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Research Papers: Design of Mechanisms and Robotic Systems

Nonlinear Assembly Tolerance Design for Spatial Mechanisms Based on Reliability Methods

[+] Author and Article Information
Yin Yin

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: yinyinjordan@163.com

Nie Hong

Professor
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: hnie@nuaa.edu.cn

Feng Fei

China Academy of Launch Vehicle Technology,
Beijing 100076, China
e-mail: 114066524@qq.com

Wei Xiaohui

Professor
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of
Aeronautics and Astronautics,
Nanjing 210016, China
e-mail: wei_xiaohui@nuaa.edu.cn

Ni Huajin

China COMAC Shanghai Aircraft Design and
Research Institute,
Shanghai 201210, China
e-mail: nihuajin@comac.cc

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 6, 2016; final manuscript received November 21, 2016; published online January 12, 2017. Assoc. Editor: Xiaoping Du.

J. Mech. Des 139(3), 032301 (Jan 12, 2017) (11 pages) Paper No: MD-16-1419; doi: 10.1115/1.4035433 History: Received June 06, 2016; Revised November 21, 2016

Assembly tolerance design for spatial mechanisms is a complex engineering problem that involves a highly nonlinear dimension chain equation and challenges in simplifying the spatial mechanism matrix equation. To address the nonlinearity of the problem and the difficulty of simplifying the dimension chain equation, this paper investigates the use of the Rackwitz–Fiessler (R–F) reliability analysis method and several surrogate model methods, respectively. The tolerance analysis results obtained for a landing gear assembly problem using the R–F method and the surrogate model methods indicate that compared with the extremum method and the probability method, the R–F method allows more accurate and efficient computation of the successful assembly rate, a reasonable tolerance allocation design, and cost reductions of 37% and 16%, respectively. Moreover, the surrogate-model-based computation results show that the support vector machine (SVM) method offers the highest computational accuracy among the three investigated surrogate methods but is more time consuming, whereas the response surface method and the back propagation (BP) neural network method offer relatively low accuracy but higher calculation efficiency. Overall, all of the surrogate model methods provide good computational accuracy while requiring far less time for analysis and computation compared with the simplification of the dimension chain equation or the Monte Carlo method.

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Figures

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Fig. 1

Tolerance design process for spatial mechanisms

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Fig. 2

Schematic diagram of the method for creating D–H coordinate systems

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Fig. 3

Flow chart of assembly tolerance design based on the R–F method

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Fig. 4

Retracting mechanism for the landing gear

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Fig. 5

Kinematic diagram of the landing gear

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Fig. 6

Distribution histogram for the upper drag brace, h5

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Fig. 7

Test prototype of the landing gear: (a) Test prototype I and (b) test prototype II

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Fig. 8

Flow chart of assembly tolerance analysis based on surrogate models

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Fig. 9

Schematic diagram of Bucher sampling design under two-dimensional conditions

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Fig. 10

BP neural network structure

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Fig. 11

Nonlinear mapping from a sample space to a characteristic space

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