Comprehensive meshing stiffness of double teeth of variable hyperbolic arc gear

After the single tooth meshing stiffness is obtained, the double tooth comprehensive meshing stiffness curve can be obtained by the method of translation and superposition of the single tooth meshing stiffness curve according to the coincidence degree of the variable hyperbolic arc gear. The variable hyperbolic arc gear is an involute tooth profile on the middle section, and the point on the middle section contacts first when it enters the mesh, so the formula of involute spur gear to calculate the coincidence degree can be used to calculate the coincidence degree of variable hyperbolic arc gear. According to the calculation formula of involute spur gear coincidence degree, the coincidence degree of variable hyperbolic arc gear can be calculated as 1.725.

By moving the single tooth time-varying meshing stiffness curve n Δ α to the left and right, the double tooth comprehensive meshing stiffness curve of variable hyperbolic arc gear pair can be obtained, as shown in the figure

Where, φ is the angle of a gear tooth of the driving wheel from entering meshing to exiting meshing.

It can be seen from the figure that in the double tooth meshing area, the comprehensive meshing stiffness of the double tooth is about twice that of the single tooth, which conforms to the expression in the formula, and indirectly verifies the correctness of the finite element method for calculating the stiffness of the variable hyperbolic arc gear and the accuracy of the calculation results.

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