A rattle index formulation for single and multiple branch geartrains

The paper proposes an analytical procedure for the generalization of the rattle index in any type of ordinary transmission layouts, single or multiple branch, both in idle and loaded conditions. Its definition is obtained by a recursive analytical formulation of the rotational dynamics of gears. Numerical analytical studies are exploited to examine the effectiveness and reliability of the introduced index. Several geartrain layouts are investigated and results show its capability to instantaneously describe the vibro-impact events related to any gear pair of the driveline. Moreover, the general definition is shown to be a proper indicator of the potential presence of mutual interactions between different gear pairs pertaining to the same driveline. The analysis of the results reveals an excellent agreement with the expected behavior of the outlined parameter.