Abstract:
This study takes the transmission shaft of a 162 kW four-wheel drive wheeled tractor as the research object and proposes a dynamic damage assessment method. By integrating multidimensional parameters and employing a dynamic weight allocation mechanism, the method overcomes the limitation of traditional Miner’s linear cumulative damage theory, which focuses solely on stress amplitude. A comprehensive damage assessment framework is established, encompassing the time-domain characteristics of loads, energy distribution in the frequency domain, and fluctuation features. First, a torque testing system based on the tractor’s transmission shaft was developed. This system integrates high-precision strain-based torque sensors and wireless data acquisition modules, enabling real-time capture of torque fluctuation signals under various operating conditions such as field operations and road transportation. The field-measured wheel torque signals were converted into equivalent torque at the transmission shaft through the wheel-side planetary reduction mechanism, central transmission, transfer case, creeper gear, and gearbox. Subsequently, the rainflow counting method was applied to identify load cycles in the torque data. Statistical characteristics of the loads were derived using statistical methods, providing a high-confidence data foundation for subsequent analysis. In the damage indicator construction phase, a composite model of "three-dimensional linear weighting–nonlinear compression" was innovatively proposed. Three indicators—load gradient, frequency-band damage energy, and load kurtosis—were linearly weighted. The weighting parameters for these three core indicators were optimized using a grid search algorithm, with the root mean square error and absolute percentage error employed to quantitatively evaluate the performance of different parameter combinations. The optimal weight allocation scheme was determined as 0.35, 0.425, and 0.225. To mitigate the influence of extreme values on the assessment results, an S-shaped compression mapping based on the sigmoid function was introduced, effectively balancing sensitivity and robustness. Subsequently, the load cycle time center was indexed within the dynamic damage intensity index window, and time-frequency characteristics were integrated into the cyclic damage for amplitude correction. A hazardous threshold based on the dynamic damage intensity index revealed exponential amplification of 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, resulting in a dynamic damage assessment methodology. Experimental results demonstrate that the improved method effectively calculates damage across load bands. The peak normalized power spectral density energy occurs at 0.1 Hz, while the maximum damage frequency band is at 0.43 Hz, with a damage value of 1.78×10
-8. The fact that the peak power spectral density energy does not coincide with the maximum damage value effectively illustrates the limitations of traditional methods that consider only amplitude, thereby validating the theoretical correctness of the proposed approach. The relative error of the traditional Miner’s damage rule was 51.11%, whereas the relative error of the proposed damage prediction method was only 0.67%. This method exhibits high accuracy and feasibility in damage prediction, advancing the study of linear damage models beyond the perspectives of loading sequence and statistical analysis, and providing a theoretical basis and new insights for future research on damage assessment methods. Furthermore, this study not only proposes a concrete and engineerable dynamic damage assessment process but also constructs a three-dimensional damage feature space incorporating load gradient, frequency-band energy, and load kurtosis. This multidimensional parameter coupling mechanism offers dual value for subsequent research: it can be directly applied to life prediction of rotating machinery such as transmission shafts and gearboxes, and can also be extended to damage assessment in new structural domains such as composite materials and additive manufacturing components, providing a novel theoretical tool and quantitative methodology for intelligent operation and predictive maintenance.