In the gear transmission system, due to the need of lubrication and the manufacturing accuracy and installation error of gear teeth, the existence of tooth side clearance in the system can not be avoided. From the previous analysis, it can be seen that the clearance nonlinear function is an important nonlinear factor in the gear transmission system of hybrid electric vehicle. According to the dynamic characteristics of the whole system, the size of tooth side clearance that makes the system in a stable running state is calculated by using simulationx simulation software.
For the system model established above, the time-varying stiffness of gear meshing is fully considered. During the operation simulation, the backlash is simulated and analyzed as follows: (1) B = 0mm; (2)b=0.1mm； (3) The magnitude of the tooth side meshing force under B = 0.2mm, the peak value of the force in the time domain and the unstable region are recorded, and these signals are analyzed in the frequency domain by fast Fourier transform. Through the simulation analysis of the whole gear system, it is found that the change trend of the gear in the composite planetary gear mechanism is similar to that in the parallel shaft gear, because the large planetary gear p1n in the composite planetary gear mechanism is the same as that of the small sun gear S1 Ring gear R and asteroid gear p2n mesh. Asteroid gear p2n meshes with large planetary gear p1n and also with large sun gear S2. The vibration characteristics of asteroid gear p2n and large planetary gear p1n are relatively complex. Therefore, the results of selecting planetary gears in composite planetary gear mechanism are analyzed in detail, as shown in Fig. 1 (a), (b), (c) and Fig. 2 (a), (b), (c).
According to the theory, the calculation of meshing vibration frequency of gap coupling model can more accurately reflect the coupling vibration characteristics of gear mechanism than that of uncoupled model, which is more in line with the actual requirements. When the gear clearance is different, the vibration characteristics of the gear transmission system are reflected in different gear clearance. It is mainly reflected in the magnitude of amplitude. With the increase of backlash, the overall amplitude increases. The peak value corresponding to backlash B = 0mm is 1.38e + 05n, the peak value corresponding to backlash B = 0.1mm is 1.62e + 05n, and the peak value corresponding to backlash B = 0.2mm is 1.65e + 05n, which indicates that the larger the backlash, the greater the meshing impact of the gear, which is in line with the actual situation; From Fig. 2 (a), (b) and (c), when the tooth side is less than 0.1mm, with the increase of the tooth side clearance, the unstable area of the gear becomes wider and a wider resonance range is obtained, but the amplitude is the same as that without clearance, which is 1400N. When the tooth side is 0.2mm, not only the unstable area of the gear becomes wider, but also the amplitude increases to 1900N. In addition, it can be seen from the spectrum that the planetary gear shows different states in the vibration process: there is no impact and unilateral impact, and the nonlinear characteristics such as amplitude jump and multivalued solution also appear near the resonance frequency of the planetary gear.
Corresponding to the above three cases of motion simulation. The excitation degree of resonance can be more clearly assigned by order analysis, and the results of these three cases are analyzed in order. The relevant results are shown in Figure 3. It can be seen from the figure that when the tooth side clearance is 0mm, the unstable area appears in the accessories of planetary gear P1 at the speed of 1300rpm ~ 1900rpm. When the tooth side clearance is 0.1mm, the unstable area appears near the speed of 1500rpm. When the tooth side clearance is 0.2mm, the unstable area of planetary gear P1 mainly appears near the speed of 4400rpm and 5300rpm, And the excitation degree of resonance is relatively high.
Through analysis and summary, too large or too small backlash will bring adverse effects. In order to ensure the stable operation of the planetary gear transmission system, we should try our best to ensure that the tooth side clearance of the planetary gear is around 0.1mm. Since the gear transmission system of the hybrid electric vehicle is composed of multiple pairs of gears, in order to ensure the stable operation of the gear transmission system, the tooth side clearance of other multiple pairs of gears in the system is studied by analyzing the planetary tooth side clearance of the composite planetary gear mechanism, It provides a reference range for the clearance of each gear pair in the system, which will not be described here. Therefore, the machining accuracy of the gear can be guaranteed in the process of gear manufacturing and processing. In the process of installation, in addition to the clearance required for lubrication between gear teeth, the installation accuracy of the gear should be guaranteed as much as possible. Through the above methods, the tooth side clearance in the system can meet the theoretical requirements, so as to improve the nonlinear dynamic characteristics of the whole hybrid electric vehicle gear transmission system and provide a method for vibration and noise reduction of the whole system.