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9 AOA, because no flange climb can occur if the L/V ratio is lower than the limit ratio. The biparameters criterion is obtained by fitting in the bilinear data range where AOA is larger than 5 mrad. It is conservative at AOA less than 5 mrad due to the non- linear characteristic. The biparameter criterion was derived based on simula- tion results for the new AAR-1B wheel on new AREMA 136-pound rail. It is only valid for vehicles Figure 2.4. Wheel/rail interaction and contact forces on with this combination of wheel and rail profiles. flange tip. Figure 2.5 shows the limiting flange-climb distance defined by the general form of flange-climb-distance crite- enough to resist the fall of the wheel and force the flange tip rion (Equation 2.4) compared to the biparameter criterion to climb on top of the rail. (Equation 2.6) for the combination of AAR-1B wheel and The flange length Len is defined as the sum of the maxi- AREMA 136 RE rail at 10 mrad AOA. The AAR-1B wheel mum flange angle arc length QP and flange tip arc length PO, has a flange angle of 75 degrees and a flange length of as shown in Figure 2.4. 0.618 in. Under this condition, the limiting flange-climb-distance given from the general form of climb-distance criterion is a 2.5 A BIPARAMETER TECHNIQUE TO DERIVE constant of 2.3 ft once the wheel L/V ratio exceeds the Nadal FLANGE CLIMB DISTANCE limit of 1.13 for a friction coefficient of 0.5, as shown by the straight line in Figure 2.5. A biparameter regression technique was also developed to The curve in Figure 2.5 gives the limiting distance crite- derive the distance criterion. The limiting distances derived rion from the biparameter criterion under the same condi- from the biparameter regression technique are more accurate tion. Once the Nadal L/V ratio is exceeded, the distance and less conservative than that defined by the general form limit is the function of the average of actual L/V ratios over of distance criterion presented in Section 2.2.1. However, the the distance that Nadal L/V ratio limit has been exceeded. It derivation must be performed for each specific wheel and can be seen from Figure 2.5 that the biparameter criterion is rail profile combination. An example of derivation of the less conservative than the general form of distance criterion distance criterion, using the biparameter method for the for wheel L/V ratio less than 2.0, especially when the wheel AAR-1B wheel contacting AREMA 136 RE rail, is demon- L/V ratio is just above the Nadal limit (1.13 in this case). In strated in this section. actual tests, sustained wheel L/V ratios greater than 2.0 are In Appendix C of this report, the bilinear characteristic uncommon. between the transformed climb distance and the two parameters, AOA and L/V ratio, was obtained through a nonlinear transformation. The accuracy of the fitting for- mula is further improved by using gradual linearization methodology. 5 Flange Climb Distance Limit (feet) As an example of this technique, a biparameter flange- 4.5 bi-parameter General form climb-distance criterion, which takes the AOA, the L/V ratio 4 as parameters, was proposed for vehicles with AAR-1B 3.5 wheel and AREMA 136-pound rail profile: 3 2.5 2 L/V Distance (feet) < 1.5 1 (2.6) 1 0.001411 * AOA + (0.0118 * AOA + 0.1155) * L/V - 0.0671 0.5 0 1 1.5 2 2.5 3 3.5 The biparameter criterion has been validated by the TLV test data. Some application limitations of the biparameter cri- Wheel L/V Ratio terion (Equation 2.6) include the following: Figure 2.5. Comparison of flange-climb-distance limit The L/V ratio in the biparameter criterion must be from the general form of distance criterion and the higher than the L/V limit ratio corresponding to the biparameter criterion.