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6 CHAPTER 2 FLANGE CLIMB DERAILMENT CRITERIA The flange climb derailment criteria proposed in this tions. The Nadal values for contact angles of 63 and 75 section include the wheel L/V ratio limit and the flange- degrees are specified in Figure 2.1 with values of 0.73 and climb-distance limit. Details of the research to develop these 1.13, respectively. If the maximum contact angle is used, criteria are reported in Appendices B and C. These criteria Equation 2.3 gives the minimum wheel L/V ratio at which were developed based on computer simulations of single flange climb derailment may occur for the given contact wheelsets. The wheel profiles used in the simulations were angle and friction coefficient . Clearly, wheels with low obtained from the transit system survey. These profiles were flange angles and high friction coefficient have a low L/V applied on both light rail and rapid transit vehicles with ratio limit and a higher risk of flange climb derailment. flange angles ranging from 60 degrees to 75 degrees and Equation 2.1 states that if the AOA is larger than 5 mrad flange lengths ranging from 0.395 to 0.754 in. or the AOA cannot be determined (which is usually the case The proposed criteria have been validated by flange-climb during on-track tests), the limiting L/V value is the Nadal test data using the TLV. This section provides an example of value determined by Equation 2.3. If the AOA can be deter- applying the criteria to a passenger car test. The limitations mined with an AOA measurement device or from simulation of the proposed criteria are also discussed. results and its value is less than 5 mrad, the limiting L/V ratio can be less conservative than the Nadal value (Equation 2.2). Equation 2.2 was developed to account for the effects of 2.1 WHEEL L/V RATIO CRITERIA increased flange climb L/V with small AOAs. Figure 2.2 shows a comparison of Equation 2.2 and the Nadal value for The L/V ratio criteria proposed for transit vehicles are a wheel with a 63 degree flange angle. stated as follows: The study included in Appendix B indicates that one rea- (1) if AOA 5 mrad or if AOA is unknown, son independently rotating wheelsets (IRW) tend to climb the rail more easily than conventional solid wheelsets is that L < q0 , (2.1) the coefficient of friction on nonflanging wheel has no effect V on the flanging wheel. Therefore, the Nadal L/V limit is accurate for IRW but can be conservative for the wheelsets (2) If AOA < 5 mrad of solid axles. The wheel L/V ratio required for flange climb for solid axles increases as the increased friction coefficient L 0.43 < q0 + , (2.2) on nonflanging wheel. If the friction coefficient on the non- V AOA + 1.2 flanging wheel approaches to zero, the L/V ratio limit for the solid axle wheel would be the same as that for IRW. where q0 is the Nadal value that is defined by Equation 2.3 and Figure 2.1 and AOA is wheelset AOA in mrad. The Nadal single-wheel L/V limit criterion (1), proposed 2.2 FLANGE-CLIMB-DISTANCE CRITERIA by M. J. Nadal in 1908 for the French Railways, has been used throughout the railroad community. Nadal proposed a In practice, a flange climbing derailment is not instanta- limiting criterion as a ratio of L/V forces: neous. The L/V ratio has to be maintained while the climb- ing takes place. If, for example, the lateral force returns to L tan( ) - = (2.3) zero before the flange has reached the top of the rail, the V 1 + tan( ) wheel might be expected to drop down again. When the flange contacts the rail for a short duration, as may be the where is the friction coefficient at the wheel/rail contact case during hunting (kinematic oscillations) of the wheelset, surface and is the wheel/rail contact angle. the L/V ratio might exceed Nadal's limit without flange Figure 2.1 shows the Nadal values for different wheel/rail climbing. For that reason, the flange-climb-distance criteria maximum contact angles and friction coefficient combina- were developed to evaluate the risk of derailment associated