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ASSOCIATION FOR THE DEVELOPMENT OF COMPUTER-AIDED

TOLERANCING SOFTWARE

User's Guide

Written by:

Dr. Kenneth W. Chase & David R. Todd

September 1, 1994

AutoCATS is a 2-D Computer-Aided Tolerancing System designed for AutoCAD. This system consists of two pieces of software: the AutoCATS 2-D Modeler and 2-D Analyzer. The AutoCATS 2-D Modeler allows designers to graphically create 2-D vector assembly models in AutoCAD. The AutoCATS 2-D Analyzer interactively assists designers in the selection and allocation of component tolerances for these assemblies in order to assure manufacturability, least cost, and minimum rejection rates.

With the AutoCATS 2-D Analyzer, vector models of 2-D mechanical assemblies created by the Modeler may be analyzed. The analysis may use worst case or statistical methods to predict the magnitude of variations and probable rejects for critical clearance, position, and other assembly specifications. Three sources of variation may be accounted for:

  1. Dimensional variations ( lengths and angles )
  2. Form and feature variations ( flatness, roundness, angularity, etc. )
  3. Kinematic variations ( small adjustments between mating parts )

In turn, the Analyzer may be used to allocate or select tolerances for an assembly to meet these same critical assembly specifications.

The AutoCATS 2-D Analyzer user interface is menu-driven with on-line help, command buffering, and global commands available at every menu. It features full-screen data editing and the ability to save design iteration data.

(c) Copyright ADCATS 1994. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission of the publisher. Printed in the United States of America, Brigham Young University.

Addition copies of this manual may be purchased for $15 through:

ADCATS
Attn: Dr. Kenneth W. Chase
Mechanical Engineering
242 CB
Brigham Young University
Provo, Utah 84602
Tel: (801) 378-6541
Fax: (801) 378-5037

 

AutoCAD is a registered trademark of Autodesk, Inc.


TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION

1.0 Motivation .........................................................................1-1

1.1 Sources of Variation ..............................................................1-2

1.2 CATS Overview ..................................................................1-3

1.3 Tolerance Analysis vs. Tolerance Allocation ..................................1-4

1.4 Tolerance Analysis Models ......................................................1-4

1.5 Tolerance Allocation Options ....................................................1-5

1.6 Cost-vs-Tolerance Options ......................................................1-6

1.7 Additional Design Features ......................................................1-6

1.8 Reference Handbook .............................................................1-6

1.9 AutoCATS 2-D Modeler .........................................................1-9


CHAPTER 2: ASSEMBLY TOLERANCE ANALYSIS

2.0 Introduction .......................................................................2-1

2.1 2-D and 3-D Tolerance Analysis ................................................2-1

2.2 A Vector Model of an Assembly ................................................2-2

2.3 Linearized Solution for the Assembly Tolerances ............................2-4

2.4 Numerical Example ...............................................................2-6

2.5 Approximating Form Variations ................................................2-8

2.6 Calculating the Contribution of Form Variations .............................2-8

2.7 Advanced Six Sigma Analysis--Accounting for Process Mean Shifts ...2-10


CHAPTER 3: TOLERANCE ALLOCATION

3.0 Tolerance Analysis vs. Tolerance Allocation ..................................3-1

3.1 Allocation by Proportional Scaling .............................................3-2

3.2 1-D Example: Worst Case Tolerance Allocation by Proportional Scaling ..3-3

3.3 Allocation by Weight Factors ...................................................3-5

3.4 1-D Example: Worst Case Allocation by Weight Factors ....................3-6

3.5 1-D Example: Statistical (RSS) Allocation by Weight Factors ..............3-7

3.6 Tolerance Allocation Using Least Cost Optimization .........................3-8

3.7 True Cost and Optimum Acceptance Fraction ...............................3-12

3.8 Advanced Allocation Features--Nominal Allocation .......................3-13


CHAPTER 4: USER INTERFACE

4.0 Program Control ..................................................................4-1

4.1 File Management ..................................................................4-4

4.2 Data Entry and Editing ...........................................................4-4


CHAPTER 5: CLUTCH EXAMPLE PROBLEM

5.0 An Introduction to AutoCATS 2-D Analysis ..................................5-1

5.1 Start Up ............................................................................

5.2 Equating Variables ................................................................5-4

5.3 Parameters .........................................................................5-5

5.4 Kinematic Assembly Variables ..................................................5-6

5.5 Tolerance Analysis Without Feature Tolerances ..............................5-7

5.6 Analysis of Design Specifications .............................................5-10

5.6.1 Worst Case Analysis .....................................................5-10

5.6.2 Statistical (RSS) Analysis ...............................................5-11

5.7 Tolerance Allocation ..............................................................5-13

5.7.1 Tolerance Allocation by Proportional Scaling .........................5-13

5.7.2 Tolerance Allocation by Weight Factors ...............................5-16

5.7.3 Tolerance Allocation by Minimum Cost ...............................5-19

5.8 Percent Contribution Chart .....................................................5-23

5.9 Sensitivity Diagram .............................................................5-24

5.10 Advanced Six-Sigma Analysis ................................................5-25

5.11 Advanced Allocation--Nominal Allocation ..................................5-27

5.12 Save Analysis Matrices .........................................................5-30

5.13 Ending the Session ..............................................................5-31


CHAPTER 6: STACKED BLOCKS EXAMPLE PROBLEM

6.0 An Introduction to the Multi-Loop Problem ...................................6-1

6.1 Start Up ............................................................................

6.2 Equating Variables ................................................................6-2

6.3 Kinematic Assembly Variations .................................................6-4

6.4 Analysis of Design Specifications ..............................................6-5

6.5 Percent Contribution Chart ......................................................6-6

6.6 Sensitivity Diagram ...............................................................6-7

6.7 Tolerance Allocation ..............................................................6-8


CHAPTER 7: REMOTE POSITIONER EXAMPLE PROBLEM

7.0 An Introduction to Open Loop Specifications .................................7-1

7.1 Start Up ............................................................................7-3

7.2 Parameters .........................................................................7-3

7.3 Kinematic Assembly Variables ..................................................7-4

7.4 Analysis of Design Specifications ..............................................7-5

7.5 Tolerance Allocation ..............................................................7-7


CHAPTER 8: 1D ANALYSIS


LIST OF FIGURES & TABLES

CHAPTER 1

Figure 1.1 Short- and far- sighted engineering ............................................1-1

Figure 1.2 Sources of variation in mechanical assemblies ..............................1-2

Figure 1.3 CATS Tolerance Selection Aids ..............................................1-3

Figure 1.4 Tolerance Analysis vs. Tolerance Allocation ................................1-4

Figure 1.5 Integrated AutoCATS modeling system for assembly tolerance analysis ..1-7


CHAPTER 2

Table 2.1 Assembly Tolerance Accumulation Models .................................2-1

Figure 2.1 Determining the number of out-of-spec assemblies ........................2-2

Figure 2.2 Vector loop model of locking computer tape hub assembly ...............2-3

Figure 2.3 Translational variations caused by form variations .........................2-8

Figure 2.4 Rotational variations caused by form variations ............................2-8

Figure 2.5 Feature tolerances added at mating surfaces of an assembly ..............2-9

Table 2.2 Specified Feature Tolerances for Tape Hub Problem ......................2-9

Figure 2.6 The location of the mean is not known precisely. .........................2-11

Figure 2.7 Effect of mean shift for all components with kstat=.25 ..................2-13


CHAPTER 3

Figure 3.1 Tolerance Analysis vs. Tolerance Allocation ...............................3-1

Figure 3.2 Graphical interpretation of tolerance allocation by proportional scaling ..3-2

Figure 3.3 Shaft and housing assembly ..................................................3-3

Figure 3.4 Tolerance range of machining processes ....................................3-3

Figure 3.5 Tolerance allocation by proportional scaling ................................3-5

Figure 3.6 Graphical interpretation of tolerance allocation by weight factors. .......3-6

Table 3.1 Comparison of Allocation Methods ..........................................3-7

Figure 3.7 Tolerance allocation by proportional scaling and weight factors ..........3-8

Figure 3.8 Optimal tolerance allocation for minimum cost ..............................3-9

Table 3.2 Proposed Cost-of-Tolerance Models .........................................3-9

Figure 3.9 Graphical interpretation of minimum cost tolerance allocation ..........3-10

Table 3.3 Minimum Cost Tolerance Allocation .......................................3-11

Figure 3.10 Comparison of minimum cost allocation results ..........................3-12

Table 3.4 Minimum True Cost ..........................................................3-13

Figure 3.11 Effects of nominal allocation options .......................................3-13


CHAPTER 4

Figure 4.1 AutoCATS 2-D Analyzer Menu Structure ...................................4-2

Table 4.1 Global Commands .............................................................4-3

Figure 4.2 Sample data editing screen ....................................................4-4


CHAPTER 5

Figure 5.1 One-way clutch assembly .....................................................5-1

Figure 5.2 Vector loop for one-way clutch ...............................................5-2

Figure 5.3 Percent contribution to assembly variable DATUM2 .....................5-23

Figure 5.4 Sensitivities of assembly variable DATUM2 ..............................5-24


CHAPTER 6

Figure 6.1 Assembly of stacked blocks ...................................................6-1

Figure 6.2 Vector loops used to solve for assembly variations of stacked blocks ....6-2

Figure 6.3 Percent Contribution to assembly variable BASE/1-4 .....................6-6

Figure 6.4 Sensitivities of assembly variable BASE/1-4 ...............................6-7


CHAPTER 7

Figure 7.1 Remote positioner assembly ..................................................7-1

Figure 7.2 Parallelism and true position design specifications. ........................7-1

Figure 7.3 Vector loops for the remote positioner. ......................................7-2


CHAPTER 8

Figure 8.1 1-D loop input screen ..........................................................8-1


 PRO-E 2 D
Modeler:
Title | Overview | Modeling | Commands
Analyzer:
Title | Overview | Analysis | Allocation | Interface
Verification: Overview

 AutoCAD 2 D
Modeler:
Title | Overview | Modeling | Commands
Analyzer: Title | Overview | Analysis | Allocation | Interface
Verification: Title | Overview

 Catia 3 D
Modeler:
Title | Overview | Modeling | Commands | Building a Tolerance Model


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