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8 TABLE 2.2 Estimation of constant c Axle Spacing Distance Vehicle Type Constant c (in.) LRV1 (with IRW) 74.8 3.08 LRV2 (Solid axles) 75 2.86 HRV (Solid axles) 82 2.04 TABLE 2.3 Conservative AOAe (mrad) for practical use Straight 5-Degree 10-Degree >10-Degree Vehicle and Truck Type Lines Curves Curves Curves Vehicle with IRW 10 15 20 Equation 2.5 + 10 Others 5 10 15 Equation 2.5 + 5 available or cannot be measured under certain circumstances, 30 an equivalent index, or effective AOA (AOAe), is proposed here in order to use the flange climb criteria. The AOAe is a 25 AOAe (mrad) function of axle spacing in the truck, track curvature, and 20 truck type. 15 The equivalent index AOAe (in milliradians) of the leading 10 axle of a two-axle truck can be obtained through a geometric 5 analysis of truck geometry on a curve (Equation 2.5): 0 0 2 4 6 8 10 12 41.67cl AOAe = 0.007272clC = (2.5) Curvature (degree) R IRW Solid Wheelset where c = a constant for different truck types, Figure 2.3. Recommended conservative AOAe for l = axle spacing distance (in.), practical use. C = curve curvature (degrees), and R = curve radius (ft). Table 2.2 lists the constant c obtained from simulations for 2.4 DEFINITION OF FLANGE CLIMB DISTANCE three types of representative transit vehicles: a Light Rail Vehicle Model 1 (LRV1) with independent rolling wheels in The climb distance used here is defined as the distance trav- the center truck, a Light Rail Vehicle Model 2 (LRV2), and eled starting from the point at which the limiting L/V ratio a Rapid Transit Vehicle (HRV). Therefore, the AOAe can be (Equation 2.1 and 2.2) is exceeded (equivalent to the point estimated according to the track curvature (C) and known "A" in Figure B-4 of Appendix B) to the point of derailment. constant c (Equation 2.5). For the purposes of these studies, the point of derailment was Due to the track perturbations and the degrading of determined by the contact angle on the flange tip decreasing wheelset steering capability, the practical wheelset AOA to 26.6 degrees after passing the maximum contact angle. could be higher than the value calculated by Equation 2.5. The 26.6-degree contact angle corresponds to the minimum Table 2.3 shows the AOAe values recommended for use in contact angle for a friction coefficient of 0.5. Figure 2.4 shows the distance criterion of Equation 2.4. These values for the wheel flange tip in contact with the rail at a 26.6-degree AOAe were considered conservative enough according to angle. Between the maximum contact angle (point Q) and the the simulation results and test data. 26.6-degree flange tip angle (point O), the wheel can slip back When the vehicle runs on a curve with the curvature lower down the gage face of the rail due to its own vertical axle load than 10 degrees and not listed in Table 2.3, it is recom- if the external lateral force is suddenly reduced to zero. In this mended that a linear interpolation between the segment condition, the lateral creep force F (due to AOA) by itself is points in Table 2.3 should be used in the criterion, as shown not large enough to cause the wheel to derail. in Figure 2.3. The statistical data from an AOA wayside When the wheel climbs past the 26.6-degree contact angle monitoring system should be used in the criterion to take into (point O) on the flange tip, the wheel cannot slip back down account the many factors affecting AOAe if such a system is the gage face of the rail due to its own vertical axle load: the available. lateral creep force F generated by the wheelset AOA is large