# Calculation and analysis of comprehensive time-varying meshing stiffness

According to the two models of contact stiffness calculation, the following are calculated and discussed respectively. Firstly, according to the calculation of time-varying meshing stiffness of gear pair considering the contact stiffness of Yang SIM model, the calculation results of time-varying meshing stiffness of three pairs of gear pair are shown in Figure 1. The change of time-varying meshing stiffness curve in the figure shows that the curve change trend of both the comprehensive stiffness of single wheelset and time-varying meshing stiffness is first increased and then decreased (convex geometry) And the stiffness of double meshing zone is greater than that of single meshing zone. Due to the different basic and geometric parameters of the three pairs of gears, the distribution of meshing area and single double meshing area of the three pairs of gears in the graphic representation of time-varying meshing stiffness is different. Through the expression of meshing area in the joint graph and the basic parameters of the gear pair, the increase of the number of teeth can lead to the narrowing of the actual meshing area of the gear teeth, and the relative reduction of the single meshing area. Because of the diversity of gear parameters, the amplitude change of stiffness can not be evaluated by specific increment / decrement.

Similarly, taking gear pair 1 as an example, the time-varying meshing stiffness curve of gear pair considering semi empirical formula contact stiffness model is drawn in Figure 2. It can be seen from the figure that compared with the time-varying meshing stiffness considering Yang sun model, both the comprehensive stiffness of single wheelset and the time-varying meshing stiffness have basically the same trend in the stiffness curve, but the stiffness amplitude is y The ang sun model is larger than the semi empirical formula. Taking this example as the analysis object, the stiffness values of the two models keep the same order of magnitude, which also shows the similarity of the two models. In Figure 2 (a), under the action of load proportioning and distribution, due to the load change at the alternate position of the single double meshing area, the stiffness curve will have a slight steep rise at this position, as shown in the figure, while it has good ride comfort stiffness change at other positions. This phenomenon does not exist when it is transformed into the time-varying meshing stiffness curve of the actual gear pair (Fig. 2 (b)), which indicates that the small phenomenon of load mutation is irrelevant and does not need to be studied deeply. It can also be seen from Figure 2 that the stiffness value also shows a weak increasing trend with the increase of load, which fully indicates that the contact stiffness of meshing stiffness component shows strong nonlinear characteristics. However, from the comparison between the change of stiffness value and the increase of load, the change of stiffness value is very small. On the other hand, it also proves that the calculation of time-varying meshing stiffness modulus considering load effect The reliability of the model. 