Dynamics of gear meshing: stiffness evaluation and vibration

In the present paper we are concerned with vibration problems in gears mesh. A 2D model is developed,which is able to create the teeth profile for the contact profile and the tooth fillet for a very large classes of 2Dgears. A single degree of freedom model is developed using lumped masses. The stiffness of the gears is cal-culated using the finite element code (MSC MARC) from different meshing position of two identical gears,using contact elements for the teeth interaction. This approach allows to evaluate accurately the variableglobal stiffness, which depends on the gear position, materials and teeth geometry. The variable stiffnessgives rise to a parametric excitation, which is periodic; therefore it gives rise to a Mathieu type instability. AFourier series of the variable stiffness is obtained from the numerical data evaluated with the FEM model.The dynamic model is analyzed by means of direct simulations and ontinuation techniques; the latter one areable to follow periodic responses and detect instabilities and dynamic bifurcations.