Abstract
This article proposes two strategies for time-dependent probabilistic fatigue analysis considering stochastic loadings and strength degradation based on the failure transformation and multi-dimensional kernel density estimation method. The time-dependent safety margin function is first established to describe the limit state of the time-dependent failure probability for mechatronics equipment with stochastic loadings and strength degradation. Considering the effective safety margin points and the corresponding number of the load cycles, two strategies for transforming the time-dependent failure probability calculation to the static reliability calculation are then proposed. Multi-dimensional kernel density estimation method is finally employed to build the probability density functions and the reliability is estimated based on the probability density functions. An engineering case of a filtering gear reducer is presented to validate the effectiveness of the proposed methods both in computational efficiency and accuracy.
Highlights
The fatigue is crucial to mechatronic products’ lifetime and it may cause catastrophic consequences
A number of researchers have sought to calculate the fatigue reliability of mechanical products based on probabilistic methods
These methods can be grossly divided into three categories: fatigue life–based reliability analysis method,[2,3,4] fatigue damage cumulative–based reliability analysis method,[2,5,6,7,8,9,10,11,12,13,14,15,16] and residual strength degradation–based reliability analysis method.[17,18,19,20]
Summary
The fatigue is crucial to mechatronic products’ lifetime and it may cause catastrophic consequences. Keywords Safety margin function, fatigue, time-dependent failure probability, kernel density estimation, stochastic loadings, strength degradation In order to estimate the time-dependent fatigue reliability efficiently and overcome the limitations in most of the current methods, following contributions in threefolds are made: (1) time-dependent security margin model based on time-dependent strength degradation model is built; (2) two transformation strategies are constructed to transform the time-dependent failure probability problem into static one; and (3) multidimensional kernel density estimation (KDE) method is employed to establish the time-dependent probabilistic fatigue analysis model.
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