The dynamic modelling of a spur gear in mesh including friction and a crack

To improve the current generation of diagnostic techniques, many researchers are actively developing advanced dynamic models of gear case vibration to ascertain the effect of different types of gear train damage. This paper details a simplified gear dynamic model aimed at exploring the effect of friction on the resultant gear case vibration. The model incorporates the effect of variations in gear tooth torsional mesh stiffness, developed using finite element analysis, as the gears mesh together. The method of introducing the frictional force between teeth into the dynamic equations is given. The comparison between the results with friction and without friction was investigated using Matlab and Simulink models developed from the differential equations. The effects the single tooth crack has on the frequency spectrum and on the common diagnostic functions of the resulting gearbox component vibrations are also shown. (C) 2001 Academic Press.