Dynamic behaviour of gearbox transmitting power to milling tool in a milling process application is considered in this paper. The gearbox is subjected to variable cutting torque induced by the milling operation. This variability will lead to fluctuating speed. The dynamic behaviour of the system should be investigated according to this non-stationary operating condition. To achieve this objective, a simple model of motor-gearbox-milling tool system is developed. The influence of variable cutting torque on driving motor speed is taken into account. The gearmesh function which describes the meshing phenomena is modified according to this specific operating condition. Simulations of the dynamic behaviour of the gearbox show a simultaneous frequency and amplitude modulation. These modulations are highlighted using time frequency representation which is necessary to implement so that it is possible to achieve a correct diagnosis of the transmission. Simulations in presence of tooth crack defect confirmed the necessity to implement time frequency techniques to characterize time varying systems.