This paper represents a mathematically rigorous and technically realistic effort of describing the idle rattle phenomenon. The two-degree-of-freedom model constitutes a relatively simple, analytical tool suitable for design and application purposes. It also introduces a new and more practical formulation of the rattle threshold. The model describes elastic-plastic collisions of meshing gears and splines, and allows for multi-harmonic excitation.
The mathematical model not only consists of differential equations of gear and spline oscillations, but also equations of collisions and separations of meshing elements. When the impacts occur, a special algorithm is used for determining energy of collisions. The model is based on the fact that impact energy levels directly correspond to idle rattle noise levels.
The computer simulation presented in this paper is to meet the pressing need for an analytical and computer design methodology for drivelines and their components. Powertrain systems are not only to accommodate rotating motion, but also to control and isolate torsional vibrations.
Using a specially developed algorithm, the computer program solves nonlinear differential equations and estimates collisions of meshing gears and splines during rattle. The program is capable of calculating energy of impacts over a large time interval during steady-state motion of the system, identifying the rattle threshold in terms of design parameters, and determining the behavior of the system during rattle.
The simulation program has been used to conduct basic studies of the rattle phenomenon. Some important results of this analysis are discussed in this paper.