Wear and fatigue analysis of UAV involute spline couplings considering the fitting error

Involute spline pairs are widely used in power transmission systems of aerospace and heavy machinery. However, manufacturing tolerances, assembly errors, and service-induced deformations inevitably lead to misalignments such as shaft misalignment, angular eccentricity, and asymmetric angular eccentricity. These misalignments cause non-uniform contact pressure distribution along the tooth surfaces, resulting in severe localized wear and a significant reduction in fatigue life. Most existing studies focus on single misalignment parameters, while the coupling effects of multiple misalignment parameters on wear and fatigue life remain insufficiently understood. This study aims to investigate the wear mechanisms of spline tooth surfaces under different misalignment conditions, develop a methodology for predicting fatigue life and locating failure points, and quantify the correlation between misalignment parameters and tooth surface wear.

Based on the Archard wear theory, the Abaqus subroutine Umeshmotion and the Lagrangian-Eulerian adaptive meshing technique were employed to study the wear mechanism of spline couplings under three typical misalignment conditions: shaft misalignment (e), angular eccentricity (β), and asymmetric angular eccentricity (β-d). The contact pressure and sliding distance along the tooth surfaces were extracted from quasi-static finite element simulations, and the wear depth at each contact point was calculated iteratively using Archard’s equation. The Smith-Watson-Topper (SWT) critical plane fatigue life model and the linear damage accumulation model were used to estimate the fatigue life of spline pairs under different fitting conditions and to locate the failure points. Furthermore, the grey relational analysis method was applied to quantify the correlation degrees of e, β, and d with the tooth surface wear.

The simulation results show that the failure initiation points are primarily concentrated at the tooth ends and roots. The fatigue life of the spline decreases significantly with increasing fitting error, and the rate of fatigue life reduction accelerates as the misalignment magnitude increases, which greatly accelerates the fatigue failure of the spline. The grey relational analysis reveals that the correlation degree between e and the tooth surface wear is the largest among all parameters, with relational grades consistently exceeding 0.85. At the axial position of x/L = 0.5, the correlation degree between d and surface wear is approximately 0.1 higher than that between β, indicating that the asymmetric angular eccentricity (β-d) exacerbates the wear process.

Misalignment significantly reduces the fatigue life of spline pairs by increasing local contact pressure and sliding distance, thereby accelerating wear at the tooth ends and roots. Among the three misalignment types, asymmetric angular eccentricity is identified as the most detrimental condition, and the shaft misalignment amount e is found to be the most influential parameter affecting tooth surface wear. These findings provide a theoretical basis for the design and assembly optimization of spline pairs in high-reliability applications.