Multibody Modeling of Gear Dynamics With 3-D Contacts: Advances and Challenges

Abstract

This paper describes the application of modeling of multibody systems to high-precision mechanical gears. Although the context of the paper is applied in nature, the objective is to present recent advances in computer-aided modeling of multibody systems with three-dimensional (3-D) contacts and to explore the limits of the technology, theory, and methods. Gear systems are traditionally modeled as single dimensional object with a simple transformation ratio. However, when we are interested in high precision gear systems, all joints and flexibility of gear shafts bearings are accounted for in the model. In this paper we discuss challenges in using recent advances in computer-aided multibody modeling (CAMM) with 3-D contacts applied to the design of a steering gear system. These advances in CAMM have made it possible to produce detailed dynamic simulation of constrained multibody motion in a much shorter time than the traditional Finite Element approach. Extracting position and velocity information from simulation of multibody models using CAMM is routine work today save for the most complex systems. However, extracting information about contact force between rigid bodies during impact subsequent rolling and sliding motions is a more challenging problem. This paper discusses these challenges and presents possible numerical and modeling solutions. Gears move in three-dimensional space, their surfaces undergoing continuous contact and separation; we distinguish between large dominant motion and microscopic motion along constraints axis. In an effort to understand motion of steering gear at the microscopic level, we modeled gears as multibody systems with their surfaces in a dynamic state of contact and separation. These models capture the dynamics of gears traveling distances of around 50 microns in less than 10 milliseconds. We applied newly developed analytic, numeric, and computer-aided tools to gain insight into gear forces, specifically, those forces responsible for the inception of mechanical knock in steering gear. The results provided a 3-D view of the sequence of events of gears with their surfaces in motion, in sudden contact, sliding, and the resulting force generation. The models include effect of friction on impact mechanics of the gears. First we briefly present a discussion of the state-of-knowledge in CAMM with three-dimensional surface contacts. Computer aided engineering requirements necessary to solve the problem are discussed together with computer hardware, software, and analysis methods that are necessary for successful modeling of multibody gear systems with 3-d contacts. We finally present a model of a generic gear system that demonstrates both the potential and the limitations of the current technology.