A comparison of tolerance analysis models for assembly

Bo, Chaowang; Zhi-hong, Yang; Wang, Linbo; Chen, Hongqian

doi:10.1007/s00170-013-4795-2

Cited by 22 publications

(10 citation statements)

References 18 publications

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“…10,11 The vectors are arranged in chains representing those dimensions that stack together to determine the resultant assembly dimensions. 16 In the assembly vector loop, each vector embodies the translation and rotation relative to the previous vector. Therefore, there are two kinds of variation sources, one is the length deviation depicting the fluctuation of length dimension and clearance between mating parts and the other is the angle deviation which expresses the change appearing in the interactive orientation relationships.…”

Section: The Parameterization Of Individual Variationmentioning

confidence: 99%

“…There are still some other tolerance analysis methods which can directly derive the stack-up functions without resorting to the assembly response function, as have been discussed by many literatures. 14–17 The Jacobian model 18 uses kinematic chains composed of functional elements to represent the stack of dimensions and variations. The Torsor model 19,20 describes the three-dimensional (3D) tolerance zones by small displacement screws.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a new method based on the free-body diagrams of force analysis was proposed for calculating the sensitivities of a two-dimensional (2D) assembly. 9 Although the representations of individual variations and tolerance accumulation in these methods are different, the resulting stack-up functions are mostly linear 14–16 and can be written in the form of formula (1).…”

Section: Introductionmentioning

confidence: 99%

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Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Zhao

Wang

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part B:

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Many existing tolerancing models deal with the tolerance analysis of mechanical assemblies using linear stack-up function, which will cause truncation errors for nonlinear assembly problem. This article proposes a new method for describing the variation propagation based on the product of exponentials formula. Both the length deviations and the angle deviations are uniformly represented by twist coordinates. Accordingly, the nonlinear stack-up functions relating the assembly functional requirements to the manufacturing variations can be derived, and no truncation errors generated. A three-dimensional assembly case is studied exploiting the proposed method and the direct linearization method, respectively. It appears that the product of exponentials formula can bring consistent tolerance analysis results with the exact geometric solutions, whereas there are some small errors in the analysis results of direct linearization method. The precision of tolerance estimation via the product of exponentials formula is improved by 0.52% at the most compared with that by the direct linearization method. Due to the elimination of local datum reference frames, the product of exponentials formula can also lead to a more concise description of tolerance accumulation than the direct linearization method.

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Section: The Parameterization Of Individual Variationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Zhao

Wang

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part B:

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“…Two analytical approaches that are the Jacobian and the vector loop have been applied to this case study in Ref. [31], and the obtained results are given in the first two lines of Table 3. The application of the VSA ® software to the case study is required to calculate five measurement operations, as shown in Figure 8, to obtain the functional requirement that is the distance between Blocks 1 and 2, once assembled.…”

Section: Case Study 2: An Assembly Of Three Blocksmentioning

confidence: 99%

Computer-Aided Techniques for Geometry Assurance

Corrado¹,

Polini²

2016

Computer-Aided Technologies - Applications in Engineering and Medicine

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Geometry assurance can be described as a number of activities, all contributing to minimize the effect of geometrical variation in a final product. This work aims to introduce a new type of comparison between a computer-aided technique for geometry assurance and some models proposed by the literature. In particular, the aim of this work is to solve, through a computer-aided technique, some case studies that were already solved by different methods of the literature. The different case studies that have been introduced and solved in this paper aim to highlight the potentialities and the limits in using a computer-aided technique for geometry assurance. Because this type of comparison is not present in the literature yet, this work wants to place the emphasis on the fact that till now there is not a unique approach to solve problems of geometry assurance and no approach can be defined as better than another, in terms of results.

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“…In general, systematic error can be eliminated by means of calibration or compensation. Thus, the majority of the studies on error analysis and error allocation focus on random error [4], [5]. However, in some technical systems, the systematic error cannot be eliminated by calibration or compensation, e.g.…”

Section: Introductionmentioning

confidence: 99%

Importance Measure Method for Sources of System Output Error Based on Decomposition of Second-Order Moment

Sun

Cui

et al. 2019

IEEE Access

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In this paper, we propose an error importance measure (EIM) method to quantify the relative contribution of error sources to the system output error. In order that the contribution of both variation and mean shift of error sources are taken into account, we use second-order moment to characterize the degree of system output deviation from ideal or target value. First, the second-order moment is decomposed into a series of terms through the Taylor series expansion, and the individual effects, the interaction effects, and the total effects for one or a group of error sources are defined accordingly. Second, we define the EIM indices as the value of total effect divided by second-order moment of output error. Third, three test models and an application case are introduced to demonstrate the effectiveness and engineering significance of the proposed EIM indices. The results show that the EIM indices can reflect both the impacts of variation and mean the shift in error sources.

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A comparison of tolerance analysis models for assembly

Cited by 22 publications

References 18 publications

Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Computer-Aided Techniques for Geometry Assurance

Importance Measure Method for Sources of System Output Error Based on Decomposition of Second-Order Moment

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