Load Spectrum Compiling for Transmission Shaft of Tracked Vehicle Based on Kernel Density Estimation

For establishing the high reliability load spectrum for transmission shaft of military tracked vehicle on the typical road, the torque and relevant vehicle data similar to that in real service conditions was collected through vehicle experiments, and the confidence level of load data samples was calculated based on the criteria of least testing times. A load spectrum compiling procedure is designed based on 2-D kernel density estimation on account of the irregular 2-D distribution of amplitude and mean values in test load data. In the load spectrum compiling procedure, two times of rain-flow counting are adopted: the first rain-flow counting result is used to deduce the extrema of amplitude and mean values, and the second rain-flow counting result is used to extrapolate the kernel density. This compiling procedure can not only obtain better fitting of amplitude and mean distribution, but also achieve the reasonable extrapolation of the experimental rain-flow matrix. Goodman equation and the equivalent damage conversion method are used to derive 8-level program block load spectrum from 2-D load spectrum, and a loading method for the combination of torque and rotational speed is presented. 0.8 times of eighth amplitude are chosen as the value of small load from the perspective of fatigue damage, and total cycles are decreased by 99.33% while total damage is decreased only by 0.29%, which can accelerate the fatigue loading test.