Static and Coulomb frictions are extensively used in automotive mechanical systems to control the synchronization between two shafts or two axles. Clutches, gearboxes and limited-slip differentials are some examples. This paper proposes a method for the efficient simulation of a wide class of automotive mechanical systems with static and Coulomb friction phenomena. The modelling approach is based on the port-Hamiltonian representation of the dynamic systems and the computation of the friction forces requires only the zero crossing detection. A slight approximation allows faster and sufficiently accurate simulations even without an accurate zero crossing detection. The proposed approach has been used to simulate the behaviour of a complex gearbox provided by some high level farm tractors.