For involute spur fixed-drive and planetary gear drive respectively, a non-linear dynamic engagement model including dynamic backlash and dynamic engagement stiffness is proposed, which can be applied to profile modification gear. The engagement model realizes feedback calculation of the non-linear dynamic model coupled with the yaw-torsion of gear drive and can be used to analyze the dynamic changes of engagement parameters during gear drive.Coupling between chemistry and vibration response.
(1) For fixed-shaft gear drive, firstly, the analytical expression of the dynamic tooth side clearance caused by the change of the center distance is deduced; secondly, the analytical expression of the engagement position and the pressure angle of the engagement point corresponding to the dynamic boundary conditions of single-tooth and double-tooth engagement and profile modification area are deduced, taking into account the profile modification, speed change, the change of the center distance and the change of the engagement state of the tooth surface and back-tooth.The method calculates the dynamic engagement stiffness, and takes the single-stage gear as an example to further analyze the influence of speed change and center distance change on the engagement stiffness, which verifies the correctness of the calculation method of dynamic engagement stiffness. Finally, the dynamic backlash and dynamic engagement stiffness are replaced by the constant backlash and quasi-static periodic time-varying engagement stiffness in the previous engagement model, and a non-linear dynamic engagement model isType A.
(2) For planetary gear drive, firstly, the analytical expression of the dynamic tooth side clearance caused by the change of center distance is deduced for the outer engagement pair formed by the sun gear planetary gear and the inner engagement pair formed by the ring gear respectively; then, the engagement position, single and double teeth engagement and back engagement state are deduced considering the profile modification, speed change, phase difference and tooth surface and back engagement state changes.The analytical expression of pressure angle of meshing point corresponding to dynamic boundary condition in the modification area is used to calculate the dynamic meshing stiffness by analytical method. Finally, the dynamic backlash and dynamic meshing stiffness are replaced by the constant backlash and quasi-static periodic time-varying meshing stiffness in the previous meshing model, and a non-linear dynamic meshing model is proposed.