Research Papers

Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation

[+] Author and Article Information
Xiaoping Du

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
290D Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500
e-mail: dux@mst.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 3, 2013; final manuscript received May 4, 2014; published online June 2, 2014. Assoc. Editor: David Gorsich.

J. Mech. Des 136(8), 081010 (Jun 02, 2014) (7 pages) Paper No: MD-13-1504; doi: 10.1115/1.4027636 History: Received November 03, 2013; Revised May 04, 2014

This work develops an envelope approach to time-dependent mechanism reliability defined in a period of time where a certain motion output is required. Since the envelope function of the motion error is not explicitly related to time, the time-dependent problem can be converted into a time-independent problem. The envelope function is approximated by piecewise hyperplanes. To find the expansion points for the hyperplanes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances of the dimension variables are small. The expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.

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Grahic Jump Location
Fig. 2

Four-bar function generator mechanism

Grahic Jump Location
Fig. 3

Motion error at the means of dimension variables

Grahic Jump Location
Fig. 4

Probability if failure on [95.5 deg,215.5 deg]



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