Dynamic meshing force and dynamic tooth force of multistage gears in shearer cutting section

Dynamic load is the direct cause of vibration and fatigue failure of transmission system. Analyzing the dynamic load of each component is a necessary step to check the bearing capacity of components and understand the dynamic characteristics of the system.

Taking the first pair of high-speed gears (gear pair 1) as an example, the dynamic load in the process of one meshing is calculated, as shown in Figure 1. The large deformation gear model takes into account the early meshing and delayed meshing caused by tooth deformation. Therefore, tooth pair 2 starts to mesh before the theoretical meshing point (0 point), and the meshing force is equal to the sum of the tooth forces of tooth pair 1 and tooth pair 2. As the meshing proceeds, the tooth pair 1 gradually withdraws from the theoretical meshing point (ε α – 1 point), and the gear pair enters the single tooth meshing state, and the meshing force is equal to the tooth force. Until the next theoretical meshing point (point 1), the tooth pair 3 starts to mesh, and the gear pair enters the double tooth meshing state again.

The peak value of dynamic tooth force is a point in Fig. 1 (a), which is caused by the tooth pair 1 out of meshing and occurs near the pitch circle of tooth pair 2. At this time, the gear pair is in single tooth meshing. The peak value of the dynamic meshing force is at point B in Fig. 1 (a), which is caused by the meshing impact of the teeth on 3. At this time, the gear pair is in double tooth meshing. It can be seen from Fig. 1 (a) that the peak value of dynamic meshing force is larger than that of dynamic tooth force. Dynamic tooth force is the actual dynamic load of a single tooth, which can be used for gear strength check. The dynamic meshing force is the sum of the forces of all the meshing teeth of a gear pair, which can be used for strength check of gear shaft and bearing and system dynamics analysis. Both dynamic meshing force and dynamic tooth force are called gear dynamic load. Figure 1 (b) compares the dynamic load coefficients of each gear pair calculated by the dynamic tooth force and the dynamic meshing force respectively. It can be seen that there is a great difference between the two. Attention should be paid to the difference in application.

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