Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation

2009 ◽  
Vol 41 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Jean-Yves Dantan ◽  
Ahmed-Jawad Qureshi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Constraint Satisfaction ◽  
Tolerance Analysis ◽  
Constraint Satisfaction Problems ◽  
Worst Case ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Statistical Tolerance Analysis Based on Constraint Satisfaction Problems and Monte Carlo Simulation

2012 ◽  
Vol 433-440 ◽  
pp. 6616-6621
Author(s):  
Yong Jun Jiang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problem ◽  
Mathematical Formulation ◽  
Tolerance Analysis ◽  
Constraint Satisfaction Problems ◽  
Statistical Tolerance ◽  
Problem Solvers ◽  
Statistical Tolerance Analysis

This paper deals with the mathematical formulation of tolerance analysis. The mathematical formulation presented simulates the influences of geometrical deviations on the geometrical behavior of the mechanism, and integrates the quantifier notion. We propose a mathematical formulation of tolerance analysis which simulates the influences of geometrical deviations on the geometrical behavior of the mechanism, and integrates the quantifier notion. To compute this mathematical formulation, two approaches based on Quantified Constraint Satisfaction Problem solvers and Monte Carlo simulation are proposed and tested.

scholarly journals A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation

2012 ◽  
Vol 44 (2) ◽  
pp. 132-142 ◽  
Author(s):  
Ahmed Jawad Qureshi ◽  
Jean-Yves Dantan ◽  
Vahid Sabri ◽  
Paul Beaucaire ◽  
Nicolas Gayton
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Tolerance Analysis ◽  
Analysis Approach ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

A Statistical Tolerance Analysis Method for Feature in Non-Normal Distribution

2010 ◽  
Author(s):  
Chang-Hsin Kuo ◽  
Jhy-Cherng Tsai
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Normal Distribution ◽  
Mechanical Design ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Normal Distributions ◽  
Tolerance Specification ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

The tolerance analysis of an assembly is an important issue for mechanical design. Among many tolerance analysis methods, the conventional statistical tolerance analysis method is the most popular one. However, the conventional statistical tolerance analysis method is based on the normal distribution. It fails to predict the resultant tolerance of an assembly with features in non-normal distributions. In this paper, the distributions of features are transferred into statistical moments first. Then, the tolerance stack-up can be handled based on these moments. Finally, the computed resultant moments can be mapped back to probability distribution to find the resultant tolerance specification of the assembly. Two examples are used to demonstrate the proposed method. Compared to the resultants by Monte Carlo simulation with 1,000,000 samples, the predicted resultant tolerance specifications by this method are only −0.868% and 0.799% differences. The predicted resultant tolerances of this method are fast and accurate.

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.

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.

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.

Application of Quasi-Monte Carlo Method Based on Good Point Set in Tolerance Analysis

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Yanlong Cao ◽  
Huiwen Yan ◽  
Ting Liu ◽  
Jiangxin Yang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Tolerance Analysis ◽  
Simulation Method ◽  
Analysis Tool ◽  
Monte Carlo Simulation Method ◽  
Worst Case ◽  
Quasi Monte Carlo ◽  
Good Point

Tolerance analysis is increasingly becoming an important tool for mechanical design, process planning, manufacturing, and inspection. It provides a quantitative analysis tool for evaluating the effects of manufacturing variations on performance and overall cost of the final assembly. It boosts concurrent engineering by bringing engineering design requirements and manufacturing capabilities together in a common model. It can be either worst-case or statistical. It may involve linear or nonlinear behavior. Monte Carlo simulation is the simplest and the most popular method for nonlinear statistical tolerance analysis. Monte Carlo simulation offers a powerful analytical method for predicting the effects of manufacturing variations on design performance and production cost. However, the main drawbacks of this method are that it is necessary to generate very large samples to assure calculation accuracy, and that the results of analysis contain errors of probability. In this paper, a quasi-Monte Carlo method based on good point (GP) set is proposed. The difference between the method proposed and Monte Carlo simulation lies in that the quasi-random numbers generated by Monte Carlo simulation method are replaced by ones generated by the method proposed in this paper. Compared with Monte Carlo simulation method, the proposed method provides analysis results with less calculation amount and higher precision.

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