Flange Climb Derailment Criteria and Wheel/Rail Profile Management and Maintenance Guidelines for Transit Operations (2005)

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CHAPTER 2 FLANGE CLIMB DERAILMENT CRITERIA The flange climb derailment criteria proposed in this section include the wheel L/V ratio limit and the flange- climb-distance limit. Details of the research to develop these criteria are reported in Appendices B and C. These criteria were developed based on computer simulations of single wheelsets. The wheel profiles used in the simulations were obtained from the transit system survey. These profiles were applied on both light rail and rapid transit vehicles with flange angles ranging from 60 degrees to 75 degrees and flange lengths ranging from 0.395 to 0.754 in. The proposed criteria have been validated by flange-climb test data using the TLV. This section provides an example of applying the criteria to a passenger car test. The limitations of the proposed criteria are also discussed. 2.1 WHEEL L/V RATIO CRITERIA The L/V ratio criteria proposed for transit vehicles are stated as follows: (1) if AOA ≥ 5 mrad or if AOA is unknown, (2.1) (2) If AOA < 5 mrad (2.2) 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 by M. J. Nadal in 1908 for the French Railways, has been used throughout the railroad community. Nadal proposed a limiting criterion as a ratio of L/V forces: (2.3) where µ is the friction coefficient at the wheel/rail contact surface and δ is the wheel/rail contact angle. Figure 2.1 shows the Nadal values for different wheel/rail maximum contact angles and friction coefficient combina- L V = − + tan( ) tan( ) δ µ µ δ1 L V AOA < + + q0 0 43 1 2 . . , L V < q0 , 6 tions. The Nadal values for contact angles of 63 and 75 degrees are specified in Figure 2.1 with values of 0.73 and 1.13, respectively. If the maximum contact angle is used, Equation 2.3 gives the minimum wheel L/V ratio at which flange climb derailment may occur for the given contact angle and friction coefficient µ. Clearly, wheels with low flange angles and high friction coefficient have a low L/V ratio limit and a higher risk of flange climb derailment. Equation 2.1 states that if the AOA is larger than 5 mrad or the AOA cannot be determined (which is usually the case during on-track tests), the limiting L/V value is the Nadal value determined by Equation 2.3. If the AOA can be deter- mined with an AOA measurement device or from simulation 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 increased flange climb L/V with small AOAs. Figure 2.2 shows a comparison of Equation 2.2 and the Nadal value for a wheel with a 63 degree flange angle. The study included in Appendix B indicates that one rea- son independently rotating wheelsets (IRW) tend to climb the rail more easily than conventional solid wheelsets is that the coefficient of friction on nonflanging wheel has no effect on the flanging wheel. Therefore, the Nadal L/V limit is accurate for IRW but can be conservative for the wheelsets of solid axles. The wheel L/V ratio required for flange climb for solid axles increases as the increased friction coefficient on nonflanging wheel. If the friction coefficient on the non- flanging wheel approaches to zero, the L/V ratio limit for the solid axle wheel would be the same as that for IRW. 2.2 FLANGE-CLIMB-DISTANCE CRITERIA In practice, a flange climbing derailment is not instanta- neous. The L/V ratio has to be maintained while the climb- ing takes place. If, for example, the lateral force returns to zero before the flange has reached the top of the rail, the wheel might be expected to drop down again. When the flange contacts the rail for a short duration, as may be the case during hunting (kinematic oscillations) of the wheelset, the L/V ratio might exceed Nadal’s limit without flange climbing. For that reason, the flange-climb-distance criteria were developed to evaluate the risk of derailment associated

with the wheel L/V ratio limit. Flange climb derailment would occur only if both wheel L/V ratio limit and distance limit are exceeded. A general form of flange-climb-distance criterion is pro- posed in this section that applies to an L/V ratio equal to or less than 1.99. 2.2.1 A General Flange-Climb-Distance Criterion A general flange-climb-distance criterion was developed by using the technique described in Appendix C of this report. Sixteen combinations of wheel flange angle and flange length, covering a wide range of these values on actual wheels, were used for the derivation. This general criterion, 7 proposed in Equation 2.4, takes the AOA, the maximum flange angle, and flange length as parameters. (2.4) where D is limiting climb distance in feet and AOA is in mrad. Coefficients A, B are functions of the maximum flange angle Ang (degrees) and flange length Len (in.) as defined in Section 2.4: The limiting climb distance for a specific transit wheel profile can be derived from the above general criterion by substituting the maximum flange angle and flange length into Equation 2.4. It is especially useful for the transit wheel pro- files that were not simulated in this report. Table 2.1 lists a range of limiting flange-climb-distance values computed using Equation 2.4 for a specified range of flange angles, flange length, and AOA. Table 2.1 indicates that at an AOA of 5 mrad, the limiting flange-climb distance increases as increased wheel flange angle and flange length. At an AOA of 10 mrad, flange length has more effect on the distance limit than flange angle. In summary, considering that flange climb generally occurs at a higher AOA, increasing wheel flange angle can increase the wheel L/V ratio limit required for flange climb and increasing flange length can increase the limiting flange climb distance. 2.3 DETERMINATION OF EFFECTIVE AOA The flange climb criteria, including both wheel L/V ratio limit and climbing distance limit, are closely related to the wheelset AOA. Because the wheelset AOA may not be Ang Len + − − 10 0 2688 0 0266 5 . . B Len = − + +     10 21 157 2 1052 0 05 . . . * Len Ang Ang − − + − + 1 0 0092 1 2152 39 031 1 232 . ( ) . . . A Ang = − + +     100 1 9128 146 56 3 1 . . . * D A B Len AOA B Len < + * * * 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 45 55 65 75 85 Flange Angle (Degree) N ad al L /V V al ue 1.0 0.5 0.1 0.2 0.3 0.4 Figure 2.1. Nadal criterion as a function of flange angle and friction coefficients in a range of 0.1 to 1.0. 0.6 0.7 0.8 0.9 1 1.1 1.2 0 5 10 15 20 AOA (mrad) W he el L /V R at io Modified Limit Nadal Limit Figure 2.2. Comparison of Nadal L/V ratio limit and modified L/V ratio limit. AOA = 5 mrad AOA = 10 mrad Flange Angle (deg) 63 deg 68 deg 72 deg 75 deg 63 deg 68 deg 72 deg 75 deg Flange Length (inch) 0.4 inch 2.0 2.2 2.4 3.3 1.5 1.5 1.5 1.9 0.52 inch 2.4 2.6 2.9 3.8 1.8 1.8 1.8 2.1 0.75 inch 3.2 3.5 3.7 4.3 2.3 2.3 2.2 2.4 TABLE 2.1 Limiting flange-climb-distance computed using Equation 2.4

available or cannot be measured under certain circumstances, an equivalent index, or effective AOA (AOAe), is proposed here in order to use the flange climb criteria. The AOAe is a function of axle spacing in the truck, track curvature, and truck type. The equivalent index AOAe (in milliradians) of the leading axle of a two-axle truck can be obtained through a geometric analysis of truck geometry on a curve (Equation 2.5): (2.5) where c = a constant for different truck types, l = axle spacing distance (in.), C = curve curvature (degrees), and R = curve radius (ft). Table 2.2 lists the constant c obtained from simulations for three types of representative transit vehicles: a Light Rail Vehicle Model 1 (LRV1) with independent rolling wheels in the center truck, a Light Rail Vehicle Model 2 (LRV2), and a Rapid Transit Vehicle (HRV). Therefore, the AOAe can be estimated according to the track curvature (C) and known constant c (Equation 2.5). Due to the track perturbations and the degrading of wheelset steering capability, the practical wheelset AOA could be higher than the value calculated by Equation 2.5. Table 2.3 shows the AOAe values recommended for use in the distance criterion of Equation 2.4. These values for AOAe were considered conservative enough according to the simulation results and test data. When the vehicle runs on a curve with the curvature lower than 10 degrees and not listed in Table 2.3, it is recom- mended that a linear interpolation between the segment points in Table 2.3 should be used in the criterion, as shown in Figure 2.3. The statistical data from an AOA wayside monitoring system should be used in the criterion to take into account the many factors affecting AOAe if such a system is available. AOAe clC cl R = =0 007272 41 67. . 8 2.4 DEFINITION OF FLANGE CLIMB DISTANCE The climb distance used here is defined as the distance trav- eled starting from the point at which the limiting L/V ratio (Equation 2.1 and 2.2) is exceeded (equivalent to the point “A” in Figure B-4 of Appendix B) to the point of derailment. For the purposes of these studies, the point of derailment was determined by the contact angle on the flange tip decreasing to 26.6 degrees after passing the maximum contact angle. The 26.6-degree contact angle corresponds to the minimum contact angle for a friction coefficient of 0.5. Figure 2.4 shows the wheel flange tip in contact with the rail at a 26.6-degree angle. Between the maximum contact angle (point Q) and the 26.6-degree flange tip angle (point O), the wheel can slip back down the gage face of the rail due to its own vertical axle load if the external lateral force is suddenly reduced to zero. In this condition, the lateral creep force F (due to AOA) by itself is not large enough to cause the wheel to derail. When the wheel climbs past the 26.6-degree contact angle (point O) on the flange tip, the wheel cannot slip back down the gage face of the rail due to its own vertical axle load: the lateral creep force F generated by the wheelset AOA is large Vehicle and Truck Type Straight Lines 5-Degree Curves 10-Degree Curves >10-Degree Curves Vehicle with IRW 10 15 20 Equation 2.5 + 10 Others 5 10 15 Equation 2.5 + 5 TABLE 2.3 Conservative AOAe (mrad) for practical use Vehicle Type Axle Spacing Distance (in.) Constant c LRV1 (with IRW) 74.8 3.08 LRV2 (Solid axles) 75 2.86 HRV (Solid axles) 82 2.04 TABLE 2.2 Estimation of constant c Figure 2.3. Recommended conservative AOAe for practical use. 0 5 10 15 20 25 30 0 2 4 6 8 10 12 Curvature (degree) AO Ae (m rad ) IRW Solid Wheelset

enough to resist the fall of the wheel and force the flange tip to climb on top of the rail. The flange length Len is defined as the sum of the maxi- mum flange angle arc length QP and flange tip arc length PO, as shown in Figure 2.4. 2.5 A BIPARAMETER TECHNIQUE TO DERIVE FLANGE CLIMB DISTANCE A biparameter regression technique was also developed to derive the distance criterion. The limiting distances derived from the biparameter regression technique are more accurate and less conservative than that defined by the general form of distance criterion presented in Section 2.2.1. However, the derivation must be performed for each specific wheel and rail profile combination. An example of derivation of the distance criterion, using the biparameter method for the AAR-1B wheel contacting AREMA 136 RE rail, is demon- strated in this section. In Appendix C of this report, the bilinear characteristic 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. As an example of this technique, a biparameter flange- climb-distance criterion, which takes the AOA, the L/V ratio as parameters, was proposed for vehicles with AAR-1B wheel and AREMA 136-pound rail profile: (2.6) The biparameter criterion has been validated by the TLV test data. Some application limitations of the biparameter cri- terion (Equation 2.6) include the following: • The L/V ratio in the biparameter criterion must be higher than the L/V limit ratio corresponding to the 0.001411 * AOA (0.0118 * AOA 0.1155) * L/V 0.0671+ + − 1 L/V Distance (feet) < 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 with this combination of wheel and rail profiles. Figure 2.5 shows the limiting flange-climb distance defined by the general form of flange-climb-distance crite- rion (Equation 2.4) compared to the biparameter criterion (Equation 2.6) for the combination of AAR-1B wheel and AREMA 136 RE rail at 10 mrad AOA. The AAR-1B wheel has a flange angle of 75 degrees and a flange length of 0.618 in. Under this condition, the limiting flange-climb-distance given from the general form of climb-distance criterion is a constant of 2.3 ft once the wheel L/V ratio exceeds the Nadal limit of 1.13 for a friction coefficient of 0.5, as shown by the straight line in Figure 2.5. The curve in Figure 2.5 gives the limiting distance crite- rion from the biparameter criterion under the same condi- tion. Once the Nadal L/V ratio is exceeded, the distance limit is the function of the average of actual L/V ratios over the distance that Nadal L/V ratio limit has been exceeded. It can be seen from Figure 2.5 that the biparameter criterion is less conservative than the general form of distance criterion for wheel L/V ratio less than 2.0, especially when the wheel L/V ratio is just above the Nadal limit (1.13 in this case). In actual tests, sustained wheel L/V ratios greater than 2.0 are uncommon. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 1 1.5 2 2.5 3 3.5 Wheel L/V Ratio Fl an ge C lim b Di st an ce L im it (fe et) bi-parameter General form Figure 2.5. Comparison of flange-climb-distance limit from the general form of distance criterion and the biparameter criterion. Figure 2.4. Wheel/rail interaction and contact forces on flange tip.

2.6 EFFECT OF SPEED ON DISTANCE TO CLIMB The above criteria, both the general formula and biparam- eter method, were derived based on the flange climb simula- tion results of a single wheelset running at a speed of 5 mph. Simulation results show the climb distance slightly increases with increasing running speed due to increased longitudinal creep force and reduced lateral creep force (2), as shown in Figure 2.6. The dynamic behavior of wheelset becomes very compli- cated at higher running speed (above 80 mph for 5 mrad AOA and above 50 mph for 10 mrad AOA). However, the distance limit derived from the speed of 5 mph should be conservative for higher operating speeds. 2.7 APPLICATION OF FLANGE CLIMB CRITERIA 2.7.1 In Simulations The application of flange climb criteria in simulations can be found in Chapter 3 of Appendix B. 2.7.2 In Track Tests In tests, when AOA is unknown or can’t be measured, the AOAe described in Section 2.3 has to be estimated using 10 Equation 2.8. The examples in the following section demonstrate the application of flange climb criteria in track tests. 2.8 EXAMPLES OF APPLICATION OF FLANGE CLIMB CRITERIA As an example of their application, the flange climb criteria were applied to a passenger car with an H-frame truck under- going dynamic performance tests at the FRA’s Transportation Technology Center, Pueblo, Colorado, on July 28, 1997. The car was running at 20 mph through a 5 degree curve with 2 in. vertical dips on the outside rail of the curve. The L/V ratios were calculated from vertical and lateral forces measured from the instrumented wheelsets on the car. Table 2.4 lists the 4 runs with L/V ratios higher than 1.13, exceeding the AAR Chapter XI flange climb safety criterion. The rails during the tests were dry, with an estimated friction coefficient of 0.5. The wheel flange angle was 75 degrees, resulting in a corresponding Nadal value of 1.13. The climb distance and average L/V in Table 2.4 were cal- culated for each run from the point where the L/V ratio exceeded 1.13. 2.8.1 Application of General Flange Climb Criterion The instrumented wheelset has the AAR-1B wheel profile with 75.13 degree maximum flange angle and 0.62 in. flange length; by substituting these two parameters into the general flange climb criterion, the flange criterion for the AAR-1B wheel profile is as follows: The axle spacing distance for this rail car is 102 in. The constant c was adopted as 2.04 since the vehicle and truck design is similar to the heavy rail vehicle in Table 2.2. According to Equation 2.5, the AOAe is about 7.6 mrad for this passenger H-frame truck on a 5-degree curve. By substi- tuting the AOAe into the above criteria, the safe climb dis- tance without derailment is 3 ft. According to Table 2.3, the conservative AOAe for a 5-degree curve should be 10 mrad; D AOAe < + 26 33 1 2 . . Runs Speed Maximum L/V Ratio Average L/V Ratio Climb Distance rn023 20.39 mph 1.79 1.39 5.8 ft rn025 19.83 mph 2.00 1.45 6.3 ft rn045 19.27 mph 1.32 1.23 0.7 ft rn047 21.45 mph 1.85 1.52 5 ft TABLE 2.4 Passenger car test results: Climb distance and average L/V measured from the point where the L/V ratio exceeded 1.13, for friction coefficient of 0.5 Figure 2.6. Effect of travel speed on distance to wheel climb. (L/V ratio = 1.99, AAR-1B wheel (75-degree flange angle) and AREMA 136 RE rail.) 0 1 2 3 4 5 0 20 40 60 80 Travel Speed (mph) Fl an ge C lim b Di st an ce (f ee t) AOA=10 mrad AOA=5 mrad

the conservative safe climb distance without derailment is 2.4 ft; however, the climb distance according to the 50 ms criterion is 1.4 ft. (The 50-ms criterion is discussed in Appen- dix B, Section B1.3.) The wheel, which climbed 0.7 ft distance in run rn045 with a 1.23 average L/V ratio (maximum L/V ratio 1.32), was run- ning safely without threat of derailment according to the cri- terion. The other three runs were unsafe because their climb distances exceeded the criterion. 2.8.2 Application of Biparameters Criterion Figure 2.7 shows the application of the biparameters cri- terion on the same passenger car test. The run (rn045) with the maximum 1.32 L/V ratio is safe, since its climb distance of 0.7 ft is shorter than the 4.3-ft criterion value calculated by the biparameter formula (Equation 2.7). The climb distance 11 is even below the 20 mrad AOAe criterion line, which sel- dom happened for an H-frame truck running on the 5-degree curve. The other three runs were running unsafely because their climb distances exceeded the 10 mrad conservative AOAe criterion line. The same conclusion is drawn by applying the general flange climb criterion and the biparameter flange climb cri- terion to the passenger car test. The climb distances of these two criteria also show that the general flange climb criterion is more conservative than the biparameter criterion. The rea- son for this is that the average L/V ratio in the test, which is 1.23, is lower than the 1.99 ratio used in the simulation to derive the general flange climb criterion. The difference between these two criteria shows the biparameter flange climb criterion is able to reflect the variation of the L/V ratio. However, the general flange climb criterion is conservative for most cases since the sustained average 1.99 L/V ratio dur- ing flange climb is rare in practice. Figure 2.7. Application of the biparameter criterion for friction coefficient of 0.5. 0 1 2 3 4 5 6 7 8 9 1.1 1.2 1.3 1.4 1.5 1.6 Average L/V Ratio during Climb Cl im b Di st an ce (f ee t) Measured Formula, 7.6 mrad AOA Formula, 10 mrad AOA Formula, 20 mrad AOA