A Parameter-Driven Methodology of Wheel Flat Modeling for Wheel–Rail Impact Dynamics

A wheel flat is a typical wheel defect that significantly impacts the wheel–rail system, posing substantial challenges to vehicle operation safety. In the existing literature, the wheel flat plane model does not account for the contribution of the width direction to the impact response and thus cannot accurately reveal the wheel–rail contact state with a flat. This paper systematically proposes a three-dimensional analytical model that considers multiple worn stages and constructs a spatial complex surface reconstruction model for flats based on NURBS technology. A vehicle–track coupled dynamics model, considering the geometry of the flat, is established to investigate the effects of flat geometry on the wheel–rail impact response and contact relationship in detail. The results show that in the subcritical regime, the wear degree of the flat predominantly affects the impact force, while in the transcritical regime, both the wear degree and velocity together determine the magnitude of the wheel–rail impact force. As the wear degree increases, the moment of wheel lateral jump occurs earlier. The spatial modeling method for flats proposed in this paper offers a novel technical approach for accurately simulating the dynamic behavior of wheel–rail contact when a flat is present.