Nonlinear dynamic modeling and test validation for a two-stage involute gear system

Here, a two-stage involute gear system was taken as a study object, the effects of variation of distances between centers due to geometric eccentricity, installation errors of distances between centers and bending displacement of gear center bearings on pressure angle and backlash were analyzed, a nonlinear dynamic meshing stiffness model was introduced, nonlinear dynamic meshing forces of each gear pair were obtained. Adopting Lagrange method, the nonlinear lateral-shimmy-torsional coupled dynamic model of the two-stage involute gear system was established considering the effects of eccentricity, backlash, time-varying pressure angle and the nonlinear dynamic meshing stiffness model. The nonlinear dynamic equations were solved with the 4th order fixed step Runge-Kutta algorithm. The theoretical calculation and tests were performed for a test device of a two-stage gear system. The test results showed that the maximum error between simulated values of angular acceleration under various conditions and tested ones obtained with angular acceleration sensors installed at symmetric positions around gear circumference is 23.51%; the maximum error between simulated values of vibration displacements and tested ones obtained with displacement sensors installed at positions of the gear box is 21.21%; the maximum error between simulated values of torsional shear stresses and tested ones obtained with strain gauges pasted on the gear shaft is 17.9%. The study results indicated that the varying trend of simulated results agrees well with that of test ones, and errors are within an acceptable range, the reasons causing errors between simulated results and tested ones are analyzed; the correctness of the proposed dynamic model and the meshing stiffness model of the gear system is verified.