Quarter-car model is examined here from a new viewpoint to consider tyre-road separation. A nonlinear model is formulated using nondimensionalisation methods which would incorporate the tyre-road discontinuities to minimise the number of parameters and generalise the analysis. The investigation of the frequency responses and fraction of the separation time has been sensitively implemented. The separation dynamics are numerically simulated to identify which values of suspension characteristics can postpone and avoid the contact-free phenomenon, which results in eliminating the potentially dangerous oscillation. Converting between the nondimensional and dimensional formulations is beneficial for investigating the tyre separation with a wide variety of vehicle suspensions. Comparing the outcomes of traditional models without separation modelling demonstrates the proposed approach has achieved more precise frequency responses that contain more realistic system dynamics. Finally, model validation is carried out in the MSC-ADAMS medium.