Application of the Nadal Limit to the prediction of wheel climb derailment is presented along with the effect of pertinent geometric and material parameters. Conditions which contribute to this climb include wheelset angle of attack, contact angle, friction and saturation surface properties, and lateral and vertical wheel loads. The Nadal limit is accurate for high angle of attack conditions, as the wheelset rolls forward in quasi-static steady motion leading to a flange climbing scenario. A detailed study is made of the effect of flange contact forces Ftan and N, the tangential friction force due to creep and the normal force, respectively. Both of these forces vary as a function of lateral load L. It is shown that until a critical value of L/V is reached, climb does not occur with increasing L since Ftan is saturated and the flange contact point slides down the rail. However, for a certain critical value of L/V (i.e. the Nadal limit) Ftan is about to drop below its saturated value and flange climb (rolling without sliding) up the rail occurs. Additionally, an alternative explanation of climb is given based on a comparison of force resultants in track and contact coordinates. The effects of longitudinal creep force Flong and angle of attack are also investigated. Using a saturated creep resultant based on both (Ftan, Flong) produces a climb prediction L/V larger (less conservative) than the Nadal limit. Additionally, for smaller angle of attack the standard Nadal assumption of Ftan = μN may lead to an overly conservative prediction for the onset of wheel climb. Finally, a useful analogy for investigating conditions for sliding and/or rolling of a wheelset is given from a study of a disk in rigid body mechanics.
Application of Nadal Limit for the Prediction of Wheel Climb Derailment
