Functional Tolerance Analysis of a Complex Mechanism Based on Analysis Line Method

2013 ◽  
Vol 373-375 ◽  
pp. 2078-2081
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Rui Li
Keyword(s):  
Tolerance Analysis ◽  
Complex Mechanism ◽  
Functional Feature ◽  
Manufacturing Costs ◽  
Line Method ◽  
Analysis Process ◽  
Functional Tolerance ◽  
Simple Assembly ◽  
Tolerance Accumulation ◽  
Analysis Line

Tolerance analysis plays an important role at the stage of product design and has great influences on the assembly quality and manufacturing costs. For each ending point on the functional feature, the displacement transfer relationship is influenced by the clearance between the two parts and the tolerances of each part. With regard to functional tolerance accumulation for the simple assembly, the tolerance analysis of a complex mechanism with three parts is conducted based on the analysis line method. The rules for the functional tolerance analysis process will be summarized in this paper.

Study on the Influences of Datum Precedence on Functional Tolerance Analysis

2013 ◽  
Vol 470 ◽  
pp. 475-478
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Jian Wei Sun
Keyword(s):  
Product Design ◽  
Tolerance Analysis ◽  
Assembly Quality ◽  
Functional Feature ◽  
Manufacturing Costs ◽  
Tolerance Specification ◽  
Geometric Deviation ◽  
Functional Tolerance ◽  
Planar Junction ◽  
Analysis Line

Tolerance analysis plays an important role at the stage of product design and has great influences on the assembly quality and manufacturing costs. A positioning mechanism composed of two parts with cylindrical and planar junction is chosen for studying the influences of datum precedence on functional tolerance analysis. For different cases, the tolerance specification is specified with ISO tolerance language and the analysis line method is applied to obtain the analytical expression between the possible displacement on functional feature and geometric deviation on each part. The results for different datum precedence are summarized in this paper.

A Comparison Study of Small Displacement Torsor and Analysis Line Methods for Functional Tolerance Analysis

2012 ◽  
Vol 605-607 ◽  
pp. 358-364
Author(s):  
Chun Li Li ◽  
Jian Xin Yang ◽  
Jun Ying Wang ◽  
Wen Xin Ma
Keyword(s):  
Computation Time ◽  
Tolerance Analysis ◽  
General Characteristic ◽  
Worst Case Analysis ◽  
Small Displacement ◽  
Worst Case ◽  
Small Displacement Torsor ◽  
Functional Tolerance ◽  
Tolerance Accumulation ◽  
Analysis Line

Tolerance analysis plays an important role in the stage of product design and has great influences on the product assembly quality and manufacturing costs. Two major methods are used for three-dimensional functional tolerance analysis, which are small displacement torsor and analysis line. A positioning mechanism with two parts is presented for tolerance accumulation calculation. Through the comparison of these two methods on computation processes and results, analysis line method can establish the explicit relationship between the functional requirement and the tolerances of the influential part, which allows finding the accumulation results in the worst-case and statistical conditions. However, it requires the determination of transfer relationship case by case. For small displacement torsor model, it permits a set of inequalities to express the tolerance zones, which yields a linear programming problem. It is applicable to different tolerance chains for its general characteristic. However it is adopted only for the worst-case analysis and requires more computation time.

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.

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 New Approach to Assemble Tolerance Analysis Based on CE/TOL

2014 ◽  
Vol 852 ◽  
pp. 634-638
Author(s):  
Xiu Heng Zhang ◽  
Peng Ba
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Functional Requirement ◽  
Modeling Tools ◽  
Manufacturing Costs ◽  
New Approach ◽  
Percentage Contribution ◽  
Technical Requirements ◽  
Processing Program ◽  
Mechanical Products

Quality indicators (precision, durability, reliability) of the mechanical products are heavily depended on their tolerance to select reasonable. According to the technical requirements and the processing program of the product in whole or in parts, the parts and components can be allocated on a reasonably tolerance, and the balance can be found between the product's features and manufacturing costs. In this paper, Pro / E modeling tools are used to design parts and assembly. In the assembly process, assembly of components designed is analyzed and synthezed by the using of CE/TOL (tolerance analysis) module of Pro/E. we obtained the percentage contribution of each unit feature to the functional requirement. A percentage contribution can help designer to decide which tolerance is tighten or loosen. The application of the tolerance analysis approacch in a simple three-dimensional sample was also discussed in this paper. Results show that this approach makes manufacturing costs and the probability of excessive interference and accuracy reduce. The accuracy of the product is improved.

A Simple Method for Mobility Analysis Using Reciprocal Screws

2006 ◽  
Author(s):  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Coordinate System ◽  
Scalar Product ◽  
Simple Procedure ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Parallel Mechanisms ◽  
Complex Mechanism ◽  
Mobility Analysis ◽  
Simple Method ◽  
Analysis Process

The goal of this paper is to demonstrate that the Modified Gru¨bler-Kutzbach Criterion when combined with a simple procedure for determining the reciprocal screws offers a direct and simple method for analysing highly complex mechanisms including the over-constrained parallel manipulators. Since the scalar product of screws is not dependent on the choice of the origin, one can quickly obtain a simple expression of screws by selecting an appropriate coordinate system. In such simple expression, the coordinates of a screw would include 0 or 1, and thus greatly simplifies the procedure for determine the number of constraints in a mechanism. Seven rules have been presented to help simplify the analysis process. The advocated approach makes it possible to determine, within minutes, the mobility of a highly complex mechanism by using a pencil and a paper. Many over-constrained mechanisms, including three parallel mechanisms, are presented as examples.

Statistical Tolerance Analysis With Sensitivities Established From Tolerance-Maps and Deviation Spaces

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Aniket N. Chitale ◽  
J. K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Coordinate Frame ◽  
Target Feature ◽  
Functional Feature ◽  
Local Reference ◽  
Design Function ◽  
Statistical Tolerance ◽  
The Relationship ◽  
Statistical Tolerance Analysis

Math models aid designers in assessing relationships between tolerances that contribute to variations of a dependent dimension that must be controlled to achieve some design function at a target (functional) feature. The Tolerance-Maps© (T-Maps©) model for representing limits to allowable manufacturing variations is applied to identify the sensitivity of a dependent dimension to each contributing tolerance of the relationship. For each contributing feature and tolerances specified on it, the appropriate T-Map is chosen from a library of T-Maps, each represented in its own respective local reference frame. Each chosen T-Map is then transformed to the coordinate frame at the target feature, and the accumulation T-Map of these is formed with the Minkowski sum. The shape of a functional T-Map/deviation space is circumscribed (fitted) to this accumulation map. Since fitting is accomplished numerically by intersecting geometric shapes, T-Maps/deviation spaces are constructed with linear half-spaces. The sensitivity for each tolerance-and-feature combination is determined by perturbing the tolerance, refitting the functional shape to the modified accumulation map, and forming a ratio of the increment of functional tolerance to the perturbation. Taking tolerance-feature combinations one by one, sensitivities for an entire stack can be built. For certain loop equations, the same sensitivities result by fitting the functional shape to the T-Map/deviation space for each feature, without a Minkowski sum, and forming the overall result as a scalar sum. Sensitivities are used to optimize tolerance assignments by identifying the tolerances that most strongly influence the dependent dimension at the target feature. Form variations are not included in the analysis.

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.

Tolerance simulation of composite wingbox assembly considering preloading-modified distribution

2016 ◽  
Vol 36 (3) ◽  
pp. 224-232 ◽  
Author(s):  
Hua Wang ◽  
Jun Liu
Keyword(s):  
Probability Distribution ◽  
Tolerance Analysis ◽  
Tolerance Allocation ◽  
Analysis Model ◽  
Element Analysis ◽  
Content Type ◽  
Analysis Process ◽  
Final Assembly ◽  
Thickness Variations ◽  
Input Probability

Purpose Tolerance simulation’s reliability depends on the concordance between the input probability distribution and the real variation. The prescribed clamp force introduced changes in parts’ variation, which should be reflected in the input probability distribution for the tolerance simulation. The paper aims to present a tolerance analysis process of the composite wingbox assembly considering the preloading-modified distribution and especially focuses on the spring-in deviation of the thin-walled C-section composite beam (TC2B). Design/methodology/approach Based on finite element analysis model of TC2B, the preloading-modified probability distribution function (PDF) of the spring-in deviation is obtained. Thickness variations of the TC2B are obtained from the data of the downscaled composite wingbox. These variations are input to the computer-aided tolerance tools, and the final assembly variations are obtained. The assembly of the downscaled wingbox illustrates the effect of preloading on the probability distribution of the spring-in deviation. Findings The results have shown that the final assembly variations estimated with the modified probability distribution is more reliable than the variation of the initial normal distribution. Originality/value The tolerance simulation work presented in the paper will enhance the understanding of the composite parts assembling with spring-in deviations, improve the chance to choose assembling processes that allow specifications to be met and help with tolerance allocation in composites assembly.

scholarly journals Comparison of Analysis Line and Polytopes Methods to Determine the Result of a Tolerance Chain

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Laurent Pierre ◽  
Bernard Anselmetti
Keyword(s):  
Mechanical System ◽  
Tolerance Analysis ◽  
Functional Surface ◽  
Functional Tolerancing ◽  
The Face ◽  
Geometric Deviations ◽  
Minkowski Sums ◽  
Outer Bound ◽  
Analysis Line

Functional tolerancing must ensure the assembly and the functioning of a mechanism. This paper compares two methods of tolerance analysis of a mechanical system: the method of “analysis lines” and the method of “polytopes.” The first method needs a discretization of the ending functional surface according to various analysis lines placed on the outer-bound of the face and oriented along the normal of the surface. The second method uses polytopes. The polytopes are defined from the acceptable limits of the geometric deviations of parts and possible displacements between two parts. Minkowski sums and intersections polytopes are then carried out to take into account all geometric variations of a mechanism.

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