Investigation of normal force and stress at the wheel-rail interface: the validity of hertzian theory in flange climbing scenarios

To predict vehicle behaviour and track degradation, the railway industry relies on Multibody System (MBS) simulations, utilising Hertzian contact mechanics for computational efficiency. However, Hertzian theory assumes a non-conformal, elliptical contact area, making its validity questionable during severe curve negotiation where the flange tightly wraps around the gauge corner. This thesis systematically investigates this theoretical boundary, evaluating how Hertzian approximations distort predicted forces and stresses under extreme conditions. To isolate fundamental kinematics, a multibody model of a Bo'Bo' locomotive was developed in the GENSYS environment. The vehicle was simulated negotiating a 1400-meter circular curve based on the VUZ Velim test circuit. Parametric sweeps of vehicle speed and static axle load were executed over an idealised track to force the wheelset into varying states of cant deficiency and flange engagement. The dynamic outputs reveal that vehicle speed is the absolute dominant parameter dictating contact interface volatility. While heavier axle loads provided a mild stabilising effect via enhanced gravitational stiffness, severe cant deficiency violently thrust the outer wheelset laterally. Crucially, during these highly conformal flange engagements, the built-in Hertzian algorithm mathematically broke down. Unable to resolve the elongated geometry of the physical contact, the software artificially compressed the calculated area, resulting in a physically unrealistic spike in the predicted maximum normal stress. By demonstrating that high-speed stress peaks at the flange root are heavily computationally inflated, this study provides vital context for railway engineers. Recognising this limitation allows for the recalibration of predictive wear models and derailment risk assessments, preventing overly conservative speed restrictions while highlighting precisely where advanced non-Hertzian algorithms become strictly necessary.