In recent years, with the popularization of electric vehicles, the requirements for vibration and noise performance of spur gear transmission system have been significantly improved. As a kind of parameter self excitation system, spur gear transmission system will generate self excitation vibration under the action of internal excitation even if it is not affected by external excitation. Time-varying meshing stiffness and comprehensive meshing error are the most important internal excitation of spur gear system. Therefore, it is of great significance to accurately calculate the time-varying meshing stiffness and comprehensive meshing error of the spur gear system, and on this basis, to study the influence of various types of errors on the dynamic characteristics of the spur gear system, and to predict and control the vibration and noise level of the spur gear system.
At home and abroad, the influence of cumulative pitch deviation, tooth profile deviation, crack failure, micro topography of tooth surface on the dynamic characteristics of spur gear transmission system has been extensively studied. In the existing research, the calculation methods of time-varying meshing stiffness can generally be divided into two categories: finite element method and analytical method. The finite element method is widely accepted and applied because of its accurate calculation results. Yuan et al. and Ma et al. studied the influence of load and tooth profile modification on time-varying meshing stiffness through finite element method. With the development of computer technology, although the finite element method has been widely used in various fields, there are still some shortcomings in calculating the time-varying meshing stiffness of spur gears. On the one hand, the calculation accuracy and mesh quality of the finite element method are
Generally, in order to improve the calculation efficiency and reduce the calculation cost, the mesh size is difficult to reach the micron level, and it is difficult to simulate the influence of spur gear machining errors on time-varying meshing stiffness; On the other hand, in order to simplify the finite element model, only part of the tooth pairs in the spur gear pair are usually considered, and the machining errors of each gear tooth are different, ignoring the influence of the gear tooth meshing order on the time-varying meshing stiffness.
Compared with the finite element method, the analytical method has higher calculation efficiency, and its calculation results are consistent with those of the finite element method. Therefore, more and more attention has been paid in recent years. The methods of material mechanics and elastic mechanics are commonly used in the analytical method, but they are mainly used to calculate the stiffness of a single tooth and the stiffness of a single tooth engagement. In the case of multi tooth engagement, the stiffness of a single tooth engagement is usually obtained by simply superimposing it. In addition, in the dynamic analysis, the ideal spur gear is often taken as the object to calculate its time-varying meshing stiffness, ignoring the impact of a series of abnormal meshing phenomena such as gear tooth disengagement, out of line contact and eccentric load caused by machining and installation errors on the time-varying meshing stiffness in the actual meshing process of spur gears.
In the dynamic analysis of spur gears, many scholars use simple harmonic functions to simulate the comprehensive meshing error of spur gears, and its amplitude is usually assumed or determined according to the tolerance value corresponding to the accuracy level of spur gears. However, the waveform and amplitude of comprehensive meshing error caused by different types of spur gear errors are quite different. In addition, the comprehensive meshing error of spur gears is deeply coupled with time-varying meshing stiffness, and it is difficult to obtain more accurate dynamic analysis results by using simple harmonic function to simulate the comprehensive meshing error of spur gears without considering the impact on time-varying meshing stiffness.
(1) Processing and installation errors affect time-varying meshing stiffness and comprehensive meshing error at the same time, and they are deeply coupled. Among the machining errors, the tooth pitch deviation is the main influencing factor of time-varying meshing stiffness and comprehensive meshing error; Under the effect of tooth pitch deviation, the comprehensive meshing error changes step by step. When the step value exceeds a certain range, the gear teeth will be disengaged, and the time-varying meshing stiffness will suddenly change; The tooth pitch deviation is also the main influencing factor of the dynamic transmission error of the gear system.
(2) Under the influence of installation error, the comprehensive meshing error is a certain value in the whole meshing cycle; The center distance error causes the instantaneous contact line to move on the tooth surface, and the time-varying meshing stiffness decreases with the increase of center distance; Axis inclination error leads to gear eccentric load, tooth contact line shortens, time-varying meshing stiffness decreases, and axis inclination error φ Inclination error of relative axis γ The influence on time-varying meshing stiffness is greater.
(3) In order to reduce the peak and peak values of dynamic transmission error of the gear system, the tooth pitch deviation shall be reasonably distributed according to the load size, and the eccentric load caused by axis tilt error shall be avoided; In addition, although the negative deviation of center distance has less influence on the peak and peak value of dynamic transmission error than the positive deviation, the negative deviation of center distance should be combined with tooth profile modification to reduce the meshing impact caused by the negative deviation of center distance.
Based on the above reasons, the error tooth surface model considering the gear machining and installation errors is firstly established, the load bearing contact analysis algorithm suitable for the error tooth surface model is proposed, and the time-varying meshing stiffness and comprehensive meshing error of the spur gear pair are accurately calculated. On this basis, the bending torsional coupling dynamic model of spur gear pair is established, and the influence of different types of errors on the dynamic characteristics of gear transmission system is studied.