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.

The comparison of the time-varying meshing stiffness under the Yang sun model and the semi empirical formula shows that they have their own characteristics. The Yang SIM model considering the macro geometric effect can quickly locate and evaluate the time-varying meshing stiffness of gear pair, and the quasi nonlinear semi empirical formula can explain the load effect on the time-varying meshing stiffness from another point of view The application of this algorithm can show the advantages of this algorithm, especially in the high precision, high parameters and high performance requirements of aviation, aerospace and other precision transmission parts. It is shown that the selection of algorithm for time-varying meshing stiffness evaluation should be based on the actual product application and demand.

The influence of the geometric parameters of gear pair on the time-varying meshing stiffness of gear pair is studied by selecting gear pair 1 and considering the semi empirical formula contact stiffness calculation model. The influence of different gear pressure angles on the stiffness is shown in Fig. 3. The time-varying meshing stiffness curve shows that the change of tooth profile pressure angle can affect the meshing area span of gear pair and the distribution ratio of single double meshing area, and the stiffness value is also affected. The curve in the figure shows that the stiffness increases with the increase of gear pressure angle.

Figure 4 shows the influence of different meshing tooth widths on the time-varying meshing stiffness of gear pair. The figure shows that the change of tooth width has no effect on the meshing interval span and stiffness curve trend of meshing stiffness, but only makes the stiffness value change, that is, the meshing stiffness value increases with the increase of meshing tooth width. From the difference of stiffness curve in the figure, the same increment of tooth width will cause different increment of stiffness value in single meshing area and double meshing area.

Figure 5 shows the influence of time-varying meshing stiffness of gear pair under the action of different shaft radius (gear matrix aperture). The simulation curve results in the figure show that the time-varying meshing stiffness increases with the increase of installation shaft radius of master-slave gears, but the incremental relationship between them is a nonlinear relationship. To sum up, the simulation results show that the reasonable selection of tooth width and shaft radius can achieve the effect of small range adjustment of meshing stiffness, optimize the meshing stiffness of gear and improve the anti torsion performance of rotor under the condition of meeting the allowable range of design load and the determination of gear parameters Basic applied research.

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