Single tooth meshing stiffness of variable hyperbolic arc gear

The comprehensive elastic deformation UN of the pair of gear teeth is extracted by finite element post-processing, and the normal contact force of the gear is calculated by torque formula. The single tooth meshing stiffness of each meshing position can be calculated by the formula.

The single tooth meshing stiffness curve can be obtained by interpolating the stiffness value with cubic polynomial, as shown in the figure. It can be seen from the figure that with the increase of gear (driving wheel) angle, the meshing stiffness curve presents an arch change trend of first increasing and then decreasing, and reaches the peak value when the angle is around 10 °. The reason is: in the process of gear meshing, the comprehensive elastic deformation of the gear changes, while the normal contact force of the gear surface remains unchanged, so the stiffness curve presents the trend as shown in the figure.

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