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Research Papers: Design Automation

Time-Dependent Reliability-Based Dimensional Synthesis for Planar Linkages With Unknown but Bounded Joint Clearances

[+] Author and Article Information
Xiaojun Wang

Institute of Solid Mechanics,
Beihang University,
No.37 XueYuan Road,
HaiDian District,
Beijing 100191, China
e-mail: xjwang@buaa.edu.cn

Xinyu Geng

Institute of Solid Mechanics,
Beihang University,
No.37 XueYuan Road,
HaiDian District,
Beijing 100191, China
e-mail: gxy20063211@126.com

Lei Wang

Institute of Solid Mechanics,
Beihang University,
No.37 XueYuan Road,
HaiDian District,
Beijing 100191, China
e-mail: LeiWang_Beijing@buaa.edu.cn

Ruixing Wang

Institute of Solid Mechanics,
Beihang University,
No.37 XueYuan Road,
HaiDian District,
Beijing 100191, China
e-mail: ruixing1989@163.com

Xiao Chen

Institute of Solid Mechanics,
Beihang University,
No.37 XueYuan Road,
HaiDian District,
Beijing 100191, China
e-mail: 307923480@qq.com

Weichao Fan

Institute of Solid Mechanics,
Beihang University,
No.37 XueYuan Road,
HaiDian District,
Beijing 100191, China
e-mail: 785149075@qq.com

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 13, 2017; final manuscript received March 8, 2018; published online April 17, 2018. Assoc. Editor: Xiaoping Du.

J. Mech. Des 140(6), 061402 (Apr 17, 2018) (12 pages) Paper No: MD-17-1271; doi: 10.1115/1.4039637 History: Received April 13, 2017; Revised March 08, 2018

Linkage mechanisms are typically designed to generate a specific functional relationship or path. Because the uncertain dimensions and joint clearances severely affect the output motion accuracy, designers urgently need a reliability-based design approach with high confidence and efficiency. However, the traditional kinematic reliability synthesis, which focuses on several discrete time points, cannot satisfy the accuracy requirement over a continuous time interval. Accordingly, to ensure high accuracy over a time period, this study presents a reliability synthesis approach that considers the time-dependency effect of motion error. The exact statistical characteristics of clearances and dimensions may be unavailable because of the limited sample information in practical engineering. Thus, by qualifying the uncertainties as unknown but bounded variables, the time-dependent reliability index is assessed based on a combination of the nonprobabilistic interval process and first-passage theories. Two engineering examples are presented to demonstrate the validity and applicability of the developed methodology.

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Figures

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Fig. 1

Illustration of linkage mechanisms

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Fig. 2

Description of clearance circle

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Fig. 3

Normalized model and rotary rectangle model

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Fig. 4

Nonprobabilistic first passage theory

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Fig. 5

Nonprobabilistic static reliability model

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Fig. 6

Flowchart of the time-dependent kinematic reliability analysis based on the Monte Carlo simulation method

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Fig. 7

Schematic of the function generation mechanism with joint clearances

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Fig. 8

Time-dependent kinematic reliability of optimal synthesis solutions

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Fig. 9

Third grade linkage mechanism

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Fig. 10

Desired motion function of the slide

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Fig. 11

Time-dependent reliability of initial design

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Fig. 12

Time-dependent reliability of synthesis solutions

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Fig. 13

Static reliability of synthesis solutions

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