A CAD model for the tolerancing of mechanical assemblies considering non-rigid joints between parts with defects

2021 ◽  
pp. 095440542110257
Author(s):  
Anis Korbi ◽  
Mehdi Tlija ◽  
Borhen Louhichi
Keyword(s):  
Tolerance Analysis ◽  
Design Stage ◽  
Small Displacement ◽  
Worst Case ◽  
Mechanical Assemblies ◽  
Proposed Model ◽  
Small Displacement Torsor ◽  
Rigid Joints ◽  
Geometrical Defects ◽  
The Ideal

During the design stage, the ideal simulation and visualization of the mechanical assemblies behavior require the modeling of parts with dimensional and geometrical defects. However, the deviations caused by parts deformations can generate an important difference between the ideal assembly and the real product. In this regard, this paper proposes a tolerance analysis method of CAD assemblies considering non-rigid joints between parts with defects. The determination of realistic rigid components with dimensional and geometrical defects is based on the worst case tolerancing approach and the Small Displacement Torsor (SDT) parameters. The Finite Element (FE) computation is executed to determine deformations of realistic non-rigid part models under external loads. Sub-algorithms to define non-rigid joints between realistic parts are developed. The tolerance analysis is established using the realistic CAD assembly. A case study is presented to evaluate the proposed model.

A Comparison Study of Mathematical Models for Tolerance Analysis

2013 ◽  
Vol 765-767 ◽  
pp. 759-762
Author(s):  
Jian Xin Yang ◽  
Zhen Tao Liu ◽  
Ben Zhao
Keyword(s):  
Tolerance Analysis ◽  
Mathematical Representation ◽  
Small Displacement ◽  
Propagation Mechanism ◽  
Comparison Study ◽  
Worst Case ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Small Displacement Torsor ◽  
Comprehensive Comparison

This paper reviews two major models (Small Displacement Torsor, Deviation and Clearance Domain) for 3D functional tolerance analysis and compares them. The underlying mathematical representation of geometric tolerances can be classified as inequalities and multi-variate region. The corresponding algebraic or geometric tolerance propagation mechanism of each model is briefly introduced for worst-case and statistical tolerancing. Through a comprehensive comparison of these models, this paper gives some suggestions for choosing the appropriate method for a given tolerancing problem.

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.

An Analysis Model to Predict Rotation Accuracy of High-Precision Spindles Considering Part Errors and Deformation

2017 ◽  
Author(s):  
Yanhui Sun ◽  
Jun Hong ◽  
Junkang Guo ◽  
Yanfei Zhang ◽  
Shaoke Wan ◽  
...  
Keyword(s):  
High Precision ◽  
Design Stage ◽  
Small Displacement ◽  
Analysis Model ◽  
Transformation Matrices ◽  
Beam Elements ◽  
Fea Model ◽  
Small Displacement Torsor ◽  
Variation Propagation ◽  
Error Accumulation

High-precision spindles have significant influence on the machining precision and finishing quality largely due to their motion errors. However, the analysis of rotation accuracy is quite not easy in design stage because of the neglecting of geometric errors and deformations of parts in the traditional dimension chains. Hence, a theoretical analysis model is built in present study to do the prediction. The 3D error accumulation path is recognized by Datum Flow Chain (DFC) and the key tolerances are modeled by Small Displacement Torsor (SDT). Thereafter, the variation propagation is conducted by Homogeneous Transformation Matrices (HTM) and the geometric misalignment in the spindle is calculated. Then, an FEA model is built with Timoshenko beam elements and the deformation is calculated after the geometric misalignment is applied to the model. As spindle rotates, the trajectory of the spindle nose is obtained. Finally, the Monte Carlo (MC) method is used to get the distribution and the range of motion errors. To verify the feasibility and reliability of the analysis model, the radial and axial motion errors of a double supported high-precision spindle are analyzed.

A small displacement torsor model for tolerance analysis in a workpiece-fixture assembly

2009 ◽  
Vol 223 (8) ◽  
pp. 1005-1020 ◽  
Author(s):  
J N Asante
Keyword(s):  
Effective Means ◽  
Experimental System ◽  
Tolerance Analysis ◽  
Geometric Error ◽  
Small Displacement ◽  
Small Displacement Torsor ◽  
Set Up ◽  
Workpiece Setup ◽  
Feature Constraints

Workpiece geometric error, locator geometric error, and clamping error are factors that influence workpiece setup in workpiece fixturing. These errors accumulate and propagate during fixturing. They may be the reason for a machined feature being out of tolerance after machining. This paper presents a methodology for modelling and analysing the combined effect of these errors on a machined feature. Deviation of a machined feature due to the combined errors is expressed in terms of the small displacement torsor parameters. Given a tolerance on the machined feature, constraints are specified for that feature to establish a relationship between the tolerance zone of the feature and the torsor parameters. These constraints provide boundaries within which the machined feature must lie. This is used for tolerance analysis of the machined feature. A case study example was used to illustrate the approach. An experimental system was also set up to verify the analytical model. The results show that this approach offers an effective means for fixturing tolerance analysis.

scholarly journals Geometrical and dimensional tolerance analysis for the radial flux type of permanent magnet generator design

2021 ◽  
Vol 12 (2) ◽  
pp. 68-80
Author(s):  
Muhammad Fathul Hikmawan ◽  
Agung Wibowo ◽  
Muhammad Kasim
Keyword(s):  
Permanent Magnet ◽  
Manufacturing Process ◽  
Cumulative Effect ◽  
Tolerance Analysis ◽  
Air Gap ◽  
Tolerance Allocation ◽  
Design Stage ◽  
Worst Case ◽  
Radial Flux ◽  
Permanent Magnet Generator

Mechanical tolerance is something that should be carefully taken into consideration and cannot be avoided in a product for manufacturing and assembly needs, especially in the design stage, to avoid excessive dimensional and geometric deviations of the components made. This paper discusses how to determine and allocate dimensional and geometric tolerances in the design of a 10 kW, 500 rpm radial flux permanent magnet generator prototype components. The electrical and mechanical design results in the form of the detailed nominal dimensions of the generator components, and the allowable air gap range are used as input parameters for tolerance analysis. The values of tolerance allocation and re-allocation process are carried out by considering the capability of the production machine and the ease level of the manufacturing process. The tolerance stack-up analysis method based on the worst case (WC) scenario is used to determine the cumulative effect on the air gap distance due to the allocated tolerance and to ensure that the cumulative effect is acceptable so as to guarantee the generator's functionality. The calculations and simulations results show that with an air gap of 1 ± 0.2 mm, the maximum air gap value obtained is 1.1785 mm, and the minimum is 0.8 mm. The smallest tolerance value allocation is 1 µm on the shaft precisely on the FSBS/SRBS feature and the rotor on the RPMS feature. In addition, the manufacturing process required to achieve the smallest tolerance allocation value is grinding, lapping, and polishing processes.

Applications of the GapSpace Model for Multidimensional Mechanical Assemblies

2003 ◽  
Vol 3 (1) ◽  
pp. 22-30 ◽  
Author(s):  
Zhihua Zou ◽  
Edward P. Morse
Keyword(s):  
Sufficient Conditions ◽  
Tolerance Analysis ◽  
Necessary And Sufficient Conditions ◽  
Important Task ◽  
Assembly Model ◽  
Worst Case ◽  
Mechanical Assemblies ◽  
Necessary And Sufficient ◽  
The Way

The most fundamental, and perhaps most important, task in the tolerance analysis of assemblies is to test whether or not the components with tolerances are actually able to fit together (called assembleability). Another important task of tolerance analysis is to check how the tolerances affect the quality or functionality of a product when they are assembled together. This paper presents the way the tolerance analyses are implemented by an assembly model, called the GapSpace model. The model can not only capture the necessary and sufficient conditions for assembleability analysis, but also transfers the functionality into the modeling variables (gaps). The assembleability analyses based on the GapSpace model for nominal components and those with worst case or statistical tolerances are introduced through an example. The problems of testing the quality of assemblies and calculating sensitivities are solved quickly and precisely using the model. The GapSpace model is more suitable for certain GD&T tolerancing methods than for parametric plus/minus tolerancing.

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.

scholarly journals Reliability-based tolerance redesign of mechanical assemblies using Jacobian-Torsor model

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110132
Author(s):  
Bingxiang Wang ◽  
Xianzhen Huang ◽  
Miaoxin Chang
Keyword(s):  
Optimization Model ◽  
Economic Effect ◽  
Tolerance Analysis ◽  
Lambert W Function ◽  
Mechanical Assembly ◽  
Assembly Tolerance ◽  
Tolerance Optimization ◽  
Geometric Tolerances ◽  
Mechanical Assemblies ◽  
Proposed Model

The purpose of this paper is to present a new method to redesign dimensional and geometric tolerances of mechanical assemblies at a lower cost and with higher reliability. A parametric Jacobian-Torsor model is proposed to conduct tolerance analysis of mechanical assembly. A reliability-based tolerance optimization model is established. Differing from previous studies of fixed process parameters, this research determines the optimal process variances of tolerances, which provide basis for the subsequent assembly tolerance redesign. By using the Lambert W function and the Lagrange multiplier method, the analytical solution of the parametric tolerance optimization model is obtained. A numerical example is presented to demonstrate the effectiveness of the model, while the results indicate that the total cost is reduced by 10.93% and assembly reliability improves by 2.12%. This study presents an efficient reliability-based tolerance optimization model. The proposed model of tolerance redesign can be used for mechanical assembly with a better economic effect and higher reliability.

Tolerance Analysis in Machining: An Approach Combining the Model of Manufactured Part and the Jacobian-Torsor Model

2008 ◽  
Author(s):  
Mojtaba Kamali Nejad ◽  
Alain Desrochers ◽  
Franc¸ois Villeneuve ◽  
Fre´de´ric Vignat
Keyword(s):  
Kinematic Chain ◽  
Tolerance Analysis ◽  
Small Displacement ◽  
Functional Requirements ◽  
Combined Approach ◽  
Functional Elements ◽  
New Approach ◽  
Nominal Model ◽  
Small Displacement Torsor ◽  
Position And Orientation

To perform tolerance analysis in machining, a combined approach which blends the benefits of the Model of Manufactured Part (the MMP model) and the Jacobian-Torsor model is proposed. The former is based on the CAD nominal model, where deviations are described relative to the nominal part using small displacement torsor. The later starts with the kinematic dimension chains and expresses the relative position and orientation of the various components of the chosen kinematic chain by Jacobian matrices. The Jacobian-Torsor model uses interval arithmetic for expressing the possible variation of the functional elements and for calculating the extreme bounds of the functional requirements. In the following sections, the two aforementioned models will first be outlined before the new combined approach for tolerance analysis in machining is presented. This new approach uses the advantages of the MMP model to simulate the machining operation, taking into account positioning and machining defects. Furthermore it takes advantages of the interval-based formulation which has been used in the Jacobian Torsor model. The combined approach is finally applied on an example.

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