Rigid-elastic modeling of meshing gear wheels inmultibody systems
Received: 9 September 2005 / Accepted: 3 May 2006
C Springer Science+Business Media B.V. 2006
Abstract In many applications in mechanical engineering, gear wheels are used to transmitpower between rotating shafts and, therefore, the ability to incorporate them into multibodysystems and to simulate contact between them has become an essential topic in multibodydynamics.
However, in some applications gear wheels may not be considered as being perfectlyrigid. Due to the effect of contact forces there occur relevant deformations in meshing teethand it is required for a high quality of the analysis to introduce some elasticities in themodel of meshing gear wheels. Therefore, in this work elastic elements between the teethand the body of each gear wheel are considered. This approach is especially well suited formultibody systems since it is a compromise between a totally rigid model and a fully elasticmodel allowing the simulation of large motions with many revolutions while still important elasticities are considered. The teeth and the body of each gear wheel are still modelled as being rigid but they are connected to each other by elastic elements. In doing so, an efficien tand physically motivated algorithm is described and implemented in order to find the effects of multi-tooth contact as well as backlash and left and right hand side contact of the meshing teeth. Some examples compare the simulation results of rigid, partially elastic and fully elastic models.
Keywords :Tangentially movable teeth . Meshing teeth . Multiple contact . Elastic gears .
Gear contact modeling . Multibody geared systems
1. Introduction
Contact modeling of gear wheels has some special difficulties which arise, e.g., from the nonlinear behavior of tooth stiffness, backlash, gear geometric parameters, see e.g. [5, 6, 21]. There exist a large number of researches which focus on modeling of meshing gear wheels using analytical approaches, see e.g. [5, 8–10]. In most of these contributions, the equation of motion for one gear pair is formulated. These formulations are basically functions of the gear geometry and some material parameters like stiffness and damping coefficients. For simplicity, contact between each gear pair is modeled through a spring-damper element which acts tangentially to the base circle of each meshing gear. In using such formulations,some important features of contact of gear wheels, such as the effect of involute meshing teeth, nonstandard teeth or multiple contact are often not taken into account and, therefore,they can not be used for the general case of contact between gear wheels. Instead, numerical approaches can handle realistic cases of contact modeling with all difficulties involved by introducing effective parameters which have a great effect on the dynamical behavior.