Calculation of optimum profile modification curve for gear pair based on complex potential method

Abstract

The optimum profile modification curve of a gear pair is usually determined according to the fluctuation minimization of static transmission error (STE). For the calculation of STE, the potential energy method dismisses the correlative tooth deflection induced by gear body elastic coupling effects, and the finite element method requires high calculation cost. In order to simultaneously obtain high calculation accuracy and efficiency, the single tooth deflection is calculated through analytical integration about the Hertz contact pressure based on the conformal map method. The correlative tooth deflection is calculated based on the power series solution of the mixed boundary problem of an elastic annulus. Via combination of deflection compatibility and the force equilibrium condition, a contact analysis model of a spur gear pair is built. Based on the model, the STE is first calculated and compared with the finite element analysis result to verify the model rationality. Then, the optimum profile modification curve which renders constant STE is calculated. For a gear pair with the obtained modification curve, fluctuation of dynamic transmission error also decreases and the optimization effect is verified.

Keywords

Conformal map method power series method complex potential method profile modification static transmission error gear pair

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