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.

Statistical Tolerance Analysis of Over-Constrained Mechanical Assemblies With Form Defects Considering Contact Types

2019 ◽  
Vol 19 (2) ◽  
Author(s):  
Edoh Goka ◽  
Lazhar Homri ◽  
Pierre Beaurepaire ◽  
Jean-Yves Dantan
Keyword(s):  
Tolerance Analysis ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Behavior Modeling ◽  
Functional Requirements ◽  
Mechanical Assembly ◽  
Mechanical Assemblies ◽  
Statistical Tolerance ◽  
The Individual ◽  
Statistical Tolerance Analysis

Tolerance analysis aims toward the verification impact of the individual tolerances on the assembly and functional requirements of a mechanism. The manufactured products have several types of contact and are inherent in imperfections, which often causes the failure of the assembly and its functioning. Tolerances are, therefore, allocated to each part of the mechanism in purpose to obtain an optimal quality of the final product. Three main issues are generally defined to realize the tolerance analysis of a mechanical assembly: the geometrical deviations modeling, the geometrical behavior modeling, and the tolerance analysis techniques. In this paper, a method is proposed to realize the tolerance analysis of an over-constrained mechanical assembly with form defects by considering the contacts nature (fixed, sliding, and floating contacts) in its geometrical behavior modeling. Different optimization methods are used to study the different contact types. The overall statistical tolerance analysis of the over-constrained mechanical assembly is carried out by determining the assembly and the functionality probabilities based on optimization techniques combined with a Monte Carlo simulation (MCS). An application to an over-constrained mechanical assembly is given at the end.

Tolerance Analysis and Diagnosis Model of Compliant Block Assembly Considering Welding Deformation

2015 ◽  
Author(s):  
Junghyun Lee ◽  
Wooyoung Choi ◽  
Minseok Kang ◽  
Hyun Chung
Keyword(s):  
Tolerance Analysis ◽  
Normal Equation ◽  
Welding Distortion ◽  
Assembly Process ◽  
Accuracy Control ◽  
Mechanical Assembly ◽  
Multi Stage ◽  
Proposed Model ◽  
Diagnosis Model ◽  
Welding Processes

This paper proposes a simplified tolerance analysis and diagnosis model including the effects of welding distortion, for accuracy control in ship block assembly processes. The variation simulation model for tolerance analysis utilizes the concepts of the sources of variation and the compliant mechanical assembly model to include the welding distortions. The proposed model utilizes welding distortion patterns and a transformation matrix to efficiently model the deformation during the joining process. The diagnosis model assumes the multi-stage assemblies and that the variations of previous stages are propagated to the current stage. It calculates the sensitivity; a linear mapping from input parts to output assembly variations, and includes the effects of welding distortion as an additional vector that deviates the assembly variation further. The diagnosis model predicts the quantitative effect of each source of variations to the final assembly’s geometrical variation, based on normal equation and assembly stage’s state space equation model. The proposed model is applied to a realistic block assembly process for validation purpose. The model can effectively simulate the propagation of welding distortion as well as quantitatively identify variation patterns and welding processes throughout the multi-stage assembly process.

A Comprehensive Tolerancing System for 3D Mechanical Assemblies

2010 ◽  
Vol 139-141 ◽  
pp. 1289-1293 ◽  
Author(s):  
Dong Ya Yang ◽  
Jun Gong
Keyword(s):  
Design Principle ◽  
Tolerance Analysis ◽  
Automatic Generation ◽  
Geometric Feature ◽  
Design Practice ◽  
Simulation Environment ◽  
Assembly Tolerance ◽  
Detail Design ◽  
Comprehensive Method ◽  
Mechanical Assemblies

A comprehensive tolerancing system is presented with its design principle, system architecture and key functions. The following functional modules, automatic generation of dimension chain, equivalent variational mechanism (EVM) modeling and visualized 3D tolerance analysis, are described in detail. Design intent is expressed by assembly tolerance specifications, which may be added to the model and used in computing predicted quality levels. A comprehensive method, based on equivalent replacement, has been developed for modeling variations in 3D mechanical assemblies. The models are constructed of common engineering elements: dimension chain, kinematic joints, assembly datums, dimensional and geometric feature tolerances, and assembly tolerance limits. The method is consistent with engineering design practice and is well suited for integration with commercial CAD systems. To make the tolerancing system robust and efficient, new functionalities are added to well-known CAD software and simulation environment. Tested by many samples, this system shows good robustness and practicability.

Visualized Equivalent Variational Modeling in Tolerance Analysis of 3D Mechanical Assemblies

2011 ◽  
Vol 201-203 ◽  
pp. 229-233
Author(s):  
Dong Ya Yang ◽  
Jun Gong
Keyword(s):  
Kinematic Model ◽  
Tolerance Analysis ◽  
Geometric Feature ◽  
Velocity Analysis ◽  
Assembly Tolerance ◽  
Variational Modeling ◽  
Mechanical Assemblies ◽  
Dimensional Variation ◽  
Kinematic Joint

This paper introduces a new, visualized approach for including all the geometric feature variations in the tolerance analysis of mechanical assemblies. It focuses on how to characterize geometric feature variations in vector-loop-based assembly tolerance models. The characterization will be used to help combine the effects of all variations within an assembly in order to perform tolerance analysis of mechanical assemblies by employing commercial 3D kinematic software (e.g. ADAMS). Equivalent variational modeling, based on TAKS method, has been developed for modeling variations in 3D mechanical assemblies. Create a library of Equivalent Variational Joints (EVJs) to allow inclusion all kinds of variations in analysis, and allow the kinematic model to include both geometric and dimensional variation in a velocity analysis. EVJ, for use in tolerance analysis, was developed for commonly used 3D kinematic joint types, and was implemented with examples to explain their use to form Equivalent Variational Mechanisms (EVMs).

Geometric tolerance analysis through Jacobian model for rigid assemblies with translational deviations

2016 ◽  
Vol 36 (1) ◽  
pp. 72-79 ◽  
Author(s):  
Wilma Polini ◽  
Andrea Corrado
Keyword(s):  
Tolerance Analysis ◽  
Geometric Error ◽  
Functional Requirements ◽  
Content Type ◽  
Geometric Tolerances ◽  
Mechanical Assemblies ◽  
Geometric Deviations ◽  
2D And 3D ◽  
Practical Implications

Purpose – The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements. Design/methodology/approach – This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed. Findings – The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational. Research limitations/implications – In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies. Practical implications – Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease of the manufacturing costs. Originality/value – The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.

Tolerance-based Variations in Solid Modeling

2003 ◽  
Vol 3 (4) ◽  
pp. 345-352 ◽  
Author(s):  
G. Moroni ◽  
W. Polini
Keyword(s):  
Tolerance Analysis ◽  
Design Stage ◽  
Tolerance Design ◽  
Functional Requirements ◽  
Mechanical Parts ◽  
Assembly Tolerance ◽  
Geometric Tolerances ◽  
Design Requirements ◽  
Optimal Values ◽  
Definition Of

Information on tolerances and attributes of mechanical parts and assemblies is crucial for many activities in a product’s life cycle. Tolerance design is a complex task because many factors (functional, technological and economical) should be considered. It is an iterative process, starting from a first tolerances assignment and ending with the definition of their optimal values. Once all tolerances have been assigned to each part of an assembly, tolerance analysis is performed. This stage aim is to evaluate if the combined effects of the assigned tolerances let the design requirements be met. Then, feasible and economical aspects are considered on the basis of both available processes and cost evaluations. The whole tolerance design stage is usually defined as tolerance synthesis. The focus of this work is the discussion of the algorithms to model the geometrical variations, of each part of an assembly, allowed by geometric tolerances. This involves the change of the boundary nominal representation of a part face on the basis of the assigned dimensional and geometric tolerances. At present, the developed algorithms are able to simulate flatness, location and orientation. The modified parts, generated by tolerance simulation, may be used to evaluate the overall assemblability and, then, to verify the assembly functional requirements.

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.

Fuzzy Tolerance Analysis of 3-D Mechanical Assemblies

1997 ◽  
Author(s):  
K. Srikanth ◽  
F. W. Liou ◽  
S. N. Balakrishnan
Keyword(s):  
Fuzzy Logic ◽  
Manufacturing Process ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
Tolerance Design ◽  
Cost Information ◽  
Assembly Tolerance ◽  
Mechanical Assemblies ◽  
Representation Scheme ◽  
Tolerance Assignment

Abstract Tolerance design is interdisciplinary in nature and is characterized by a highly uncertain environment. In recent years, fuzzy logic has appeared as a credible alternative for tolerance design. In this paper a fuzzy based tolerance representation scheme is presented to model three dimensional (3-D) tolerances. With this representation, relative assembly tolerance constraints can be expressed. A fuzzy tolerance generation and assignment process for assembly is discussed. Fuzzy tolerance equations are generated for 3-D assembly considerations. Manufacturing process information, along with uncertain cost information modeled in fuzzy terms, is added to the system to arrive at a cost-optimal tolerance assignment.

The Tolerance Optimization Problem Using a System of Experimental Design

1994 ◽  
Author(s):  
M. H. Gadallah ◽  
H. A. ElMaraghy
Keyword(s):  
Experimental Design ◽  
Optimization Problem ◽  
State Of The Art ◽  
Tolerance Analysis ◽  
Synthesis Methods ◽  
Manufacturing Cost ◽  
Mechanical Assembly ◽  
Manufacturing Tolerance ◽  
Mechanical Assemblies ◽  
Analysis And Synthesis

Abstract A new algorithm for manufacturing tolerance synthesis is proposed. In complex mechanical assemblies, most tolerance analysis and synthesis methods tend to be impractical. In this article, a methodology is proposed to minimize manufacturing cost by tightening important dimensional and/or geometrical tolerances. Analysis of variance and experimental design techniques are used to discriminate among various design dimensions to the overall functional requirement of the mechanical assembly. In this case, some, but not all, design dimensions will be controlled. This paper reviews the state-of-the art in the area of tolerance analysis and synthesis and highlights the contribution of this work.

Assembly tolerance analysis based on the Jacobian model and skin model shapes

2019 ◽  
Vol 39 (2) ◽  
pp. 245-253 ◽  
Author(s):  
Ting Liu ◽  
Yan-Long Cao ◽  
Qijian Zhao ◽  
Jiangxin Yang ◽  
Lujun Cui
Keyword(s):  
Product Life Cycle ◽  
Tolerance Analysis ◽  
Quality Level ◽  
Functional Requirements ◽  
Skin Model ◽  
Content Type ◽  
Kinematic Chains ◽  
Assembly Tolerance ◽  
Geometric Tolerances ◽  
Functional Features

Purpose The purpose of this paper is to carry out an assembly tolerance analysis by means of a combined Jacobian model and skin model shape. The former is based on small displacements modeling of points using 6 × 6 transformation matrices of open kinematic chains in robotics. The latter easily models toleranced features with all kinds of geometric deviations. Design/methodology/approach This paper presents the procedure of performing tolerance analysis by means of the Jacobian model and skin model shape for assemblies. The point cloud-based discrete representative is able to model the actual toleranced surfaces instead of the ideal or associated ones in an assembly, which brings the simulation tools closer to reality. Findings The proposed method has the advantage of skin model shape which is suitable for geometric tolerances management along the product life cycle and contact analysis of kinematic small variations, as well as, with the Jacobian, enabling transformation of locally expressed parts deviations to globally expressed functional requirements. The result of the case study shows the accuracy of the method. Research limitations/implications The proposed approach has not been developed fully; other functional features such as the pyramid are still ongoing challenges. Practical implications It is an effective method for supporting design, manufacturing and inspection by providing a quantitative analysis of the effects of multi-tolerances on the final functional key characteristics and for predicting the quality level. Originality/value The paper is original in taking advantages of both Jacobian model and skin model shape to consider all geometric tolerances in assembly.

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