Establishment of the dynamic BTAP model and load-sharing analysis of herringbone gear planetary system with cracks

To reveal the influence of component cracks on the dynamic load-sharing characteristics of the herringbone gear planetary system (HGPS), a 55-DOF bending-torsional-axial-pendular (BTAP) nonlinear dynamic model of the system was constructed, taking into account parameters of different crack degrees (depth, angle, length), as well as factors such as manufacturing error (ME) and installation error (IE), time-varying mesh stiffness (TVMS), time-varying support stiffness, damping, and friction. The TVMS model of components with cracks was established using the cumulative potential energy method, and the mathematical quantification relationship between different crack parameters and TVMS was studied. Based on the theory of elastohydrodynamic lubrication (EHL), calculate the time-varying friction coefficient and friction force of each gear pair. Using the nonlinear elastic theory of rolling elements and raceways, the time-varying support stiffness of each component is obtained. Using the Runge-Kutta numerical integration method to solve the dynamic differential equations, and analyzed the load-sharing characteristics and sensitivity influence law of the system when the sun gear, planetary gear, and internal gear ring contain cracks respectively. Built a vibration test bench for the HGPS with cracks, and the experimental results were compared with the theoretical results. The results show that as the crack intensifies, the TVMS value decreases at the crack tooth. When the sun gear contains cracks, there will be obvious protruding excitation in the system’s load-sharing curve, and the internal meshing load-sharing characteristics are better than the external meshing load-sharing characteristics. At the same time, as the degree of cracks increases, the system load-sharing characteristics first improve and then deteriorate. At the same crack, as manufacturing and installation errors increase, the load-sharing characteristics of the internal and external meshing pairs deteriorate. When the internal gear ring contains cracks, the dynamic load-sharing coefficients of the internal and external meshing pairs of the system are 7.96 and 4.10, respectively, which have the highest impact on the dynamic load-sharing coefficient and sensitivity of the internal and external meshing pairs of the system. The experimental results are consistent with the theoretical results, verifying the correctness of the model.