Nonlinear dynamic modeling and analysis of spur gears considering dynamic contact state under misalignment errors

Traditional gear dynamic models take the mesh stiffness obtained under static conditions as an internal excitation. Under practical conditions, misalignment errors are unavoidable and will affect the contact state and mesh stiffness. The contact state and mesh stiffness under misalignment errors are dynamic force-dependent (DFD) since they are also affected by the violently fluctuating dynamic meshing force (DMF). Consequently, developing a dynamic model based on statically obtained mesh stiffness is inappropriate under misalignment errors. This study presents a torsional dynamic model of spur gears considering the DFD mesh stiffness and contact state change caused by misalignment errors. The mesh stiffness and torsional dynamic model of the proposed model are jointly solved. Parametric studies are conducted to reveal the differences in the dynamic responses between the proposed and traditional models under different misalignment errors. The dynamic responses of spur gears in resonance and off-resonance regions show that, compared with the traditional model, the proposed model under misalignment errors is more likely to undergo non-periodic and chaotic motion due to contact loss. In addition, misalignment errors lead to a significant increase in the maximum value and oscillation amplitude of the DMF of the proposed model.