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Further investigation of wheel climb initiation: Three-point contact

In previous research, a set of nonlinear algebraic kinematic constraint equations were developed that describe the configuration of a wheelset in contact with a track at two distinct points. In such a case of two points of contact, a simplified wheelset model that has the lateral displacement and angle of attack as the independent variables can be developed. In the current investigation, this approach is extended to the new case of a wheelset in contact with a tangent track at three distinct points. The solution of this three-point contact problem requires specifying the wheelset angle of attack only. This wheelset configuration is significant in derailment investigations because it is a possible configuration at the initiation of a wheel climb derailment. In order to study this wheel climb initiation configuration, a set of nonlinear kinematic constraint equations is developed as a function of the wheelset angle of attack and solved for the unknown system coordinates and contact surface parameters using an iterative Newton–Raphson algorithm. The wheelset angle of attack during wheel climb derailments can be determined forensically at the derailment site, making this approach of practical significance. It is shown in this investigation that the system configuration can be fully defined for wheel climb derailment initiation, which allows for the investigation of various derailment parameters such as the wheel–rail contact angle. It is then reinforced in this study that the wheelset flange angle, which is the angle between the tangent to the wheel surface at the contact point and the wheelset axle, is not representative of the wheel–rail contact angle, which is the angle between the tangent to the contact surfaces and the lateral common tangent to the two railheads; this distinction can only be demonstrated through full definition of the system configuration that accounts for the wheelset roll angle. This investigation therefore calls into question the Nadal L / V derailment limit as well as any investigation that chooses to neglect the wheelset orientation or the effect of such orientation on the wheel/rail contact geometry. This new formulation is validated and supported using a three-dimensional fully nonlinear unconstrained multibody system wheel climb derailment model recently proposed in a previous study. Using this model, new results demonstrate that initiation of the wheel climb motion is correctly predicted using proper geometry definitions in the derailment criteria, whereas previous results demonstrated such motion was not correctly predicted using the geometry definitions used by Nadal. This investigation is not intended as a derailment criteria proposal, but rather as support and rationalization for the use of correct contact geometry in derailment investigations. This investigation reiterates the important result that the Nadal L / V derailment limit is not conservative, and demonstrates that, with proper formulation, more accurate and justifiable derailment criteria can be developed.