Tolerance Design : A Handbook for Developing Optimal Specifications

by Creveling, Clyde M.

• ISBN13: 9780201634730
• ISBN10: 0201634732
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-01-01
• Publisher: Prentice Hall

Summary

Whether an engineer, designer, drafter, or technician, each member of the design engineering team has a valuable role to play in the development of product specifications. Tolerance Design recognizes this development process as the responsibility of the entire team and provides practical solutions that each team member can readily apply. The step-by-step details of analytical and experimental tolerance development methods are clearly explained, and as a result, you will be able to develop tolerances more economically. The blend of practical examples with substantive case studies provides a comprehensive process approach to tolerance development. Students of design and engineering will find this book invaluable as they prepare to enter a competitive job market where practical design optimization skills are at a premium.

Table of Contents

Preface	xv	(4)
Acknowledgments	xix
Section I: Setting the Stage for Understanding the Science of Tolerancing	1	(84)
1 Introduction to Tolerancing and Tolerance Design	3	(22)
The Historical Roots of Tolerancing	3	(3)
The State of the Art in Tolerancing Techniques	6	(3)
What Should a Modern Tolerance Development Process Look Like?	6	(1)
The Relationship between Traditional Tolerancing Methods and the Taguchi Approach	6	(3)
Developing Tolerances: The Role of Engineers and Designers	9	(1)
Concepts, Definitions, and Relationships	10	(2)
Matching Design Tolerances with Appropriate Manufacturing Processes	12	(1)
Introduction to the Taguchi Approach to Tolerance Analysis	12	(11)
Review of the Three Phases of a Quality Engineering--Based Product--Development Process	13	(7)
Taguchi's Approach to Tolerancing	20	(3)
Summary	23	(1)
References	24	(1)
2 The Relationship of Quality Engineering and Tolerancing to Reliability Growth	25	(26)
The Three Initial Phases of Product Development	26	(22)
Phase 1: Subsystem Concept Selection and Robustness Optimization	28	(11)
Gate 1	39	(1)
Phase 2: System Robustness Optimization	39	(3)
Gate 2	42	(1)
Phase 3: Product Design	42	(5)
Gate 3	47	(1)
The Reliability Bathtub Curve and Tolerancing	48	(1)
Summary	49	(1)
References	50	(1)
3 Introductory Statistics and Data Analysis for Tolerancing and Tolerance Design	51	(34)
The Role of Data in Tolerance Analysis	51	(1)
Graphical Methods of Data Analysis	52	(3)
The Histogram	54	(1)
Quantitative Methods of Data Analysis	54	(1)
Introduction to the Fundamentals of Descriptive Statistics	55	(7)
The First Moment of the Data about the Mean -- The Arithmetic Average	55	(1)
The Second Moment about the Mean: The Variance	56	(1)
The Standard Deviation	57	(1)
The Third Moment about the Mean: The Skew	58	(1)
The Fourth Moment about the Mean: The Kurtosis	59	(2)
The Coefficient of Variation	61	(1)
The Use of Distributions	62	(1)
The Use of Distributions in Taguchi's Parameter and Tolerance Design	62	(1)
The Use of Distributions in Traditional Tolerance Analysis	63	(1)
Introduction to the Fundamentals of Inferential Statistics	63	(9)
The Z Transformation Process	63	(3)
The Student--t Transformation Process	66	(1)
The Adjusted Z Transformation Process for Working with Nonnormal Distributions	67	(5)
Manufacturing Process Capability Metrics	72	(4)
Six Sigma Process Metrics	76	(3)
The Relationship between the Quality--Loss Function, Cp, and Cpk	79	(2)
Summary	81	(2)
References	83	(2)
Section II: Traditional Tolerance Analysis	85	(114)
4 Using Standard Tolerance Publications and Manufacturer's Process Capability Recommendations	87	(14)
Starting the Tolerance Design Process	87	(1)
The Three Sigma Paradigm	88	(2)
Processes for Establishing Initial Tolerances	90	(6)
Establishing Process Capability and Process Control for Identifying Initial Tolerances	96	(3)
Creating a Library for Process Capabilities as a Data Base	98	(1)
Summary	99	(1)
References	99	(2)
5 Linear and Nonlinear Worst--Case Tolerance Analysis	101	(23)
Standard Worst--Case Methods	101	(21)
Six Sigma Worst--Case Tolerance Analysis	102	(2)
Analysis for Nonlinear Tolerance Stacks Using the Worst--Case Method	104	(1)
Process Diagrams for Worst--Case Analysis for the Stackup of Tolerances in Assemblies	105	(4)
A Case Study for a Linear Worst--Case Tolerance Stackup Analysis	109	(2)
A Process for Modeling Worst--Case Nonlinear Tolerance Stackup Problems	111	(11)
Summary	122	(1)
References	123	(1)
6 Linear and Nonlinear Statistical Tolerance Analysis	124	(25)
The Root Sum of Squares (RSS) Approach	126	(6)
The Z Transformation Process	127	(1)
One--Dimensional Tolerance Stacks	127	(3)
Motorola's Dynamic Root Sum of Squares Approach	130	(1)
Motorola's Static Root Sum of Squares Approach	131	(1)
The Nonlinear RSS Case Method	132	(1)
Process Diagrams for the StatisticalMethods of Tolerance Stackup Analysis	133	(12)
The Linear RSS Method	133	(5)
The Dynamic RSS Method	138	(1)
The Static RSS Method	139	(6)
The Nonlinear RSS Example	145	(2)
Summary	147	(1)
References	148	(1)
7 Sensitivity Analysis and Related Topics	149	(11)
The Various Approaches to Performing Sensitivity Analysis	149	(5)
Mathematical Sensitivity Analysis	149	(1)
Tolerance--Range Sensitivity Analysis	150	(1)
Component Manufacturing Process Output Distribution Sensitivity Analysis	151	(1)
Nonlinear Tolerance Sensitivity Analysis	151	(1)
The Steps for Basic Nonlinear Sensitivity Analysis	152	(1)
Empirical Sensitivity Analysis	153	(1)
ANOVA Sensitivity Analysis	153	(1)
One--Factor--at--a--Time Sensitivity Analysis	153	(1)
Using Sensitivity Analysis in Concept Design	154	(2)
An Example of the Use of Sensitivity Analysis in Concept Development	156	(2)
Summary	158	(1)
References	159	(1)
8 Computer Aided Tolerancing Techniques	160	(27)
Various Software and Platform Options to Support CAT Analysis	161	(2)
Commercially Available Pro/ENGINEER--Based Tolerance Analysis Software	162	(1)
Monte Carlo Simulations in Tolerance Analysis	163	(4)
Characterizing Probability Distributions for Tolerance Analysis Applications	167	(5)
The Common Probability Distributions Available in Crystal Ball	167	(1)
The Less Common Probability Distributions Available in Crystal Ball	168	(2)
Step--by--Step Process Diagrams for a Crystal Ball Monte Carlo Analysis	170	(2)
Sensitivity Analysis Using Crystal Ball	172	(3)
How to Use Crystal Ball	175	(6)
Running the Monte Carlo Simulation	181	(3)
Preparing Engineering Analysis Reports	184	(1)
Another Computer--Aided Tolerance Approach	185	(1)
Summary	185	(1)
References	186	(1)
9 Introduction to Cost--Based Optimal Tolerancing Analysis	187	(4)
Skills Required for Cost--Based Optimal Tolerance Analysis	188	(1)
The Various Approaches to Cost--Based Optimal Tolerance Analysis	188	(2)
Cost versus Tolerance Plots	190	(1)
Summary	190	(1)
References	190	(1)
10 Strengths and Weaknesses of the Traditional Tolerance Approaches	191	(8)
Using Standard Tolerance Publications and Manufacturer's Process Capability Recommendations	192	(1)
Worst--Case Tolerance Analysis	193	(1)
The Statistical Methods of Tolerance Analysis	193	(1)
The Root Sum Square Approach	193	(1)
The Dynamic Root Sum of Squares Approach	193	(1)
The Static Root Sum of Squares Approach	194	(1)
The Nonlinear Tolerance Approaches	194	(1)
Sensitivity Analysis	194	(1)
Computer--Aided Tolerancing	194	(1)
Cost--Based Optimal Tolerance Analysis	195	(1)
How the Six Processes Relate to the Overall Product Tolerancing Process	195	(1)
Summary	196	(1)
References	197	(2)
Section III: Taguchi's Approach to Tolerancing and Tolerance Design	199	(162)
11 The Quality--Loss Function in Tolerancing and Tolerance Design	201	(23)
Linking Cost and Functional Performance	201	(1)
An Example of the Cost of Quality	202	(4)
The Step Function: An Inadequate Description of Quality	206	(1)
The Customer Tolerance	207	(1)
The Quality--Loss Function: A Better Description of Quality	208	(1)
The Quality--Loss Coefficient	209	(1)
An Example of the Quality--Loss Functions	210	(9)
The Types of Quality--Loss Functions	210	(9)
Developing Quality--Loss Functions in a Customer's Environment	219	(1)
Constructing the Quality--Loss Economic Coefficient	220	(2)
Summary	222	(1)
References	223	(1)
12 The Application of the Quadratic Loss Function to Tolerancing	224	(22)
The Difference between Customer, Design, and Manufacturing Tolerances	224	(1)
Customer Tolerances	224	(1)
Design and Manufacturing Tolerances	225	(1)
The Taguchi Tolerancing Equations	225	(4)
Taguchi's Economical Safety Factor	225	(1)
The Derivation of Taguchi's Tolerance Equation and the Factor of Safety	226	(3)
Relating Customer Tolerances to Engineering Tolerances	229	(1)
An Example of Tolerancing Using the Loss Function (Nominal--the--Best Case)	229	(1)
Relating Customer Tolerances to Subsystem and Component Tolerances	230	(1)
The Linear Sensitivity Factor	231	(1)
Using the Loss Function for Multiple--Component Tolerance Analysis	232	(1)
An Example of Applying the Quality--Loss Function to a Multicomponent Problem	233	(1)
Setting Up the Problem	234	(1)
Identifying Critical Parameters	234	(3)
Mapping the Critical Parameters and Their Sensitivities	235	(2)
Converting the Traditional Tolerance Problem into a Quality--Loss	237	(1)
How to Evaluate Aggregated Low Level Tolerances	238	(2)
Case 1: Ratio of Losses are Much Less than Unity	239	(1)
Case 2: Ratio of Losses are Much Greater than Unity	239	(1)
Case 3: Ratio of Loss Approximately Equal Unity	239	(1)
Using the Loss Function Nonlinear Relationships	240	(1)
Developing Tolerances for Deterioration Characteristics in the Design	241	(1)
Tolerancing the Deterioration Rate of a Higher Level Product Characteristic	242	(1)
Determining Initial and Deterioration Tolerances for a Product Characteristic	243	(1)
Summary	244	(1)
References	245	(1)
13 General Review of Orthogonal Array Experimentation for Tolerance Design Applications	246	(16)
Developing Tolerances Using a Designed Experiment	246	(1)
Use of Orthogonal Arrays in Tolerance Design	247	(1)
The Build--Test--Fix Approach	248	(1)
Introduction to Full Factorial Experiments	248	(7)
Designed Experiments Based on Fractional Factorial Orthogonal Arrays	249	(2)
Degrees of Freedom: The Capacity to do Experimental Analysis	251	(1)
Degrees of Freedom for the Full Factorial	251	(1)
The DOF for the Fractional Factorial Orthogonal Array	251	(1)
DOF for Two--Level Full Factorial Arrays	252	(3)
Methods to Account for Interactions within Tolerance Design Experiments	255	(5)
Interactions Defined	255	(2)
Quantifying the Effect of an Interaction	257	(2)
Defining the Degrees of Freedom Required for Evaluating Interactions	259	(1)
Summary	260	(1)
References	261	(1)
14 Introducing Noise into a Tolerance Experiment	262	(16)
Defining Noises and Creating Noise Diagrams and Maps	262	(15)
Selecting Noise Factors for Inclusion in a Tolerance Experiment	264	(1)
Noise Diagrams and System Noise Maps	265	(2)
Experimental Error and Induced Noise	267	(4)
The Noise Factor Experiment	271	(1)
Creating Compound Noise Factors	272	(1)
Setting Up and Running the Noise Experiment	273	(1)
Analysis of Means for the Noise Experiment	274	(2)
Verification of the Predicted Response	276	(1)
Summary	277	(1)
References	277	(1)
15 Setting Up a Designed Experiment for Variance and Tolerance Analysis	278	(28)
Preparing to Run a Statistical Variance Experiment	279	(13)
Selecting the Right Orthogonal Array for the Experiment	279	(2)
Special Instructions for Running Three--Level Statistical Variance Experiments	281	(11)
Using the V.3 Transformation	292	(4)
A Comparison of Output Statistics	296	(4)
Conducting a Tolerance Experiment for Worst--Case Conditions	300	(1)
An L9 Experiment and Monte Carlo Simulation Using Levels Assuming Uniform Distributions	301	(3)
Metrology and Experimental Technique	304	(1)
Summary	304	(1)
References	305	(1)
16 The ANOVA Method	306	(19)
Accounting for Variation Using Experimental Data	307	(1)
A Note on Computer--Aided ANOVA	308	(1)
An Example of the ANOVA Process	308	(3)
Degrees of Freedom in ANOVA	311	(1)
Error Variance and Pooling	312	(1)
Error Variance and Replication	312	(1)
Error Variance and Utilizing Empty Columns	313	(1)
The F--Test	313	(1)
A WinRobust ANOVA Example	314	(4)
An ANOVA--TM Example	318	(5)
Summary	323	(1)
References	324	(1)
17 The Tolerance Design Process: A Detailed Case Study	325	(36)
The Steps for Performing the Tolerance Design Process	325	(2)
Option 1: A Company Cost--Driven Process	327	(1)
Option 2: A Manufacturing Capability and Cost--Driven Process	328	(2)
The ASI Circuit Case Study	330	(4)
Identifying the Parameters for Tolerancing	330	(1)
Improving Quality in Cases where Parameter Design was Not Done	331	(1)
Constructing the Loss Function	332	(2)
Setting Up and Running the Experiment	334	(3)
Two--versus Three--Level Experiments	337	(1)
Techniques for Putting Noise into the Tolerance Experiment	338	(1)
Running the Experiment	338	(2)
Data Entry	340	(3)
Measuring the Proper Response Characteristic	343	(1)
Interactions in Tolerance Experiments	343	(1)
Analyzing the Data	344	(1)
Applying ANOVA	344	(5)
Relating the ANOVA Data to the Loss Function and Process Capability (Cp)	349	(1)
Defining the Critical to Function (CTF) Factors	350	(1)
Defining the Cost Improvement Parameters (CIP)	351	(1)
Identifying and Quantifying the Costs Associated with Improving Quality	352	(1)
Working with Suppliers to Lower Customer Losses through Reducing the Component Parameter Standard Deviations	352	(1)
Calculating New Variances and MSD Values Using the Variance Equation	353	(1)
Quantifying the Cost of Reducing the Parameter Standard Deviations	354	(2)
Identifying and Quantifying the Opportunities for Lowering Costs	356	(1)
Relaxing Tolerances and Material Specifications of CIPs to Balance Cost and Quality	356	(1)
New Loss and Cp after Upgrading the Critical To Function Factors and Downgrading the Cost Improvement Parameters	357	(1)
Using Tolerance Design to Help Attain Six Sigma Quality Goals	357	(1)
Using Tolerance Design to Improve System Reliability	357	(1)
Summary	358	(1)
References	359	(2)
Section IV: Industrial Case Studies	361	(28)
18 Drive System Case Studies	363	(26)
The Drive System	364	(1)
The Drive Module	365	(2)
Case 1: Defining Tolerances for Standard Drive Module Components	367	(2)
Tolerancing Custom Parts to Assemble with Standard Parts	368	(1)
Case 2: Drive Module for Worst--Case Assembly Analysis	369	(2)
Worst--Case Linear Stack Analysis	369	(2)
Case 3: Drive Module for Computer--Aided Assembly Analysis	371	(2)
RSS Case Linear Stack Analysis	371	(2)
Case 4: Drive Module for Computer--Aided Assembly Analysis	373	(7)
Case 5: Drive System Aided by the Use of a Designed Experiment	380	(8)
Preparing for the Drive System Tolerance Developmental Experiment	381	(1)
Setting Up the Experiment	382	(3)
Data Acquisition	385	(1)
Results from the L9 Experiment	386	(2)
Summary	388	(1)
Appendix A: The Z Transformation Tables and the t Transformation Table	389	(4)
Appendix B: The Adjusted Z Transformation Tables	393	(10)
Appendix C: The F Tables	403	(6)
Appendix D: Additional References for Tolerance Design	409	(2)
Appendix E: Suppliers for Tolerance Design	411	(2)
Index	413

Excerpts

This is the first book in the history of engineering science to comprehensively address the analytical and experimental methods available for the development of tolerances. This indicates, on one hand, an unfortunate legacy of neglecting a very important engineering topic. On the other hand, it provides an opportunity for engineering practitioners, students, and educators to fill a void in their skill sets.This book is written for a fairly diverse audience. It is intended to be used as a handbook for industrial applications as well as a course text in technology and engineering science programs at the college and university level. It is structured so that undergraduate technology and engineering students at the associate and baccalaureate levels can equally share in its informational value. The author views the tolerance development process as the responsibility of the design engineering team. This requires that the book be suitable for engineers, designer/drafters, and technicians. Each of these engineering team members has a valuable role to play in the development of product specifications.Tolerance Designcontains detailed information for each of these team members.This book is broad in scope. It reviews the three initial phases of the product-development process where tolerance development resides as the final cost-versus-quality balancing process. It explains, in detail, how tolerance design relates to concept design and parameter design. It also relates the tolerance design process to many other engineering and product development tools and tasks, including reliability growth activities. It covers all the basic analytical methods that exist in modern and traditional tolerancing techniques. It also rigorously covers the latest experimental methods that can be employed in the tolerance design process.This text details step-by-step the analytical and experimental tolerance-development methods so the reader can more easily and properly develop tolerances. Many examples and case studies are used to convey the process of defining the right tolerances so they can be properly communicated to the manufacturing, assembly, and service communities. The text illustrates how to balance product cost and quality through the tolerance development process. Great emphasis is placed on how the engineering and manufacturing teams must work harmoniously and concurrently to develop optimal tolerances.Tolerance Designinstills a philosophy that tolerance development is as much about cost optimization as it is about functional integrity.This book has been heavily critiqued and scrutinized, on your behalf, by many of the top experts in the U.S. engineering, tolerance analysis, and tolerance communication communities. Much of their work has been included in this text. This was done to make the depth and breadth of the book rock solid. Since the book is the first of its kind, the author and publisher believed it had to be thoroughly evaluated, perhaps even more rigorously than usual, so that it could stand as a major contribution to engineering literature for many years to come. The book was "engineered" to meet your needs so you can meet your customer's needs.The world is so competitive now that there is simply no way to keep our industries economically viable by using the same ad hoc engineering processes that have evolved over the past 50 years. With this in mind, a major focus in this text is given to the disciplined methods of quality engineering as defined by Dr. Genichi Taguchi. Engineering processes are now being taught in universities and applied in industries all over the United States. This book is very process oriented. It strives to teach discipline in the development of tolerances. In fact, you will have difficulty succeeding in tolerance optimization if the engineering processes that follow the tolerancing process are void of rigor and discipline. Taguchi's approach to product development provides an