Analytical and Numerical Dynamic Analysis of Gears in the Presence of Engine Acyclism

A one degree of freedom model is set up which incorporates time-varying mesh stiffness functions and the influence of unsteady input rotations due to engine acyclism. In order to investigate spur and helical gears, a piecewise and a sine function are used to simulate mesh stiffness fluctuations. Contact conditions are considered in order to deal with contact losses and back strikes, i.e., when contacts occur on the back flanks of the teeth. The dynamic response is determined by combining several analytical and numerical techniques. It is shown that acyclism modulations can generate additional response peaks on either side of the main resonance area. This is due to frequency and amplitude modulations between the mesh excitations and the harmonics of the engine rotational speed. The analytical results compare particularly well with those delivered by a time-step numerical integration by Newmark’s method with controlled variable time-step coupled with a contact algorithm. This excellent agreement shows that Newmark’s method can be extended to the dynamic simulation of geared drives with unsteady rotational speeds provided that time-steps are carefully calibrated and readjusted. Finally, the influence of gear geometry (module, tooth number, speed ratio) along with the acyclism parameters (frequencies, amplitudes) is studied and some general trends are presented concerning the resulting dynamic tooth loads.