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

Abstract

This work develops an envelope approach to timedependent 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 timedependent problem can be converted into a timeindependent 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 timedependent mechanism reliability is then estimated by a multivariable normal distribution at the expansion points. As an example, analytical equations are derived for a fourbar function generating mechanism. The numerical example shows the significant accuracy improvement.