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10 2.6 EFFECT OF SPEED ON DISTANCE TO CLIMB Equation 2.8. The examples in the following section demonstrate the application of flange climb criteria in track The above criteria, both the general formula and biparam- tests. eter method, were derived based on the flange climb simula- tion results of a single wheelset running at a speed of 5 mph. Simulation results show the climb distance slightly increases 2.8 EXAMPLES OF APPLICATION OF FLANGE with increasing running speed due to increased longitudinal CLIMB CRITERIA creep force and reduced lateral creep force (2), as shown in As an example of their application, the flange climb criteria Figure 2.6. were applied to a passenger car with an H-frame truck under- The dynamic behavior of wheelset becomes very compli- going dynamic performance tests at the FRA's Transportation cated at higher running speed (above 80 mph for 5 mrad Technology Center, Pueblo, Colorado, on July 28, 1997. The AOA and above 50 mph for 10 mrad AOA). However, the car was running at 20 mph through a 5 degree curve with 2 in. distance limit derived from the speed of 5 mph should be vertical dips on the outside rail of the curve. The L/V ratios conservative for higher operating speeds. were calculated from vertical and lateral forces measured from the instrumented wheelsets on the car. 2.7 APPLICATION OF FLANGE CLIMB CRITERIA Table 2.4 lists the 4 runs with L/V ratios higher than 1.13, exceeding the AAR Chapter XI flange climb safety criterion. 2.7.1 In Simulations The rails during the tests were dry, with an estimated friction coefficient of 0.5. The wheel flange angle was 75 degrees, The application of flange climb criteria in simulations can resulting in a corresponding Nadal value of 1.13. be found in Chapter 3 of Appendix B. The climb distance and average L/V in Table 2.4 were cal- culated for each run from the point where the L/V ratio exceeded 1.13. 2.7.2 In Track Tests In tests, when AOA is unknown or can't be measured, the 2.8.1 Application of General Flange Climb AOAe described in Section 2.3 has to be estimated using Criterion The instrumented wheelset has the AAR-1B wheel profile with 75.13 degree maximum flange angle and 0.62 in. flange 5 Flange Climb Distance (feet) length; by substituting these two parameters into the general 4 flange climb criterion, the flange criterion for the AAR-1B wheel profile is as follows: 3 26.33 2 D< AOAe + 1.2 1 0 The axle spacing distance for this rail car is 102 in. The 0 20 40 60 80 constant c was adopted as 2.04 since the vehicle and truck Travel Speed (mph) design is similar to the heavy rail vehicle in Table 2.2. AOA=10 mrad AOA=5 mrad According to Equation 2.5, the AOAe is about 7.6 mrad for this passenger H-frame truck on a 5-degree curve. By substi- Figure 2.6. Effect of travel speed on distance to wheel tuting the AOAe into the above criteria, the safe climb dis- climb. (L/V ratio = 1.99, AAR-1B wheel (75-degree flange tance without derailment is 3 ft. According to Table 2.3, the angle) and AREMA 136 RE rail.) conservative AOAe for a 5-degree curve should be 10 mrad; TABLE 2.4 Passenger car test results: Climb distance and average L/V measured from the point where the L/V ratio exceeded 1.13, for friction coefficient of 0.5 Maximum Average L/V Runs Speed Climb Distance L/V Ratio Ratio rn023 20.39 mph 1.79 1.39 5.8 ft rn025 19.83 mph 2.00 1.45 6.3 ft rn045 19.27 mph 1.32 1.23 0.7 ft rn047 21.45 mph 1.85 1.52 5 ft
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11 the conservative safe climb distance without derailment is is even below the 20 mrad AOAe criterion line, which sel- 2.4 ft; however, the climb distance according to the 50 ms dom happened for an H-frame truck running on the 5-degree criterion is 1.4 ft. (The 50-ms criterion is discussed in Appen- curve. The other three runs were running unsafely because dix B, Section B1.3.) their climb distances exceeded the 10 mrad conservative The wheel, which climbed 0.7 ft distance in run rn045 with AOAe criterion line. a 1.23 average L/V ratio (maximum L/V ratio 1.32), was run- The same conclusion is drawn by applying the general ning safely without threat of derailment according to the cri- flange climb criterion and the biparameter flange climb cri- terion. The other three runs were unsafe because their climb terion to the passenger car test. The climb distances of these distances exceeded the criterion. two criteria also show that the general flange climb criterion is more conservative than the biparameter criterion. The rea- son for this is that the average L/V ratio in the test, which is 2.8.2 Application of Biparameters Criterion 1.23, is lower than the 1.99 ratio used in the simulation to derive the general flange climb criterion. The difference Figure 2.7 shows the application of the biparameters cri- between these two criteria shows the biparameter flange terion on the same passenger car test. The run (rn045) with climb criterion is able to reflect the variation of the L/V ratio. the maximum 1.32 L/V ratio is safe, since its climb distance However, the general flange climb criterion is conservative of 0.7 ft is shorter than the 4.3-ft criterion value calculated by for most cases since the sustained average 1.99 L/V ratio dur- the biparameter formula (Equation 2.7). The climb distance ing flange climb is rare in practice. 9 8 7 Climb Distance (feet) 6 5 4 3 2 1 0 1.1 1.2 1.3 1.4 1.5 1.6 Average L/V Ratio during Climb Measured Formula, 7.6 mrad AOA Formula, 10 mrad AOA Formula, 20 mrad AOA Figure 2.7. Application of the biparameter criterion for friction coefficient of 0.5.