Self-excited torsional vibrations in the wheelset axle may lead to undesired phenomena, such as passengers’ discomfort, wheel polygonization or press-fit instability. The main cause is a sudden adhesion change in the wheel-rail contact, which modifies the contact energy. Measurement data from three different vehicle types including more than 30,000 torsional vibration events were analyzed to develop a new transient creep force model. This model uses only a single degree of freedom, which is later related to a physical quantity, i.e., frictional power. It requires a low computational effort and allows a straightforward statistical analysis of the results. Herein, the model is applied to one full dataset. It provides a creep curve for each point in time. Thus, it reproduces all the contact energies and the wheel-rail adhesion coefficients during a transient adhesion cycle. The results show a good agreement to measured data. The developed model can be used to simulate the torsional vibrations, it provides a physical-based explanation of the involved phenomena occurring in the wheel-rail contact, reduces time and cost of the measurement campaigns, and improves the assessment of torsional vibration events in the design stage.