Fatigue Damage Analysis Of Automobile Rear Subframe Based On Kernel Density Estimation Via Diffusion

Extrapolation of load spectrum is an important step in the compilation of load spectrum,which is to extend the short-time load spectrum to the whole life domain according to the distribution law.Probability density estimation of load spectrum is the key link of load spectrum extrapolation.The accuracy of load spectrum probability density estimation by different schemes is different.To solve the problem of boundary deviation of traditional kernel density estimation,kernel density estimation method via diffusion is introduced into the process of load spectrum extrapolation.Based on this,this paper takes the rear sub-frame as the research object,adopts parameter extrapolation method,non-parameter extrapolation method and kernel density estimation method via diffusion,calculates the probability kernel density function according to the distribution law of load spectrum,and carries out load spectrum extrapolation to calculate the fatigue damage.The load spectrum extrapolation scheme was compared and analyzed from the fitting effect diagram,fitting priority,extrapolated extreme value of load spectrum,cumulative cycle number and fatigue damage value,so as to clarify the optimal probability density estimation scheme of load spectrum and provide support for the fatigue durability research of vehicle parts.The road test was designed and carried out,and the six component force signals of the wheel core and the key points of the vehicle body were measured.The finite element model of the rear sub-frame and the multi-body dynamics model of the whole vehicle were established and verified by experiments.The time history of the load at the danger point of the rear sub-frame is obtained by the displacement inversion method and the modal superposition method,which provides data for the extrapolation of the load spectrum.The rain flow count was used to calculate the load spectrum of the sub-frame hazard point,and the rain flow matrix was obtained.For the one-dimensional range-mean matrix that passed the independence test,the probability density function was calculated by using three schemes:parameter estimation,Gaussian kernel density estimation and diffusion kernel density estimation.The results show that the probability density function estimation by the kernel density estimation method via diffusion is better than other methods,and the boundary deviation problem of kernel density estimation is solved.At the same time,the load cycles of the extrapolated load spectrum obtained from the diffusion kernel density estimation is most close to 10~6times,which is equivalent to the actual conditions.It is proved that the kernel density estimation method via diffusion is suitable for rain basin extrapolation of one dimensional load spectrum.The kernel density estimation method via diffusion is extended to the two-dimensional load spectrum extrapolation,according to from-to rain flow matrix,kernel density estimation method via diffusion and Gaussian kernel density estimation method could be used to fit load distribution,comparison and analysis show that kernel density estimation method via diffusion of fitting effect is better,the fitting priority indicators are better than the kernel density estimation method.For the extrapolated load spectrum,the extrapolated load spectrum obtained by the kernel density estimation method via diffusion is close to the actual working condition,which proves that the kernel density estimation method via diffusion is suitable for the extrapolation of two-dimensional load spectrum.The S-N curve of the material was modified to the S-N curve of the rear sub-frame,and the fatigue damage analysis of the rear sub-frame was carried out.From the fatigue damage matrix analysis,it can be seen that the damage contribution of small values in the extrapolated load spectrum increases,which proves the accuracy of the extrapolated load spectrum methods.The load spectrum fatigue damage obtained by the non-parametric rain flow extrapolation using the kernel density estimation method via diffusion is larger,which is suitable for fatigue damage analysis of vehicle parts requiring high fatigue durability and reliability.The applicability of the diffused kernel density estimation method in the process of load spectrum compilation is proved,which provides a reliable technical route for the fatigue damage research of automobile parts.