PREDICTION AND MITIGATION OF THE GROWTH OF WHEEL POLYGONISATION

Wheel polygonisation is a significant railway degradation phenomenon that can increase wheel–rail forces, vibration, noise and maintenance costs. Although extensive numerical, field and experimental studies have investigated its formation, direct analytical prediction of polygon growth remains limited. This paper formulates wheel polygonisation as a regenerative wear instability and derives closed-form expressions for the growth rate, dominant order and amplitude evolution of circumferential wheel-profile harmonics. A modal representation of the coupled wheel–rail system is combined with rolling-contact, wear and regenerative time-delay mechanics. In this formulation, an initial wheel-profile perturbation excites dynamic contact forces, which produce a non-uniform wear response that can reinforce the perturbation over successive wheel revolutions. The model is verified using four published laboratory, roller-rig and field cases covering a wide range of speeds, polygon order and metro to high-speed operating conditions, with generally less than ±2% deviation between predicted and measured polygonisation growth amplitudes. The results support the interpretation of polygonisation as an exponential surface-evolution instability, with growth governed by wheel–rail modal dynamics, wear sensitivity, operating speed and the regenerative time-delay mechanics. The model predicts instability onset, dominant polygon orders and measured growth trends across the investigated operating conditions and also reveals and quantifies the mechanisms of suppressing polygon growth such as via speed control. For instance, for a high-speed train case, the model reproduces the suppression of detectable polygon growth following a speed reduction from 250 to 200 km/h, corresponding to a predicted fourfold reduction in exponential growth rate. Sensitivity analysis identifies wear reduction, modification of the relevant modal response, and control of mean speed or speed variation as the most effective mitigation routes. The verified model provides a computationally efficient (> 6 orders of magnitude faster than numerical simulation) tool for predicting, understanding and mitigating wheel polygonisation while offering new physical insight into the exponential growth mechanisms responsible for this important surface-evolution instability including for potentially analogous phenomena such as fifth octave rolling mill chatter, milling chatter and rail corrugations.