Nonlinear Vibration of Gears With Tooth Surface Modifications

Abstract

This work provides an analytical solution for the nonlinear vibration of gear pairs that exhibit partial and total contact loss. Partial contact loss is where parts of contact lines lose contact although other parts remain in contact. The gear tooth surface modifications admit an arbitrary combination of profile and lead modifications. Modifications are a source of partial contact loss. The analysis also applies for total contact loss. Unlike models in the literature that are excited by static transmission error or time-varying mesh stiffness, the excitation and the nonlinearity are not a priori specified. Instead, the force-deflection function of the gear pair is provided by an independent source, such as a finite element model or Hertz contact formula. The manipulation of the single-degree-of-freedom oscillator equation of motion yields the excitation and the nonlinearity that arise from Fourier and Taylor series expansions of the force-deflection function. These expansions capture the essential contact behavior that includes tooth profile and lead modifications as well as the bending and shear flexibility of the gear teeth and gear blanks. The method of multiple scales gives the steady-state dynamic response in terms of a frequency-amplitude relation. Comparisons with gear vibration experiments and simulations from the literature that include spur and helical gears with tooth profile and lead modifications verify the method.