Application of the Jacobian–torsor theory into error propagation analysis for machining processes

Zuo, Xiaoyan; Li, Beizhi; Yang, Jing; Jiang, Xin

doi:10.1007/s00170-013-5088-5

Cited by 21 publications

(7 citation statements)

References 21 publications

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“…Ghie 15,16 and Ghie et al 17 introduced the application of the unified Jacobian-Torsor model for deterministic and statistical tolerance analysis. Zuo et al 18 presented a methodology of error propagation analysis based on the Jacobian-Torsor theory in manufacturing processes. Chen et al 19 further presented a modified method for the unified Jacobian-Torsor model considering the constraints between components of torsor, then they introduced a statistical way to implement tolerance allocation based on the modified model.…”

Section: Literature Reviewmentioning

confidence: 99%

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A statistical approach for three-dimensional tolerance redesign of mechanical assemblies

Peng

Wang

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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The unified Jacobian–Torsor model has been developed for performing three-dimensional tolerance analysis in both deterministic and statistical situations. The aim of this paper is to develop a statistical approach for three-dimensional tolerance redesign of mechanical assemblies by integrating the unified Jacobian–Torsor model and Monte Carlo simulation to guide the designer to choose tolerances more economically. To implement the proposed approach, a unified Jacobian–Torsor model is created based on the assembly functional requirement and assigned initial tolerance values. The Monte Carlo simulation is employed to iteratively evaluate the model using sets of random numbers as inputs so as to make this deterministic model become a stochastic one. The simulation is stopped as the number of iterations increases to the pre-specified number of iterations, the statistical results of functional requirement are obtained as well as corresponding contribution percentage of each functional element to the total functional requirement is calculated. The results are verified by comparing the statistical results of functional requirement with the specified design specification, while the contribution percentage chart can help the designer determine which tolerance should tighten or loosen. After several iterations, once the statistical result of functional requirement is sufficiently close to the design specification, the final result of tolerance values can be obtained and three-dimensional tolerance redesign of mechanical assembly is achieved. A numerical example is given to demonstrate the application of the proposed method, and the comparison with the deterministic tolerance redesign method exhibits that the proposed method has better economic effect.

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Section: Literature Reviewmentioning

confidence: 99%

“…Zuo et al. 18 presented a methodology of error propagation analysis based on the Jacobian–Torsor theory in manufacturing processes. Chen et al.…”

Section: Literature Reviewmentioning

confidence: 99%

A statistical approach for three-dimensional tolerance redesign of mechanical assemblies

Peng

Wang

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Many studies [12][13][14][15][16][17][18][19] have involved the application of these two jacobian models. In the manufacturing process, the study of X.Y.Zou [20] treated workpieces, fixtures, and machine tools as an assembly, and formulated the corresponding error propagation model using the Jacobian-Torsor theories. A group of constraints to variations were added to the Jacobian-Torsor model by H. Chen [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Tolerance Design and Robust Study for The Joint Clearances of Landing Gear Retraction Mechanisms

2020

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Joint clearances inevitably affect the kinematic accuracy and robustness of landing gear retraction mechanisms. However, the complexity and uncertainty of the clearances lead to difficulty in establishing mathematic models and analyzing effects. In the interest of assessing the clearance effects on the kinematic accuracy of landing gears, an integrated tolerance theory is proposed in this paper. In the theory proposed, Jacobian–Torsor model is combined with robust analysis to establish the kinematic accuracy model and predict the influences of clearances. The overall steps to apply the theory presented in practice are given. A typical landing gear retraction mechanism is chosen for the case study and the results show that the tendencies of clearances can be observed. Through the process of tolerance design, robust study, and tolerance redesign, the kinematic accuracy is significantly improved. The integrated tolerance theory proposed and the study conducted will provide designers new insights for the clearance analysis of landing gear mechanisms.

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“…Whitney et al [11] proposed a closed-form algorithm for modeling variations caused by geometric deviations. Zuo et al [12] and Shen et al [13] used Jacobian-Torsor model to provide mathematical models of tolerance analysis. Armillotta [14] puts forward that assembly requirements which have been used in a rule-based geometric reasoning procedure select datum reference frames for each part and assign tolerance types to part features.…”

Section: Introductionmentioning

confidence: 99%

A novel tolerance analysis for mechanical assemblies based on Convex Method and non-probabilistic set theory

Zhu

Xuan

2015

Int J Adv Manuf Technol

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Tolerance directly affects the performance and cost of the mechanical product. Tolerance analysis is a very useful approach for evaluating the accumulation of uncertainties caused by individual part tolerances. Worst Case (W-C) method and statistical methods are commonly used tolerance analysis methods. However, the result of W-C method is overly pessimistic, and the statistical methods adopt idealized distribution assumptions. In this paper, a novel C-NPS method combing Convex Method and non-probabilistic set theory (NPS) is put forward to address the above tolerance analysis problem. In this method, uncertainties of both part tolerances and assembly variations are modeled using NPS, then these part uncertainties are accumulated together to calculate the assembly function using Convex Method. Thus, the variation caused by each feature in the mechanical assembly can be estimated. C-NPS method is more suitable for tolerance analysis of different tolerances when the tolerance probability distributions are unavailable. The application of the method is illustrated through a one-way clutch mechanism assembly problem, and the advantages of this method are presented. The proposed method can be regarded as an attractive supplement to the tolerance analysis field.

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Application of the Jacobian–torsor theory into error propagation analysis for machining processes

Cited by 21 publications

References 21 publications

A statistical approach for three-dimensional tolerance redesign of mechanical assemblies

A statistical approach for three-dimensional tolerance redesign of mechanical assemblies

Tolerance Design and Robust Study for The Joint Clearances of Landing Gear Retraction Mechanisms

A novel tolerance analysis for mechanical assemblies based on Convex Method and non-probabilistic set theory

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