Torsional vibrations in differentials of Rear Wheel Drive vehicles are of major importance for the automotive industry. Hypoid transmissions, forming the motion transfer mechanism from the driveshaft to the wheels, suffer from severe vibration issues. The latter are attributed to improper mesh between the mating gear flanks due to misalignments, variation of contact load and shifting of the effective mesh position. For certain operating conditions, the gear pair exhibits high amplitude motions accompanied with separation of the mating surfaces. Ultimately, single or even double-sided vibro-impact phenomena evolve, which have been related to noise generation. This thesis attempts to address these issues by effectively analysing the dynamic behaviour of a hypoid gear pair under torsional motion. The case study considered is focused on a commercial light truck. The major difference of the employed mathematical model to prior formulations is the usage of an alternative expression for the dynamic transmission error so that the variation of contact radii and transmission error can be accounted for. This approach combined to a correlation of the resistive torque in terms of the angular velocity of the differential enables the achievement of steady state, stable periodic solutions. The dynamic complexity of systems with gears necessitates the identification of the various response regimes. A solution continuation method (software AUTO) is employed to determine the stable/unstable branches over the operating range of the differential. The ensuing parametric studies convey the importance of the main system parameters on the dynamic behaviour of the transmission yielding crucial design guidelines. A tribo-dynamic investigation aims at expanding the dynamic model from pure dry conditions to a more integrated elastohydrodynamic (EHL) approach. Analytical and extrapolated solutions are applied for the derivation of the film thickness magnitude based on the kinematic and loading characteristics of the dynamic model. The temperature rise is governed mainly by conduction due to the thin lubricant films. The generated friction is also computed as a function of the viscous shear and asperity interactions. The effective lubricant viscosity is greatly affected by the pressure increase due to the resonant behaviour of the contact load. The final part of this work is involved with a feasibility study concerning the application of Nonlinear Energy Sinks (NES) as vibration absorbers, exploiting their ability for broadband frequency interaction. Response regimes associated with effective energy absorption are identified and encouraging results are obtained, showing the potential of the method.

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