The dynamics of automotive differentials have been studied extensively to improve their efficiency and additionally, in recent years, generated noise and vibration. Various mathematical models have been proposed to describe the contact/impact of gear teeth pairs. However, the influence of vehicular cruising speed on the resisting torque has not been considered in sufficient detail. This can lead to unrealistic predictions with regards to loss of contact of teeth pair, a phenomenon which leads to NVH issues. The current work presents a torsional model of a hypoid gear pair. The resisting torque is a function of the traction force and aerodynamic drag, whilst the vehicle is cruising at nominally constant speed. The pinion input torque is derived through assumed instantaneous equilibrium conditions. In this approach, realistic excitation capturing the vehicle's driving conditions is imposed on the dynamics of the hypoid gear pair. The dependence of the gear pair meshing stiffness on the torque amplitude is also considered using Tooth Contact Analysis (TCA). As a result the natural frequency of the system is subject to condition-based variations. The dynamic response of the system is presented at various cruising speeds. Frequency response spectra are derived to illustrate the limiting speed when gear flank separation occurs. The novelty of this model is related to the accurate prediction of gear teeth impacts, leading to the appearance of the axle whine phenomenon. The validation of the numerical findings with published experimental data is part of the planned future work.