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 Comparative Study of Tolerance Analysis Methods

2004 ◽  
Author(s):  
Zhengshu Shen ◽  
Gaurav Ameta ◽  
Jami J. Shah ◽  
Joseph K. Davidson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Tolerance Analysis ◽  
3 Dimensional ◽  
Analysis Methods ◽  
Simulation Based ◽  
Comprehensive Comparison ◽  
Tolerance Charts ◽  
Assembly Constraints ◽  
Tolerance Accumulation

This paper reviews four major methods for tolerance analysis and compares them. The methods discussed are (1) 1D tolerance charts, (2) variational analysis based on Monte Carlo simulation, (3) vector loop (or kinematic) based analysis, and (4) ASU T-Maps© based tolerance analysis. Tolerance charts deal with 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. Monte Carlo simulation based tolerance analysis is based on parametric solid modeling; its inherent drawback is that simulation results highly depend on the user-defined modeling scheme, and its inability to obey 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. ASU T-Maps based tolerance analysis method can model geometric tolerances and their interaction in truly 3-dimensional context. It is completely consistent with Y14.5 standard but its use by designers may be quite challenging. T-Maps based tolerance analysis 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. No guidelines exist for such a purpose. Through a comprehensive comparison of these methods, this paper will develop some guidelines for selecting the best method to use for a given tolerance accumulation problem.

Worst Case Tolerance Analysis with Nonlinear Problems

1988 ◽  
Vol 110 (3) ◽  
pp. 232-235 ◽  
Author(s):  
W. H. Greenwood ◽  
K. W. Chase
Keyword(s):  
Iterative Method ◽  
Significant Influence ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Tolerance Analysis ◽  
Rational Basis ◽  
Worst Case ◽  
Manufactured Products ◽  
Engineering Drawings ◽  
Tolerance Accumulation

When designers assign tolerances on engineering drawings, they have a significant influence on the resulting cost and producibility of manufactured products. A rational basis for assigning tolerances involves constructing mathematical models of tolerance accumulation in assemblies of parts. However, tolerance stacks in two or three-dimensional problems or other nonlinear assembly functions may distort the resultant assembly tolerances, altering the range and symmetry. An iterative method is described for adjusting the nominal dimensions of the component parts such that the specified assembly limits are not violated.

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.

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.

A New Tolerance Analysis Method for Designers and Manufacturers

1987 ◽  
Vol 109 (2) ◽  
pp. 112-116 ◽  
Author(s):  
W. H. Greenwood ◽  
K. W. Chase
Keyword(s):  
Tolerance Analysis ◽  
New Method ◽  
Analysis Method ◽  
Worst Case ◽  
Assembly Tolerance ◽  
Naturally Occurring ◽  
Methods Of Analysis

Even when all manufactured parts for an assembly are produced within limits, these parts still may not assemble properly if the assembly tolerance analysis was inadequately performed. Naturally occurring shifts in a process can produce biased distributions which can result in increased assembly problems and a greater number of rejects than anticipated. The most common methods of analysis of assembly tolerance buildup are worst case and root sum squares. The limitations of each of these methods are discussed and a simple new method is proposed which accounts for expected bias. This new method includes both worst case and root sum squares as extreme cases.

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.

Application of a Unified Jacobian—Torsor Model for Tolerance Analysis

2003 ◽  
Vol 3 (1) ◽  
pp. 2-14 ◽  
Author(s):  
Alain Desrochers ◽  
Walid Ghie ◽  
Luc Laperrie`re
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Small Displacement ◽  
Manufacturing Processes ◽  
Functional Requirements ◽  
Tolerance Zone ◽  
Kinematic Chains ◽  
Final Assembly ◽  
Novel Method ◽  
Assembly Constraints

Because of uncertainties in manufacturing processes, a mechanical part always shows variations in its geometrical characteristics (ex. form, dimension, orientation and position). Quality then often reflect how well tolerances and hence, functional requirements, are being achieved by the manufacturing processes in the final product. From a design perspective, efficient methods must be made available to compute, from the tolerances on individual parts, the value of the functional requirement on the final assembly. This is known as tolerance analysis. To that end, existing methods, often based on modeling of the open kinematic chains in robotics, are classified as deterministic or statistical. These methods suppose that the assembled parts are not perfect with regard to the nominal geometry and are rigid. The rigidity of the parts implies that the places of contacts are regarded as points. The validation or the determination of a tolerance zone is therefore accomplished by a series of simulation in specific points subjected to assembly constraints. To overcome the limitations and difficulties of point based approaches, the paper proposes the unification of two existing models: the Jacobian’s matrix model, based on the infinitesimal modeling of open kinematic chains in robotics, and the tolerance zone representation model, using small displacement screws and constraints to establish the extreme limits between which points and surfaces can vary. The approach also uses interval algebra as a novel method to take tolerance boundaries into account in tolerance analysis. The approach has been illustrated on a simple two parts assembly, nevertheless demonstrating the capability of the method to handle three-dimensional geometry. The results are then validated geometrically, showing the overall soundness of the approach.

A small displacement torsor model for 3D tolerance analysis of conical structures

2014 ◽  
Vol 229 (14) ◽  
pp. 2514-2523 ◽  
Author(s):  
Sun Jin ◽  
Hua Chen ◽  
Zhimin Li ◽  
Xinmin Lai
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Dimensional Euclidean Space ◽  
Small Displacement ◽  
Analysis Method ◽  
Tolerance Zone ◽  
Geometric Tolerances ◽  
Small Displacement Torsor ◽  
Conical Surfaces ◽  
Conical Structures

The small displacement torsor model is a classic three-dimensional tolerance analysis method. It uses three translational vectors and three rotational vectors to represent tolerance information in three-dimensional Euclidean space. However, the target features of this model mainly focused on planes and cylinders in previous studies. Little attention is invested to conical features and their joints which are used widely and more complex than the planar and cylindrical features. The objective of this article is to present a three-dimensional mathematical method of tolerance representation about conical surfaces and their joints based on the small displacement torsor model, and propose a mathematical model of variations and constraint relations of components of the small displacement torsor for conical surfaces caused by geometric tolerances limited by its tolerance zone. In addition, a simple example involving conical structures is used to demonstrate three-dimensional conical tolerance propagation. Both deterministic and statistical results are obtained by this model.

Three-dimensional tolerance analysis of discrete surface structures based on the torsor cluster model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chuanyuan Zhou ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Mathematical Model ◽  
Cluster Model ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Discrete Elements ◽  
Content Type ◽  
Dimensional Tolerance ◽  
Discrete Surfaces ◽  
Discrete Surface

Purpose The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products. Design/methodology/approach The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method. Findings The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model. Research limitations/implications The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation. Practical implications The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly. Originality/value This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

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