Compilation and bench test of traction force load spectrum of tractor three-point hitch based on optimal distribution fitting

Abstract: This study aims to clarify the working load characteristics and distribution of tractor three-point suspension devices, further to predict the life of parts and product reliability analysis. A load spectrum preparation was also proposed using optimal distribution fitting, in order to verify the multi-peak and uncertain probability distribution of the operating load. A mixed distribution model was established with the mean value following the Gaussian mixture and the amplitude following the Weibull mixture. The number of optimal basis functions in the mixed distribution was determined to combine the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Furthermore, the Expectation-Maximization algorithm was selected to estimate the optimal parameters of the mixed distribution, particularly on the optimal solution and curve fitting. Taking the measured load of tractor three-point suspension traction as the research object, the optimal distribution fitting was carried out to determine the estimation parameters of the mixed distribution. Specifically, the determination coefficients of mixed Gaussian and Weibull distribution increased by 3.45% and 6.02%, respectively, the correlation coefficients increased by 1.73% and 4.87%, respectively, the root mean square errors decreased by 31.38% and 40%, respectively, and the residual sum of squares decreased by 52.92% and 64.01%, respectively, compared with the single distribution fitting. The extreme value and frequency were extrapolated using the optimal distribution fitting, thereby preparing the two-dimensional program load spectrum. The damage of the two-dimensional load spectrum was equivalently converted into the one-dimensional load spectrum, according to the Miner fatigue cumulative damage theory and S-N curve. A comparison was made on the statistical characteristics and rain flow counting of the extrapolated double load spectrum and the original load. The results show that the range of the extrapolated extreme value was expanded for the load, indicating the consistent load distribution. The bidirectional extrapolation of the average amplitude was realized under the premise of retaining the original load characteristics. The extrapolated traction load spectrum was then applied to the indoor bench loading system of tractor three-point suspension traction. The feedback regulation and the loading of suspension traction were realized using a PID control. A loading test of the three-point suspension frame was also performed on the bench loading system. The loading test results show that the maximum overshoot of the system was 5.19%, the maximum stability time was 0.2 s, and the maximum delay was 0.4 s, indicating an excellent response characteristic of the system. Correspondingly, the indoor bench system can fully meet the loading and reproduction of the three-point suspension traction in the tractor. The rain flow counting analysis was also made on the external traction load spectrum, further to acquire the feedback traction load spectrum. Anyway, there were consistent mean and amplitude frequency of the rain flow counting, indicating the consistent fatigue damage caused by the two parts. The finding can also provide a theoretical reference for the tractor indoor bench test using the load spectrum.