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

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B-1 APPENDIX B: Investigation of Wheel Flange Climb Derailment Criteria for Transit Vehicles (Phase I Report)

SUMMARY This research investigated wheelset flange climb derailment with the intent of develop- ing limiting criteria for single-wheel L/V ratios and distance to climb for transit vehicles. The investigations used simulations of single wheelsets and representative transit vehicles. Based on the single wheelset simulation results, preliminary L/V ratio and climb-distance criteria for transit vehicle wheelsets are proposed. The proposed criteria are further val- idated through simulation of three types of transit vehicles. This research has been based on the methods previously used by the research team to develop flange climb derailment criteria for the North American freight railroads. The following conclusions are drawn from single wheelset and vehicle simulations: • New single wheel L/V distance criteria have been proposed for transit vehicles with specified wheel profiles: Wheel 1 profile: Wheel 2 profile: Wheel 3 profile: L/V Distance (feet) if AOA 10 mrad= ≥1 8. , L/V Distance (feet) 0.136 * AOA 1 if AOA 10 mrad< + < 4 2. , L/V Distance (feet) if AOA 0 mrad= ≥1 6 1. , L/V Distance (feet) 0.16 * AOA 1 if AOA 10 mrad< + < 4 1. , L/V Distance (feet) if AOA 10 mrad= ≥2 2. , L/V Distance (feet) 0.13 * AOA 1 if AOA 10 mrad< + < 5 , INVESTIGATION OF WHEEL FLANGE CLIMB DERAILMENT CRITERIA FOR TRANSIT VEHICLES (PHASE I REPORT)

B-4 Wheel 4/5 profile: Wheel 6 profile: where AOA is in mrad. In situations where AOA is not known and cannot be mea- sured, the equivalent AOA (AOAe) calculated from curve curvature and truck geometry should be used in the above criteria. • In situations where AOA is known and can be measured, more accurate new single wheel L/V ratio criteria based on AOA have also been proposed (see correspond- ing equation in Chapter 2 of this appendix). • Simulation results for transit vehicles assembled with different types of wheel pro- files confirm the validity of the proposed criteria. • An incipient derailment occurs for most conditions when the climb distance exceeds the proposed criteria value. • The proposed climb distance criteria are conservative for most conditions. Under many conditions, variations of AOA act to reduce the likelihood of flange climb. • The single wheel L/V ratio required for flange climb derailment is determined by the wheel maximum flange angle, friction coefficient, and wheelset AOA. • The L/V ratio required for flange climb converges to Nadal’s value at higher AOA (above 10 mrad). For the lower wheelset AOA, the wheel L/V ratio necessary for flange climb becomes progressively higher than Nadal’s value. • The distance required for flange climb derailment is determined by the L/V ratio, wheel maximum flange angle, wheel flange length, and wheelset AOA. • The flange climb distance converges to a limiting value at higher AOAs and higher L/V ratios. This limiting value is highly correlated with wheel flange length. The longer the flange length, the longer the climb distance. For the lower wheelset AOA, when the L/V ratio is high enough for the wheel to climb, the wheel-climb distance for derailment becomes progressively longer than the proposed flange-climb-distance limit. The wheel-climb distance at lower wheelset AOA is mainly determined by the maximum flange angle and L/V ratio. • Besides the flange contact angle, flange length also plays an important role in pre- venting derailment. The climb distance can be increased through use of higher wheel maximum flange angles and longer flange length. • The flanging wheel friction coefficient significantly affects the wheel L/V ratio required for flange climb. The lower the friction coefficient, the higher the single wheel L/V ratio required. • For conventional solid wheelsets, a low nonflanging wheel friction coefficient has a tendency to cause flange climb at a lower flanging wheel L/V ratio, and flange climb occurs over a shorter distance for the same flanging wheel L/V ratio. • The proposed L/V ratio and flange-climb-distance criteria are conservative because they are based on an assumption of a low nonflanging wheel friction coefficient. L/V Distance (feet) if AOA 10 mrad= ≥2 2. , L/V Distance (feet) 2 * AOA if AOA 10 mrad< + < 49 2 2. , L/V Distance (feet) if AOA 10 mrad= ≥1 3. , L/V Distance (feet) 2 * AOA 1.5 if AOA 10 mrad< + < 28 ,

B-5 • For independent rotating wheelsets, the effect of the nonflanging wheel friction coefficient is negligible because the longitudinal creep force vanishes. • The proposed L/V ratio and flange-climb-distance criteria are less conservative for independent rotating wheels because independent rotating wheels do not generate significant longitudinal creep forces. • For the range of track lateral stiffness normally present in actual track, the wheel- climb distance is not likely to be significantly affected by variations in the track lateral stiffness. • The effect of inertial parameters on the wheel-climb distance is negligible at low speed. • At high speed, the climb distance increases with increasing wheelset rotating inertia. However, the effect of inertial parameters is not significant at a low nonflanging wheel friction coefficient. • Increasing vehicle speed increases the distance to climb. Phase I of this project proposed specific L/V ratio and flange-climb-distance criteria for several specific wheel/rail profile combinations. Preliminary validation of these cri- teria was made using derailment simulations of several different passenger vehicles. To provide further validation of the criteria, the main task in Phase II of this project was to perform comparisons with results from full-scale transit vehicle tests. The conditions and limitations for the application of the criteria were also proposed. Since the climb distance limit is highly correlated with the flange parameters (flange angle, length, and height), a general climb distance criterion that depends on both the AOA and flange parameters was further investigated in Phase II.

CHAPTER 1 INTRODUCTION The research team conducted a full-scale wheel-climb derailment test with its TLV during 1994 and 1995 (1). The primary objective of the test was to reexamine the current flange climb criteria used in the Chapter XI track worthiness tests described in M-1001, AAR Manual of Standards and Recommended Practices, 1993. In 1999, the research team conducted extensive mathe- matical modeling of a single wheelset flange using its dynamic modeling software (2). The objective of this work was to gain a detailed understanding of the mechanisms of flange climb. This research resulted in the proposal of a new single-wheel L/V ratio criterion and a new flange-climb- distance criterion for freight cars. Subsequently, some revi- sions were made to the proposed criteria (3). Both of these projects were jointly funded by the FRA and the AAR. The proposed L/V and distance-to-climb criteria were developed for freight cars with an AAR1B wheelset with a 75-degree flange angle. These were developed based on fit- ting L/V and distance-to-climb curves to numerous simula- tions of flange climb derailment. These were verified by comparison to the single wheel flange climb test results. Because the test and simulation results showed considerable sensitivity to axle AOA, the criteria were proposed in two forms. The first is for use when evaluating test results where the AOA is being measured, and the second, which is more conservative, is for use when the AOA is unknown or cannot be measured. The following are the proposed criteria. Because mea- surement of AOA is usually quite difficult, the second forms are most likely to be used. The criteria are shown graphically in Figures B-1 and B-2. (1) With capability to measure AOA during the test: (a) Wheel < 1.0 {for AOA > 5 mrad} (b) Wheel {for AOA < 5 mrad} (2) Without ability to measure AOA, Wheel < 1.0L V L V 12 AOA (mrad) 7< + L V B-6 Correspondingly, the L/V distance criterion was proposed as: (1) With onboard AOA measurement system, (a) L/V Distance (ft) < {for AOA > −2 mrad} (b) L/V Distance (ft) = {for AOA < −2 mrad}∞ 16 AOA (mrad) 1.5+ Figure B-1. Proposed single wheel L/V criterion with wheelset AOA measurement. Figure B-2. Proposed L/V distance limit with wheelset AOA measurement. (Dots represent results; line represents the proposed distance limit.) 0 2 4 6 8 10 12 14 –2 Angle of attack (mrad) . )tf( ti mil ec natsid V/L 50 msec duration at 50 mph 50 msec duration at 25 mph 0 2 4 6 8 10 12

(2) Without onboard AOA measurement system, the L/V distance criterion is proposed relating to the track curvature: L/V Distance (ft) < The research to develop these criteria was based primarily on tests and simulations of wheel and rail profiles and load- ing conditions typical for the North American freight rail- roads. Analyses were also limited to 50 mph. The research team is conducting further research to finalize these proposed criteria for adoption by the AAR. Currently, no consistent flange climb safety criteria exist for the North American transit industry. Wheel and rail pro- file standards and loading conditions vary widely for differ- ent transit systems and for different types of vehicles used in light rail and rapid transit services. Therefore, the proposed flange climb criteria developed by the research team for freight cars may not be directly applicable to any particular transit system. The purpose of this project was to use similar analytical methods to develop flange climb derailment safety criteria, specifically for different types of transit systems and transit vehicles. The research team undertook a program of developing wheel/rail profile optimization technology and flange climb criteria at the request of the NCHRP. This program included two phases, as listed Table B-1. This report describes the methodology and results derived from the work performed in Task 2 of Phase I of this program. Wheel and rail profile data, and vehicle and track system data gathered as a part of Phase I, Task 1, were used to develop the inputs to the simulations of flange climb derailment. 1.1 BACKGROUND Wheel-flange-climb derailments occur when the forward motion of the axle is combined with an excessive ratio of L/V wheel/rail contact forces. This usually occurs under conditions of reduced vertical force and increased lateral force that causes the wheel flange to roll onto the top of the rail head. The climb 16 Curve (degree) 3.5+ B-7 condition may be temporary, with wheel and rail returning to normal contact, or it may result in the wheel climbing fully over the rail. Researchers have been investigating the wheel flange climb derailment phenomena since the early 20th cen- tury. As a result of these studies, six flange climb criteria have been proposed. These criteria have been used by railroad engi- neers as guidelines for safety certification testing of railway vehicles. Briefly, they are the following: • Nadal Single-Wheel L/V Limit Criterion • Japanese National Railways (JNR) L/V Time Duration Criterion • General Motors’ Electromotive Division (EMD) L/V Time Duration Criterion • Weinstock Axle-Sum L/V Limit Criterion • FRA High-Speed Passenger Distance Limit (5 ft) • AAR Chapter XI 50-millisecond (ms) Time Limit The Nadal single-wheel L/V limit criterion, proposed by Nadal in 1908 for the French Railways, has been used through- out the railroad community. Nadal established the original for- mulation for limiting the L/V ratio in order to minimize the risk of derailment. He assumed that the wheel was initially in two-point contact with the flange point leading the tread. He concluded that the wheel material at the flange contact point was moving downwards relative to the rail material, due to the wheel rolling about the tread contact. Nadal further theorized that wheel climb occurs when the downward motion ceases with the friction saturated at the contact point. Based on his assumptions and a simple equilibrium of the forces between a wheel and rail at the single point of flange contact, Nadal pro- posed a limiting criterion as a ratio of L/V forces: The expression for the L/V criterion is dependent on the flange angle δ and friction coefficient µ. Figure B-3 shows the solution of this expression for a range of values, appro- priate to normal railroad operations. The AAR developed its L V = − + tan( ) tan( ) δ µ µ δ1 TABLE B-1 Wheel/rail profile optimization and flange climb criteria development tasks Program: Development of Wheel/Rail Profile Optimization Technology and Flange Climb Criteria Task 1 Survey the transit industry and define common problems and concerns related to wheel/rail profiles in transit operation Phase I Task 2 Propose preliminary flange climb derailment criteria for application to transit operation Task 1 Develop a general methodology of wheel/rail profile assessment applicable to transit system operation Phase II Task 2 Propose final flange climb derailment criteria validated by test data

Chapter XI single-wheel L/V ratio criterion based on Nadal’s theory using a friction coefficient of 0.5. Following a large number of laboratory experiments and observations of actual values of L/V ratios greater than the Nadal criterion at incipient derailment, researchers at JNR proposed a modification to Nadal’s criterion (4). For time durations of less than 0.05 s, such as might be expected dur- ing flange impacts due to hunting, an increase was given to the value of the Nadal L/V criterion. However, small-scale tests conducted at Princeton University indicated that the JNR criterion was unable to predict incipient wheel-climb derailment under a number of test conditions. A less conservative adaptation of the JNR criterion was used by General Motors EMD in its locomotive research (5). More recently, Weinstock, of the United States Volpe National Transportation Systems Center, observed that this balance of forces does not depend on the flanging wheel alone (6). Therefore, he proposed a limit criterion that utilizes the sum of the absolute value of the L/V ratios seen by two wheels of an axle, known as the “Axle Sum L/V” ratio. He proposed that this sum be limited by the sum of the Nadal limit (for the flanging wheel) and the coefficient of friction (at the non- flanging wheel). Weinstock’s criterion was argued to be not as overly conservative as Nadal’s at small or negative AOA and less sensitive to variations in the coefficient of friction. Based on the JNR and EMD research, and considerable experience in on-track testing of freight cars, a 0.05-s (50-ms) time duration was adopted by the AAR for the Chapter XI cer- tification testing of new freight cars. This time duration has since been widely adopted by test engineers throughout North America for both freight and passenger vehicles. A flange-climb-distance limit of 5 ft was adopted by the FRA for their Class 6 high speed track standards (7). This dis- tance limit appears to have been based partly on the results of the joint AAR/FRA flange climb research conducted by the research team and also on experience gained during the test- ing of various commuter rail and long distance passenger cars. B-8 A review of recent flange climb and wheel/rail interaction literature has been conducted as part of the work (shown in the Appendix B-1). Although several other teams are cur- rently active in the field of flange climb research, no signifi- cant new flange climb criteria have been reported. Therefore, it was concluded that the development of new cri- teria for the transit industry would be based on applying the research and analytical methods used in the research team’s previous flange climb research. To develop wheel-climb derail- ment criteria for transit vehicles, some parameters—such as forward speed, inertial parameters of wheelsets, and wheel and rail profiles used in the transit industry—would need to be fur- ther investigated. The criteria also need to be further validated through simulations and tests of representative transit vehicles. Previous research has also shown that flange climb is strongly influenced by wheelset AOA. Transit vehicles are likely to experience considerably different conditions of AOA than freight vehicles. Further, AOA is very difficult to measure. Thus, the proposed flange climb criteria are based on conservative expectations for AOA in different ranges of track curvature. 1.2 OBJECTIVE The objectives of Phase I of this project were the following: • To further investigate wheel/rail flange climb mecha- nisms for transit vehicles. • To evaluate and propose wheelset flange climb derail- ment criteria for transit systems using simulations of single wheelsets. • To validate the criteria through simulations of represen- tative transit vehicles. 1.3 METHODOLOGY 1.3.1 Single Wheelset Flange Climb Derailment Simulations The effects of different parameters on derailment were inves- tigated through single-wheelset simulation. Based on these sim- ulation results, the L/V ratio and climb distance criteria for six different kinds of transit wheelsets were proposed. To minimize the number of variables and focus on wheel/rail interaction, a computer simulation model of a sin- gle wheelset was used. The wheel and rail profiles, inertia parameters, and vertical wheel loads were adopted from actual transit vehicle drawings and documents. Much of this data had been gathered as a part of the surveys being con- ducted for Phase I, Task 1 of this TCRP research project (8). The same basic simulation methods used in the research team’s previous flange climb studies were adopted here. To perform the flange climb derailment simulations, the wheelset AOA was set at a fixed value. A large yaw stiffness Figure B-3. Nadal criterion values. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 50 55 60 65 70 75 80 85 Flange Angle (Degree) N ad al L /V V al ue 0.1 0.2 0.3 0.4 0.5 0.6

between the axle and ground ensured that the AOA remained approximately constant throughout the flange climb process. A vertical wheel load that corresponded to the particular vehicle axle load was applied to the wheelset to obtain the appropriate loading at the wheel/rail contact points. The magnitude of the external lateral force and the wheelset AOA controls the flanging wheel L/V ratio. To make the wheel climb the rail and derail, an external lateral force was applied, acting towards the field side of the derail- ing wheel at the level of the rail head. Figure B-4 shows a typical lateral force history. During a constant speed move- ment, an initial lateral force was applied at either 50 percent or 80 percent of the expected L/V ratio for steady-state climb (based on Nadal’s theory). This initial load level was held for 5 ft of travel to ensure equilibrium. The lateral force was then increased to the final desired L/V ratio (starting from A in Figure B-4). This high load was held until the end of the sim- ulation. From this point, the wheel either climbed on top of the rail or it traveled a distance of 40 ft without flange climb; the latter was considered as no occurrence of derailment. Flange climb results from each of the six different wheelsets were analyzed to develop and propose limiting flange climb L/V criteria and distance-to-climb criteria for the different types of transit systems. 1.3.2 Vehicle Derailment Simulations As a preliminary validation of the proposed flange climb derailment criteria, three hypothetical passenger vehicles representing heavy rail and light rail transit vehicles were B-9 modeled. The vehicle models included typical passenger car components, such as air bag suspensions, primary rubber suspensions, and articulation joints. To generate the large AOA, a large lateral force and vertical wheel unloading typical of actual flange climb con- ditions were used. The track input to the models used a mea- sured track file, with variations in curvature, superelevation, gage, cross level, and alignment perturbations along the track. The wheelset L/V ratio and climb distance for vehicles assembled with different wheelsets were obtained through vehicle simulations at different running speeds. The pro- posed flange climb derailment criteria were then evaluated by applying them to the vehicle simulation results. Figure B-4. Lateral force step input. 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 5 10 15 20 25 30 35 40 Distance (feet) )bl( ecroF laretaL deilppA A

CHAPTER 2 SINGLE WHEELSET FLANGE CLIMB DERAILMENT SIMULATIONS The dynamic behavior of six different transit wheelsets were investigated through simulations of single wheelsets. The wheel profiles were taken from the transit system survey conducted as part of Phase I, Task 1 of this TCRP project. The basic parameters of these six wheelsets are listed in Table B-2. Besides the wheel profiles, other parameters in the models—such as wheelset mass, inertia and axle loads— were adopted from drawings or corresponding documents to represent the real vehicle conditions in the particular transit systems. For Wheels 1 through 5 (light rail and heavy rail) the sim- ulations used a new AREMA 115 lb/yd rail section. For Wheel 6 (commuter rail) the AREMA 136 RE rail profile was used. Flange climb results and the corresponding proposed lim- iting flange climb criteria are presented in the following sec- tions for each of the six wheel profiles. A very detailed dis- cussion is provided for Wheel 1. Since the same method was B-10 used for all profiles, only a synopsis of results is provided for the other five wheel profiles. 2.1 TRANSIT VEHICLE WHEELSET 1 Vehicle derailment usually occurs because of a combina- tion of circumstances. Correspondingly, the indexes for the evaluation of derailment, the wheel L/V ratio, and climb dis- tance are also affected by many factors. To evaluate the effects of these factors, case studies are presented for each of them in this section. 2.1.1 Definition of Flange Climb Distance An important output parameter from the simulations is flange climb distance. The climb distance here is defined as the distance traveled from the final step in lateral force (point “A” in Figure B-4) to the point of derailment. For the purposes of Parameter Wheel 1 Wheel 2 Wheel 3 Wheel 4 Wheel 5 Wheel 6 Maximum Flange Angle (degree) 63.361 63.243 60.483 75.068 75.068 75.125 Nominal Wheel Diameter (in.) 28 27 27 26 26 36 Nadal Value 0.748 0.745 0.671 1.130 1.130 1.132 Flange Height (mm) (in.) 26.194 1.031 17.272 0.680 20.599 0.811 19.177 0.755 19.177 0.755 28.042 1.104 Flange Length (mm) (in.) 19.149 0.754 11.853 0.467 17.232 0.678 10.038 0.395 10.038 0.395 15.687 0.618 Source WMATA SEPTA- GRN SEPTA- 101 NJ-Solid NJ-IRW AAR-1B Type of Service Heavy rail Light rail Light rail Light rail Light rail, independent Commuter cars rotating wheels TABLE B-2 Wheel profile parameters

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 of 63.3 degrees for Wheelset 1. The 26.6-degree contact angle corresponds to the minimum contact angle for a friction coefficient of 0.5. Figure B-5 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 wheelset can slip back down the gage face of the rail due to its own vertical axle load if the external lateral force is sud- denly 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 wheelset 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 enough to resist the fall of the wheel and force the flange tip to climb on top of the rail. As shown in Figure B-5, the flange length is defined as the sum of the maximum flange angle arc length QP and flange tip arc length PO. 2.1.2 Effect of Wheelset AOA Figure B-6 shows the effect of AOA on wheel flange climb for Wheel 1 for a range of wheel L/V ratios. A friction coef- ficient of 0.5 was used on the flange and the tread of the derailing wheel. Figure B-6 indicates that wheel climb will not occur for an L/V ratio less than the asymptotic value for each AOA. This asymptotic L/V value corresponds to the quasi-steady derail- ment value for this AOA. For L/V values higher than this, derailment occurs at progressively shorter distances. As AOA is decreased, the wheel quasi-steady derailment L/V value increases and the distance to climb also increases. This result clearly indicates that the Nadal criterion is con- servative for small AOAs, while for AOAs greater than 10 mrad flange climb occurs in distances less than 5 ft for L/V ratios that are slightly greater than the Nadal value. B-11 2.1.3 Effect of Flanging Wheel Friction Coefficient As indicated by Nadal's criterion (Figure B-3), the L/V ratio required for quasi-steady derailment is higher for a lower flanging wheel friction coefficient. Figure B-7 shows the effect on distance-to-climb of reducing the friction coef- ficient from 0.5 to 0.3. Compared with Figure B-6, the asymptotic L/V ratio for flanging wheel friction coefficient 0.3 in Figure B-7 is higher. However, as with the 0.5 coeffi- cient of friction cases, for AOAs greater than 10 mrad flange climb still occurs in less than 5 ft for L/V ratios that are slightly greater than the Nadal value. Figure B-8 compares the simulation results with Nadal's val- ues for coefficients of friction of 0.1, 0.3, and 0.5 for a 5-mrad wheelset AOA. The dashed lines represent Nadal's values. The Figure B-5. Wheel/rail interaction and contact forces on flange tip. Figure B-6. Effect of wheelset AOA on distance to climb, u = 0.5 (Wheel 1). 0 5 10 15 20 25 30 0.5 Flanging Wheel L/V Ratio )t e ef( s e c n at si D b mil C 0mrad 2.5mrad 5mrad 10mrad 20mrad Nadal 21 1.5 2.5 Figure B-7. Effect of wheelset AOA on distance to climb, u = 0.3 (Wheel 1). 0 5 10 15 20 25 30 0.5 Flanging Wheel L/V Ratio )teef( ec natsiD b milC 0mrad 2.5mrad 5mrad 10mrad 20mrad Nadal 21 1.5 2.5

asymptotic value increases with decreasing friction coefficient. A lower flange friction coefficient significantly increases the quasi-steady L/V ratio required for derailment but has almost no effect on the L/V distance limit if this L/V ratio is much exceeded. 2.1.4 Effect of Nonflanging Wheel Friction Coefficient Figure B-9 shows the effect of the nonflanging wheel fric- tion coefficient µnf with a flanging wheel friction coefficient of 0.5 and a 5-mrad wheelset AOA. At a very low µnf, the non- flanging wheel lateral and longitudinal creep forces were neg- ligible; the initial high flanging wheel longitudinal creep force quickly decreased to the same small amplitude but in the reverse direction as the nonflanging longitudinal creep force. B-12 When the nonflanging wheel friction coefficients are increased, the lateral creep forces on the nonflanging wheel side and the longitudinal creep forces on both sides become higher. As the longitudinal creep forces increase, the lateral creep force on the flanging wheel decreases with the satura- tion of resultant creep force. As a result, the quasi-steady wheel L/V ratio required for derailment increases, as shown in Figure B-9. However, if the L/V ratio is large enough to cause derailment (above 1.4 in Figure B-9), the climb distance is not affected by the nonflanging wheel friction coefficient. This result indicates that a low nonflanging wheel friction coefficient has a tendency to cause flange climb at a lower flanging-wheel L/V ratio and climbs in a shorter distance than a wheelset with the same friction coefficient on both wheels. Low friction on the nonflanging wheel therefore rep- resents the worst-case condition resulting in the shortest dis- tances for flange climb. Thus, to produce conservative results, most of the single wheelset derailment simulations discussed in this report were performed with a very low non- flanging wheel friction coefficient (0.001). 2.1.5 Effect of Track Lateral Stiffness Figure B-10 shows the effect of lateral track stiffness on the wheel flange climb at 5 mrad wheelset AOA. The difference of lateral track stiffness of 105 lb/in. and 106 lb/in. are negli- gible. As the lateral track stiffness decreases to 104 lb/in., the climb distance increases by 9 ft compared to the other two stiffness values. With stiffness of regular track normally in the range of 105 to 106 lb/in., the flange-climb distance is not likely to be significantly affected by the track lateral stiffness. Note that the simulations do not allow the rail to roll. Therefore, the effect of reducing the track stiffness is to allow only increased lateral motion of the rails. In actual conditions of reduced lateral track stiffness it is common to have reduced Figure B-8. Effect of coefficient of friction, 5 mrad AOA (Wheel 1). 0 5 10 15 20 25 30 0.5 Flanging Wheel L/V Ratio )teef( ec natsiD b milC mu=0.1 mu=0.3 mu=0.5 mu=0.1 mu=0.3 mu=0.5 21 1.5 2.5 3 Figure B-9. Effect of nonflanging wheel friction coefficient, 5 mrad AOA (Wheel 1). 0 5 10 15 20 25 30 0.5 Flanging Wheel L/V Ratio )t e ef( e c n at si D b milC mu-nf=0.001 mu-nf=0.3 mu-nf=0.5 21 1.5 Figure B-10. Effect of track lateral stiffness, 5 mrad AOA (Wheel 1). 0 5 10 15 20 25 30 0.5 1 1.5 2 2.5 Flanging Wheel L/V Ratio )teef( ec natsi D b milC 1.0E4 1.0E5 1.0E6

rail roll restraint as well. It is recommended that the effects of rail roll restraint and rail roll be studied at a future date. 2.1.6 Effect of Wheel L/V Base Level As described in Section 1.3.1 (Figure B-4), all the simula- tions were performed with an initial lateral force applied to the wheelset to bring the wheelset towards flange contact and cre- ate a base L/V ratio. The base level represents the different L/V ratio that might be present due to steady state curving conditions or yaw misalignments of truck and/or axles in real vehicles. Figure B-11 shows the effect of L/V ratio base level on the wheel flange climb at 5 mrad AOA. The climb distance decreases by a small amount as the L/V base level increases. The vertical dashed line in the plot is the quasi-steady L/V value for a 5-mrad AOA, which corresponds to the asymptotic line in Figure B-6. If the maximum L/V level is less than this value, flange climb derailment cannot occur for any L/V base level. The climb distance is affected by the base L/V level, but the effect is much less significant than for a 75-degree- maximum-flange-angle wheelset (2). Compared to the low-flange-angle wheelset, the high-flange-angle wheelset requires greater effort to climb over the maximum flange angle and travels a farther distance at the same base L/V level. It is recommended that this difference be explored in greater detail in Phase II of this project. It is expected that the flange angle and the length of flange face that is maintained at the maximum contact angle will affect the climb distance. 2.1.7 Effect of Running Speed and Wheelset Inertial Parameters Figure B-12 shows the effect of running speed on wheel flange climb at 5 mrad AOA. The climb distance increases with increases in running speed. As the stabilizing force B-13 for wheel derailment, a significant initial longitudinal creep force is generated at high speed and resists wheel climb. The dynamic forces due to increased wheelset mass and rotating inertia become higher as the running speed increases. Figure B-13 shows the effect of inertial parame- ters on the climb distance for low speed (5 mph) and high speed (100 mph). The nominal wheelset rotating inertia was increased by two times, the wheelset mass and rolling and yawing inertia were also increased correspondingly. As seen in Figure B-13, at low speed, the effect of inertial pa- rameters is negligible. At 100 mph, the climb distance of the double rotating inertia wheelset is increased by 0.5 to 1.0 ft at lower L/V ratios, but the effect of inertial parame- ters is negligible at high L/V ratios. The effect of inertia parameters is not significant at low nonflanging wheel fric- tion coefficient. Figure B-11. Effect of L/V base level, 5 mrad AOA (Wheel 1). 2 3 4 5 6 7 8 9 10 0.5 1 1.5 2 Wheel L/V Ratio )teef( ec natsi D b milC Base-0.0 Base-0.25 Base-0.5 Base-0.8 Figure B-12. Effect of speed on distance to climb for two different maximum wheel L/V ratios, 5 mrad AOA (Wheel 1). 0 2 4 6 8 10 12 14 16 18 20 0 Travel Speed (mph) )teef( sec natsiD b milC L/V max=0.97 L/V max=1.06 15050 100 Figure B-13. Effect of rotating inertia at 5 mph and 100 mph, 5 mrad AOA (Wheel 1). 0 2 4 6 8 10 12 14 0.5 1 1.5 2 Wheel L/V Ratio )teef( ec natsiD b milC 2Iy,5mph Iy,100mph Iy, 5mph 2Iy,100mph

2.1.8 Wheel 1 Maximum Single Wheel L/V Ratio Criterion Based on the above analysis, the AOA has the most signif- icant effect on wheelset L/V ratio and climb distance. The fol- lowing L/V ratio criteria for the Wheel 1 profile is proposed: (B-1) (B-2) (B-3) Equations B-1 and B-3 are Nadal’s limiting value for Wheel 1, which has a flange angle of 63 degrees. Equation B-2 was developed to account for the effects of increased flange climb L/V with small AOAs. This was done in a sim- ilar manner to previous TTCI research (2). Figure B-14 shows the L/V ratio limit from the simulations compared to the proposed L/V ratio criterion for the Wheel 1 profile. Compared to the Nadal criterion, the new criterion is less conservative for AOA below 5 mrad. The proposed cri- terion, however, is more conservative than the simulations. This allows for the possibility of track and vehicle conditions that might cause localized increases in the AOA. If a measurement of AOA is not available, a single value wheel L/V ratio criterion is proposed, as shown in Equation B-3. 2.1.9 Wheel 1 L/V Flange-Climb-Distance Criterion The maximum wheel L/V ratio is constrained by the wheel L/V criterion proposed in Section 2.1.8. The maximum dis- tance over which the L/V is permitted is given by the L/V distance criterion proposed below. The single wheelset sim- ulation results, described above, show that the climb distance L V if AOA unknown< 0 74. , L V AOA(mrad) 10.3 if AOA 5 mrad< + < 11 3. , L V if AOA 5 mrad< ≥0 74. , B-14 is strongly dependent on wheelset AOA. The following is the proposed L/V distance criterion for the Wheel 1 profile: With onboard AOA measurement system, (B-4) (B-5) Figure B-15 shows the simulation results of L/V climb dis- tance and the proposed climb distance criterion for the Wheel 1 profile. All the simulation points are above the pro- posed criterion line. Therefore, the proposed flange-climb- distance criterion represents the worst case for all simulation cases and can be considered to be reasonably conservative. When wheelset AOA is not available, an 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: (B-6) where c = a constant for different truck types, l = axle spacing distance in inches, and C = the curve curvature, in degrees. The relationship between the quasi-steady axle AOA on curve and the curve curvature was further investigated through a group of vehicle equilibrium position simulations. The vehicle model used is described below in Section 3.1.1. Simulation results show the trailing axle of an H frame truck tends to align to a radial position while running through the curve. As a result, the leading axle AOA is increased correspondingly. When the curve curvature is larger than 4 degrees, the dynamic AOA/curvature ratio is AOAe = 0 007272. clC L/V Distance (feet) if AOA 10 mrad= ≥2 2. , if AOA 10 mrad< L/V Distance (feet) 0.13 * AOA 1 < + 5 , Figure B-14. Comparison of proposed wheel L/V ratio criterion with simulation (Wheel 1). 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0 Angle of Attack (mrad) ti miL oitaR V/L Simulation Proposed 5 10 15 20 Figure B-15. Comparison of proposed L/V distance criterion with simulation (Wheel 1). 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Wheel Set Angle of Attack (mrad) )t e ef( e c n at si D b mil C Simulation Proposed

1–1.13, shown in Figure B-16, the constant c for the H frame truck is approximately 2 (1.8–2.1, as calculated by using Equation B-6 for the H frame truck with 75 in. axle spacing). The simulation results in Figure B-16 also show the leading axle quasi-steady AOA value is smaller than the curve curva- ture at low curvature curve (below 5 degrees the ratio of AOA/curvature < 1), but larger than curvature at high curvature curve, the ratio of AOA/curvature > 1. Because the criterion is sensitive to low AOA, another constraint for Equation B-6 is added: (B-7) For the situation without an onboard AOA measurement system, a criterion based on the track curvature is proposed: (B-8) AOAe (mrad) is the equivalent AOA calculated from curve curvature according to Equations B-6 and B-7. 2.2 TRANSIT VEHICLE WHEELSET 2 Figure B-17 shows the effect of wheelset AOA on wheel flange-climb distance for a range of Wheelset 2 flanging wheel L/V ratios. Coefficient of friction on the flanging wheel was 0.5. Results are generally similar to Wheel 1, with increased AOA requiring decreased distance to climb, although for each AOA the distances to climb are somewhat shorter. 2.2.1 Wheel 2 Maximum Single Wheel L/V Ratio Criterion Based on the simulations, a proposed single wheel L/V criterion was developed for Wheel 2. Figure B-18 shows the NUCARS simulation L/V ratio limit and the proposed L/V ratio criterion for Wheel 2. The relationship of Wheel 2 L/V ratio versus AOA is quite similar to that of Wheel 1, L/V Distance (feet) 0.13 * AOAe 1 < + 5 AOAe if degree and AOAe= < >C C C, 5 B-15 because both wheels have the same 63-degree maximum flange angle. Therefore, the proposed L/V ratio criterion for the Wheel 2 is the same as that for Wheel 1 and is given by Equations B-1 to B-3. 2.2.2 Wheel 2 L/V Flange-Climb-Distance Criterion Though the proposed L/V ratio criterion for Wheel 2 is the same as Wheel 1, the difference of its flange-climb distance is not negligible. The reasons are discussed in Section 2.7. The following is the proposed L/V distance criterion for Wheel 2: With onboard AOA measurement system, (B-9) (B-10)L/V Distance (feet) if AOA 0 mrad= ≥1 6 1. , if AOA 10 mrad< L/V Distance (feet) 0.16 * AOA 1 < + 4 1. , Figure B-17. Effect of wheelset AOA on distance to climb, u = 0.5 (Wheel 2). 0 5 10 15 20 25 30 0.5 1 1.5 2 2.5 Flanging Wheel L/V Ratio )teef( sec natsiD b milC 0mrad 2.5mrad 5mrad 10mrad Nadal Figure B-18. Comparison of proposed wheel L/V ratio criterion with simulation (Wheel 2). 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0 5 10 15 20 Wheel Set Angle of Attack (mrad) oitaR ti miL V/L Simulation Proposed Figure B-16. Quasi-steady lead axle AOA as a function of curvature for an H-frame truck. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 2 4 6 8 10 12 Curvature (Degree) Ax le 1 AO A( mr ad )/C ur va tu re (de g)

Without onboard AOA measurement system, (B-11) Figure B-19 shows the simulation results of L/V climb distance and the proposed climb distance criterion for Wheel 2. 2.3 TRANSIT VEHICLE WHEELSET 3 Figure B-20 shows the effect of wheelset AOA on flange- climb distance for a range of Wheelset 3 flanging wheel L/V ratios. The Nadal L/V flange climb limit is shown as a dashed line. Coefficient of friction on the flanging wheel was 0.5. Results are generally similar to Wheel 1, with increased AOA requiring decreased distance to climb. Distances to climb are slightly shorter and the Nadal limit is slightly lower due to the smaller flange angle of Wheel 3. L/V Distance (feet) 0.16 * AOAe 1 < + 4 1. B-16 2.3.1 Wheel 3 Maximum Single Wheel L/V Ratio Criterion Based on the simulations, a proposed single wheel L/V crite- rion was developed for Wheel 3. This is different than for Wheel 1 and Wheel 2 due to the lower flange angle and corresponding lower Nadal limit. Figure B-21 shows the simulation L/V ratio limit and the proposed L/V ratio criterion for the Wheel 3. The following is the proposed L/V ratio criterion for Wheel 3: (B-12) (B-13) (B-14) 2.3.2 Wheel 3 L/V Flange-Climb-Distance Criterion Figure B-22 compares simulation results of L/V climb dis- tance and the proposed climb distance criterion for Wheel 3. The following is the proposed L/V distance criterion: With onboard AOA measurement system, (B-15) (B-16) Without onboard AOA measurement system, (B-17)L/V Distance (feet) 0.136 * AOAe 1 < + 4 2. L/V Distance (feet) if AOA 10 mrad= ≥1 8. , if AOA 10 mrad< L/V Distance (feet) 0.136 * AOA 1 < + 4 2. , L V if AOA unknown< 0 66. , L V AOA(mrad) 11.38 if AOA 5 mrad< + < 10 8. , L V if AOA 5 mrad< ≥0 66. , Figure B-19. Comparison of proposed L/V distance criterion with simulation (Wheel 2). 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Wheel Set Angle of Attack (mrad) Cl im b Di st an ce (fe e t) Simulation Proposed Figure B-20. Effect of wheelset AOA on distance to climb, u = 0.5 (Wheel 3). 0 5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 Flanging Wheel L/V Ratio )teef( sec natsi D b milC 0mrad 2.5mrad 5mrad 10mrad Nadal Figure B-21. Comparison of proposed wheel L/V ratio criterion with simulation (Wheel 3). 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0 5 10 15 20 Wheel Set Angle of Attack (mrad) oita R V/L Simulation Proposed

2.4 TRANSIT VEHICLE WHEELSET 4 (SOLID) Figure B-23 shows the effect of wheelset AOA on flange- climb distance for a range of Wheelset 4 flanging wheel L/V ratios. The Nadal L/V flange climb limit is shown as a dashed line. Coefficient of friction on the flanging wheel was 0.5. Results are generally similar to Wheel 1, with increased AOA requiring decreased distance to climb. Although the Nadal limit is higher than for Wheel 1 due to a larger flange angle, the distances to climb are much shorter. This is due to a very short flange length, as discussed in Section 2.7. 2.4.1 Wheel 4 Maximum Single Wheel L/V Ratio Criterion Based on the simulations, a proposed single wheel L/V cri- terion was developed for Wheel 4. This is different form Wheel 1 due to the larger flange angle and correspondingly higher Nadal limit. Due to the 75-degree flange angle, this B-17 criterion is the same as the L/V criterion proposed for freight vehicles (2). Figure B-24 shows the simulation L/V ratio limit and the proposed L/V ratio criterion for Wheel 4. The following is the proposed L/V ratio criterion for Wheel 4: (B-18) (B-19) (B-20) 2.4.2 Wheel 4 L/V Flange-Climb-Distance Criterion Figure B-25 shows the simulation results of L/V climb dis- tance and the proposed climb distance criterion for Wheel 4. It can be seen that some simulation points are below the pro- posed criterion line. However, bearing in mind that the L/V ratio of these points is much higher than the actual L/V ratio, which can be measured in practice, the proposed criterion is considered to be reasonable. The following is the proposed L/V distance criterion: With onboard AOA measurement system, (B-21) (B-22) Without onboard AOA measurement system, (B-23)L/V Distance (feet) 2 * AOAe 1.5 < + 28 L/V Distance (feet) if AOA 10 mrad= ≥1 3. , if AOA 10 mrad< L/V Distance (feet) 2 * AOA 1.5 < + 28 , L V if AOA unknown< 1 0. , L V AOA(mrad) 7 if AOA 5 mrad< + < 12 , L V if AOA 5 mrad< ≥1 0. , Figure B-22. Comparison of proposed L/V distance criterion with simulation (Wheel 3). 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Wheel Set Angle of Attack (mrad) )teef( ec natsiD b milC Simulation Proposed Figure B-23. Effect of wheelset AOA on distance to climb, u = 0.5 (Wheel 4). 0 5 10 15 20 25 30 1 1.5 2 2.5 3 Flanging Wheel L/V Ratio )teef( ec natsiD b milC 0mrad 2.5mrad 5mrad 10mrad Nadal Figure B-24. Comparison of proposed wheel L/V ratio criterion with simulation (Wheel 4). 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 0 5 10 15 20 Wheel Set Angle of Attack (mrad) ti miL oitaR V/L Simulation Proposed

The proposed flange-climb-distance criterion for Wheel 4 is shorter than that proposed for the AAR-1B wheel (Section 2.6), which has the same flange angle. This is because the flange length on Wheel 4 is much shorter than for the AAR-1B wheel. 2.5 TRANSIT VEHICLE WHEELSET 5 (INDEPENDENT ROTATING WHEELS) Wheel 4 and Wheel 5 have the same profile shape and flange angle. However, the left and right wheels of Wheelset 5 are allowed to rotate independently of each other, while Wheelset 4 has the wheels mounted on a solid axle. For Wheelset 5, this means the individual wheels are not con- strained to rotate at the same speed, resulting in considerably different axle steering response. 2.5.1 Comparison of Solid and Independent Rotating Wheelsets As discussed in Section 2.1.4, a low, nonflanging wheel friction coefficient represents the worst case for a conven- tional solid wheelset. Figure B-26 shows the effect of the nonflanging wheel friction coefficient µnf for Wheelset 4, with a flanging wheel friction coefficient of 0.5 and a 5-mrad wheelset AOA. With the increase of nonflanging wheel fric- tion coefficients, the quasi-steady wheel L/V ratio required for derailment increases, and the climb distance also increases when the L/V ratio is lower than 2.2. But the IRW wheelset situation is quite different because the spin constraint between the two wheels is eliminated. Figure B-27 shows the effect of the nonflanging wheel fric- tion coefficient µnf for the independent rotating Wheelset 5, with a flanging wheel friction coefficient of 0.5 and a 5-mrad wheelset AOA. In contrast to the situation of the conven- tional solid wheelset, when µnf = 0.001, 0.3, 0.5, and 0.8, the longitudinal creep forces on both wheels vanish as expected. Therefore, longitudinal creep forces have no effect on lateral creep forces. For the independently rotating wheels at differ- B-18 ent nonflanging wheel friction coefficient levels, the rela- tionship between flanging L/V ratio and flange-climb dis- tance converge to the same values. Figure B-28 compares the conventional solid wheelset (Wheel 4) and independent rotating wheelset (Wheel 5) at different nonflanging wheel friction coefficients µnf. The difference is significant at large µnf. However, the results are virtually the same at small µnf, because for both cases there are almost no longitudinal creep forces present. 2.5.2 Wheel 5 Maximum Single Wheel L/V Ratio Criterion The analyses in Section 2.5.1 show that the L/V ratios for independent rotating wheels and solid axles with low non- flanging wheel coefficient of friction are the same. Since Wheel 4 and Wheel 5 have the same wheel profile shape, the L/V criterion for Wheel 5 is the same as for Wheel 4 (Equations B-18 to B-20). Figure B-25. Comparison of proposed L/V distance criterion with simulation (Wheel 4). 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 Wheel Set Angle of Attack (mrad) )t e ef( e c n at si D b mil C Simulation Proposed Figure B-26. Effect of nonflanging wheel friction coefficient, 5 mrad AOA (Wheel 4). 0 2 4 6 8 10 12 14 16 18 20 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Flanging Wheel L/V Ratio )teef( ec natsi D b milC mu-nf=0.001 mu-nf=0.3 mu-nf=0.5 mu-nf=0.8 Figure B-27. Effect of nonflanging wheel friction coefficient, 5 mrad AOA (Wheel 5—independent rotating wheels). 0 2 4 6 8 10 12 14 16 18 20 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Flanging Wheel L/V Ratio )teef( ec natsi D b milC mu-nf=0.001 mu-nf=0.3 mu-nf=0.5 mu-nf=0.8

2.5.3 Wheel 5 L/V Flange-Climb-Distance Criterion L/V Distance Criterion The analyses in Section 2.5.1 show that the distances to climb for independent rotating wheels and solid axles with low nonflanging wheel coefficient of friction are the same. Since Wheel 4 and Wheel 5 have the same wheel profile shape, the distance-to-climb criteria for Wheel 5 is the same as for Wheel 4 (Equations B-21 to B-23). 2.6 COMMUTER CAR WHEELSET 6 The commuter car wheelset uses the AAR-1B wheel profile, which has a 75-degree flange angle. Figure B-29 shows the effect of wheelset AOA on wheel flange-climb distance for a range of Wheelset 6 flanging wheel L/V ratios. The Nadal L/V B-19 flange climb limit is shown as a dashed line. Coefficient of fric- tion on the flanging wheel was 0.5. Results are generally simi- lar to Wheel 1, with increased AOA requiring decreased distance to climb. The Nadal limit is higher than for Wheel 1 due to a larger flange angle; and the distances to climb are somewhat longer, probably due to a longer flange length. The distances to climb for Wheel 6 are also longer than for Wheels 4 and 5, which also have the 75 degree flange angle. This is because of the longer flange length of the AAR-1B wheel profile. 2.6.1 Wheel 6 Maximum Single Wheel L/V Ratio Criterion Based on the simulations, a proposed single wheel L/V crite- rion was developed for Wheel 6. This is different than for Wheel 1 due to the larger flange angle and corresponding higher Nadal limit. Because this is the AAR-1B wheel with a 75-degree flange angle, this criterion is the same as the L/V criterion proposed for freight vehicles, as well as for Wheels 4 and 5. Figure B-30 com- pares the simulation L/V ratio limit and the proposed L/V ratio criterion for Wheel 6. The proposed L/V ratio criterion for Wheel 6 is therefore given in Equations B-18 to B-20. 2.6.2 Wheel 6 L/V Flange-Climb-Distance Criterion Figure B-31 shows the simulation results of L/V climb dis- tance and the proposed climb distance criterion for Wheel 6. The following is the proposed L/V distance criterion: With onboard AOA measurement system, (B-24) (B-25)L/V Distance (feet) if AOA 10 mrad= ≥2 2. , if AOA 10 mrad< L/V Distance (feet) 2 * AOA < + 49 2 2. , Figure B-29. Effect of wheelset AOA on distance to climb, u = 0.5 (Wheel 6). 0 5 10 15 20 25 30 0.5 1 1.5 2 2.5 3 3.5 Flanging Wheel L/V Ratio )teef( ec natsiD b milC 0mrad 2.5mrad 5mrad 10mrad Nadal Figure B-28. Comparison of solid and IRW wheelset, 5 mrad AOA. 0 2 4 6 8 10 12 14 16 18 20 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Flanging Wheel L/V Ratio Cl im b Di st an ce (f ee t) IRW, mu-nf=0.001 Solid, mu-nf=0.001 IRW, mu-nf=0.5 Solid, mu-nf=0.5 Figure B-30. Comparison of proposed wheel L/V ratio criterion with simulation (Wheel 6). 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 0 5 10 15 20 Wheel Set Angle of Attack (mrad) ti miL V/L Simulation Proposed

Without onboard AOA measurement system, (B-26) Although Wheel 6 is the same profile shape as used for freight cars, the proposed distance criterion is less conserv- ative (longer distances) than the proposed distance criterion for freight cars. This is because the passenger vehicles nor- mally have truck designs that control axle yaw angles better than standard freight cars and in some instances have softer primary suspensions that provide for better axle steering, resulting in lower AOA and longer flange climb distances. 2.7 COMPARISONS AND ANALYSIS Figure B-32 compares all the above flange-climb-distance criteria and the proposed criterion for freight cars (3). As dis- cussed in Section 2.1, the wheel L/V ratio decreases with the increase of wheelset AOA and converges to the Nadal value. L/V Distance (feet) 2 * AOAe 2.2 < + 49 B-20 Figure B-32 shows that climb distances of all these different wheelsets decrease with increasing wheelset AOA and also converge to a corresponding asymptotic value. To under- stand the meaning of the asymptotic value, the wheel climb- ing process has to be examined in detail. The wheelset climbing process is divided into two phases that are dependent on the wheel/rail contact positions. In the first phase, the flanging wheel contacts the rail at the maximum flange angle and begins to climb. The maximum flange angle is maintained for a certain length on the flange. For example, the length of Wheel 1 for maximum flange angle (63 degrees) is about 0.331 in. (8.4 mm). When the wheel climbs above the maximum flange angle, the wheel contacts the rail at the flange tip and begins the second climbing phase, with the contact angle reducing as the climb continues. The whole climbing process ends when the flange angle reaches 26.6 degrees. This is the point at which the wheelset can no longer fall back down the gage face of the rail by itself if the lateral flanging force is suddenly removed (corresponding to a friction coefficient of µ = 0.5, as described in Section 2.1). Figures B-33 and B-34 show the flanging wheel contact angle during climb and L/V ratio at 10 mrad AOA. The Figure B-31. Comparison of proposed L/V distance criterion with simulation (Wheel 6). 0 5 10 15 20 25 0 2 4 6 8 10 12 Wheel Set Angle of Attack (mrad) )teef( ec natsiD b milC Simulation Proposed Figure B-32. L/V distance comparison for different wheelset profiles. 0 5 10 15 20 25 0 2 4 6 8 10 Curve Curvature (degree) )teef( ec natsiD b milC Wheel 1 Wheel 2 Wheel 3 Wheel 4/5 Wheel 6 Freight Car[3] Wheel 1: D=5/(0.13*AOAe+1) Wheel 2: D=4.1/(0.16*AOAe+1) Wheel 3: D=4.2/(0.136*AOAe+1) Wheel 4/5: D=28/(2*AOAe+1.5) Figure B-33. Wheelset 1 contact angle, 10 mrad AOA. -70 -60 -50 -40 -30 -20 -10 0 0 2 4 6 8 10 12 Travel Distance (feet) )eergeD( elg nA tcat n oC a b Figure B-34. Wheelset 1 L/V ratio, 10 mrad AOA. -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 0 2 4 6 8 10 12 Travel Distance (feet) oit a R V/ L l e e h W a b

climbing distances are defined as “a” and “b” corresponding to the two climbing phases. In the first phase, where the con- tact stays on the maximum flange angle part of the flange (corresponding to arc QP in Figure B-5), a climbing ratio can be defined as a/(a+b). Figure B-35 shows that when the L/V ratio is greater than 1 and the AOA is greater than 10 mrad, the first phase climbing ratio is about 30 percent. This means that, for these conditions, 30 percent of the climb distance is on the maximum flange angle and 70 percent of the climb distance is on the flange tip. As shown in Figures B-35 through B-39, for different wheel profiles, the whole climbing process is dominated by the phase of climbing on the flange tip (corresponding to arc PO in Figure B-5) for large wheelset AOA (above 5 mrad) and large L/V ratios (above 1.5 for 63 or 60 degrees maxi- mum flange angle, above 2 for 75 degrees maximum flange angle). However, when the wheelset AOA is relatively small and the L/V ratio is lower, the whole climbing process is B-21 dominated by the first climbing phase and the wheelset mainly climbs on the maximum flange angle parts and then quickly derails. Based on the above analysis, the wheel-climb distance is controlled by both the wheel/rail contact angle and the flange length, which includes the maximum flange angle length and the flange tip length. At a low AOA (<5 mrad) and a low L/V ratio, the wheel-climb distance is mainly determined by the maximum wheel flange angle—the higher the angle, the longer the climb distance. At a high AOA (>5 mrad) and a high L/V ratio, the wheel-climb distance converges to a lim- iting value. This limiting value is correlated with the wheel flange length, as demonstrated by the simulations. In very simple terms, the longer the flange length, the longer the climb distance limit. A comparison of Nadal value and the proposed climb dis- tance limits for the six different wheel profiles are listed in Table B-3. Figure B-35. Wheel 1 staying ratio with varying L/V ratio and AOA. 0 10 20 30 40 50 60 70 80 90 100 0.5 1 1.5 2 2.5 Flanging Wheel L/V Ratio elg nA eg nalF xa M no g niyatS ) %(oitaR 0mrad 2.5mrad 5mrad 10mrad 20mrad Figure B-37. Wheel 3 staying ratio with varying L/V ratio and AOA. 0 10 20 30 40 50 60 70 80 90 elg nA eg nalF xa M no g niyatS ) %(oitaR 0.50 1 1.5 2 2.5 Flanging Wheel L/V Ratio 0mrad 2.5mrad 10mrad5mrad Figure B-36. Wheel 2 staying ratio with varying L/V ratio and AOA. 0 10 20 30 40 50 60 70 80 90 100 elg nA eg nalF xa M no g niyatS ) %( oitaR 0.5 1 1.5 2 2.5 Flanging Wheel L/V Ratio 0mrad 2.5mrad 5mrad 10mrad Figure B-38. Wheel 4 staying ratio with varying L/V ratio and AOA. 0 10 20 30 40 50 60 70 80 90 elg nA eg nalF xa M no g niyatS ) %( oitaR 31 1.5 2 2.5 Flanging Wheel L/V Ratio 0mrad 2.5mrad 5mrad 10mrad

Figure B-40 shows the relationship between the flange- climb-distance limit and flange length. In general, the climb distance limit increases with increasing flange length. This conclusion means both the flange contact angle and the flange length play an important role in preventing derail- ment: increasing both the maximum flange angle and the flange length can increase the climb distance, thus improving derailment safety. The climb distance criterion, dependent on the AOA and flange parameters, will be further investigated in Phase II of this program. 2.8 CONCLUSIONS FOR SINGLE WHEELSET SIMULATIONS Based on the single wheelset simulation results, wheel flange climb derailment criteria for transit vehicles have been proposed that are dependent on the particular wheel profile characteristics. The following conclusions can be drawn from the analyses performed: • New single wheel L/V distance criteria have been pro- posed for transit vehicles with specified wheel profiles: B-22 (1) Wheel 1 profile: (2) Wheel 2 profile: (3) Wheel 3 profile: (4) Wheel 4/5 profile: (5) Wheel 6 profile: L/V Distance (feet) if AOA 10 mrad= ≥2 2. , if AOA 10 mrad< L/V Distance (feet) 2 * AOA < + 49 2 2. , L/V Distance (feet) if AOA 10 mrad= ≥1 3. , if AOA 10 mrad< L/V Distance (feet) 2 * AOA 1.5 < + 28 , L/V Distance (feet) if AOA 10 mrad= ≥1 8. , if AOA 10 mrad< L/V Distance (feet) 0.136 * AOA 1 < + 4 2. , L/V Distance (feet) if AOA 0 mrad= ≥1 6 1. , if AOA 10 mrad< L/V Distance (feet) 0.16 * AOA 1 < + 4 1. , L/V Distance (feet) if AOA 10 mrad= ≥2 2. , if AOA 10 mrad< L/V Distance (feet) 0.13 * AOA 1 < + 5 , Figure B-39. Wheel 5 staying ratio with varying L/V ratio and AOA. 0 10 20 30 40 50 60 70 80 90 oitaR elg nA eg nalF xa M no g niyatS ) %( 1 1.5 2 2.5 3 Flanging Wheel L/V Ratio 0mrad 2.5mrad 5mrad 10mrad Items Wheel 1 Wheel 2 Wheel 3 Wheel 4/5 Wheel 6 Maximum Flange Angle (Degree) 63.361 63.243 60.483 75.068 75.125 Nadal Value 0.748 0.745 0.671 1.130 1.132 Flange Length (mm) (in.) 19.149 0.754 11.853 0.467 17.232 0.678 10.038 0.395 15.687 0.618 Climb Distance in feet (at 10 mrad AOA) 2.174 1.577 1.780 1.302 2.207 TABLE B-3 Nadal values and climb distance limits for different wheelset profiles

where AOA is in mrad. In situations where AOA is not known and cannot be measured, the equivalent AOA (AOAe) calculated from curve curvature and truck geometry should be used in the above criteria. • If the AOA is known and can be measured, more accu- rate new single wheel L/V ratio criteria based on AOA have also been proposed (see corresponding equation in Chapter 2). • The single wheel L/V ratio required for flange climb derailment is determined by the wheel maximum flange angle, friction coefficient, and wheelset AOA. • The L/V ratio required for flange climb converges to Nadal’s value at higher AOAs (above 10 mrad). For lower wheelset AOAs, the wheel L/V ratio necessary for flange climb becomes progressively higher than Nadal’s value. • The distance required for flange climb derailment is determined by the L/V ratio, wheel maximum flange angle, wheel flange length, and wheelset AOA. • The flange-climb distance converges to a limiting value at higher AOAs and higher L/V ratios. This limiting value is highly correlated with wheel flange length. The longer the flange length, the longer the climb distance. B-23 For lower wheelset AOAs, when the L/V ratio is high enough for the wheel to climb, the wheel-climb distance for derailment becomes progressively longer than the proposed flange-climb-distance limit. The wheel-climb distance at lower wheelset AOAs is mainly determined by the maximum flange angle and L/V ratio. • Besides the flange contact angle, flange length also plays an important role in preventing derailment. The climb distance can be increased through the use of higher wheel maximum flange angles and longer flange length. • The flanging wheel friction coefficient significantly affects the wheel L/V ratio required for flange climb: the lower the friction coefficient, the higher the single wheel L/V ratio required to climb the rail. • For conventional solid wheelsets, a low nonflanging wheel friction coefficient has a tendency to cause flange climb at a lower flanging wheel L/V ratio. Flange climb occurs over a shorter distance for the same flanging wheel L/V ratio. • The proposed L/V ratio and flange-climb-distance crite- rion are conservative because they are based on an assump- tion of a low nonflanging wheel friction coefficient. • For independent rotating wheelsets, the effect of the nonflanging wheel friction coefficient is negligible because the longitudinal creep force vanishes. • The proposed L/V ratio and flange-climb-distance crite- rion are less conservative for independent rotating wheels because independent rotating wheels do not gen- erate significant longitudinal creep forces. • For the range of track lateral stiffness normally present in actual track, the wheel-climb distance is not likely to be significantly affected by variations in the track lateral stiffness. • The effect of inertial parameters on the wheel-climb dis- tance is negligible at low speeds. • At high speeds, the climb distance increases with increasing wheelset rotating inertia. However, the effect of inertial parameters is not significant at a low non- flanging wheel friction coefficient. Figure B-40. Relation between the climb distance limit and the flange length. 0 0.5 1 1.5 2 2.5 9 11 13 15 17 19 Flange Length (mm) )teef( ti miL ecnatsiD b milC

CHAPTER 3 TRANSIT VEHICLES FLANGE CLIMB DERAILMENT SIMULATIONS An AOA measurement is not usually available in practice. Therefore, the proposed criteria based on curvature will nor- mally be used. These are validated in this section of this report. Three types of hypothetical passenger cars represent- ing heavy rail and light rail transit vehicles have been mod- eled. The proposed criteria were applied to the simulation results to evaluate the validity of the proposed criteria. The vehicle models include typical passenger car connec- tions, such as air bag suspensions and articulated units. The wheel/rail connection parameters in the vehicle models cor- respond to the values adopted in the single wheelset model in Chapter 2. Other suspension parameters were estimated according to the research team’s previous experience in sim- ulation of passenger vehicles. 3.1 HEAVY RAIL VEHICLE 3.1.1 The Vehicle Model The vehicle modeled is a typical heavy rail transit system vehicle. It has H-frame trucks, chevron primary suspension and secondary air suspension. The principal dimensions of the car are as follows: (1) car length over couplers 67 ft 10 in., (2) rigid wheel base 6 ft 10 in., (3) wheel diameter 28 in., and (4) truck centers 47 ft 6 in. A loaded car weight of 108,664 pounds was used to calculate the required car body mass and mass moment of inertias for the vehicle model. Overall, a total of 12 bodies and 60 connections were used to assemble the simulation model. 3.1.2 Track Geometry Input Data The track input to the simulations comprises track geome- try data and track curve data. The track geometry data is used to specify perturbed track input to the model and consists of lateral and vertical perturbation amplitudes of each rail at spec- ified positions along the track. The track curve data is used for specifying the superelevation and curvature of the track. For these simulations, measurements of actual track with a large alignment and cross level perturbation in a curve were adopted because they were expected to generate conditions that could lead to wheel flange climb derailment. The input data included the curvature, superelevation, gage, cross level, B-24 profile, and alignment perturbations along the track. Figures B-41 through 46 show the curvature, superelevation, and per- turbations. A large drop in left rail vertical direction, align- ment, and cross level perturbation can be found at the 558-ft distance. The track geometry coordinate system follows right-hand rules. The longitudinal axis is parallel to the track centerline, with positive displacements in the direction of travel. The lateral axis is perpendicular to the track centerline and is pos- itive pointing to the left, when viewed in the direction of motion. The vertical axis is positive pointing upward to Figure B-41. Track curvature. –7 –6 –5 –4 –3 –2 –1 0 0 100 200 300 400 500 600 700 800 Distance (feet) )eergeD( erutavruC Figure B-42. Track superelevation. 0 100 200 300 400 500 600 700 800 Distance (feet) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 )hcni( noitavelerepuS

B-25 3.1.3 Heavy Rail Vehicle Simulation Results Simulations for the heavy rail vehicle were made for two different wheel profiles to validate the corresponding pro- posed L/V ratio and distance-to-climb criteria. The first wheel/rail profile combination used was Wheel 1 on standard AREMA 115-10 lb/yd rail. These are the same as used for the Wheel 1 single wheelset simulations discussed in Section 2.1. The rail/wheel friction coefficient is 0.5. The second wheel/rail profile combination used was Wheel 2 on standard AREMA 115-10 lb/yd rail. These are the same as used for the Wheel 2 single wheelset simulations discussed in Section 2.2. The rail/wheel friction coefficient is 0.5. Both wheel profiles have a 63-degree flange angle, but Wheel 2 has a much shorter flange length and a correspond- ingly shorter distance-to-climb criterion. The simulations were conducted for a range of speeds to generate a range of flange climbing conditions: • Contact with maximum flange angle but not flange climbing. • Flange beginning to climb up the rail but not derailing (incipient derailment). • Flange climbing that terminated in derailment. This range of conditions represents what happens to actual vehicles when they encounter severe track perturbations. The proposed criteria were evaluated by comparing them to the results for these different flange climb conditions. 3.1.3.1 Heavy Rail Vehicle Assembled with Wheelset 1 Simulation results show that the first axle begins to climb at a track location of 555.5 ft (distance referred to the first axle). This is the location of the large lateral and vertical Figure B-43. Left rail lateral position. –0.4 –0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 )hc ni( n oitis oP liaR tfeL laretaL 0 100 200 300 400 500 600 700 800 Distance (feet) Figure B-44. Right rail lateral position. –0.8 –0.6 –0.4 –0.2 0 0.2 0.4)hc ni( n oitis oP liaR thgiR laretaL 0 100 200 300 400 500 600 700 800 Distance (feet) Figure B-45. Left rail vertical position. –0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 )hc ni( noitisoP liaR tfeL lacitreV 0 100 200 300 400 500 600 700 800 Distance (feet) Figure B-46. Right rail vertical position. –0.2 –0.1 0.0 0.1 0.2 0.3 0.4 hc ni( noitisoP liaR thgiR lacitreV ) 0 100 200 300 400 500 600 700 800 Distance (feet) complete the coordinate system. Negative curvature indi- cates a right-hand curve; positive superelevation is for a superelevated right-hand curve. Correspondingly, the left wheel climbs on the left rail while the vehicle travels through the right-hand curve.

track geometry perturbations. Distance histories of wheel L/V ratio along the track at speeds of 40, 50, and 60 mph are given in Figure B-47. As the speed increases, the high L/V ratio is sustained for a longer distance. This results in the wheel being at the maximum flange angle for a longer dis- tance, as shown in Figure B-48, corresponding to a longer flange climb distance. For Wheelset 1, the Nadal value is 0.748. According to Equation B-3, the proposed L/V ratio limiting value is 0.74. B-26 This value is based on the single wheelset simulations pre- sented in Chapter 2, with a flanging wheel friction coefficient of 0.5 and a nonflanging wheel friction coefficient of 0.001. Because the whole vehicle simulations are made with a fric- tion coefficient of 0.5 on both wheels, the criterion given by Equation B-3 is conservative. It is appropriate to use the con- servative value because of the uncertainty of actual friction coefficients in service. When the wheel L/V ratio is over the limiting value, the wheel begins climbing on the flange and the climbing process ends at the point when the L/V ratio is lower than the limit- ing value. This climb distance calculation method is used for the analysis of all vehicle simulation results in Chapter 3. This is a more conservative and practical definition than used in Chapter 2, which was defined based on the flange angle of 26.6 degrees on the flange tip. The corresponding climb distances listed in Table B-4 show that the climb distance becomes longer with increasing speed. The curvature at this track location is 1.95 degrees (see Figure B-41). According to Equation B-4, the climb distance limit is 4.0 ft. When the vehicle travels at speeds lower than 50 mph, the climb distance is less than or equal to the limit- ing value, the wheel climbs to the maximum flange angle, and the contact angle remains at 63 degrees (Figure B-48). However, when the running speed is increased to 60 mph, the climb distance is 5.6 ft, which is over the limiting value. The wheel climbs above the maximum flange angle and reaches the flange tip between the distances of 557.5 and 559 ft. The contact angle changes from 63 degrees to 61.5 degrees, and the L/V ratio drops. As seen in Figure B-49, the RRD also increases signifi- cantly, indicating that the wheel is climbing the flange and making contact on the flange tip. Although the wheel falls back from flange contact to wheel tread contact after the climb process, it is regarded as an incipient derailment. It is a high risk for a vehicle to run in this situation; a small dis- turbance during practical running could lead to a derailment. As shown above, when the climb distance is greater than the proposed criterion value, the wheel climbs over the maximum flange angle onto the flange tip. Derailment could happen due to any small disturbance. Although derailment has not actually occurred, in practical terms it is considered an unsafe condi- tion when the climb distance exceeds the proposed criterion. The vehicle simulation results confirm the methodology and criterion proposed for Wheelset 1 in Section 2.1. TABLE B-4 First axle wheel-climb distance (ft) (Heavy Rail Vehicle, Wheel 1) Climb Distance 40 mph 555.5 558.5 3 50 mph 555.5 559.5 4 60 mph 555.2 560.5 5.3 Speed Start Climbing Point End Climbing Point Figure B-47. Wheel L/V ratio at different speeds (Heavy Rail Vehicle, Wheel 1). –1.00 –0.90 –0.80 –0.70 –0.60 –0.50 –0.40 –0.30 –0.20 –0.10 0.00 551 553 555 557 559 561 563 565 567 569 Travel Distance (feet) oita R V/L leeh W 40mph 50mph 60mph Nadal value Figure B-48. Wheel contact angle at different speeds (Heavy Rail Vehicle, Wheel 1). 0 10 20 30 40 50 60 551 553 555 557 559 561 563 565 567 569 Travel Distance (feet) )eerge D( elg n A tcat n oC 40mph 50mph 60mph

3.1.3.2 Heavy Rail Vehicles Assembled with Wheelset 2 Simulations for vehicles assembled with Wheelset 2 also show similar results to Wheelset 1: the climb distance becomes longer with the increasing speed, as shown in Table B-5 and Figure B-50. The Nadal value for the Wheel 2 profile is 0.745, the pro- posed L/V ratio limit value is 0.74, and the climb distance limit is 3.1 ft according to Equation B-11. When the vehicle travels at 50 mph, the climb distance is 4.0 (longer than the limiting value 3.1), the wheel still climbs on the maximum flange angle parts, and the contact angle stays at 63 degrees as seen in Figure B-51. This indi- cates that the proposed criterion for Wheel 2 is conserva- tive for this situation. Figure B-53 shows the variation of wheelset AOA dur- ing climb. According to the analysis in Chapter 2, the decrease of AOA leads to an increase of climb distance. But the climb distance is 5.6 ft when the running speed is increased to 60 mph, which is above the limiting value. The wheel climbs over the maximum flange angle and onto the flange tip between the distances of 558 and 561 ft. The con- tact angles changes from 63 degrees to 57 degrees, with a significant drop in the L/V ratio and contact angle. As seen in Figure B-52, the RRD also increases significantly when the wheel contacts at flange tip positions. B-27 In contrast to Wheel 1, when climbing onto the flange tip occurs, the contact angle of Wheel 2 reduces by 3 degrees while Wheel 1 reduces by only 1.5 degrees. Wheel 2 also climbs even farther onto the tip of the flange. As noted in Table B-3, the flange length of Wheel 2 is 9 mm shorter than that of Wheel 1. Therefore, although both wheels have the same maximum flange angle, the safety margin for Wheel 2 is even smaller, and its derailment probability is significantly increased. The simulation results for the heavy rail vehicles assembled with two different types of wheel profiles confirm the method- ology and criteria proposed for Wheel 1 and 2 in Chapter 2. Figure B-49. The wheel RRD at different speeds (Heavy Rail Vehicle, Wheel 1). –0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 551 553 555 557 559 561 563 565 567 569 Travel Distance (feet) )hc ni( ec nereffiD s uidaR g nill oR 40mph 50mph 60mph TABLE B-5 First axle wheel-climb distance (ft) (Heavy Rail Vehicle, Wheel 2) 40 556.4 560 3.6 50 556.4 560.4 4.0 60 556.4 562 5.6 Speed (mph) Start Climbing Point End Climbing Point Climb Distance Figure B-50. Wheel L/V ratio at different speeds (Heavy Rail Vehicle, Wheel 2). –1.00 –0.80 –0.60 –0.40 –0.20 0.00 555 558 560 563 565 568 570 Travel Distance (feet) oita R V/L leeh W 40mph 50mph 60mph Nadal Value Figure B-51. Wheel contact angle at different speeds (Heavy Rail Vehicle, Wheel 2). 0 10 20 30 40 50 60 555 557.5 560 562.5 565 567.5 570 Travel Distance (feet) )eerged( elg n A tcat n oC 40mph 50mph 60mph

3.2 ARTICULATED LOW FLOOR LIGHT RAIL VEHICLE (MODEL 1) 3.2.1 The Vehicle Model The vehicle modeled is a typical articulated low floor light rail transit vehicle. It is composed of three car bodies with three trucks. The end car bodies are each mounted on a single truck at one end and connected to an articulation unit at the other end. The center car body is the articulation unit riding on a single truck with independent rotating wheels. The prin- cipal dimensions of the vehicle are as follows: (1) rigid wheel base 74.8 in., (2) solid wheel diameter 28 in., (3) independent rotating wheel diameter 26 in., and (4) truck centers 289.4 in. Overall, a total of 26 bodies and 138 connections were used to assemble the simulation model. The rail/wheel friction coefficient is 0.5. The track input model is the same as used for the heavy rail vehicle as described in Section 3.1.2. B-28 3.2.2 Low Floor Light Rail Vehicle (Model 1) Simulation Results Simulations for the articulated low floor light rail vehicle (Model 1) were made for four different wheel profiles to validate the corresponding proposed L/V ratio and distance- to-climb criteria. The first wheel/rail profile combination used was Wheel 4 on standard AREMA 115 10-lb/yd rail. This is the same as that used for the Wheel 4 single wheelset simulations dis- cussed in Section 2.4. The rail/wheel friction coefficient is 0.5. This combination was applied to the end trucks of the articulated light rail vehicle. The second wheel/rail profile combination used was Wheel 5 (IRW) on standard AREMA 115 10-lb/yd rail. This is the same as that used for the Wheel 5 single wheelset sim- ulations discussed in Section 2.5. The rail/wheel friction coefficient is 0.5. This combination was applied to the mid- dle truck on the articulation unit of the light rail vehicle. Both of these wheel profiles have identical shapes with a 75-degree flange angle. However, Wheel 5 has independent rotating wheels. The third wheel/rail profile combination used was Wheel 3 on standard AREMA 115 10-lb/yd rail. This is the same as that used for the Wheel 3 single wheelset simulations dis- cussed in Section 2.3. The flange angle is 60 degrees and the rail/wheel friction coefficient is 0.5. This combination was applied to the end trucks of the articulated light rail vehicle. The fourth combination is the same profile as the third, but modified to have independent rotating wheels for application to the middle truck on the articulation unit of the light rail vehicle. The simulations were conducted for a range of speeds to generate a range of flange climbing conditions: • Contact with maximum flange angle, but not flange climbing. • Flange beginning to climb up the rail, but not derailing (incipient derailment). • Flange climbing that terminated in derailment. This range of conditions represents what happens to actual vehicles when they encounter severe track perturbations. The proposed criteria were evaluated by comparing them to the results for these different flange climb conditions. 3.2.2.1 Low Floor Light Rail Vehicle (Model 1) Assembled with Wheelsets 4 and 5 The first simulations of the light rail vehicle Model 1 were conducted with Wheelset 4 on the end trucks and Wheelset 5 (independent rotating wheels) on the center Figure B-52. The wheel RRD at different speeds (Heavy Rail Vehicle, Wheel 2). -0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 555 557.5 560 562.5 565 567.5 570 Travel Distance (feet) ) h c ni( e c n er effi D s ui d a R g nill o R 40mph 50mph 60mph Figure B-53. Wheelset AOA at different speeds (Heavy Rail Vehicle, Wheel 2). –4.0E-03 –2.0E–03 0.0E+00 2.0E–03 4.0E–03 6.0E–03 8.0E–03 1.0E-02 555 Travelling Distance (feet) m ra d) ( kcattA f o elg nA 40mph 50mph 60mph 557.5 560 562.5 565 567.5 570

truck under the articulation unit. Simulation results show the following: • The third axle begins to climb near the location of 579 ft distance (distance referred to the third axle). • The climb distance becomes progressively longer at higher speeds, as shown in Table B-6 and Figure B-54. • The third wheelset (Wheel 5, IRW) derails at the speed of 39 mph. For Wheel 5 profile, the Nadal limiting L/V ratio is 1.13. According to Equation B-20, the proposed L/V ratio limiting value is 1.0. The curvature at this location is 1.95 degrees and the climb distance limit is 5.2 ft, according to Equation B-23. When the vehicle travels at speeds lower than 30 mph, the flange-climb distance is less than the limiting value. The wheel climbs onto the maximum flange angle and the contact angle stays at 75 degrees, as seen in Figure B-55. However, when the running speed is increased to 37 mph, the climb dis- tance increases to 8.5 ft, which is over the limit value, and the wheel climbs over the maximum flange angle and reaches the flange tip between the distances of 581.7 and 582.3 ft. The contact angle changes from 74.5 degrees to 73.9 degrees, with an insignificant drop in the L/V ratio. However, the RRD B-29 (shown in Figure B-56) increases significantly when the wheel contacts at the flange tip position, clearly showing that the wheel has climbed over the maximum flange angle and is running on the flange tip. As shown in Figures B-54 through B-56, the third axle derails when the running speed is further increased to 39 mph. TABLE B-6 Third axle wheel-climb distance (ft) (Light Rail Vehicle 1, Wheel 5) Speed (mph) Start Climbing Point End Climbing Point Climb Distance 20 579.8 582.8 3 30 579.8 584.6 4.8 37 578.9 587.4 8.5 Figure B-56. Wheel RRD at different speeds (Light Rail Vehicle 1, Wheel 5). 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 578 580 582 584 586 588 590 Travel Distance (feet) hc ni( ec n er effi D s uid ar g nill o R ) 20mph 30mph 37mph 39mph Figure B-54. Wheel L/V ratio at different speeds (Light Rail Vehicle 1, Wheel 5). –2.30 –2.10 –1.90 –1.70 –1.50 –1.30 –1.10 –0.90 –0.70 –0.50 –0.30 –0.10 0.10 578 580 582 584 586 588 590 Travel Distance (feet) oit a R V/L l e eh W 20mph 30mph 37mph 39mph Nadal Value Figure B-55. Wheel contact angle at different speeds (Light Rail Vehicle 1, Wheel 5). 0 10 20 30 40 50 60 70 578 580 582 584 586 588 590 Travel Distance (feet) ) e erg e D( elg nA tc at n oC 20mph 30mph 37mph 39mph

This result gives a better demonstration of the high risk for vehicles to run when the climb distance is over the limiting value. The simulation results also confirm the validation of the proposed climb distance criteria discussed in Chapter 2. 3.2.2.2 Low Floor Light Rail Vehicles Assembled with Solid and IRW Wheelset 3 The second set of simulations of the light rail vehicle Model 1 were conducted with Wheelset 3 on the end trucks and Wheelset 3 modified with independent rotating wheels on the center truck under the articulation unit. Simulation results show the following: • The third axle begins to climb at the location of 580 ft distance (distance referred to the third axle). • The climb distance becomes longer with increasing speed before derailment occurs, as shown in Table B-7 and Figure B-57. • The third wheelset (independent rotating wheels) derails at a speed of 11 mph. For the Wheel 3 profile, the Nadal value is 0.67. Accord- ing to Equation B-14, the proposed L/V ratio limiting value B-30 is 0.66. The curvature at this location is 1.95 degrees and the climb distance limit is 3.3 ft according to Equation B-15. When the vehicle travels at speed lower than 10 mph, the climb distance is less than or equal to the limiting value. The wheel climbs onto maximum flange angle and the contact angle stays at 60 degrees, as seen in Figure B-58. However, when the vehicle travels at a speed of 10 mph, the climb distance equals the limiting value. Although the wheel still stays at the maximum flange angle, it has climbed farther up the flange than at 7 mph, as shown by the RRD in Figure B-59. When the running speed is increased a little more to 11 mph, the wheel climbs above the maximum flange angle, over the flange tip, and ultimately derails. In contrast to Wheel 5 discussed in the previous section, the IRW Wheel 3 is unacceptable for this kind of light rail vehicle. When derailment occurred, the climb distance was very rapid and much shorter than the proposed limiting value, which is to be expected. Compared to Wheel 5, the RRD for IRW Wheel 3 in Fig- ure B-59 increases significantly even when the wheel is still climbing on the maximum flange angle. This is an impor- tant characteristic for low maximum flange angle profile wheels. In other words, the very low maximum flange angle makes it easy for the wheelset to climb up on the flange tip, TABLE B-7 Third axle wheel-climb distance (ft) (Light Rail Vehicle 1, IRW Wheel 3) Speed (mph) Start Climbing Point End Climbing Point Climb Distance 7 580.1 581.9 1.8 10 580.2 583.5 3.3 11 580.2 581.5 1.3,Derail Figure B-57. Wheel L/V ratio at different speeds (Light Rail Vehicle 1, Wheel 3). –0.74 –0.64 –0.54 –0.44 –0.34 –0.24 –0.14 –0.04 0.06 Travel Distance (feet) oit a R V/L e eh W 7mph 10mph 11mph Nadal Value Figure B-58. Wheel contact angle at different speeds (Light Rail Vehicle 1, Wheel 3). 0 10 20 30 40 50 60 579 581 583 585 587 589 591 Travel Distance (feet) ) e erg e D( elg nA tc at n oC 7mph 10mph 11mph

even though there may be a longer maximum flange angle length. The simulation results for light rail vehicles assembled with Wheel 5 and Wheel 3 IRW profile wheelsets also con- firm the methodology and criteria proposed for them in Chapter 2. The significant difference in the simulation results for these two wheel profiles shows that optimization of wheel profiles are extremely important in the design of a particular vehicle. 3.3 ARTICULATED HIGH FLOOR LIGHT RAIL VEHICLE (MODEL 2) 3.3.1 The Vehicle Model The articulated high floor light rail vehicle Model 2, com- posed of two car bodies and three trucks, represents another typical type of articulated transit system vehicle. The two car bodies articulate on the middle truck, with all three trucks having solid wheelsets. The principal dimensions of the vehicle are as follows: (1) rigid wheel base 75 in., (2) wheel diameter 26 in., and (3) truck centers 275.5 in. Over- all, a total of 18 bodies and 85 connections were used to assemble the simulation model. The rail/wheel friction coef- B-31 ficient is 0.5. The track input model is the same as described in Section 3.1.2. 3.3.2 High Floor Light Rail Vehicle (Model 2) Simulation Results Simulations for the high floor articulated light rail vehicle ratio (Model 2) were made for two different wheel profiles to validate the corresponding proposed L/V ratio and distance- to-climb criteria. The first wheel/rail profile combination used was Wheel 2 on standard AREMA 115 10-lb/yd rail. This combination is the same as that used for the Wheel 2 single wheelset simu- lations discussed in Section 2.2. The rail/wheel friction coef- ficient is 0.5. The flange angle is 63 degrees. The second wheel/rail profile combination used was Wheel 3 on standard AREMA 115 10-lb/yd rail. This is the same as that used for the Wheel 3 single wheelset simulations discussed in Section 2.3. The rail/wheel friction coefficient is 0.5. The flange angle is 60 degrees. The simulations were conducted for a range of speeds to generate a range of flange climbing conditions: • Contact with maximum flange angle, but not flange climbing. • Flange beginning to climb up the rail, but not derailing (incipient derailment). • Flange climbing that terminated in derailment. This range of conditions represents what happens to actual vehicles when they encounter severe track perturbations. The proposed criteria were evaluated by comparing them to the results for these different flange climb conditions. 3.3.2.1 High Floor Light Rail Vehicle (Model 2) Assembled with Wheelset 2 Simulation results show the following: • The first axle begins to climb near the location of 555 ft distance (distance referred to the third axle). • The climb distance becomes progressively longer with increasing speed, as shown in Table B-8 and Figure B-60. Figure B-59. Wheel RRD at different speeds (Light Rail Vehicle 1, Wheel 3). 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 579 581 583 585 587 589 591 Travel Distance (feet) )hc ni( ec nereffiD s uidaR g nill oR 7mph 10mph 11mph Speed (mph) Start Climbing Point End Climbing Point Climb Distance 20 30 40 555.2 555.1 555 558.5 3.2 559 3.9 560 5 TABLE B-8 Third axle wheel-climb distance (ft) (Light Rail Vehicle 2, Wheel 2)

The Nadal value and proposed criterion for Wheel 2 have been listed in Section 3.1.3.2. The proposed L/V ratio limit- ing value is 0.74, and the proposed flange-climb-distance limit is 3.1 ft. When the vehicle travels at speeds lower than 30 mph, the climb distance is longer than the limiting value. The wheel climbs to the maximum flange angle face, and the contact angle stays at 63 degrees, as seen in Figure B-61. The pro- posed criterion for Wheel 2 is conservative for this situation (the same conclusion has been found in 3.1.3.2). However, when the running speed is increased to 40 mph, the climb distance is 5 ft—much higher than the limiting value. The wheel climbs above the maximum B-32 flange angle and onto the flange tip between the distances of 557.2 and 557.9 ft. The contact angle reduces from 63 degrees to 59.5 degrees, with a significant drop in the L/V ratio. At the same time, the RRD (shown in Figure B-62) increases significantly when the wheel contacts the rail on the flange tip. The vehicle is running unsafely in this condition. The simulation results of light rail vehicles (Model 2) assembled with Wheel 2 show that the criterion proposed for Wheel 2 in Section 2 is conservative at low speed, which is consistent with the conclusion in Section 3.1.1.2 for heavy rail vehicles assembled with the same profile wheelsets. However, the proposed criterion is still valid when the climb distance is much higher than the limit. 3.3.2.2 High Floor Light Rail Vehicle (Model 2) Assembled with Wheelset 3 The Nadal value and proposed criterion for Wheel 3 have been listed in Section 3.2.2.2. The proposed L/V ratio limit value is 0.66, the proposed climb distance limit is 3.3 ft. The simulation results for light rail vehicles (Model 2) assembled with Wheel 3 are shown in Table B-9 and Figures B-63 through B-65. In general the results are simi- lar to those of Wheel 2. The simulation results also show that the proposed climb distance criterion for Wheel 3 is valid when the climb distance is very much over the limit value, although it is con- servative for low speed situations. In contrast to Wheel 2, Wheel 3 takes more distance to climb at the same speed even though it has a smaller flange angle. This is because Wheel 3 has a longer flange length, which allows the wheel to climb in a longer distance. Figure B-60. Wheel L/V ratio at different speeds (Light Rail Vehicle 2, Wheel 2). –1.50 –1.30 –1.10 –0.90 –0.70 –0.50 –0.30 –0.10 0.10 554 556 558 560 562 564 566 Travel Distance (feet) oit a R V/L l e eh W 20mph 30mph 40mph Nadal Value Figure B-61. Wheel contact angle at different speeds (Light Rail Vehicle 2, Wheel 2). 0 10 20 30 40 50 60 554 556 558 560 562 564 566 Travel Distance (feet) Co nt ac t A ng le (d eg ree ) 20mph 30mph 40mph Figure B-62. Wheel RRD at different speeds (Light Rail Vehicle 2, Wheel 2). 0.00 0.10 0.20 0.30 0.40 0.50 0.60 554 556 558 560 562 564 566 Travel Distance (feet) R ol lin g Ra di us D iff er en ce (in ch ) 20mph 30mph 40mph

B-33 proposed in Chapter 2. The incipient derailment can be pre- dicted by applying these criteria in vehicle dynamics simula- tion analysis. The simulation results also show that the proposed climb distance criteria for low-maximum-flange-angle wheelsets are conservative at low speeds. For the simulations shown, once the flange climb reached the maximum flange angle the AOA began to reduce for two reasons: • Increased rolling radius causes the wheelset to start steering back (this does not happen for the IRW). • The track perturbation geometry changes, reducing the AOA. This reduction in AOA increases the effective L/V ratio limit and lengthens the effective flange-climb-distance limit. This has the effect, in general, of making the proposed crite- ria conservative. Because the L/V ratios and climb distance are sensitive to the wheelset AOA, the effects of AOA variation during climb need to be further investigated both by single wheelsets and vehicles simulations. Figure B-63. Wheel L/V ratio at different speeds (Light Rail Vehicle 2, Wheel 3). -1.3 -1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1 554 556 558 560 562 564 566 568 570 Travel Distance (feet) W he el L /V R at io 15mph 20mph 35mph Nadal Value Figure B-64. Wheel contact angle at different speeds (Light Rail Vehicle 2, Wheel 3). 0 10 20 30 40 50 60 554 556 558 560 562 564 566 568 570 Travel Distance (feet) )eergeD( elgnA tcatnoC 15mph 20mph 35mph Figure B-65. Wheel RRD at different speeds (Light Rail Vehicle 2, Wheel 3). 0.00 0.10 0.20 0.30 0.40 0.50 0.60 554 556 558 560 562 564 566 568 570 Travel Distance (feet) )hc ni( ec n er effi D s uid a R g nill o R 15mph 20mph 35mph TABLE B-9 Third axle wheel-climb distance (ft) (Light Rail Vehicle 2, Wheel 3) Start Climbing Point End Climbing Point Climb Distance Speed (mph) 15 20 35 555.5 559 555.3 555.1 559.3 560.7 3.5 4.0 5.6 3.4 VEHICLE SIMULATION SUMMARY In general, the simulation results for these three types of transit vehicles assembled with five different types of wheel profiles confirm the validity of the methodology and criteria

CHAPTER 4 CONCLUSIONS AND DISCUSSIONS 4.1 CONCLUSIONS Based on the single wheelset and vehicle simulation results, the following conclusions are drawn: • New single wheel L/V distance criteria have been pro- posed for transit vehicles with specified wheel profiles: Wheel 1 profile: Wheel 2 profile: Wheel 3 profile: Wheel 4/5 profile: Wheel 6 profile: L/V Distance (feet) if AOA 10 mrad= ≥2 2. , if AOA 10 mrad< L/V Distance (feet) 2 * AOA < + 49 2 2. , L/V Distance (feet) if AOA 10 mrad= ≥1 3. , if AOA 10 mrad< L/V Distance (feet) 2 * AOA 1.5 < + 28 , L/V Distance (feet) if AOA 10 mrad= ≥1 8. , if AOA 10 mrad< L/V Distance (feet) 0.136 * AOA 1 < + 4 2. , L/V Distance (feet) if AOA 0 mrad= ≥1 6 1. , if AOA 10 mrad< L/V Distance (feet) 0.16 * AOA 1 < + 4 1. , L/V Distance (feet) if AOA 10 mrad= ≥2 2. , if AOA 10 mrad< L/V Distance (feet) 0.13 * AOA 1 < + 5 , B-34 where AOA is in mrad. In situations where AOA is not known and cannot be measured, the equivalent AOA (AOAe) calculated from curve curvature and truck geometry should be used in the above criteria. • If AOA is known and can be measured, more accurate new single wheel L/V ratio criteria based on AOA have also been proposed (see corresponding equation in Chapter 2). • The simulation results for transit vehicles assembled with different types of wheel profiles confirm the valid- ity of the proposed criteria. • For most conditions, an incipient derailment occurs when the climb distance exceeds the proposed criterion value. • The proposed climb distance criteria are conservative for most conditions. Under many conditions, variations of AOA act to reduce the likelihood of flange climb. • The single wheel L/V ratio required for flange climb derailment is determined by the wheel maximum flange angle, friction coefficient, and wheelset AOA. • The L/V ratio required for flange climb converges to Nadal’s value at higher AOAs (above 10 mrad). For lower wheelset AOAs, the wheel L/V ratio necessary for flange climb becomes progressively higher than Nadal’s value. • The distance required for flange climb derailment is determined by the L/V ratio, wheel maximum flange angle, wheel flange length, and wheelset AOA. • The flange-climb distance converges to a limiting value at higher AOAs and higher L/V ratios. This limiting value is highly correlated with wheel flange length. The longer the flange length, the longer the climb distance. For lower wheelset AOAs, when the L/V ratio is high enough for the wheel to climb, the wheel-climb distance for derailment becomes progressively longer than the proposed flange-climb-distance limit. The wheel-climb distance at lower wheelset AOA is mainly determined by the maximum flange angle and L/V ratio. • Besides the flange contact angle, flange length also plays an important role in preventing derailment. The climb distance can be increased through use of higher wheel maximum flange angles and longer flange length. • The flanging wheel friction coefficient significantly affects the wheel L/V ratio required for flange climb; the lower the friction coefficient, the higher the single wheel L/V ratio required. • For conventional solid wheelsets, a low nonflanging wheel friction coefficient has a tendency to cause flange

climb at a lower flanging wheel L/V ratio, and flange climb occurs over a shorter distance for the same flang- ing wheel L/V ratio. • The proposed L/V ratio and flange-climb-distance crite- ria are conservative because they are based on an assump- tion of a low nonflanging wheel friction coefficient. • For independent rotating wheelsets, the effect of the nonflanging wheel friction coefficient is negligible because the longitudinal creep force vanishes. • The proposed L/V ratio and flange-climb-distance crite- ria are less conservative for independently rotating wheels because they do not generate significant longi- tudinal creep forces. • For the range of track lateral stiffness normally present in actual track, the wheel-climb distance is not likely to be significantly affected by variations in the track lateral stiffness. • The effect of inertial parameters on the wheel-climb dis- tance is negligible at low speeds. • At high speeds, the climb distance increases with increasing wheelset rotating inertia. However, the effect of inertial parameters is not significant at low nonflang- ing wheel friction coefficients. • Increasing vehicle speed increases the distance to climb. 4.2 DISCUSSION An AOA measurement is not usually available in practice. Therefore, the proposed climb distance criteria based on curvature will normally be used. For the situation of a vehi- cle running on tangent track, the equivalent AOAe is zero because the tangent line curvature is zero. However, under certain track perturbations and running speeds, the wheelset AOA could in practice be very large for some poor-steering trucks, such as typical freight car trucks, very worn passen- ger trucks, trucks with axle misalignments, and trucks with large turning resistance. Although certain types of trucks (H-frame passenger car trucks, trucks with soft primary sus- pension) could have small AOAs due to a better steering abil- ity, the criteria must be conservative enough to identify potential bad performance. For the cases on tangent lines, the criteria based on a zero AOAe may not be conservative enough to capture bad trucks. Most passenger rail cars (including transit and intercity cars) have truck designs that control axle yaw angles better than standard freight cars; and, in some instances, passenger cars have softer primary suspensions that provide for better axle steering, resulting in lower AOAs and longer flange climb distances. Therefore, the proposed criteria for transit cars are made less conservative than freight cars. However, there is no guarantee that all rail passenger cars have better truck designs, and the criteria must be made sufficiently con- servative to capture poor performance either from poor track quality or from poor axle steering. Rail passenger cars with good truck designs and good axle steering will meet the more conservative criteria because of their better steering B-35 capabilities. The more conservative criteria will provide a greater margin of safety for the better performing vehicles and ensure that the poor performing trucks are captured. Based on the single wheelset and complete car simulation results, both the L/V ratio and climb distance converge to cor- responding limit values when the wheelset AOA is over 10 mrad. Therefore, the 10-mrad AOA situation represents the most conservative case for wheelset climb derailment, which could be used as an alternative criterion for both tangent and curved track line cases together with the proposed criterion in this report. This has the significant advantage of proposing only one L/V criterion and one distance-to-climb criterion for a particular wheel/rail profile combination and they are not dependent on knowing AOA, curvature, truck design, or track perturbation conditions. The resulting criteria for Wheelset 1 using the AOA of 10 mrad would be: Although onboard AOA measurement is not available in practice, the wheelset AOA at a specific location can be mea- sured by a wayside measurement system. This system makes the 10-mrad criteria operational in practical running and tests. The 10-mrad criteria need further investigation and evaluation in comparison to the criteria proposed thus far. A significant concern with the proposed criteria is that they are specific to the particular wheel/rail profile combinations that were analyzed. The criteria appear to be dependent on details of the particular wheel and rail profile shapes. Although similar analyses could be performed to develop new criteria for a specific wheel and rail profile pair, it is rec- ognized that the transit industry would prefer to have some general formulas for calculating flange climb safety criteria for any conditions. Another concern is that the proposed criteria have been developed based on some simple assumptions of likely wheelset AOA in curved and straight track. Uncertainties regarding differences in the axle steering characteristics of different vehicles and the likelihood of encountering track geometry deviations that can cause local increases in wheelset AOA require that conservative assumptions be made, result- ing in proposed criteria that may be too conservative. The friction coefficient varies with the rail and wheel sur- face conditions and has important effects on derailment. A climb distance criterion taking the variation of friction coef- ficients into account will provide more valuable information for wheel/rail interaction mechanisms and rail vehicle safety. Under the conditions of flange climb, large lateral forces are likely to be present that may cause the rail to roll—espe- cially if the track structure is weak. Rail roll will change the wheel/rail contact conditions and may result in lower effec- tive contact angles and shorter effective maximum flange L/V Distance (feet) if AOA mrad< ≥2 2 10. , L V if AOA mrad< ≥0 74 10. ,

angle lengths, with consequent reductions in L/V limits and flange climb distances. The following are specific recommendations for work in the future to complete the validation efforts and to address some of these concerns: • Perform comparisons with results from full-scale tests to further validate the criteria proposed for transit vehicles. • Since the climb distance limit is highly correlated with the flange parameters (flange angle, length, height), fur- ther investigate and propose a general climb distance criterion that depends on both the AOA and flange parameters. B-36 • Because the L/V ratios and the climb distance are sen- sitive to the wheelset AOA, further investigate the effect of variations of AOA during flange climb using simula- tions of both single wheelsets and full vehicles. • Further develop flange-climb-distance criteria to account for the effects of carrying friction coefficient. • Perform additional single wheel simulations to investi- gate the effects of rail rotation. Because of the complexity of derailments and due to lim- ited funding, only a few of these tasks can be accomplished in Phase II. The rest of the recommended work may need continuing efforts in the future.

B-37 APPENDIX B-1: LITERATURE REVIEW B1.1 INTRODUCTION The research work performed for this project was based on methods developed by the research team during tests and analyses performed from 1994 to 1999 (1, 2). In recent years, other organizations have also been performing flange climb derailment research. A literature review was conducted to ensure their findings were understood prior to performing this research project. B1.2 BLADER (9) F. B. Blader (9) has given a clear description and discus- sion of wheel-climb research and safety criteria that had been examined or adopted by railroad operators and railroad test facilities as guidelines for safety certification testing of rail- way vehicles. Briefly, they are the following: • Nadal’s Single-Wheel L/V Limit Criterion. • Japanese National Railways’ (JNR) L/V Time Duration Criterion. • GM Electromotive Division’s (EMD) L/V Time Dura- tion Criterion. • Weinstock’s Axle-Sum L/V Limit Criterion. The Nadal single-wheel L/V limit criterion, proposed by Nadal in 1908 for the French Railways, has been used throughout the railroad community. Nadal established the original formulation for limiting the L/V ratio in order to minimize the risk of derailment. He assumed that the wheel was initially in two-point contact with the flange contact point leading the tread, and he concluded that the wheel material at the flange contact point was moving downwards relative to the rail material, due to the wheel rolling about the tread contact point. Nadal further theorized that wheel climb occurs when the downward motion ceases with the friction saturated at the contact point. Based on his assumption and a simple equilibrium of the forces between a wheel and rail at the single point of flange contact, Nadal proposed a limiting criterion as a ratio of L/V forces: L V = − + tan( ) tan( ) δ µ µ δ1 The expression for the L/V ratio criterion is dependent on the flange angle δ and friction coefficient µ. Figure B1-1 shows the solution of this expression for a range of values appropriate to normal railroad operations. The AAR has based its Chapter XI single-wheel L/V ratio criterion on Nadal’s theory using a friction coefficient of 0.5. Following several laboratory experiments and observations of actual values of L/V ratios greater than the Nadal criterion at incipient derailment, researchers at the Japanese National Railways (JNR) proposed a modification to Nadal’s criterion (4). For time durations of less than 0.05 s, such as might be expected during flange impacts due to hunting, an increase was given to the value of the Nadal L/V criterion. However, small-scale tests conducted at Princeton University indicated that the JNR criterion was unable to predict incipient wheel- climb derailment under a number of test conditions. A less conservative adaptation of the JNR criterion was used by the Electromotive Division of General Motors (EMD) in its locomotive research (5). More recently, Weinstock of the United States Volpe National Transportation Systems Center observed that this balance of forces does not depend on the flanging wheel alone (6). Therefore, he proposed a limit criterion that uti- lizes the sum of the absolute value of the L/V ratios seen by two wheels of an axle, known as the “Axle Sum L/V” ratio. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 50 55 60 65 70 75 80 85 Flange Angle (Degree) N ad al L /V V al ue 0.1 0.2 0.3 0.4 0.5 0.6 Figure B1-1. Nadal criterion values.

B-38 He proposed that this sum be limited by the sum of the Nadal limit (for the flanging wheel) and the coefficient of friction (at the nonflanging wheel). Weinstock’s criterion was argued to be not as overly conservative as Nadal’s at small or nega- tive AOA and less sensitive to variations in the coefficient of friction. The Weinstock criterion retains the advantage of simplic- ity. It can be measured with an instrumented wheelset, which measures the values of L/V ratio on both wheels. It is not only more accurate than Nadal’s criterion, it also has the merit of being less sensitive to errors or variations in the coefficient of friction. B1.3 50-MS DISTANCE CRITERION Based on the JNR and EMD research, and considerable experience in on-track testing of freight vehicles, a 0.05-s (50-ms) time duration was adopted by the AAR for the Chap- ter XI certification testing of new freight vehicles. This time duration has since been widely adopted by test engineers throughout North America for both freight and passenger vehicles. B1.4 FRA TRACK SAFETY STANDARDS (7) A flange-climb-distance limit of 5 ft was adopted by the FRA for their Class 6 high speed track standards (7). This distance limit appears to have been based partly on the results of the joint AAR/FRA flange climb research conducted by TTCI and also on experience gained during the testing of var- ious commuter rail and long distance passenger vehicles. B1.5 PREVIOUS TTCI RESEARCH (1–3) The results of wheel climb (also called flange climb) derailment testing and mathematical simulations performed with the TLV at the TTCI are summarized in Reference 1. The important conclusions are the following: • Large flanging rail friction and nonflanging friction dur- ing the test resulted in axle sum L/V ratios at wheel climb that were lower than the Chapter XI limit of 1.5. • All L/V force ratios found in the tests and with NUCARS simulations converged to the Nadal and Weinstock values at higher AOAs (10 to 15 mrad). At lower and negative AOAs, the predicated and measured L/V ratios exceeded Nadal and Weinstock values. • The wheel/rail coefficient of friction, the maximum wheel/rail contact angle, and the wheelset AOA have a major influence on the potential for wheel climb. • Vertical load unbalance does not affect the critical L/V values as computed by the Weinstock and Nadal equa- tions and the L/V ratios measured experimentally. Nadal’s original formulation assumes the worst sce- nario—that of a zero longitudinal creepage between wheel and rail. Shust et al. (1) propose a modified formulation using the effective coefficient of friction to replace the friction coefficient in Nadal’s formulation. The modified formulation is considered less conservative as it accounts for the presence of longitudinal creep forces that tend to provide a stabilizing effect to the wheel climb. Following the extensive tests of Reference 1, TTCI per- formed theoretical simulations of flange climb using the NUCARS model. This resulted in proposing a new maximum L/V ratio limit and flange-climb-distance limit (2). These were subsequently revised and presented in Reference 3. B1.6 DYNAMIC SAFETY (DYSAF) RESEARCH (10, 11) Kik et al.’s “Comparison of Result of Calculations and Measurements of DYSAF-tests” (10) compares results of calculations and measurements from this research project: DYSAF (assessment of vehicle-track interaction with special reference to DYnamic SAFety in operating conditions). A test running gear was developed to test derailment of a wheelset in guiding and unloaded conditions. The aim of this project was to investigate safety limits of derailment at high speed. The test was carried out in Velim, Czech Republic, in August 2000 to analyze derailment conditions at higher speeds up to 160 km/h. The test was performed in quasi- stationary conditions on a small circuit at low speeds (from 20 to 75 km/h) and dynamic conditions on a great circuit at high speed (from 80 to 160 km/h). The influence of AOA L/V ratio and duration of L/V were investigated in different test series. An extension to the existing Nadal’s formula was developed, but parameter identification in this formula has not been done yet. The lateral, vertical, and roll movement of rails and lateral movement of sleepers were included in the simulation model of 21 rigid bodies with 93 degrees of freedom (DOF). Mea- sured track irregularities, including gage as well as lateral and vertical alignment of left and right rail, were also stud- ied in the simulation. Special effort was made in the identifi- cation of simulation parameters such as friction coefficients. The authors reached the following conclusions: • For the higher velocity, the L/V ratio is much more dominated by higher frequency dynamics and it can no longer be neglected. Measurement of track irregularities should be improved to include the smaller wavelength defects. • A reasonable threshold of L/V ratio as a derailment cri- terion or a general multicriterion based on L/V ratio could not be derived until now. Simulation might be the best solution for safety investigations of railway vehicles.

B-39 Results of single wheelset derailment simulations, con- ducted as a part of the DYSAF research project, are presented by Parena et al. in “Derailment Simulation, Parametric Study” (11). The simulation cases were based on a wheelset model forced to derail by a lateral force on the level of track with and without excitations in vertical and roll direction, and excitations in the lateral direction. The influence of rail/wheel geometric and friction parameters, vertical load- ing, and lateral loading duration was investigated. The fol- lowing conclusions were reached: • Without influence of lateral sliding, a revised Nadal for- mula with 3/4 friction coefficient is quite useful to com- pute maximum L/V ratio. • Maximum L/V ratio occurs higher up the flange than the maximum angle of the flange, seemingly due to the lat- eral sliding of the wheel on the rail. • Nonsymmetric, low frequency vertical loading or lat- eral force excitation of longer duration reduces the maximum lateral force that the wheelset resists until derailment. • In any case, bounce and the lower sway of a vehicle should have different Eigen frequencies. If they are excited with nearly the same frequency, only very low lateral force might let the vehicle derail. B1.7 CLEMENTSON AND EVANS (12) Two real derailment incidents were investigated by Clementson and Evans (12). The first case study concerned the derailment of a loaded train of two-axle coal hopper cars on straight track. This derailment was caused by a combina- tion of cyclic twist and lateral and vertical alignment in the rails causing rocking of the cars. Dynamic simulations showed the build up of a swaying motion in the vehicle and the wheels lifting substantially off the rails at the point of derailment. The body roll and wheel loads confirmed a rolling response to the track geometry that resulted in the cyclic unloading of the wheels. At the derailment speed, it was found that the wheelsets were hunting. The second case study concerned the derailment by flange climbing of a loaded steel coil-carrying car fitted with Y25 bogies. Dynamic simulations showed that unequal dips in the two rails caused a pitching and swaying response of the wagon, which unloaded the leading outer wheel just as it ran into a lateral misalignment giving rise to a very high L/V ratio and subsequent flange climbing. An additional contributory factor was a fault in the vehicle suspension giving rise to an unequal static load distribution across the leading wheelset, combined with offset loading of the steel coil above the lead- ing bogie. Simulations were carried out at 40, 45, and 50 mph with three different load conditions. For nominal vehicles, the L/V ratio increased and was sustained for a longer distance. As the speed increased, the flange climbed to 3 mm and then dropped back. For the asymmetric vehicle, the flange climbed 22 mm to the flange tip and then derailed. B1.8 CHEN AND JIN (13) In “On a New Method for Evaluation of Wheel Climb Derailment,” Chen and Jin (13) propose a derailment index for evaluation of the wheel-climb derailment with the mea- surement of primary suspension forces. The purpose of the adoption of primary suspension forces was to replace the quasi-steady wheel/rail contact forces with dynamic suspen- sion forces for the calculation of derailment index. The derailment index was dependent on the wheelset AOA and vertical unloading ratio. B1.9 LITERATURE REVIEW SUMMARY Although considerable research into flange climb is under- way, there were no new criteria proposed. The only new cri- teria, single wheel L/V ratio criterion and L/V distance crite- rion for freight cars, were proposed by Wu and Elkins (2) and revised by Elkins and Wu (3). These were developed through wheel/rail interaction analysis and extensive NUCARS sim- ulations. The criteria are strongly dependent on AOA. If AOA cannot be measured, a reduced limit depending on cur- vature is recommended.

B-40 REFERENCES 1. Shust, W.C., Elkins, J., Kalay, S., and EI-Sibaie, M., “Wheel- Climb Derailment Tests Using AAR’s Track Loading Vehicle,” AAR report R-910, Association of American Railroads, Wash- ington, D.C., December 1997. 2. Wu, H., and Elkins, J., “Investigation of Wheel Flange Climb Derailment Criteria,” AAR report R-931, Association of Amer- ican Railroads, Washington, D.C., July 1999. 3. Elkins, J., and Wu, H., “New Criteria for Flange Climb De- railment,” IEEE/ASME Joint Railroad Conference paper, Newark, New Jersey, April 4-6, 2000. 4. Matsudaira, T., “Dynamics of High Speed Rolling Stock,” Japanese National Railways RTRI Quarterly Reports, Special Issue, 1963. 5. Koci, H.H., and Swenson, C.A., “Locomotive Wheel-Loading— A System Approach,” General Motors Electromotive Division, LaGrange, IL, February 1978. 6. Weinstock, H., “Wheel Climb Derailment Criteria for Evalua- tion of Rail Vehicle Safety,” Proceedings, ASME Winter Annual Meeting, 84-WA/RT-1, New Orleans, Louisiana, 1984. 7. Federal Railroad Administration, Track Safety Standards, Part 213, Subpart G, November 1998. 8. Wu, H., Shust, W.C., and Wilson, N.G., “Effect of Wheel/Rail Profiles and Wheel/Rail Interaction on System Performance and Maintenance in Transit Phase I Report,” Transit Coopera- tive Research Program report, February 2004. 9. Blader, F.B, “A Review of Literature and Methodologies in the Study of Derailments Caused by Excessive Forces at the Wheel/Rail Interface,” AAR report R-717, Association of American Railroads, Washington, D.C., December 1990. 10. Kik, W., et al., “Comparison of Result of Calculations and Measurements of DYSAF-tests, a Research Project to Investi- gate Safety Limit of Derailment at High Speeds,” Vehicle Sys- tem Dynamics, Supplement, Vol. 37, 2002, pp. 543-553. 11. Parena, D., Kuka, N., Masmoudi, W., and Kik, W., “Derail- ment Simulation, Parametric Study,” Vehicle System Dynam- ics, Supplement, Vol. 33, 1999, pp. 155-167. 12. Clementson, J., and Evans, J., “The Use of Dynamics Simula- tion in the Investigation of Derailment Incidents,” Vehicle Sys- tem Dynamics Supplement, Vol. 37, 2002, pp. 338-349. 13. Chen, G., and Jin, X., “On a New Method for Evaluation of Wheel Climb Derailment,” IEEE/ASME Joint Railroad Con- ference paper, Newark, New Jersey, April 4-6, 2000.