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Research Papers

Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method

[+] Author and Article Information
Xufang Zhang

Assistant Professor
School of Mechanical
Engineering and Automation,
Northeastern University,
Shenyang,
Liaoning 110819, China
e-mail: zhangxf@me.neu.edu.cn

Mahesh D. Pandey

Professor
NSERC Chair
Civil and Environmental Engineering,
University of Waterloo,
Waterloo, ON N2L 3G1, Canada
e-mail: mdpandey@uwaterloo.ca

Yimin Zhang

Professor
Changjiang Scholar of China,
School of Mechanical
Engineering and Automation,
Northeastern University,
Shenyang,
Liaoning 110819, China
e-mail: ymzhang@mail.neu.edu.cn

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 25, 2012; final manuscript received November 12, 2013; published online April 17, 2014. Assoc. Editor: Xiaoping Du.

J. Mech. Des 136(6), 061006 (Apr 17, 2014) (11 pages) Paper No: MD-12-1538; doi: 10.1115/1.4026270 History: Received October 25, 2012; Revised November 12, 2013

The paper presents a computationally efficient method for system reliability analysis of mechanisms. The reliability is defined as the probability that the output error remains within a specified limit in the entire target trajectory of the mechanism. This mechanism reliability problem is formulated as a series system reliability analysis that can be solved using the distribution of maximum output error. The extreme event distribution is derived using the principle maximum entropy (MaxEnt) along with the constraints specified in terms of fractional moments. To optimize the computation of fractional moments of a multivariate response function, a multiplicative form of dimensional reduction method (M-DRM) is developed. The main benefit of the proposed approach is that it provides full probability distribution of the maximal output error from a very few evaluations of the trajectory of mechanism. The proposed method is illustrated by analyzing the system reliability analysis of two planar mechanisms. Examples presented in the paper show that the results of the proposed method are fairly accurate as compared with the benchmark results obtained from the Monte Carlo simulations.

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References

Figures

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Fig. 1

A four-bar linkage mechanism [17]: L1 = 500 mm, L2 = 150 mm, L3 = 400 mm, L4 = 450 mm, L5 = 150 mm, θ5 = π/9rad, and operating angle θ2 = 2π/3rad

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Fig. 2

Target output trajectory of the four-bar linkage

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Fig. 3

Output positioning error of the four-bar linkage: errors of input parameters ɛL1 = 1.0mm,ɛL2 = 1.0mm,ɛL3 = 1.0mm,ɛL4 = 1.0mm,ɛL5 = 1.0mm,and ɛθ1 = ɛθ2 = π/1.8deg

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Fig. 4

Autocorrelation function of output errors of the four-bar linkage example: θ2 = [0:π/25:2π]rad

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Fig. 5

Distribution of the system maximum output error. ME-FM, MaxEnt with three orders of fractional moment and MCS, Crude Monte Carlo simulation with 106 samples.

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Fig. 6

System failure probability of the four-bar planar linkage with various accuracy thresholds

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Fig. 7

A crank-shaper quick-return mechanism: model parameters L1 = 120 mm, L2 = 50 mm, L3 = 375 mm, L4 = 425 mm, and L5 = 60 mm

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Fig. 8

Distribution of the maximum displacement error of the crank-shaper quick-return mechanism

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Fig. 9

System failure probability of the crank-shaper quick-return mechanism

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