Automation of Linear Tolerance Charts and Extension to Statistical Tolerance Analysis

2003 ◽  
Author(s):  
Zhengshu Shen ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Statistical Analysis ◽  
Tolerance Analysis ◽  
Automated Analysis ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Tolerance Charting ◽  
Tolerance Charts ◽  
Statistical Tolerance ◽  
Tolerance Accumulation ◽  
Statistical Tolerance Analysis

Manual construction of tolerance charts is a popular technique for analyzing tolerance accumulation in parts and assemblies. But this technique has some limitations: (1) it only deals with the worst-case analysis, and not statistical analysis (2) it is time-consuming and errorprone (3) it considers variations in only one direction at a time, i.e. radial or linear. This paper proposes a method to automate 1-D tolerance charting, based on the ASU GD&T global model and to add statistical tolerance analysis functionality to the charting analysis. The automation of tolerance charting involves automation of stackup loop detection, automatic application of the rules for chart construction and determination of the closed form function for statistical analysis. The automated analysis considers both dimensional and geometric tolerances defined as per the ASME Y14.5 – 1994 standard at part and assembly level. The implementation of a prototype charting analysis system is described and two case studies are presented to demonstrate the approach.

Virtual Part Arrangement in Assemblies for Automatic Tolerance Chart Based Stackup Analysis

2006 ◽  
Author(s):  
Zhengshu Shen ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Worst Case Analysis ◽  
Worst Case ◽  
Tolerance Charting ◽  
Geometric Tolerances ◽  
Design Tolerance ◽  
Tolerance Chart ◽  
Loop Detection ◽  
Tolerance Charts ◽  
Tolerance Accumulation

Manual construction of design tolerance charts is a popular technique for analyzing tolerance accumulation in parts and assemblies, even though it is limited to one-dimensional worst-case analysis. Since charting rules are GD&T (geometric dimensioning & tolerancing) specification dependent, and the user has to remember all the different rules to construct a valid tolerance chart, manual charting technique is time-consuming and error-prone. The computer can be used for automated tolerance charting, which can relieve the user from the tedious and error-prone procedure while obtain the valid results faster. The automation of tolerance charting, based on the ASU GD&T mathematical model, involves (1) automation of stackup loop detection, (2) formulation of the charting rules for different geometric tolerances and determination of the closed form function for statistical analysis, (3) automatic part arrangement for an assembly level chart analysis, (4) development of the algorithms for chart analysis and automatic application of the charting rules. Since the authors’ previous DETC/CIE’03 paper already discussed tasks 1~2 and part of task 4, this paper will focus upon task 3, i.e. virtual part arrangement in assemblies for tolerance charts, and update the analysis algorithm (related to task 4). These two papers together will provide a complete coverage of automated tolerance charting technique popularly used in industry. The implementation will be briefly discussed as well, and case studies will be provided to demonstrate the approach to virtual part arrangement.

Algebraic Representation of Geometric and Size Tolerances

1995 ◽  
Author(s):  
S. H. Mullins ◽  
D. C. Anderson
Keyword(s):  
Tolerance Analysis ◽  
Design Analysis ◽  
Algebraic Representation ◽  
Dimensional Metrology ◽  
Algebraic Form ◽  
Worst Case ◽  
Mechanical Component ◽  
Analysis And Synthesis ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Abstract Presented is a method for mathematically modeling mechanical component tolerances. The method translates the semantics of ANSI Y14.5M tolerances into an algebraic form. This algebraic form is suitable for either worst-case or statistical tolerance analysis and seeks to satisfy the requirements of both dimensional metrology and design analysis and synthesis. The method is illustrated by application to datum systems, position tolerances, orientation tolerances, and size tolerances.

A Design-and-Build Project to Introduce Concepts Relating to Dimensional Variation

1998 ◽  
Vol 26 (4) ◽  
pp. 259-272
Author(s):  
S. M. Panton ◽  
P. R. Milner
Keyword(s):  
Classroom Environment ◽  
Tolerance Analysis ◽  
Cylinder Block ◽  
Worst Case ◽  
Good Design ◽  
Minimum Number ◽  
Dimensional Variation ◽  
Assembly Problem ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

A design-and-build project which has been used to introduce Year 2 students of Mechanical Engineering to the concepts of dimensional variation and the influence of dimensional variation on function and assembly. The project simulates the cylinder head cylinder block assembly problem and specifies requirements in terms of a tolerance on concentricity of the cylinders in the head and block, and the interchangeable assembly of the head and block. Materials which are easily and cheaply sourced and tools which are easily manufactured and safe to use in a classroom environment are used throughout. During the project the students are exposed to concepts such as worst-case and statistical tolerance analysis, sensitivity analysis, geometric moment effects, minimum constraint design, co-variance and gauging. The exercise also emphasizes that good design means components that function and assemble with the minimum number of tight tolerances.

A Nonlinear Tolerance Analysis Method Using Worst-Case and Matlab

2011 ◽  
Vol 201-203 ◽  
pp. 247-252
Author(s):  
Mei Qiong Yu ◽  
Yan Yan ◽  
Jia Hao ◽  
Guo Xin Wang
Keyword(s):  
Mathematical Formulation ◽  
Tolerance Analysis ◽  
Worst Case Analysis ◽  
Analysis Method ◽  
Worst Case ◽  
Analysis Methods ◽  
Precision Design ◽  
Basic Parameters ◽  
Statistical Tolerance ◽  
Production Requirement

The tolerance analysis methods are usually used to test the result of product design and assembly; moreover the tolerance analysis also is a fundamental technique in precision design process. So far, there are two kinds of tolerance analysis methods: statistical tolerance analysis and worst-case analysis; they have their own characteristics and drawbacks. In this paper, it presents a nonlinear tolerance analysis method which uses Matlab tool to construct the nonlinear tolerance analysis mathematical formulation and calculate the result of nonlinear tolerance analysis based on the principle of worst-case tolerance analysis. All the processes are dealt with and tested by computer. The engineers only enter some basic parameters through the standardized interface, and then the result can be obtained without artificial intervention. In addition, the accuracy of calculation result meets the production requirement. The system of the nonlinear tolerance analysis is easier for engineers to use.

Validation of the Tolerance Analysis of Compliant Assemblies

1999 ◽  
Author(s):  
Eric Sellem ◽  
Alain Rivière ◽  
Charles André De Hillerin ◽  
André Clement
Keyword(s):  
Sensitivity Analysis ◽  
Mechanical Model ◽  
Tolerance Analysis ◽  
Assembly Process ◽  
Worst Case ◽  
Key Characteristics ◽  
Statistical Tolerance ◽  
Compliant Parts ◽  
Complex Parts ◽  
Statistical Tolerance Analysis

Abstract Current statistical tolerance analysis of assemblies are generally based on Monte Carlo simulation or Worst Case. The available software tools using this technique model the assembly of rigid parts, by only considering the kinematic laws. Sellem (1998) proposed a linear mechanical model taking both deformation and assembly process into account in the computation of tolerance assemblies of compliant parts. This paper presents the validation of this method by a comparison with measurements performed on an actual assembly of four complex parts. Some improvements in the modeling of the assembly process are also presented and described a sensitivity analysis approach to identify the key characteristics of the assembly.

A Comparative Study Of Tolerance Analysis Methods

2005 ◽  
Vol 5 (3) ◽  
pp. 247-256 ◽  
Author(s):  
Zhengshu Shen ◽  
Gaurav Ameta ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Patent Application ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Worst Case ◽  
Analysis Methods ◽  
Tolerance Charts ◽  
Parametric Constraint ◽  
Assembly Constraints ◽  
Tolerance Accumulation

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are: (1) one-dimensional tolerance charts; (2) parametric tolerance analysis, especially parametric analysis based on the Monte Carlo simulation; (3) vector loop (or kinematic) based tolerance analysis; and (4) ASU Tolerance-Map® (T-Map®) (Patent pending; nonprovisional patent application number: 09/507, 542 (2002)) based tolerance analysis. Tolerance charts deal with worst-case tolerance analysis in one direction at a time and ignore possible contributions from the other directions. Manual charting is tedious and error prone, hence, attempts have been made for automation. The parametric approach to tolerance analysis is based on parametric constraint solving; its inherent drawback is that the accuracy of the simulation results are dependent on the user-defined modeling scheme, and its inability to incorporate all Y14.5 rules. The vector loop method uses kinematic joints to model assembly constraints. It is also not fully consistent with Y14.5 standard. The ASU T-Map® based tolerance analysis method can model geometric tolerances and their interaction in truly three-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. The T-Map® based tolerance analysis method is still under development. Despite the shortcomings of each of these tolerance analysis methods, each may be used to provide reasonable results under certain circumstances. Through a comprehensive comparison of these methods, this paper will offer some recommendations for selecting the best method to use for a given tolerance accumulation problem.

A Comparison Study of Small Displacement Torsor and Analysis Line Methods for Functional Tolerance Analysis

2012 ◽  
Vol 605-607 ◽  
pp. 358-364
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Jun Ying Wang ◽  
Wen Xin Ma
Keyword(s):  
Computation Time ◽  
Tolerance Analysis ◽  
General Characteristic ◽  
Worst Case Analysis ◽  
Small Displacement ◽  
Worst Case ◽  
Small Displacement Torsor ◽  
Functional Tolerance ◽  
Tolerance Accumulation ◽  
Analysis Line

Tolerance analysis plays an important role in the stage of product design and has great influences on the product assembly quality and manufacturing costs. Two major methods are used for three-dimensional functional tolerance analysis, which are small displacement torsor and analysis line. A positioning mechanism with two parts is presented for tolerance accumulation calculation. Through the comparison of these two methods on computation processes and results, analysis line method can establish the explicit relationship between the functional requirement and the tolerances of the influential part, which allows finding the accumulation results in the worst-case and statistical conditions. However, it requires the determination of transfer relationship case by case. For small displacement torsor model, it permits a set of inequalities to express the tolerance zones, which yields a linear programming problem. It is applicable to different tolerance chains for its general characteristic. However it is adopted only for the worst-case analysis and requires more computation time.

Computer-Aided Linear Tolerance Analysis and Optimal Tolerance Distribution for Cylindrical Machined Parts

1998 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Chin-Ming Shih
Keyword(s):  
Tolerance Analysis ◽  
Optimization Techniques ◽  
Worst Case ◽  
Tolerance Chart ◽  
Computer Aided ◽  
Machined Parts ◽  
Cylindrical Parts ◽  
Statistical Tolerance ◽  
Tolerance Distribution ◽  
Tolerance Accumulation

Abstract Quality and cost are among the most important concerns for a product. While tolerance is one of the typical metrics for quality, it is a trade-off between tolerances and costs in product development though the two factors often conflict with each other. This paper describes a systematic approach to compute linear tolerance accumulation for cylindrical parts by machining operations based on the tolerance chart. A computer-aided tolerance chart system is developed to assist the construction of the corresponding tolerance chart and the computation of accumulated linear tolerances for a given process plan. Tolerance distribution to each machining operation by optimization techniques is also investigated. The goal is to minimize machining cost subject to constraints on tolerance accumulation and process capability. It shows that the machining cost of a sample part with the worst-case tolerance analysis can be reduced by 39%, compared to that by experience, and can be further reduced if statistical tolerance analysis applies.

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