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.

scholarly journals Statistical Tolerance Analysis with T-Maps for Assemblies

Procedia CIRP ◽  
2018 ◽  
Vol 75 ◽  
pp. 220-225 ◽  
Author(s):  
Gaurav Ameta ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Tolerance Analysis ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Statistical Tolerance Analysis of Over-Constrained Mechanical Assemblies With Form Defects Considering Contact Types

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Edoh Goka ◽  
Lazhar Homri ◽  
Pierre Beaurepaire ◽  
Jean-Yves Dantan
Keyword(s):  
Tolerance Analysis ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Behavior Modeling ◽  
Functional Requirements ◽  
Mechanical Assembly ◽  
Mechanical Assemblies ◽  
Statistical Tolerance ◽  
The Individual ◽  
Statistical Tolerance Analysis

Tolerance analysis aims toward the verification impact of the individual tolerances on the assembly and functional requirements of a mechanism. The manufactured products have several types of contact and are inherent in imperfections, which often causes the failure of the assembly and its functioning. Tolerances are, therefore, allocated to each part of the mechanism in purpose to obtain an optimal quality of the final product. Three main issues are generally defined to realize the tolerance analysis of a mechanical assembly: the geometrical deviations modeling, the geometrical behavior modeling, and the tolerance analysis techniques. In this paper, a method is proposed to realize the tolerance analysis of an over-constrained mechanical assembly with form defects by considering the contacts nature (fixed, sliding, and floating contacts) in its geometrical behavior modeling. Different optimization methods are used to study the different contact types. The overall statistical tolerance analysis of the over-constrained mechanical assembly is carried out by determining the assembly and the functionality probabilities based on optimization techniques combined with a Monte Carlo simulation (MCS). An application to an over-constrained mechanical assembly is given at the end.

Tolerance Analysis Method Using Improved Convolution Method

2012 ◽  
Vol 271-272 ◽  
pp. 1463-1466
Author(s):  
Shao Gang Liu ◽  
Qiu Jin
Keyword(s):  
Linear Dimension ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Analysis Methods ◽  
Statistical Tolerance ◽  
Nonlinear Dimension ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

Convolution method is studied to analyze statistical tolerance for linear dimension chain and nonlinear dimension chain. Hybrid convolution method is proposed, which is the integration of analytical convolution and numerical convolution. In order to reduce the algorithm errors, improved convolution method is proposed. Comparing with other statistical tolerance analysis methods, this method is faster and accurate. At last, an example is used to demonstrate the method proposed in this paper.

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