Firstly, under the quasi-static condition, the influence of tooth profile modification parameters on meshing stiffness and load distribution coefficient between teeth is analyzed; secondly, based on the nonlinear dynamic model of yaw coupling, the influence rules of modification amount on dynamic load under different modification types and different modification lengths are analyzed, and the influence of modification on tooth strength is further analyzed; finally, the dynamic load coefficient and the dynamic load distribution coefficient are respectively calculated The sum of the amplitude corresponding to the first seven order meshing frequency of the static transmission error is taken as the optimization objective. The static and dynamic performance optimization models are established, and the multi parameter optimization design is carried out. The main conclusions of this chapter are as follows:
(1) According to the analysis results under quasi-static condition, in order to effectively alleviate the sharp change of meshing stiffness caused by the alternation of single and double teeth, realize the smooth transition of load change in the process of gear transmission, and ensure the degree of gear coincidence, the amount of modification should be the deformation at the highest point of single tooth meshing under the constant design load, and the selection of modification length should meet the requirement that the double teeth meshing area is all in the modification area In the region, because the modification type mainly affects the curve form of meshing stiffness and load change in the modification region, the machining difficulty of the modification type should be mainly considered, and the modification type easy to machining should be selected. At the same time, the tooth profile modification parameters and the external load have a great influence on the corresponding amplitude of each order of meshing frequency of the meshing stiffness. Previous studies have shown that the dynamic characteristics of the gear transmission system are sensitive to the change of the amplitude corresponding to the mesh frequency of each order of the mesh stiffness, which shows that the tooth profile modification will inevitably affect the dynamic characteristics of the gear transmission system.
(2) Under different modification types, there is an optimal modification amount to minimize the dynamic load of the gear, and the optimal modification amount is less than the deformation amount of the highest point of single tooth meshing under the action of the average torque of the engine; when the modification amount exceeds a certain critical value, the dynamic load of the modified gear exceeds the dynamic load of the unmodified gear; compared with other modification types, the dynamic load of the linear modification decreases the most, However, the critical modification amount is the smallest; under the optimal modification amount, the meshing force of the modified gear obviously decreases on the amplitude corresponding to the higher-order meshing frequency, and the meshing impact load produced by the alternation of single and double teeth obviously decreases, but the meshing force in the single tooth meshing area increases; under the critical modification amount, the meshing force of the modified gear obviously increases on the amplitude corresponding to the second-order and third-order meshing frequency, although The impact load of meshing is obviously reduced, but the meshing force is obviously increased in the meshing area of single and double teeth, and there is the phenomenon of de toothing at the same time. Under the optimal modification, the coincidence degree of gears is basically unchanged, while under the critical modification, when the meshing force is small, the coincidence degree of gears is reduced.
(3) With the increase of shape modification amount, the dynamic load coefficients of different shape modification lengths all change in the form of ”, but the optimal shape modification amount, critical shape modification amount and minimum dynamic load coefficient are obviously different. The optimal shape modification amount of the short modification is less than the deformation amount of the highest point of single tooth engagement under the action of the average torque of the engine, and the modification length should not be too short, otherwise the dynamic load reduction is not obvious, and the critical shape modification amount exists in the short modification. The optimal amount of long profile modification is larger than the deformation of the highest point of single tooth mesh under the action of engine average torque, and it can reduce the dynamic load of gear more effectively, and there is no critical amount of profile modification. Under the optimal amount of short modification, the coincidence degree of gears is basically unchanged, while under the optimal amount of long modification, when the meshing force is small, the coincidence degree of gears is reduced.
(4) According to the influence of tooth profile modification on the strength of gear teeth, tooth profile modification has a great influence on the strength of gear teeth at different meshing positions. The strength of short modified gear teeth in the middle of single tooth meshing area and double tooth meshing area decreases, while the strength of gear teeth at other meshing positions increases; while the strength of long modified gear teeth only decreases near the top of gear teeth. With the increase of the modification amount or the decrease of the modification length, the strength of the teeth in the single tooth meshing area decreases gradually.
(5) The modification type of two gears is the same. When any two modification parameters change, the dynamic load coefficient has a global optimum. Compared with the optimization results of tooth profile modification based on static characteristics, the optimization results of tooth profile modification based on dynamic characteristics can effectively reduce the dynamic load coefficient of the gear transmission system, verify the effectiveness of the optimization model, and provide theoretical basis for the design of low vibration and low noise gear transmission system.