A torsional model of multi-stage gears – influence of external excitations and tooth shape modifications

¹ INSA Lyon, LaMCoS, 18-20 rue des Sciences, 69100 Villeurbanne, France
² Hispano-Suiza, 18 Boulevard Louis Seguin, 92700 Colombes, France

^a Corresponding author: Philippe.Velex@insa-lyon.fr

Received: 18 May 2015
Accepted: 6 November 2015

Abstract

In this paper, a torsional dynamic model of multi-stage idler spur and helical gears is presented which combines mesh internal excitations and external forcing terms such as time-varying external torque. Each contact line in the various base planes is discretized in elemental cells which are all attributed a time-varying mesh stiffness element and initial separation to account for tooth shape deviations from ideal involute flanks. The mesh stiffness functions are estimated from the formulae of Weber & Banaschek and their relative phasing is determined based on gear geometry and relative positioning. The corresponding non-linear differential system is solved by combining a Newmark’s numerical time-step integration scheme and a normal contact algorithm. A number of simulation results are presented on the combined influence on dynamic tooth loads of errors and shape deviations along with external excitations.