Half Width & Phasing Method for reduction of Instabilities of Mesh Stiffness Variation in Two-Stage Gear

Abstract

ABSTRACT Parametric instabilities alongside severe vibration within gear systems are as due to variation in mesh stiffness, the meshing tooth stiffness changes with changes in the number of contact teeth. Two-stage gear trains are used in the investigation of the operation conditions resulting in parametric instability, among them idler gear alongside configurations of the countershaft. Two gear pairs with half the breadth as the one of the primary gear pair are used in replacing each of the traditional two-mesh gear pairs. An investigation is done into the primary, secondary, as well as combination instabilities. An analysis is conducted on the impacts of the parameters of the mesh stiffness, among the frequency of mesh, amplitudes of stiffness variation, and contact ratio alongside mesh phasing on such instability. Design formulas have been developed for the case of mesh stiffness variations having rectangular waveforms for regulation of the instability regions through adjustments to the mesh phasing as well as contact ratios. Numerical solutions are applied in the validation of the analytical findings where it is noted that the substituted four gear pairs having proper mesh stiffness parameters remove the instability regions of a traditional two-stage gear train.