Methodology for compiling torque load spectra of tractor power take-off shafts based on nonlinear damage accumulation

To obtain the load spectrum of the Power Take-Off (PTO) shaft during field operations under the rotary tillage condition of tractors, and in light of the limitations of traditional fatigue damage models for load spectra, a nonlinear damage model based on the Lemaitre model is proposed. This paper first establishes a dynamic torque stress testing system to acquire the PTO shaft torque loads at an engine speed of 2000 rpm, which are then preprocessed. Subsequently, the four-point rainflow counting method is employed to statistically count the mean and range values of the load signals, and a Q-Q plot is used for distribution testing. Following this, the time-domain method is utilized for frequency extrapolation to establish an 8x8 two-dimensional load spectrum, which is then converted into a one-dimensional load spectrum using the mean value method. Finally, damage assessment and life prediction of the load spectrum are conducted based on the Miner theory, the Corten-Dolan theory, and the nonlinear damage model based on the Lemaitre model. The results indicate that the mean values of the load signals follow a normal distribution, while the range values follow a Weibull distribution, and that the mean and range values are mutually independent. The peak threshold obtained through time-domain extrapolation is 380 N.m, and the trough threshold is 120 N.m, with the statistical characteristics of the extrapolated signal remaining largely consistent with those of the original signal. The fatigue life predicted by the nonlinear damage model based on the Lemaitre model is 1.76E8, which is the closest to the actual life compared to the other two models, with a calculation accuracy 724 times that of the Miner theory and 239 times that of the Corten-Dolan theory. This verifies the effectiveness and accuracy of the proposed method, providing a reference for future load spectrum life prediction and fatigue bench tests of tractors.