Research on Nonlinear Dynamics of Involute Spur Gear Drive System

Nonlinear dynamic model of yaw-torsion coupling was established for involute spur fixed-shaft gear drive and planetary gear drive respectively, and a non-linear dynamic engagement model was put forward. Vibration characteristics test and model verification were carried out for two-stage fixed-shaft gear drive and single-stage planetary gear drive respectively. Single-stage gear drive was analyzed based on yaw-torsion coupling non-linear dynamic model.Dynamic and non-linear dynamic characteristics of stage gear drive system under steady-state and no-load conditions; for single-stage gear drive system, the influence of profile modification parameters on static and dynamic characteristics is analyzed, and the optimal design of profile modification is carried out; for tracked vehicle gear drive system, the dynamic characteristics of gear drive system under gears are systematically analyzed and established.An optimization model considering the dynamic characteristics of each gear is developed and the optimization design is carried out.The main research results and conclusions are as follows:

(7) From the analysis results under quasi-static conditions, in order to effectively mitigate the sharp change of meshing stiffness caused by the alternation of single and double teeth, realize the smooth transition of load change during gear transmission and ensure the overlap of gears, the amount of modification should be the amount of deformation at the highest point of single teeth meshing under the fixed design load, and the length of modification should be selected to satisfy the requirement that the double teeth meshing area is fully in the modification area.In the area where the modification type mainly affects the curve form of meshing stiffness and load variation, the modification type that is easy to machine should be selected.At the same time, the profile modification parameters and external loads have a great influence on the corresponding amplitudes of each order of meshing frequency of meshing stiffness.

(8) Under different modification types, there is an optimum modification quantity to minimize the dynamic load of the gear and the optimum modification quantity is less than the maximum deformation of the single-tooth engagement under the average engine torque; when the modification quantity exceeds a certain critical value, the dynamic load of the modified gear exceeds the dynamic load of the non-modified gear; compared with other modification types, the dynamic load of linear modification reduces the most greatly.However, the critical modification quantity is the smallest; under the optimum modification quantity, the meshing force of the modified gear significantly decreases in the corresponding amplitude of high-order meshing frequency, while the meshing impact load produced when single and double teeth alternate significantly decreases, but the meshing force in the single teeth meshing area increases; under the critical modification quantity, the meshing force of the modified gear increases significantly in the corresponding amplitude of second and third-order meshing frequency, althoughRolling impact load produced by alternating single and double teeth is significantly reduced, but meshing force in single teeth meshing area is significantly increased, and tooth disengaging occurs.The overlap of gears remains unchanged at the optimum profile modification, while it decreases at the critical profile modification when the meshing force is small.

(9) With the increase of modification quantity, the dynamic load coefficient presents a V-shaped change under different modification lengths, but there are obvious differences between the optimal, critical and minimum dynamic load coefficient.The optimum modification quantity of short modification is less than that of the highest point of single tooth engagement under the average engine torque, and the modification length should not be too short, otherwise the dynamic load reduction is not obvious, and critical modification quantity exists for both short modifications.The optimum modification amount for long modification is greater than the deformation amount at the highest point of single tooth engagement under the average engine torque, and it can reduce the dynamic load of the gear more effectively without the critical modification amount.Under the optimum modification corresponding to the short modification, the gear overlap basically remains unchanged, while under the optimum modification corresponding to the long modification, the gear overlap decreases when the meshing force is small.