Probabilistic analysis of rattle occurrence in the gap of automotive interior parts

Abstract

An efficient approach is developed to evaluate probability of rattle occurrence in the gap of automotive interior parts under forced vibration, in which the probabilistic analysis is conducted by employing the combined modal sensitivity and Monte-Carlo simulation of frequency responses. Design sensitivity analysis technique is applied to obtain the first-order approximation of the modal response. Monte-Carlo simulation is applied to generate random samples of eigen pairs due to the variability of input parameters, which are used to obtain the frequency responses via modal superposition technique. To calculate the probability of rattle occurrence, a rattle index is introduced, defined as by the overlapped area of the displacements at the points in potential contact. Commercial code NASTRAN is employed for the modal frequency response and its sensitivity using the SOL 111 and SOL 200, respectively. For the illustration of the method, a simple problem with two cantilever beams with small gap is considered. Probabilistic frequency response analysis is conducted with the thickness and material properties being random variables. The probability of rattle occurrence is evaluated and its accuracy is examined by comparing with that by the crude Monte-Carlo simulation.