On the modelling of spur and helical gear dynamic behaviour

TL;DR

This paper introduces fundamental concepts and analytical models for the dynamic behavior of spur and helical gears, emphasizing transmission errors and simplified analytical results over complex numerical simulations.

Contribution

It presents a set of analytical models for gear dynamics, including lumped and thin-slice approaches, and discusses the role of transmission errors in gear behavior.

Findings

Analytical models clarify gear dynamic phenomena.

Transmission errors significantly influence gear vibrations.

Extensions to continuous models are proposed.

Abstract

This chapter is aimed at introducing the fundamentals of spur and helical gear dynamics. Using three-dimensional lumped models and a thin-slice approach for mesh elasticity, the general equations of motion for single-stage spur or helical gears are presented. Some particular cases including the classic one degree-of-freedom model are examined in order to introduce and illustrate the basic phenomena. The interest of the concept of transmission errors is analysed and a number of practical considerations are deduced. Emphasis is deliberately placed on analytical results which, although approximate, allow a clearer understanding of gear dynamics than that provided by extensive numerical simulations. Some extensions towards continuous models are presented.