Dynamic analysis of gear pairs with a gross motion effect using the dynamic stiffness matrix method

A continuum approach using the dynamic stiffness matrix (DSM) method (DSMM) is presented for the dynamic analyses of spur gear pairs incorporating the gross motion effect. A continuum dynamic model of spur gears was formulated based on the dynamic stiffness using the non-uniform Timoshenko beam theory. A systematic DSM for a gear pair was assembled including the elemental DSMs of two mating gears and non-linear Hertzian contact stiffness. The DSMs were updated at each computing step to reflect the time-varying property due to the moving mesh points. A bisection procedure was used to calculate the natural frequencies as the systematic DSM of the gear pair became singular. The mass and stiffness matrices were calculated by taking a numerical derivative of the systematic DSM. Finally, the gear dynamic responses caused by the external torque and gross motion excitation resulted. The effect of gross motion is also discussed.