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.

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.

NON-NORMAL STATISTICAL TOLERANCE ANALYSIS USING ANALYTICAL CONVOLUTION METHOD

2008 ◽  
Vol 07 (01) ◽  
pp. 127-130 ◽  
Author(s):  
S. G. LIU ◽  
P. WANG ◽  
Z. G. LI
Keyword(s):  
Normal Distribution ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Accurate Method ◽  
Probability Density Functions ◽  
Triangular Distribution ◽  
Normal Distributions ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

In statistical tolerance analysis, it is usually assumed that the statistical tolerance is normally distributed. But in practice, there are many non-normal distributions, such as uniform distribution, triangular distribution, etc. The simple way to analyze non-normal distributions is to approximately represent it with normal distribution, but the accuracy is low. Monte-Carlo simulation can analyze non-normal distributions with higher accuracy, but is time consuming. Convolution method is an accurate method to analyze statistical tolerance, but there are few reported works about it because of the difficulty. In this paper, analytical convolution is used to analyze non-normal distribution, and the probability density functions of closed loop component are obtained. Comparing with other methods, convolution method is accurate and faster.

Statistical Tolerance Analysis With Sensitivities Established With Tolerance-Maps

2018 ◽  
Author(s):  
Aniket N. Chitale ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Coordinate Frame ◽  
Target Feature ◽  
Functional Feature ◽  
Design Function ◽  
Statistical Tolerance ◽  
The One ◽  
The Relationship ◽  
Statistical Tolerance Analysis

The purpose of math models for tolerances is to aid a designer in assessing relationships between tolerances that contribute to variations of a dependent dimension that must be controlled to achieve some design function and which identifies a target (functional) feature. The T-Maps model for representing limits to allowable manufacturing variations is applied to identify the sensitivity of a dependent dimension to each of the contributing tolerances to the relationship. The method is to choose from a library of T-Maps the one that represents, in its own local (canonical) reference frame, each contributing feature and the tolerances specified on it; transform this T-Map to a coordinate frame centered at the target feature; obtain the accumulation T-Map for the assembly with the Minkowski sum; and fit a circumscribing functional T-Map to it. The fitting is accomplished numerically to determine the associated functional tolerance value. The sensitivity for each contributing tolerance-and-feature combination is determined by perturbing the tolerance, refitting the functional map to the accumulation map, and forming a ratio of incremental tolerance values from the two functional T-Maps. Perturbing the tolerance-feature combinations one at a time, the sensitivities for an entire stack of contributing tolerances can be built. For certain classes of loop equations, the same sensitivities result by fitting the functional T-Map to the T-Map for each feature, one-by-one, and forming the overall result as a scalar sum. Sensitivities help a designer to optimize tolerance assignments by identifying those tolerances that most strongly influence the dependent dimension at the target feature. Since the fitting of the functional T-Map is accomplished by intersection of geometric shapes, all the T-Maps are constructed with linear half-spaces.

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.

Comparison of Assembly Tolerance Analysis by the Direct Linearization and Modified Monte Carlo Simulation Methods

1995 ◽  
Author(s):  
Jinsong Gao ◽  
Kenneth W. Chase ◽  
Spencer P. Magleby
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Loop ◽  
Great Influence ◽  
Tolerance Analysis ◽  
Linearization Method ◽  
Direct Linearization ◽  
Highly Nonlinear ◽  
Assembly Features ◽  
Assembly Constraints

Abstract Two methods for performing statistical tolerance analysis of mechanical assemblies are compared: the Direct Linearization Method (DLM), and Monte Carlo simulation. A selection of 2-D and 3-D vector models of assemblies were analyzed, including problems with closed loop assembly constraints. Closed vector loops describe the small kinematic adjustments that occur at assembly time. Open loops describe critical clearances or other assembly features. The DLM uses linearized assembly constraints and matrix algebra to estimate the variations of the assembly or kinematic variables, and to predict assembly rejects. A modified Monte Carlo simulation, employing an iterative technique for closed loop assemblies, was applied to the same problem set. The results of the comparison show that the DLM is accurate if the tolerances are relatively small compared to the nominal dimensions of the components, and the assembly functions are not highly nonlinear. Sample size is shown to have great influence on the accuracy of Monte Carlo simulation.

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