Abstract
This paper did a theoretical study on the Nadal’s L/V ratio. The analysis is based on a mechanical model of an object sliding on an incline (or slope), which is widely used in college physics. The key is that the direction of frictional forces is always opposite to the direction of the motion of the sliding object. Therefore, there are two directions (upward or downward) for the frictional forces between the object and incline depending on the states of motion of the object. Thus, there must be two L/V ratios for the object sliding on the incline for the same reason. The theoretical demonstration shows that Nadal’s L/V is the same with the L/V which governs the downward motion of the object on the incline, because the direction of frictional force between the object and the incline is set to be upwards in the derivation of the Nadal’s L/V. Thus, Nadal’s L/V is for the object going down the incline. A detail examination was performed on the Nadal’s L/V for some typical configurations, such as the critical angle; the zero and 90 degrees angles, further proving that the Nadal’s L/V is not for an object going up on the incline, thus cannot be used as the criterion for wheel climb. A new L/V ratio was created by setting the direction of frictional force downwards to simulate the object going up on the incline, and was named as Huang’s L/V. Wheel flange/rail contact produces frictional forces between them to consume the pulling power, like a braking to slowdown wheel rotation. Thus, wheel climb is only 1/3 of the whole story of wheel flange/rail contact. The other two are 1). A retarder derailment mode is created by the braking and 2). A braking, large enough, will cause a wheel locked. Therefore, there are two derailment modes with wheel/flange rail contact, wheel climb modes and retarder mode. A method to determine which mode was initiated was demonstrated in the paper. Angle of Attack (AoA) introduces a complicated scenario for wheel climb calculations. It is almost impossible to determine a correct L/V ratio under AoA.
Highlights
Nadal’s Limit L/V ratio [4] has been introduced to the railroad industry for a long time, and has been widely used to do wheel derailment analysis
Where L and V are the lateral force and vertical force exerted on truck wheel respectively, α is the flange angle of the wheel, and μ is the friction coefficient between wheel and rail
Based on the L/V ratios from various flange angles and friction coefficients, some researchers and organizations, such as AAR (Association of American Railroads), have adopted L/V=1 as the maximum value for a railroad truck wheel stability. This Nadal’s Limit L/V ratio has been used as the criterion to railroad derailment in The United States of America and other countries
Summary
Nadal’s Limit L/V ratio [4] has been introduced to the railroad industry for a long time, and has been widely used to do wheel derailment analysis. It can be found, in literature, that researches and tests have been done on Nadal’s Limit by many scientists and organizations [1, 6, 9, 1-13]. This Nadal’s Limit L/V ratio has been used as the criterion to railroad derailment in The United States of America and other countries. The real meaning and the boundary of Nadal’s Limit L/V ratio will be understood thoroughly, and a truck wheel derailment criterion can be derived
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