3D Dynamic Modelling of Flexible Gear-Bar Mechanical Systems: A Specific Finite Element Approach

Abstract

Abstract A mechanical system considered here consists of gear, bar, shaft and bearing. The objective of the study is to develop a unified and systematic procedure to build a dynamic model for such complex mechanical systems taking into account as many as factors. These factors include the flexibility of all components and gear transmission errors. Existing literature provides a separate studies of dynamic behaviors on gear transmissions and multi-body systems (usually excluding gear transmission or at most considered as two disks with pure rolling). In this paper we propose to apply a specific finite element theory that has been widely successful in multi-body dynamics. This specific finite element theory promises that a dynamic model will be systematically established provided that an appropriate type of finite element is defined which of course should represent the dynamic features of a real world system. For this reason, we develop a new type of finite element that can describe the transmission behavior of a pair of gears with parallel axes. This new type of finite element is 3D, therefore we can demonstrate to build a dynamic model for such complex systems with consideration of rotational, transverse and axial deformations and gear transmission errors. A case study is provided.