scholarly journals A Method for Three Dimensional Tolerance Analysis and Synthesis Applied to Complex and Precise Assemblies

2008 ◽  
pp. 55-65 ◽  
Author(s):  
Frédéric Germain ◽  
Dimitri Denimal ◽  
Max Giordano
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Dimensional Tolerance ◽  
Analysis And Synthesis

A comprehensive study of three dimensional tolerance analysis methods

2014 ◽  
Vol 53 ◽  
pp. 1-13 ◽  
Author(s):  
Hua Chen ◽  
Sun Jin ◽  
Zhimin Li ◽  
Xinmin Lai
Keyword(s):  
Three Dimensional ◽  
Tolerance Analysis ◽  
Dimensional Tolerance ◽  
Analysis Methods ◽  
Comprehensive Study

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.

A quasi-Monte Carlo statistical three-dimensional tolerance analysis method of products based on edge sampling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chuanyuan Zhou ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Monte Carlo ◽  
Three Dimensional ◽  
Sampling Strategy ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Content Type ◽  
Dimensional Tolerance ◽  
Quasi Monte Carlo ◽  
Edge Sampling ◽  
The Impact

Purpose The conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems. Design/methodology/approach With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements. Findings The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously. Research limitations/implications The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model. Practical implications The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection. Originality/value The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

Three dimensional tolerance investigations on assembly of ITER vacuum vessel

2009 ◽  
Author(s):  
J. Reich ◽  
J-J. Cordier ◽  
B. Macklin ◽  
B. Giraud ◽  
D. Wilson ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Vacuum Vessel ◽  
Dimensional Tolerance

A CAD/CAM Representation Model Applied to Tolerance Transfer Methods

1998 ◽  
Author(s):  
Alain Desrochers
Keyword(s):  
Three Dimensional ◽  
Dimensional Representation ◽  
One Dimensional ◽  
Dimensional Tolerance ◽  
Representation Model ◽  
Three Dimensional Representation ◽  
Tolerance Chart ◽  
Cad Cam ◽  
Tolerance Charts

Abstract This paper presents the adaptation of tolerance transfer techniques to a model called TTRS for Technologically and Topologically Related Surfaces. According to this model, any three-dimensional part can be represented as a succession of surface associations forming a tree. Additional tolerancing information can be associated to each TTRS represented as a node on the tree. This information includes dimensional tolerances as well as tolerance chart values. Rules are then established to simulate tolerance chains or stack up along with tolerance charts directly from the graph. This way it becomes possible to combine traditional one dimensional tolerance transfer techniques with a powerful three-dimensional representation model providing high technological contents.

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

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.

Computer Aided Tolerance Analysis of Parts and Assemblies

1989 ◽  
Author(s):  
R. T. Scott ◽  
G. A. Gabriele
Keyword(s):  
Real World ◽  
Probability Distributions ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
The Real ◽  
Assembly Tolerance ◽  
Computer Aided ◽  
Probability Information ◽  
Exact Constraint

Abstract An exact constraint scheme based on the physical contacting constraints of real part mating features is used to represent the process of assembling the parts. To provide useful probability information about how assembly dimensions are distributed when the parts are assembled as intended, the real world constraints that would prevent interference are ignored. This work addresses some limitations in the area of three dimensional assembly tolerance analysis. As a result of this work, the following were demonstrated: 1. Assembly of parts whose assembly mating features are subjected to variation; 2. Assemble parts using a real world set of exact constraints; 3. Provide probability distributions of assembly dimensions.

Information Architecture for Design Tolerancing: From Conceptual to the Detail Design

1999 ◽  
Author(s):  
U. Roy ◽  
R. Sudarsan ◽  
R. D. Sriram ◽  
K. W. Lyons ◽  
M. R. Duffey
Keyword(s):  
Design Process ◽  
Tolerance Analysis ◽  
Detailed Knowledge ◽  
Functional Requirements ◽  
Physical Entity ◽  
Data Set ◽  
Analysis And Synthesis ◽  
And Behavior ◽  
Synthesis Of Tolerances ◽  
Assembly Models

Abstract Tolerance design is the process of deriving a description of geometric tolerance specifications for a product from a set of specifications on the desired properties of the product. Existing approaches to tolerance analysis and synthesis entail detailed knowledge of geometry of assemblies and are mostly applicable during advanced stages of design, leading to a less than optimal design process. During the design process of assemblies, both assembly structure and associated tolerance information evolve continuously and significant gains can be achieved by effectively using this information to influence the design of an assembly. Any pro-active approach to the assembly or tolerance analysis in the early design stages will involve decision making with incomplete information models. In order to carry out early tolerance synthesis and analysis in the conceptual stages of the product design, we need to devise techniques for representing function-behavior-assembly models that will allow analysis and synthesis of tolerances, even with the incomplete data set. A ‘function’ (what the system is for) is associated with the transformation of an input physical entity into an output physical entity by the system. The problem or customer’s need, initially described by functional requirements on an assembly, and associated constraints on the functional requirements derives the concept of an assembly. This specification of functional requirements and constraints define a functional model for the assembly. Many researchers have studied functional representation (function based taxonomy and ontology), function to form mapping, and behavior representation (behavior means how the system/product works). However, there is no comprehensive function-assembly-behavior (FAB) integrated model. In this paper, we discuss the integration of function, assembly, and behavior representation into a comprehensive information model (FAB models). To do this, we need to develop appropriate assembly models and tolerance models that would enable the designer to incrementally understand the build-up or propagation of tolerances (i.e., constraints) and optimize the layout, features, or assembly realizations. This will ensure ease of tolerance delivery.

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