Combining Finite Element Analysis and Analytical Modelling for Efficient Simulations of Non-Linear Gear Dynamics

Abstract

Although gears have been used in mechanical industry for a long time and first systematic research activities, aimed at understanding gear meshing, started in the '50s, still nowadays a lack of accurate description for several physical phenomena represents a limitation for transmission design. One of the main causes of such limitations is the threedimensional (3D), local and non-linear nature of contact problems. Given the complexity of these problems, a variety of modelling techniques with different levels of fidelity and required computational effort have been set up. Among the available methodologies, analytical modelling, which has been developed for a vast variety of applications from the early days of gear dynamics research, still attracts the interest of researchers thanks to the low computational requirements and to the capability to efficiently describe specific phenomena. Among analytical models, one-dimensional (1D) description aims at studying the torsional gear vibrations around the rotational axes and can be used to simulate either gear whine or gear rattle phenomena. The aim of this paper is to illustrate a numerical approach, based on 3D (Finite Element) FE simulations, to estimate the mass and inertia properties of a 1D gear pair model. The proposed approach is based on pre-strained modal analyses, carried out on the 3D FE model of a pair of meshing gears, from which the variable meshing stiffness and modal mass values in a given system configuration are derived and used to calibrate the equivalent 1D model. An application example of the proposed method is provided by analyzing a pair of identical spur gears, for which the 1D model is created and used to estimate the dynamic TE at different rotation speeds and under constant external load in steady-state conditions.

Multiobjective Design Optimization of Lightweight Gears

“…Lumped-parameter (LP) modeling [16][17][18][19][20] aims to (semi)analytically lump mechanical and contact properties of a system through the most relevant, yet few, parameters (e.g., meshing stiffness, damping, and inertias) and states (e.g., angular positions and velocities). It allows for efficiently representing the overall load distribution and approximating the system-level statics/dynamics with simple and quick-to-solve equations.…”