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.

Sequential Algorithm Based on Number Theoretic Method for Statistical Tolerance Analysis and Synthesis

2000 ◽  
Vol 123 (3) ◽  
pp. 490-493 ◽  
Author(s):  
Zhige Zhou ◽  
Wenzhen Huang ◽  
Li Zhang
Keyword(s):  
Tolerance Analysis ◽  
Optimization Method ◽  
Computational Effort ◽  
Tolerance Allocation ◽  
Sequential Algorithm ◽  
Theoretic Method ◽  
Analysis And Synthesis ◽  
Number Theoretic Method ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Tolerancing is one of the most important tasks in product and manufacturing process design. In the literature, both Monte Carlo simulation and numerical optimization method have been widely used in the process of statistical tolerance analysis and synthesis, but the computational effort is huge. This paper presents two techniques, quasi random numbers based on the Number Theoretic Method and sequential algorithm based on the Number Theoretic net, to calculate yield and to perform tolerance allocation. An example demonstrates the optimal tolerance allocation design and is employed to investigate the efficiency and accuracy of this solution. This algorithm can efficiently obtain the global optimum, and the amount of calculation is considerably reduced.

Worst Case and Statistical Tolerance Analysis of the Daughter Card Assembly

1992 ◽  
Author(s):  
James Guilford ◽  
M. Sethi ◽  
Joshua Turner
Keyword(s):  
Tolerance Analysis ◽  
Worst Case ◽  
Cad System ◽  
Geometric Tolerancing ◽  
Design Function ◽  
Simplifying Assumptions ◽  
Analysis Package ◽  
Statistical Tolerance ◽  
Analysis Models ◽  
Statistical Tolerance Analysis

Abstract Designers are increasingly finding the need for an automated tolerance analysis package which interprets tolerances according to established tolerancing standards. Unfortunately, most of the commercial packages available make simplifying assumptions for the conventional plus-minus tolerances and do not support geometric tolerancing at all. Construction of a tolerance analysis models with these packages can be time consuming. GEOS is an automated tolerance analysis package which overcomes these shortcomings. It is based on variational modeling and feasibility space approaches. This report presents the results for a worst case amd statistical tolerance analysis done on an industrial assembly using GEOS. For this analysis, no special models had to be created as GEOS can accept the 3-D CAD model directly. The models used both conventional plus-minus tolerances as well as geometric tolerances. A GEOS graphical front-end, integrated with a commercial CAD system, was used to define the assembly relations, design function, and analysis parameters.

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.

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