A Critical Plane Method For Determining Random Vibration Fatigue Of Structures

Due to the harsh vibration environment of aerospace structure,it is extremely important to solve the problem of fatigue failure during service.The method for calculating the fatigue life of single-axis vibration has been mature.But in the case of multi-axis vibration,the vibration fatigue life is simulated by single-axis sequential loading,then the final result is multiplied by a constant.Result calculated by this method is accurate in some case,but it is very difficult to determine the coefficient accurately.This paper presents a method to find the maximum shear stress variance by using the directional cosine of the plane at the dangerous point,and compares it with the existing method of finding the critical plane position based on five angles of Euler angle rotation.Finally,the multiaxial stress state is equivalent to the uniaxial stress state through the normal stress and shear stress in the critical plane for calculating the fatigue life.Then the specific work of this paper is as follows:(1)First,the fatigue properties of metals and the theory of fatigue damage accumulation are briefly introduced.Then,several time-domain and frequency-domain methods for calculating fatigue life of structures under uniaxial random vibration are summarized.At last,two methods to determine the critical plane of multiaxial random vibration fatigue are presented.The first method is based on the power spectral density matrix of stress response to determine the direction of the average stress principal axis from a statistical point of view,so as to further determine the position of the critical plane.The second method is based on the three directional cosines of the normal out of the critical plane,and the critical plane is obtained by maximizing the variance of shear stress.By linear combination of normal stress and shear stress on the critical plane,a fatigue life calculation method of multiaxial random vibration is established.A hybrid method combining the results of commercial finite element software and self-compiled multi-axis random vibration fatigue life calculation program is established,which can be used to calculate the multi-axis random vibration fatigue life of structures.(2)Based on theoretical analysis and calculation,two kinds of cantilever beams with notches and matching fixtures are designed,then the finite element modeling calculation is carried out,and the excitation spectrum is determined according to the calculation results.Two algorithms for determining critical plane are compiled by MATLAB,at last their random vibration fatigue life is calculated.(3)A multi-axis random vibration fatigue test system was designed,and several test pieces were tested.The experimental results were compared with the simulation results,and the causes of errors were analyzed.(4)In order to solve the problem that the stress state of the dangerous point of the test piece is quite different from that of the structure under real multi-axis excitation,the test piece is redesigned and the fatigue life of the structure under multi-axis random vibration is calculated.