangle Feature

(d) Double-D Feature

(e) Oblong Feature

Fig. 4.2: Internal Stamped Feature Library [23]

External Stamped Features

Fig. 4.3: External Stamped Feature Library [23]

(a) Arc-Notch

Feature

(b) V-Notch Feature

(c) Straight U-Notch

Feature

(d) Arc U-Notch

Feature

34

The methodology for feature extraction is described below,

4.1.1 Internal feature extraction

The sheet metal part is first flattened by unsuppressing the flat pattern feature and

then each of the loops except the outermost loop of the base face is extracted. Each of

these loops is then the input to the Internal Feature Extraction Algorithm. They are

classified into one of standard features listed above or else they are classified as Custom

Features. An example of internal feature identification is shown below in figure 4.4.

Single-D Feature:

Fig. 4.4: Internal Stamped

Feature Extraction:

W

R

(180- /2)

1. Check if the loop has two edges

2. Check if one of the edges in the loop is a

arc.

Feature Information Stored:

1. Length of the feature L = Diameter of the

2. Angle of the arc

Single D Feature [23]

L

C

straight line and the second edge is an

arc

35

3. Width of the feature W = R (1 + cos (180-/2))

4. Center of the feature, C, which is the center of the arc.

4.1.2 External feature extraction

The external feature extraction uses a feature string pattern to identify and classify

external features.

Based on the connectivity between the adjacent edges, i.e. whether a particular vertex

is convex or concave, a value of 0 or 1 is assigned to the second edge in the pair of edges

considered. The entire loop is traversed, and all the edges are assigned a value depending

on the connectivity between that edge and the earlier edge. In the loop, all the edges are

traversed in a counter clockwise manner. The following figures explain the methodology

of assigning a value of 1 or 0 to second edge in the pair.

Terminolog

The

directed ou

assigned a

string the f

direction ca

6

E5

E4 E3

E2

EFig. 4.5: Feature String Pattern formation-1 [23]

y:

--- Going into the plane of the paper (Inward normal)

--- Coming out of the plane of the paper (Outward normal)

cross product of the two edges E1 and E2 will result in a normal, which is

t of the plane of the paper. In this case, the second edge in the pair E2 is

value of 1. But, in order to develop an algorithm for developing the feature

ollowing technique is used. The face normal for the surface in the outward

n be calculated and then the dot product of the face normal and the normal

E1

36

vector corresponding to the cross product of vectors along E1 and E2 are taken. This dot

product will be positive if the normal vector is along the direction of the face normal, and

negative if the normal vector is in the opposite direction to the face normal. So depending

on if the value is positive or negative, a value of 0 or 1 is assigned to the corresponding

edge. The feature pattern for the above figure will be as follows:

Fig. 4.6: Explanation of Feature String Pattern forma

So the feature string is: 1-1-0-1-1

If one of the edges is an arc, it is approximated as two stra

chords, one joining the start point and mid point of the chord. The

case discussed for straight edges. An example of a part with a circ

below.

Fig. 4.7: Explanation of Feature String Pattern forma

The feature string for the above figure is: 1-1-0-1-1.

An example of external feature extraction is shown below, a S

Feature in figure 4.8.

1

1 1

1

0 1

1

0 1

tion-2 [23]

ight edges, by two

n the rest is same as the

ular edge is shown

tion-3 [23]

traight U Notch

1

37

Fig. 4.8: Explanation of Feature String Pattern formation-4 [23]

Feature Pattern String:

(E1 E2 E3 E4): 1-0-0-1

Feature Extraction:

1

0

0

1

1. Search the feature pattern of the loop for the feature pattern string 1-0-0-1

2. Check if all the four edges corresponding to the feature pattern string elements are

straight lines.

Feature Information:

Information stored about the feature is:

1. Co-ordinates of the Start-Point of the notch (S)

2. Co-ordinates of the Mid-Point of the notch (M)

3. Co-ordinates of the End-Point of the notch (E)

4. Width of the Notch (W)

5. Depth of the Notch (D)

The external feature extraction module can also identify nested features. It uses an

incremental feature filling technique to identify the nested features.

4.1.3 Bend feature extraction

The Bend information from any bend feature is the Bend Radius and the angle of

bend. This information can be obtained for each bend by traversing through the feature

38

manager and getting access to the bend feature and then accessing the feature definition

of the bend.

The Bend features can be classified as:

Base-Bends Edge Bends Sketched Bends Miter Bends 4.2 Intra-Feature Design Checking

Intra-feature checking involves checking if the dimensions of the feature conform to

the design rules for that feature. The intra-feature checking module carries that out

simultaneously with the feature extraction process. An example of the intra-feature rule

and its implementation for the single-D feature (figure 4.4) is shown below. For detailed

description refer to [23].

Design Advisor:

1. Check L > 1.5 x Sheet metal thickness

2. Check W > 1.5 x Sheet metal thickness

3. Check L < 5 x W

4.3 Inter-Feature Rule Checking

This section describes the methodology used for checking if the part designed

satisfies the inter-feature rules described in section 3.3. Inter feature rule checking

involves checking the various design constraints between features. These constraints

involve distance and location considerations as described in chapter 3. The module

39

developed checks for the various distance constraints between features that might lead to

design violations.

The following features are defined as standard features for the inter-feature rule-

checking module.

1. Holes (Round, Oblong, Single-D, Double-D and custom shapes)

2. Bends

3. Slots

4. Extruded Holes

5. External Edges

6. Forms.

The methodology used for inter feature rule checking is as follows.

1. Profile Offsetting: - The profile for each feature, which consists of edges, is

offset by a safe distance. These distances are defined for each type of feature

based on the various design rules collected. This offsetting generates a closed

offset profile. The inner features in a part are offset outwards (towards the

boundary) and the outer profile of the part is offset inwards, thus the offset

profiles define a safe region for each feature. If there are any design violations,

these offset profiles will intersect.

40

Fig 4.9: Example Sheet Metal Part Fig 4.10: Offset directions for individual edges

2. Intersection Checking: - The second part of the module checks the offset

profiles for interference. We use a recursive spatial sub-division technique,

similar to a quadtree to check for intersection. This method is used to avoid the

combinatorial explosion that might occur while checking each edge in a profile

against all edges in other profiles for intersection.

Table 4.1 gives us the safe design distances to be maintained during a sheet metal part

design, between various features. The distances are usually specified in terms of the

thickness of the part t. These distances are calculated based on the design rules specified

in chapter 3. These distances can be changed based on the design practices followed in

the industry.

41

Table 4.1: Distances between features

Holes Bend Slot Extruded Holes

External Edge

Forms

Hole 2 t or 0.060, whichever is greater

1.5 t + rb = 3 t

2 t or 0.060, whichever is greater

3 t ~ 4 t 2 t or 0.060, whichever is greater

3 t + rf = 4.5t~5t

Bend 4 t if the slot is parallel to the bend

4t+ rf1+rf2 = 6t

Slot 2 t or 0.060, whichever is greater

3 t ~ 4 t 2 t or 0.060, whichever is greater

3 t + rf = 4t~5t

Extruded Holes

6 t 4 t

External Edge

4 t + rf1 = 5t

Forms 8t+rf1+rf2=10t

Based on the above table, the profile of each feature is offset by a certain

distances. The various offset distances d for each profile are listed below.

1. Holes: d = t or 0.030 inches, whichever is greater.

2. Bends: d = 3 t or 3 * 0.030 inches, whichever is greater.

3. Slots: d = t or 0.030 inches, whichever is greater.

4. Extruded Holes: d = 3 t or 3 * 0.030 inches, whichever is greater.

5. External Edges: d = t or 0.030 inches, whichever is greater.

6. Forms: d = 5 t or 5 * 0.030 inches, whichever is greater.

The offset distances are so defined such that, if there are any distance considerations

between features are not satisfied, the offset profiles will intersect. These offset distances

42

are based on the rules collected in the literature. They can be easily modified according to

the company standards and design practices followed.

Profile Offsetting

A profile P is defined as a collection of curves (edges) Pi (1 i n), such that the end point of Pi coincides with the start point of Pi+1. The profile is closed if the start point

of the first edge and the end point of the last edge in the profile are the same. Except for

end point linkages, we allow no pair wise intersections among curves in the profile. The

input to the algorithm requires a closed profile (loop). The edges in the profile consist of

straight lines and arcs.

Each loop can be traversed either clockwise or in a counter-clockwise manner.

A closed profile P of n curves can be defined as,

P = [Pi, 1 i n] where, each Pi is either a straight line or an arc.

The algorithm presented here is a modification of the Tiller-Hanson [16]

algorithm. This was implemented in the GEOMOD solid modeler. There are various

other methods that have been studied for profile offsetting. Devaranjan[26] uses the same

Tiller-Hanson algorithm for profile offsetting, which is used for feature recognition and

tool mapping. M. Held[27] discusses the application of voronoi diagrams for offsetting

curvilinear polygons.

The inputs for the algorithm are,

1. Closed profile for each feature.

2. For edges of each profile, the type of edge (i.e. belonging to a bend feature, form

feature, outer edge of body or hole.)

43

3. The face normal (outward) for the face or the face on which the feature lies.

The algorithm consists of 3 separate modules

1. Preliminary offsetting: - In this stage the edges in each loop are offset

individually. The offset direction for the each loop is set and all the edges are

offset by the safe distances specified in table 4.1. The output of this stage is a set

of curves that do not form a closed loop. Various degeneracies may occur as

shown in the figures below.

2. Pair wise processing: - The offset edges are processed pair wise, so that that the

offset loop is closed. An extra edge is added or edges trimmed as required.

If two tangential edges are offset, then the offset edges are also tangential. In this case

there is no need of trimming the offset edges or inserting edges between them.

Fig. 4.11: Offset of tangential edges

If convex edges are offset, then it becomes necessary to insert an extra edge between

the offset edges to get a closed offset profile.

Original profile Offset Profile

44

Fig. 4.12: Offset of convex edges

If non-convex edges are offset these edges need to be trimmed so that the end point of

the first edge is the start point of the second edge.

Fig. 4.13: Offset of non-convex edges

Original profile

Offset line

Inserted Arc

Offset line

Original profile

3. Final Check and Post Processing: - In this module the edges are checked for

direction, isolated island loops processed. If any of the vertices in the final loop

needs post-processing, the post-processing module is invoked.

4.3.1.1 Preliminary Offsetting

This is the first stage of the offsetting process.

The inputs for this stage are,

1. The loops (profiles of each feature) on the face.

2. The features that these edges in the loop belong to.

45

3. Outwards face normal for the face.

Offsetting Straight lines Let O, P be the closed offset profile and the original feature profiles respectively.

Let Oi 1 be the start point and Oi 2 be the end point of the offset curve Oi.

Oi 1 = Pi1 + d*Ni and Oi 2 = Pi2 + d*Ni

where, d = offset distance

Ni = unit normal vector in the offset direction.

The offset distance d is the distance that each edge is offset, based on the type of

feature, described above.

The offset direction Ni (for the outer loop) is calculated as follows,

Ni = unit ( f x Ei )

where, Ei = is a vector in the direction of the edge to be offset.

f = face normal for the face or feature.

Fig. 4.14: Offset Direction for Outer Edges

The edges in a profile (loop) are traversed in a counter-clockwise sense for the outer

loop and in a clockwise manner for the inner loops. This ensures that the direction of

vector Ei is inverted for outer and inner loops. Hence the cross product of f and Ei is also

in the opposite direction. This sets the direction of the outer loop inwards and the inner

Ni

Ei

f

46

loops outwards. The offset directions for each edge of a simple sheet metal part are

shown in figure 4.10.

Offsetting arcs and circular curves The offset directions for the points on the arc are based on the whether the arc lies in

the outer or the inner loop. The new offset points are obtained by adding or subtracting

the offset distance in the direction of the vector formed by the center of the arc and the

end point.

Oi = Pi d * Ni

Where, d = offset distance.

Ni = unit vector in the direction of vector formed between center of arc and

point to be offset.

It is necessary to check if the arcs are convex or non-convex and if they lie on the

inner or outer loops to determine the offset direction.

This preliminary offsetting gives us the preliminary offset chain. The offset edges do

not form a loop, i.e. the end point of edge Oi might not necessarily be the start point of

edge Oi+1. These edges need to be processed further for obtaining a closed loop profile.

The edges output from this stage act as an input for further processing in the next step.

47

Fig 4.15: Output of preliminary offsetting module

4.3.1.2 Pair wise processing of edges

The output from the preliminary offsetting stage is input to the pair-wise processing

module. The edges are processed pair wise so as to maintain the relationship between

adjacent edges to for a loop. This is required because of the various degeneracies that

arise when non-tangential edges are offset as explained earlier.

The offset edges are then processed in a pair wise manner.

(P1, P2), (P2, P3), (P3, P4),, (Pn-1, Pn), (Pn , P1).

We classify the end points for each edge as accepted or rejected. An edge is accepted

as a member of the offset loop only if both the endpoints of the edge are accepted.

The end points of each curve are classified as accepted or rejected as follows,

Calculate tangent Tie to Pi at end point of Pi (i.e. Pie) and the tangent Tsi+1 to Psi+1 at the start point of Pi+1 (Ps).

Form the lines Li = Pe + i * Tie and Li+1 = Psi+1 + i+1 * Ts i+1 If the lines intersect denote, let oi and oi+1 be the parameter values

corresponding to the point of intersection.

48

The various cases are

1. If Li and Li+1 do not intersect, or if oi < 0 and oi+1 > 0, then Osi and Oei+1 the two offset edges are checked if they intersect and if they do, then the edges are

clipped and the intersection point are accepted else they are rejected and the

post processing flag is set.

2. If oi > 0 and oi+1 > 0, or if oi < 0 and oi+1 < 0, then the two points are classified as rejected and post processing flag is set.

3. If oi > 0 and oi+1 < 0. The points are accepted. This calls for a inserted between the edges.

This algorithm is sufficient for simple cases, but for special cases a p

processing module is necessary and is incorporated.

Fig. 4.16: Output pair wise processing of edges

O

n arc to beost-Offset Profile

riginal Profile

49

4.3.1.3 Post-Processing Phase and Check

The direction of each edge is checked with respect to the direction of the original

edge. If the edge changes direction, then the end points are classified as rejected and the

post-processing flag is set. This is carried out for all edges. For arcs, if the direction of

offset, for the end points is towards the center and if the offset distance is greater than the

radius, the offset curve changes direction. In such a case, we eliminate this offset curve

from the offset profile O and both the end points are flagged rejected.

In this phase the edges having rejected end points are processed.

1. If both the end points of a curve are flagged rejected, then the curve is not a part

of the offset profile.

2. The offset edges adjacent to this curve are checked for intersection with other

edges. The edges are trimmed and the invalid edges removed.

3. The loop removal procedure is to check the direction of each loop and only the

loops having a counter-clockwise sense are retained, while the other loops are

discarded.

4.3.1 Intersection Checking

The next stage for interfeature rule checking is checking for intersection between the

offset profiles of each feature on each face. If the brute-force approach is used to carry

out checking then each edge from each feature has to be checked against all edges

belonging to profiles of other features to see if they intersect. In case of parts where there

are a large number of features present on each face, this might lead to a combinatorial

explosion. We use a spatial decomposition technique, a variant of the PM2 quadtree, to

reduce the computation.

50

The term quadtree is used to describe a class of hierarchical data structures whose

common property is that they are based on the principle of recursive decomposition of

space. In two dimensions, a square planar region is recursively sub divided into four

rectangular parts until each part contains data that is sufficiently simple enough. The

decomposition may be into congruent parts of the same shape as the original planar

region, this is termed as regular decomposition, or it may be governed by the input.

An example of a quadtree is an edge quadtree. The edge quadtree as presented by

Shneier [28] is a region containing a vector feature, or part thereof, is repeatedly divided

into sub-quadrants until each quadrant contains a curve that can be approximated as a

straight line. Each leaf node contains the following information about the edge passing

through it: magnitude, direction, intercept and a directional error term (i.e. the error

resulting from the approximation of the curve by a straight line using a measure such as

least squares). If a line segment terminates within a node a special flag is set.

Fig. 4.17: Edge Quadtree

The sub-division technique used here draws a parallel from the PM2 quadtree an

adaptation of the PR quadtree and has been developed by H. Samet and R. Webber [21].

The PM quadtree (PM, PM1 and PM2) have been developed to store a collection of

51

polygons. The PR quadtree data structure that stores point information. Since it stores

point information for regions (polygonal maps) it has been called a PR quadtree. PR

quadtrees store point information only in leaf (terminal) nodes. Regular decomposition is

applied until no quadrant contains any more than one data point.

Fig. 4.18: PR quadtree

The PM, PM1, PM2 quadtrees are adaptations of the PR quadtree modified to store

polygonal maps and collection of polygons. In the next section the PM2 quadtree is

explained in brief.

PM2 quadtree

The decomposition criteria for PM2 quadtrees are,

1. At most one vertex can lie in a region represented by a quadtree leaf.

2. If a region contains a vertex, then it can contain no q-edge that does not include

that vertex.

3. If a region contains no vertices, then it can contain only those q-edges that meet at

a common vertex exterior to the region.

4. All leaf nodes are maximal.

A q-edge is segments of edges that are formed by clipping an edge of the edge against

the border of the region represented by a quadtree node. Line QR is a q-edge, in figure

4.18.

52

Fig. 4.19: PM2 Quadtree

We use a modification of the above sub-division technique to reduce the search for

intersecting edges.

Methodology

The criterion for sub-division of all profiles on a face is as follows,

1. All vertices in a leaf node belong to the same loop, i.e. all the vertices must have

the same loop id.

2. If the node contains vertices, it contains no edge that does not belong to any of

these vertices.

3. If the node contains no vertices, then it can only contain q-edges belonging to the

same loop.

4. Each leaf node is maximal.

If the decomposition described above is successful, it implies that there are no

intersecting edges between any of the profiles and all design conditions are satisfied. The

depth of decomposition can be set beforehand. If the decomposition is unsuccessful, i.e.

after the maximum depth of the tree is reached and still there exist nodes that do no

satisfy the above conditions, then the edges that belong to that node are checked for

intersection between themselves.

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The offset profiles on each face comprise of straight lines and arcs. These edges are

spatially decomposed and stored in nodes of a quadtree type data structure. The

decomposition process is a regular decomposition process.

The following information is stored in each node.

1. Locational information: Each node is described by its center co-ordinates (x,y),

since it is a 2-D decomposition process.

2. Pointers to the four sons for each node if any.

3. An array list of all the edges that lie in the node.

4. An array of all the vertices that lie in the node.

5. A special flag (leaf-node) is set if the node is a leaf node.

6. A flag is set if the node is at the greatest depth specified for the decomposition

and it doesnt satisfy the constraints described above.

The various considerations in the decomposition process are addressed below.

Starting square used for decomposition. It is assumed that the outer loop of each face bounds all other features in the face.

It is possible to get the smallest rectangle that contains all the edges on the face. To get

the location and dimensions for the initial polygon, we set the length of the side of the

square equal to the length of the larges side of this rectangle.

The edges on the face are then processed to check them for intersection. This parent node

is checked if it satisfies the conditions described above. If the conditions are satisfied,

then the node is set as a leaf node. If the array of edges does not satisfy the criteria, then

the node is decomposed into 4 sons, NE, NW, SE and SW. Each of these nodes is again

processed as described above. Only those edges that lie in the parent node are checked, if

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they lie in the children nodes, thus reducing the number of edges processed with

increasing depth of decomposition.

The following checks are carried out to check if the edge lies in the node.

Straight Lines 1. Check if end points lie in the node. If they do the edge lies in the node.

2. If endpoints do not lie in the node then check if the line intersects any of the 4

boundaries of the node. The following cases may be eliminated, and if the line

satisfies the following conditions, it definitely doesnt lie in the node. Let x, y be

the co-ordinates of the center of the node and d be the length of each side of the

node. Let xu, xl, and yu, yl are the greater and lesser x and y co-ordinates of the

start and end points. The length of each side of the node is represented by d.

a. If xu < x d/2 and yu < y d/2

b. Or xl > x + d/2 and yl > y + d/2

Arcs 1. Check if end points lie in the node, if they do then the arc lies in the node.

2. Check if the center of the arc lies in the node

a. If center lies in the node and radius of arc ( r ) > 2 * d, then the arc does not intersect the node, else check the arc for intersection with boundaries

of node.

b. If center does not lie in the node, then calculate distance between center of

node and center of arc l. If l > r + d / 2 or r > l + d / 2 then arc does not intersect the node.

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Fig. 4.20: Example of decomposition of offset profiles

Figure 4.19 shows the decomposition process applied to the offset profiles. The

nodes highlighted in red show the intersection that occurs within profiles. Thus if an

intersection is detected it constitutes a design violation. This is output to the designer so

that the design can be modified.

The depth of the decomposition process can heavily influence the number of

intersection checks that have to be carried out once the decomposition process reaches

the maximum depth. An estimate on the depth has to be intelligently made beforehand.

The dimension d of the node at the maximum depth can be used to decide the

decomposition depth.

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CHAPTER 5

SOLIDWORKS API DESCRIPTION

This chapter describes the various class objects defined in Visual basic and a brief

description of a few important modules developed for the offsetting process.

The following class modules have been defined in Visual Basic for the offsetting

algorithm.

5.1 Class Modules

5.1.1 CofVertex

This is a class for the Offset Vertex Object defined in SolidWorks. It provides

interfaces to the underlying properties of the vertex. An important property is if the offset

vertex is classified as accepted or rejected as a part of the offset profile.

5.1.2 CofFace

This is a class for the SolidWorks Face Object. This class has access to all the

underlying information such as the underlying loops, edges, curves and vertices.

5.1.3 CofLoop

This is a class for the SolidWorks Offset Loop Object. This class has handles to

underlying information such as edges and vertices of the offset Loops.

5.1.4 IofEdge

This is an interface, which captures the general characteristics of any curve

irrespective of its type such as the offset Straight Line, Arc or Circle. These general

parameters are the type of curve, if the curve is closed or open. These general properties

of any type of curve are captured in this Interface. Then there are classes which

implement this interface like CofStraightLine, CofCircle and CofArc, and add and set the

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other properties of the object such as Start Vertex, End Vertex for a Straight Line; Start

Vertex, End Vertex, Radius and Center for an Arc and Radius and Center for a Circle.

5.1.5 CofStraightLine

This class implements the IofEdge class. Other properties of a straight line such as

Start Vertex and End Vertex are set in this class. Visual Basic does not support

implementation inheritance and only supports interface inheritance.

5.1.6 CofCircle

This class implements the IofEdge class. Other properties of a circle such as Center

and Radius are set in this class. Visual Basic does not support implementation inheritance

and only supports interface inheritance.

5.1.7 CofArc

This class implements the IofEdge class. Other properties of an arc such as Start

Point, End Point, Mid Point, Center and Radius are set in this Class. Visual Basic does

not support implementation inheritance and only supports interface inheritance.

5.2 Main Code Modules

5.2.1 Main Module

a. Main Procedure

This procedure calls all the individual modules, which handle each stage of the

offsetting process. The main procedure gets the face normal for each face and also

the offset distance for each edge. It also contains procedures that draw the offset

profiles for each face.

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b. InitializeSolidWorks

In this function, all the start up work is done. A handle to the active SolidWorks

Object is obtained through OLE interface provided by VB. Then the feature Flat-

Pattern is accessed and the base face and face normal are obtained.

5.2.2 Preliminary Offsetting Module

a. calcLineOffset

This function calculates the offset end points for each line in the profile. A new

cofstraightline object is created and its properties are set.

b. calcArcOffset

This function calculates the offset end points, mid-point and radius for each arc

in the profile. A new cofarc object is created and its properties are set.

c. circleOffset

This function calculates the offset end points and radius for each circle in the

face. A new cofcircle object is created and its properties are set.

5.2.3 Pair-wise Processing Module

a. PairEdgeProcess

This function processes the output of the preliminary offsetting module pair

wise. It calls the various intersection functions or inserts an extra edge in the loop

wherever necessary.

b. getIntersection

This function computes the intersection points for edges, both line-line and line

arc intersections are handled.

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getLambda

This function returns the value of the parameter lambda, used for decision

making for either trimming the edges or adding an extra edge.

c. Getpoints

This function returns the point of intersection of an straight line and an arc

5.2.4 swConst

This module stores all the constant variable declarations used by SolidWorks. Some

of the new constant variables, which have been declared and used in the code have also

been declared over in this module.

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CHAPTER 6

CONCLUSIONS AND FUTURE DIRECTIONS

This chapter discusses the conclusions of this research and future scope for

research and development, to make this advisory system comprehensive and complete.

6.1 Conclusions

1. Comprehensive collection of rules

This research presents a comprehensive set of design rules for sheet metal part

design. These rules have been collected from the available literature and can be

customized according to the need of the specific industry and the design practices that it

follows. The approach used is simple and can be very easily modified to suit industry

practices. The research also provides a methodology of implementing, both the inter-

feature and intra-feature rules. The methodology presented is simple and can be easily

implemented.

2. Intuitive and Simple Methodology

The distances between various features (inter-feature rules) are defined according

to the ability of the metal to bear the shear stresses during press operation. The

methodology presented is very intuitive; we define a safe area around each feature.

Failure of the metal would occur if any other feature were to be created within that area.

The method presented checks if other features lie within the safe area, thus ensuring

that the required distances are maintained. The combinatorial explosion that occurs while

checking distance of all the edges of each feature against edges of other features is

avoided by using the described spatial decomposition process. The offsetting method can