Dynamic damage assessment of high horsepower tractor transmission based on measured load spectrum

Conventional Miner’s linear cumulative damage can focus only on the stress amplitude. In this study, a dynamic damage assessment was proposed for the high-horsepower tractor using the measured load spectrum. The research object was taken as the transmission shaft of a 162 kW four-wheel drive wheeled tractor. Multidimensional parameters were integrated to employ a dynamic weight allocation. A framework of the damage assessment was also established using the loads in the time domain, energy distribution in the frequency domain, and fluctuation features. Firstly, a torque test was developed using the transmission shaft of a tractor. The high-precision strain torque sensors were integrated with the wireless data acquisition. Torque fluctuation signals were captured under various conditions in real time, such as field operations and road transportation. The wheel torque signals were measured in the field, and then converted into the equivalent torque at the transmission shaft, according to the wheel-side planetary reduction mechanism, central transmission, transfer case, creeper gear, and gearbox. Subsequently, the rainflow counting was applied to identify the load cycles in the torque data. Statistical features of the loads were derived from high-confidence data for subsequent analysis. A composite model of the "three-dimensional linear weighting–nonlinear compression" was proposed to construct the damage indicator. Furthermore, three indicators—load gradient, frequency-band damage energy, and load kurtosis—were linearly weighted. The weighting parameters of these three indicators were optimized using a grid search algorithm. The root mean square error and absolute percentage error were employed to quantitatively evaluate the performance of different parameter combinations. The optimal weight allocation was determined as 0.350, 0.425, and 0.225. An S-shaped compression mapping with the sigmoid function was introduced to mitigate the influence of extreme values on the assessment, effectively balancing the sensitivity and robustness. The center of the load cycle time was indexed within the intensity index window of the dynamic damage. Time-frequency features were integrated into the cyclic damage for the amplitude correction. A hazardous threshold with the dynamic damage intensity index represented the exponential amplification of the cyclic amplitudes. The Goodman formula was then used to convert the torque signals into equivalent zero-mean stress amplitudes. And the S-N curve of the transmission shaft was applied to compute the damage. As such, a systematic assessment was realized on the dynamic damage. Experimental results demonstrate that the improved model effectively calculated the damage over the load bands. The peak normalized power spectral density energy occurred at 0.1 Hz, while the maximum damage frequency band was at 0.43 Hz, with a damage value of 1.78×10^-8. There was no coincidence between the peak power spectral density energy and the maximum damage. The theoretical correctness of the improved model was validated because the conventional approach only considered the amplitude. The relative error of the conventional Miner’s damage rule was 51.11%, whereas the relative error of the damage prediction was only 0.67%. The high accuracy and feasibility exhibited in the damage prediction. The linear damage models were advanced beyond the loading sequence and statistical analysis, thus providing the theoretical basis and insights for future assessment of the damage. Furthermore, a three-dimensional space of the damage feature was incorporated with the load gradient, frequency-band energy, and load kurtosis. The multidimensional parameter mechanism can be directly applied to the life prediction of the rotating machinery, such as the transmission shafts and gearboxes, or the damage assessment in the structural domains, such as the composite materials and additive manufacturing components. The finding can provide a theoretical and quantitative tool for the intelligent operation and prediction.