Taking the effect of actual surface topography under elastohydrodynamic lubrication (EHL) conditions on the contact state of gear pairs into consideration, a combination model with the analytical sliced method and two-dimensional (2D) EHL model is proposed to characterize the three-dimensional (3D) meshing characteristics of spur gears. Firstly, the surface topology of gears is tested by a surface profiler, which reflects that the topography of tooth surface accords with fractal characteristics. Thus, by adopting the Weierstrass–Mandelbrot (W-M) fractal function, the gear surface is characterized. Secondly, the numerical 2D EHL model with fractal roughness is established, and distributions of oil film pressure (OFP) and oil film thickness (OFT) at different meshing positions are obtained. Finally, considering the different topography distributions in the direction of face width, time-varying mesh stiffness (TVMS) is calculated based on the analytical sliced method. Thus, the influence of 3D surface topography can be considered. The Hertz contact stiffness is substituted by the time-varying lubricating oil film stiffness (OFS). The influences of tooth surface topography and lubricant film characteristics on meshing characteristics are investigated. The results show that the 3D rough tooth surface may be well characterized by a fractal function with random phase. Moreover, there is a great difference in the distribution of OFP and OFT between rough and smooth surfaces, which certainly influences the gear meshing characteristics.

The tooth root crack fault is a common fault type of the spiral bevel gear pair (SBGP). Affected by the strong bearing capacity, the early crack fault of the SBGP cannot be found in time. In this study, a finite element (FE) model of the SBGP is established and assembled through the tooth contact analysis. The maximum tooth root stress is analyzed considering the variation of assembly errors. Meanwhile, this study simulates the tooth root crack fault of the bevel pinion with different crack degrees. The initial position of the crack is located where the maximum tooth root stress appears. The time-varying mesh stiffness (TVMS) of the SBGP considering different degrees of the pinion tooth root crack fault is obtained. The TVMS and the non-load transmission error are brought into a hybrid FE dynamic model, and steady responses are solved. Based on this, the sensitivities of various statistical indicators for identifying the tooth root crack fault of SBGP under the influence of assembly errors are verified. This paper can provide the necessary theoretical basis for the analysis and diagnosis of tooth root crack faults in the SBGP transmission system.