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This paper aims to develop a method to improve the accuracy of tolerance analysis considering the spatial distribution characteristics of part surface morphology (SDCPSM) and local surface deformations (LSD) of planar mating surfaces during the assembly process.

First, this paper proposes a skin modeling method considering SDCPSM based on Non-Gaussian random field. Second, based on the skin model shapes, an improved boundary element method is adopted to solve LSD of nonideal planar mating surfaces, and the progressive contact method is adopted to obtain relative positioning deviation of mating surfaces. Finally, the case study is given to verify the proposed approach.

Through the case study, the results show that different SDCPSM have different influences on tolerance analysis, and LSD have nonnegligible and different influence on tolerance analysis considering different SDCPSM. In addition, the LSD have a greater influence on translational deviation along the z-axis than rotational deviation around the x- and y-axes.

The surface morphology with different spatial distribution characteristics leads to different contact behavior of planar mating surfaces, especially when considering the LSD of mating surfaces during the assembly process, which will have further influence on tolerance analysis. To address the above problem, this paper proposes a tolerance analysis method with skin modeling considering SDCPSM and LSD of mating surfaces, which can help to improve the accuracy of tolerance analysis.

The purpose of this paper is to compare two different tools for tolerance analysis. Tolerance analysis is an important task to design and manufacture high-precision mechanical assemblies; it has received considerable attention in the literature. Many are the tools required to carry out a tolerance analysis, and may be divided into two categories: the analytical models and the statistical software packages. No comparison exists in the literature among these two categories.

This work presents a comparison between two different approaches to tolerance analysis: an analytical method, the variational model, and a statistical software, eM-Tolmate. The comparison has been developed on the same aeronautical case study that constitutes an actual product.

The proposed approach has been applied to an aeronautical case study. The results of the case study show how, when 2D tolerance analysis problems need to be solved, the two adopted tools give the same results. When the complexity of the tolerance analysis problems increases, the statistical software becomes the only choice to use. The new findings of the present paper are related to the fact that computer-aided tolerance analysis software packages remain the only choice to approach actual complex industrial products despite the extensive development of theoretical research.

This paper deals with a unique case study. However, the two adopted approaches and the obtained results are general, that is, they may be applied to any assembly.

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.

Many are the tools for tolerance analysis, such as different analytical models and different commercial software packages. Some are the comparisons among the different tools in the literature, but they are not exhaustive. Therefore, when a user has to solve an assembly problem to foresee the geometric interferences during the design stage, he/she does not know what to choose. The original contribution of the paper is to address the user’s choice through a comparison between an analytical model and a statistical software to solve the tolerance analysis problems of an actual aeronautical assembly.

The purpose of this paper is to present a new efficient method for the tolerance–reliability analysis and quality control of complex nonlinear assemblies where explicit assembly functions are difficult or impossible to extract based on Bayesian modeling.

In the proposed method, first, tolerances are modelled as the random uncertain variables. Then, based on the assembly data, the explicit assembly function can be expressed by the Bayesian model in terms of manufacturing and assembly tolerances. According to the obtained assembly tolerance, reliability of the mechanical assembly to meet the assembly requirement can be estimated by a proper first-order reliability method.

The Bayesian modeling leads to an appropriate assembly function for the tolerance and reliability analysis of mechanical assemblies for assessment of the assembly quality, by evaluation of the assembly requirement(s) at the key characteristics in the assembly process. The efficiency of the proposed method by considering a case study has been illustrated and validated by comparison to Monte Carlo simulations.

The method is practically easy to be automated for use within CAD/CAM software for the assembly quality control in industrial applications.

Bayesian modeling for tolerance–reliability analysis of mechanical assemblies, which has not been previously considered in the literature, is a potentially interesting concept that can be extended to other corresponding fields of the tolerance design and the quality control.

The assembly simulation in tolerance analysis is one of the most important steps for the tolerance design of mechanical products. However, most assembly simulation methods are based on the rigid body assumption, and those assembly simulation methods considering deformation have a poor efficiency. This paper aims to propose a novel efficient and precise tolerance analysis method based on stable contact to improve the efficiency and reliability of assembly deformation simulation.

The proposed method comprehensively considers the initial rigid assembly state, the assembly deformation and the stability examination of assembly simulation to improve the reliability of tolerance analysis results. The assembly deformation of mating surfaces was first calculated based on the boundary element method with optimal initial assembly state, then the stability of assembly simulation results was assessed by the density-based spatial clustering of applications with noise algorithm to improve the reliability of tolerance analysis. Finally, combining the small displacement torsor theory, the tolerance scheme was statistically analyzed based on sufficient samples.

A case study of a guide rail model demonstrated the efficiency and effectiveness of the proposed method.

The present study only considered the form error when generating the skin model shape, and the waviness and the roughness of the matching surface were not considered.

To the best of the authors’ knowledge, the proposed method is original in the assembly simulation considering stable contact, which can effectively ensure the reliability of the assembly simulation while taking into account the computational efficiency.

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.

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.

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.

The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation.

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.

This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

This paper aims to propose a method to automate the tolerance analyses of mechanical assembly using STandard for the Exchange of Product model data-Application Protocol Part 242 (STEP AP 242) files derived from the 3-D computer-aided design (CAD) models.

Product manufacturing information and mating information available in ISO 10303 STEP AP242 files resulting from the 3-D CAD model of mechanical assembly are extracted. The extracted geometric attributes, geometric dimensioning and tolerancing (GD&T) and mating information are used to automatically generate assembly graph and mating edges required for the tolerance analyses of the mechanical assembly by using the matrix approach.

The feasibility of the proposed method is verified through two mechanical assembly case studies. The results of manual calculations and tolerance values computed by the automated method are very closely matching.

Tolerance analysis is an integral part of product development that directly influences the cost and performance of a product. Apart from the academic interest, the work is expected to have positive implications for the digital design and smart manufacturing industry that involve in the development of solutions for automation of design and manufacturing system functions.

The approach presented in the paper that aids the automation of tolerance analyses of mechanical assembly is an innovative application of the STEP AP 242 file. The automation of tolerance analyses would improve the productivity and efficiency of the product realization process.

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.

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.

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.

The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model.

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.

The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

The traditional precision design only takes the influence of geometric tolerance of the parts and does not involve the load deformation in the assembly process. This paper aims to analyze the influence mechanism of flexible parts deformation on the geometric precision, and then to ensure the reliability and stability of the mechanical system.

Firstly, this paper adopts the N-GPS to analyze the influence mechanism of flexible parts deformation on the geometric precision and constructs a coupling 3D tolerance mathematical model of the geometric tolerance and the load deformation deviation based on the SDT theory, homogeneous coordinate transformation theory and surface authentication idea. Secondly, the least square method is used to fit the deformation surface of the mating surface under load so as to complete the conversion from the non-ideal element to the ideal element.

This paper takes the horizontal machining center as a case to obtain the deformation information of the mating surface under the self-weight load. The results show that the deformation deviation of the parts has the trend of transmission and accumulation under the load. The terminal deformation cumulative amount of the system is up to –0.0249 mm, which indicated that the influence of parts deformation on the mechanical system precision cannot be ignored.

This paper establishes a comprehensive 3D tolerance mathematical model, which comprehensively considers the effect of the dimensional tolerance, geometric tolerance and load deformation deviation. By this way, the assembly precision of mechanical system can be accurately predicted.

This paper aims to present a method for the tolerance analysis of mechanical assemblies that is suitable to nonlinear problems where explicit functional equations are difficult or even impossible to write down. Such cases are usually modelled by linearised tolerance chains, whose coefficients (or sensitivities) are calculated from assembly data.

The method is based on the free-body diagrams of force analysis, which are shown to be related to the sensitivities of linearised functional equations. Such an analogy allows the conversion of a tolerance chain into a corresponding static problem, which can be solved by common algebraic or graphical procedures.

The static analogy leads to a correct treatment of tolerance chains, as the analysis of several examples has confirmed by comparison to alternative methods.

Currently, the method has only been tested on two-dimensional chains of linear dimensions for assemblies with nonredundant kinematic constraints among parts.

The proposed method lends itself to ready application by using simple operations with minimal software assistance. This could make it complementary to current methods for calculating sensitivities, which are mathematically complex and require software implementation for deployment in industrial practice.

Analogy with force analysis, which has not been previously highlighted in the literature, is a potentially interesting concept that could be extended to a wider range of tolerancing problems.

Due to technological and financial limitations, nominal dimension may not be able achievable during manufacturing process. Therefore, tolerance allocation is of significant importance for assembly. Conventional tolerance analysis methods are limited by the assumption of the part rigidity. Every mechanical assembly consists of at least one or more flexible parts which undergo significant deformation due to gravity, temperature change, etc. The deformation has to be considered during tolerance design of the mechanical assembly, in order to ensure that the product can function as intended under a wide range of operating conditions for the duration of its life. The purpose of this paper is to determine the deformation of components under inertia effect and temperature effect.

In this paper, finite element analysis of the assembly is carried out to determine the deformation of the components under inertia effect and temperature effect. Then the deformations are suitably incorporated in the assembly functions generated from vector loop models. Finally, the tolerance design problem is optimized with an evolutionary technique.

With the presented approach, the component tolerance values found are the most robust to with stand temperature variation during the product's application. Due to this, the tolerance requirements of the given assembly are relaxed to certain extent for critical components, resulting in reduced manufacturing cost and high product reliability. These benefits make it possible to create a high‐quality and cost‐effective tolerance design, commencing at the earliest stages of product development.

With the approach presented in the paper, the component tolerance values found were the most robust to withstand temperature variation during the product's application. Due to this, the tolerance requirements of the given assembly are relaxed to a certain extent for critical components, resulting in reduced manufacturing cost and high product reliability. These benefits make it possible to create a high‐quality and cost‐effective tolerance design, commencing at the earliest stages of product development.