Dynamic analysis of a reverse-idler gear pair with concurrent clearances

Abstract Concurrent non-linearities may be defined as multiple local non-linearities which are linked kinematically to an inertial body in a multi-degree-of-freedom mechanical system. A practical example is found in the reverse-idler gear system which may rattle or undergo vibro-impacts under very light mean loads. Since very little is known about such torsional systems with two or more clearances, an analytical investigation has been undertaken to gain a better understanding of the resulting non-linear behavior. New coupling and scaling procedures are developed to reduce computational difficulties. In an attempt to quantify the average impact behavior in the concurrent gear meshes, the concept of effective stiffness is introduced and calculated from the non-linear response in several ways. Response-variant natural frequencies obtained from these effective stiffnesses are then used to study the spectral interaction in a system in which two non-linearities are present simultaneously. Results of the Galerkin method (multi-term harmonic balance) match well with predictions of the numerical integration techniques. Both methods are used to study periodic responses, while the Floquet theory is used to study the stability of such solutions. Techniques for embedding the concept of effective stiffness into each method are also examined. Although the emphasis is on periodic steady state solutions, quasi-periodic responses have been briefly examined due to their prevalence in a system with concurrent nonlinearities.