In the double-tooth auxiliary meshing area, according to the corresponding relationship of the meshing position, the meshing rigidity of the two single-tooth pairs is superimposed, and the meshing rigidity of the gear running process should be obtained. This calculation is relatively simple, but it is quite different from the actual working conditions. This conventional algorithm of meshing stiffness assumes that the gear meshing stiffness is a periodic rectangular wave shape.
The state space form of the gear vibration equation describes the transient and dynamic response problems. Therefore, the change of the gear meshing stiffness as one of the input conditions is very important, and it is the key to analyzing the dynamic meshing characteristics of the gear. The change of gear meshing stiffness is affected by many factors, such as the tooth surface load of the gear pair and the load distribution between the gear teeth. This naturally includes the gear tooth error, the tooth shape modification, the gear tooth elastic deformation, and the gear coincidence. Degree and positional changes of the meshing contact points, and the like. The real solution of this model needs to be assisted by the principle of conjugate surface, and the solution process is very complicated. In order to simplify the calculation, it is assumed that the meshing of the gear pairs occurs on the meshing line. As long as the single tooth secondary meshing average stiffness is calculated, the average meshing stiffness of the double tooth pair can be obtained. In this way, at any meshing position, the calculation of the system matrix is ​​simplified to the ratio of the meshing stiffness of the meshing tooth pairs at the position to the average meshing stiffness. In this way, each location is easy to calculate. Once this problem is solved, the equation of state is easy to solve. The calculation flow chart is a logical summary of this solution idea, according to which it is easy to write its computer program.
In general, the stiffness matrix of the gear vibration system is singular, which increases the complexity of solving the gear vibration equation. Therefore, it is necessary to seek to take into account the influence of the gear spoke stiffness without causing the gear vibration equation to solve an excessively complex gear dynamics model. The state space analysis method of modern control theory is used to solve the simplified model of gear dynamics. According to the condition of the periodic solution of the gear vibration equation, the initial state can be directly recursive without repeating this step. Compared with the commonly used methods and numerical methods such as the difference method, it has great advantages. In particular, the selection of those quantities with obvious physical meaning as state variables makes the solution process more intuitive.
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