Limiting High Speed Dynamic Forces on the Track Structure; The Amtrak Acela Case Allan M. Zarembski Ph.D., PE.; President, ZETA-TECH Associates, Inc. Joseph W. Palese, MCE, PE; Director Analytical Engineering, ZETA-TECH Associates John G. Bell, BSCE, MBA Program Director, High Speed Trainsets, Amtrak Abstract As vehicle operating speeds increase, the dynamic wheel/rail impact forces applied to the track structure likewise increase. This results in the potential for increased track degradation, component failure, and corresponding increased track maintenance costs. In the case of Amtrak s new generation high speed trains, a specific requirement for the design of the new equipment was to avoid any increase in dynamic forces applied to the track in spite of the increase in operating speed from 125 to 150 mph. In order to achieve this, and maintain (or possibly decrease) the dynamic wheel/rail forces, key equipment design characteristics, to include vehicle unsprung mass and suspension characteristics, were evaluated from this point of view. This report describes the process of examining alternative high-speed equipment designs from the perspective of the track structure and the level of dynamic force applied to the track. This includes the process used to evaluate the dynamic wheel/rail forces generated by both the older 125-mph equipment and the new generation high-speed (150-mph) equipment and the comparison between load levels. This also includes the methodology used to evaluate the potential for track damage (e.g. cracking of the concrete ties on the Northeast Corridor) associated with both the older equipment and the new high speed equipment.
Introduction and Background As vehicle operating speeds increase, the dynamic wheel/rail impact forces applied to the track structure likewise increase. This is particularly true for high-speed operations, where research shows potential for significant increases in wheel/rail dynamic forces in the higher speed ranges. This results in the potential for increased track degradation, component failure, and corresponding increased track maintenance costs. The challenge facing Amtrak in its introduction of it s new generation high speed trains was to minimize any increase in track maintenance associated with this new equipment as well as minimize any potential increase in damage to the track on the Northeast Corridor. The concrete ties on the corridor were a particular source of concern in light of the tie cracking problems that had been experienced by Amtrak in the 1980s. Noting this potential impact of high speed operations, a specific requirement for the design of the new equipment was to avoid any increase in dynamic vertical wheel/rail forces applied to the track from its current levels, in spite of the proposed increase in operating speed from 125 to 150 mph on the electrified Northeast Corridor. For non-electric (fossil fuel) operations, the criterion was similar, to avoid any increase in dynamic vertical forces from its current levels at operating speeds of up to 90 mph. The baseline loadings, set for current equipment and operations include operation of the AEM7 electric locomotive at 125 mph, the then maximum speed on the Northeast Corridor. The non-electric baseline was set for the F40 diesel locomotive operating at 90 mph. Note, locomotives were used for the baseline analysis because they had the highest axle loads and generated the greatest wheel/rail forces. The proposed vehicles that were analyzed came from three potential vendor teams; the vendor identities are masked in the technical discussion;
Consortium consisting of ABB and General Electric Consortium consisting of Siemens, MK, and Fiat Consortium consisting of Bombardier and Alsthom The specific trainset configurations are summarized in Table 1 below showing team, power source [electric (EL) or fossil fuel (FF)] and proposed maximum speed. Table 1 Trainset Fuel Maximum Speed A-1 EL 150 A-2 FF 125 B-1 EL 150 B-2 FF 125 C 1 EL 150 C 2 FF 125 D-1 FF 125 D-2 FF 125 D-3 FF 125 Note, categories A, B and C contain one proposed electric configuration and one proposed fossil fuel configuration from each consortium. The additional proposed configurations were consolidated in category D. Electric powered trainsets (EL) are designed for operation on the Northeast Corridor at speeds of 150 mph. The Fossil Fuel (FF) powered trainsets were for use in non-electrified territory and are designed for speeds of 125 mph. The baseline for the Electric powered trainsets is the AEM7 operating at 125 mph while the baseline for the fossil fuel trainsets is the F40 operating at 90 mph.
Analysis Approach As has already been noted, this paper examines the dynamic evaluation of the different configurations of high-speed trainsets for Amtrak and the comparison of the dynamic load levels with the loads generated by existing equipment operating on Amtrak s Northeast Corridor. Specifically, this analysis examines the dynamic impact forces applied by the new high speed trainsets as compared to the existing equipment, and determines whether there is an increase in loading (and thus potential damage) to the track structure. The dynamic impact forces examined are the P 1 and P 2 forces, as illustrated in Figure 1. As can be seen in this Figure, the P 1 force is a high amplitude short duration (high frequency) dynamic impact force, which is usually rapidly attenuated by the track structure. However, in the case of Amtrak s Northeast Corridor track, the P 1 forces are important from the point of view of damage (cracking) of concrete ties, a situation which Amtrak encountered in the late 70s early 1980s and corrected at that time. The P 2 force, on the other hand is a lower amplitude, longer duration (lower frequency) load. Because of its dynamic characteristics, P 2 forces are those forces that contribute most to track degradation, particularly degradation of track geometry, which is the largest maintenance expense on the corridor. Thus, for this evaluation, both the P 1 and P 2 forces were analyzed.
Figure 1. P1 and P2 Forces Diagram analysis. The P 1 and P 2 formulas defined by Jenkins in 1974 [1] and Ahlbeck in 1980 [2] were used in this For the P 1 force, the following formula was utilized: P = P + αv 1 0 2 Kh M' M' 1+ M u (1) where: P 0 = Static Wheel Load, (lbs) α = Rail Joint Dip Angle, (rad) V = Vehicle Speed, (in/sec) K h = Hertzian Contact Stiffness, (lb/in) M = Effective Mass of Rail and Tie, (lb-sec 2 /in) M u = Unsprung Vehicle Mass, (lb-sec 2 /in) Several of the input variables to the above equation were developed from individual component weights and characteristics using the set of equations listed below, originally developed by Jenkins [1].
It should be noted that the Hertzian Contact Stiffness (K h ) was taken as the linearized portion of the deflection equation for two elastic bodies in contact according to Hertzian contact stress theory. Further noting that the value for the dynamic force (P 1 ) is included in the equation for the Hertzian Contact Stiffness (K h ), this results in an iterative approach being necessary for finding the value of P 1. Since the equation converges rapidly, this was found to be a reasonable technique for determining P 1. For the P 2 force, the following formula was utilized: P M 2 t = P + 1 πξ [ 2α V] M + M 2 0 u t K M t u M u M + M u t 1 2 (2) where: P 0 = Static Wheel Load, (lbs) ξ = Track Effective Damping Ratio M t = Effective Track Mass, (lb-sec 2 /in) M u = Unsprung Vehicle Mass, (lb-sec 2 /in) α = Rail Joint Dip Angle, (rad) V = Vehicle Speed, (in/sec) K t = Effective Track Stiffness, (lb/in) As with the P 1 equation, several of the input variables to the above equation were developed from individual component weights and characteristics. The above theoretical formulas were used as the basis for calculating the dynamic impact forces. However, In order to relate these equations to specific Amtrak experience on the Northeast Corridor, actual dynamic wheel impact data from Amtrak s Impact Detector was used to calibrate these equations. Calibration of Dynamic Impact Force Equations: In order to calibrate the dynamic impact force equations, actual wheel load impact data for Amtrak operations on the Northeast Corridor was used. This wheel impact data, which was gathered by Amtrak s Impact Detector, was determined to be representative of the P 1 forces. Therefore the
calibration was performed for the P 1 equation. This equation uses vehicle and track specific data as input. The only variable that lends itself to calibration is the Hertzian Contact Stiffness (K h ), which has been the subject of some dispute by various authors. This is illustrated in Table 2 below. Table 2 Method K h (lb/in) Jenkins, Coned Wheel 10.79 x 10 6 Jenkins, Worn Wheel 12.93 x 10 6 Roark 8.27 x 10 6 Hertzian Theory 8.76 x 10 6 Ahlbeck 1 7.62 x 10 6 Ahlbeck 2, (Joint) 8.93 x 10 6 Ahlbeck 3, (Wheel Flat) 9.69 x 10 6 It can be seen that there is as much as a 70% variation in the values that can be used for the Hertzian Contact Stiffness (K h ). Therefore, the actual Amtrak impact data was used to calculate a reasonable value for this parameter. The first step in the calibration process was to collect locomotive wheel impact data from the impact detector. Data for a total of 101 trains was collected over a period of two days to include both static and dynamic load values for each wheel on each locomotive of each train This data was then analyzed with questionable outliers eliminated. The remaining data was determined to be representative of existing Northeast Corridor operations for AEM7 and F40 locomotives traveling at speeds greater than 80 mph. These two sets of locomotives were separated and a statistical mean and standard deviation were calculated for each locomotive as well as by axle position of each locomotive. The mean, standard deviation, and maximum statistical dynamic impact force are summarized below along with the average static force and average speed. The maximum statistical dynamic impact force is calculated as follows: P1 = P1 + 4 σ max P1 (3)
Where P 1max = maximum dynamic impact force P 1 σ P1 = Average dynamic impact force = Standard deviation of dynamic impact force In the above equation the mean is added to 4 times the standard deviation, thus defining the level of loading for 99.997% of all dynamic wheel loads (which are less than or equal to the P 1max value). Table 3 Locomotive Avg. Avg. Speed Static P 1 σ P1 P 1max (mph) (kips) (kips) (kips) (kips) AEM7 112.2 25.2 33.1 6.4 58.7 F40 98.4 32.2 42.0 5.2 62.8 The values presented in Table 3 above, were utilized in the P 1 dynamic impact force equation together with the relevant inputs as defined in Table 4. Table 4 Variable Value for Concrete Ties m r 136 RE Rail (0.0098 lb-sec 2 /in 2 ) m s 1.04 lb-sec 2 /in L 20 in EI 2.85 x 10 9 lb-in 2 α 0.003 radians (nominal track) V 90/125 mph Note that the rail joint dip angle (α) used during the calibration process was defined as 0.003 radians which represents track in nominal FRA Class 6 condition as expected in the location of the impact detector. Note; the joint dip angles used in the impact force equations are representative of any surface discontinuity or defect in the track such as at a joint of battered weld. The value of 0.003 was taken to be representative of normal Amtrak track, while a value of 0.006 was taken to be a worst case track condition. In fact, current FRA high-speed track classes (Classes 6 through 9) allow a maximum railhead mismatch of 1/8, which over a 36 length corresponds to a dip angle of 0.003,
consistent with the calibration results. Note; this work was performed prior to the change in FRA Track Classes in November 1998. Therefore, Class 6, as referred to here, represents 110 mph track, which was being operated at speeds of up to 125 mph on an FRA waiver to Amtrak. During the calculation of worse case forces, a value of 0.006 is used. This corresponds to a rail head mismatch of the order of 7/32 (over a 36 inch length) which is between Class 3 (3/16 ) and Class 2 (¼ ) and thus corresponds directly to a worst case track condition. The calibration constant was introduced into the Hertzian Contact Stiffness equation using the equation: K = P P A 1 0 h 2 3 G P1 P 2 3 0 (4) Where A is a calibration constant and the rest of the terms are as defined previously. An iterative approach was used to determine the calibration constants for the AEM7 and F40 based on the input data collected and the appropriate equations. The resulting calibration constants were calculated to be: A AEM7 = 0.57670 A F40 = 0.61975 These calibration constants were used in the remainder of the analyses. Analysis of Dynamic Impact Forces Calculation of Baseline Forces (P 1 and P 2 ): The baseline dynamic impact forces are those forces generated by existing Amtrak locomotives, specifically the AEM7 and F40. These forces were determined for wood and concrete crosstie track using the vehicle and track characteristics (Table 5) as follows:
Table 5 Variable Value for Wood Ties Value for Concrete Ties M r 136 RE Rail (0.0098 lb-sec 2 /in 2 ) 136 RE Rail (0.0098 lb-sec 2 /in 2 ) M s 0.26 lb-sec 2 /in 1.04 lb-sec 2 /in L 20 in 20 in EI 2.85 x 10 9 lb-in 2 2.85 x 10 9 lb-in 2 α 0.003/0.006 radians 0.003/0.006 radians (normal/poor) V-two cases (normal/poor) 90/125 mph for Fossil Fuel (Base/Proposed) 125/150 mph for Electric (Base/Proposed) Again, note that a rail joint dip angle (α) of 0.003 was used to represent normal track conditions and a value of 0.006 was used here to represent worse case track condition. The baseline dynamic impact forces (Table 6a and 6b) (existing equipment and operations) were determined as follows. The reference to new and worn is to the wheels. A new wheel has a greater mass and a larger radius than a worn wheel. Table 6a α =0.003: Wood Ties Concrete Ties P 1 P 2 P 1 P 2 No. Manu. New Worn New Worn 1 AEM7 47,045 48,498 44,001 60,238 62,688 52,293 2 F40 48,731 49,840 47,395 58,569 60,426 54,182 Based on Amtrak s successful application of the F-40 at up to 90 mph and the AEM-7 at 125 mph on the NEC the values at α =.003 are the acceptance values.
Table 6b α =0.006: Wood Ties Concrete Ties P 1 P 2 P 1 P 2 No. Manu. New Worn New Worn 1 AEM7 70,138 73,177 62,814 97,960 103,132 79,399 2 F40 65,600 67,892 62,290 86,085 89,965 75,865 These baseline dynamic impact forces for the existing Amtrak locomotives can then be compared to the P 1 and P 2 forces calculated for the proposed trainset configurations. Calculation of New Trainset Forces: The trainset configurations proposed by the three vehicle consortiums were used as input to the dynamic impact force equation using the method (Table 7a and 7b) described previously. The resulting dynamic impact forces for the different proposed trainsets are summarized below: Table 7a α =0.003: Wood Ties Concrete Ties P 1 P 2 P 1 P 2 No. Manu. New Worn New Worn 1 A1 48,011 49,834 42,465 63,125 66,201 50,856 2 A2 45,546 47,093 40,789 58,478 61,083 48,020 3 B1 50,021 51,809 43,405 65,242 68,254 51,384 4 B2 55,580 57,125 49,036 68,780 71,367 55,685 5 C1 47,488 49,268 39,253 62,112 65,104 46,063 6 C2 48,520 50,043 41,090 61,139 63,690 46,887 7 D1 48,467 49,990 40,562 60,942 63,490 46,057 8 D2 55,235 56,787 48,051 68,212 70,808 54,250 9 D3 51,170 52,700 44,984 64,236 66,803 51,544
Table 7b: α =0.006: Wood Ties Concrete Ties P 1 P 2 P 1 P 2 No. Manu. New Worn New Worn 1 A-1 75,213 79,044 62,430 107,299 113,826 79,213 2 A-2 68,622 71,860 57,828 95,945 101,451 72,291 3 B-1 77,568 81,322 62,670 109,851 116,237 78,629 4 B-2 79,291 82,504 65,090 107,006 112,444 78,389 5 C1 74,698 78,442 56,506 105,800 112,155 70,127 6 C2 71,768 74,951 55,679 98,402 103,787 67,274 7 D-1 71,661 74,843 54,624 97,998 103,375 65,624 8 D-2 78,811 82,040 63,334 106,070 111,527 75,732 9 D-3 74,686 77,878 60,949 102,197 107,607 74,247 Comparing these calculated dynamic impact forces to the baseline forces for the existing Amtrak equipment gives the results shown in Tables 8a and 8b. Note the results are presented as the percentage of baseline loads. Percentages greater than 100% indicate that the impact forces generated by the proposed equipment/speed combinations are greater than those generated by current operations. Table 8a. Comparison of High Speed Trainsets with Existing Equipment α =0.003: Wood Ties Concrete Ties P 1 P 2 P 1 P 2 No. Manu. New Worn New Worn 1 A-1 102.05% 102.75% 96.51% 104.79% 105.60% 97.25% 2 A-2 93.46% 94.49% 86.06% 99.84% 101.09% 88.63% 3 B-1 106.33% 106.83% 98.65% 108.31% 108.88% 98.26% 4 B-2 114.05% 114.62% 103.46% 117.43% 118.11% 102.77% 5 C1 100.94% 101.59% 89.21% 103.11% 103.85% 88.09% 6 C2 99.57% 100.41% 86.70% 104.39% 105.40% 86.54% 7 D-1 99.46% 100.30% 85.58% 104.05% 105.07% 85.00% 8 D-2 113.35% 113.94% 101.38% 116.46% 117.18% 100.12% 9 D-3 105.01% 105.74% 94.72% 109.68% 110.55% 95.13%
Table 8b. Comparison of High Speed Trainsets with Existing Equipment α =0.006: Wood Ties Concrete Ties P 1 P 2 P 1 P 2 No. Manu. New Worn New Worn 1 A-1 107.24% 108.02% 99.39% 109.53% 110.37% 99.77% 2 A-2 104.61% 105.84% 92.84% 111.45% 112.77% 95.29% 3 B-1 110.59% 111.13% 99.77% 112.14% 112.71% 99.03% 4 B-2 120.87% 121.52% 104.49% 124.30% 124.99% 103.33% 5 C1 106.50% 107.19% 89.96% 108.00% 108.75% 88.32% 6 C2 109.40% 110.40% 89.39% 114.31% 115.36% 88.68% 7 D-1 109.24% 110.24% 87.69% 113.84% 114.91% 86.49% 8 D-2 120.14% 120.84% 101.68% 123.22% 123.97% 99.83% 9 D-3 113.85% 114.71% 97.85% 118.72% 119.61% 97.87% As can be seen from the above tables, for nominal track (α = 0.003), 8 of the 9 trainsets generated higher P 1 forces on wood ties (between 1 and 15% higher) and all 9 trainsets generated higher P 1 forces on concrete ties (between 1 and 18%) than the existing equipment. However, only two of the 9 proposed trainsets generated higher P 2 forces. (This is due to the different sensitivities of the P 1 and P 2 forces to speed and vehicle unsprung mass.) In the case of track with larger dip angle (α = 0.006), all trainsets generated higher P 1 forces for both wood and concrete with increases ranging from 5% to 25%. However, only 2 of the trainsets generated higher P 2 forces. Calculation of Equivalent Damage Speed: As noted above, virtually all of the trainsets generate P 1 forces greater than those generated by the existing Amtrak equipment. This increased P 1 force can alternately be presented in terms of a reduction in operating speed. This equivalent damage speed is the operating speed at which the P 1 forces generated by the proposed high-speed trainsets will be equal to those generated by the existing Amtrak equipment.
These equivalent damage speeds (EDS) are calculated by setting the P 1 force levels to those generated by the existing Amtrak equipment (AEM7 or F40) and calculating the speed that would generate that level of dynamic impact force (P 1 ). These Equivalent Damage Speeds (Table 9a and 9b) are thus: Table 9a. Equivalent Damage Speeds α =0.003: Wood Ties EDS Concrete Ties EDS No. Manu. New Worn New Worn 1 A-1 145 143 140 139 2 A-2 125 125 125 123 3 B-1 133 133 133 132 4 B-2 88 88 90 90 5 C1 147 146 143 142 6 C2 125 124 116 114 7 D-1 125 124 117 115 8 D-2 90 90 92 92 9 D-3 112 110 106 105 Table 9b. Equivalent Damage Speeds α =0.006: Wood Ties EDS Concrete Ties EDS No. Manu. New Worn New Worn 1 A-1 136 135 135 134 2 A-2 117 115 109 108 3 B-1 130 130 130 130 4 B-2 89 89 91 91 5 C1 138 137 137 136 6 C2 109 108 105 104 7 D-1 109 108 105 104 8 D-2 90 90 92 92 9 D-3 101 101 99 98
Noting that the calibration to Northeast Corridor force data was performed at the normal (α = 0.003) level, then the appropriate limiting condition, for evaluation of the new generation equipment would correspond to worn wheel conditions on concrete ties with a joint dip angle of α = 0.003. These results are summarized in Tables 10 and 11 for the P 1 and P 2 forces respectively. No. Trainse t Fuel Table 10. P 1 Allowable Speed % P 1 Increase * Equivalent Damage Speed 1 A-1 EL 150 106% 139 2 A-2 FF 125 101% 123 3 B-1 EL 150 109% 132 4 B-2 FF 125 118% 90 5 C1 EL 150 104% 142 6 C2 FF 125 105% 114 7 D-1 FF 125 105% 115 8 D-2 FF 125 117% 92 9 D-3 FF 125 111% 105 Based on maximum operating speed Table 11. P 2 No. Trainset Fuel Allowable Speed % P 2 Increase * Equivalent Damage Speed 1 A-1 EL 150 97% 150 2 A-2 FF 125 89% 125 3 B-1 EL 150 98% 150 4 B-2 FF 125 103% 117 5 C1 EL 150 88% 150 6 C2 FF 125 87% 125 7 D-1 FF 125 85% 125 8 D-2 FF 125 101% 125 9 D-3 FF 125 95% 125 Based on maximum operating speed
Looking first at the P 2 forces, only two trainsets generated higher forces, B-2 and D-2. The remaining equipment all generated force levels that were less than the existing equipment operations. This is of particular importance, since as was noted previously, the P 2 forces are the forces that most contributed to track degradation, particularly degradation of track geometry, which is the largest maintenance expense on Amtrak s Northeast Corridor. Based on Table II, only trainsets, B-2 and D-2 exceeded the base case to the level of requiring some amount of train slow-down. In the case of the P 1 forces presented in Table 10, all of the trainsets present some level of increased P 1 forces, thus requiring some level of slow-down to exactly match existing equipment. Note, however, that 6 out of the 9 trainsets generated increases of less than 10% and four out of the 9 generated increases less than 5%. However, as was noted previously, P 1 forces are of potential importance primarily from the point of view of damage (cracking) of concrete ties, a situation which Amtrak encountered in the late 70s early 1980s and corrected at that time. For other damage, particularly the expensive track geometry maintenance associated with the Northeast Corridor, the P 1 forces are not as significant as the P 2 forces discussed above. Thus the effect of the P 1 forces on potential concrete tie degradation/damage must be examined further to determine if there is a potential for damage in this area from the new higher speed equipment. This was addressed through an additional analysis of potential concrete tie cracking. Analysis of Concrete Tie Cracking The analysis of concrete tie cracking used here was based on the analytical studies and field tests performed by Battelle Columbus Laboratories on the Northeast Corridor in the early to mid 1980s [3,4,5]. At that time, there was a series of concrete tie cracking problems that had developed under 125 mph operations and a corresponding detailed investigation undertaken to define the loading levels required to crack these concrete ties (and their relationship to train operations and impact forces).
The levels of loading determined by these investigations [3,4,5] which can initiate concrete tie cracking are defined here-in in terms of a set of upper and lower limits as follows: Lower Cracking Level: 57,252 lbs (corresponding to a bending moment of 375,000 in-lbs) - Level below which cracking will never occur. Upper Cracking Level: 91,603 lbs (corresponding to a bending moment of 600,000 in-lbs) - Level at which cracking will always occur. Thus, if the dynamic load level is maintained below the Lower Cracking Level, concrete tie cracking will not occur. For dynamic loads above the Upper Cracking Level, concrete tie cracking will always occur. Between these two levels is an area of uncertainly, due to such factors as variations in strength of individual concrete ties, dynamic attenuation characteristics of the tie/fastener system, support conditions of the ties (which effects its dynamic response characteristics) etc. Also included is the dynamic loading characteristics of the rolling stock. Calculation of the dynamic P 1 forces for all of the equipment, including the baseline AEM7 shows that for the worn wheel condition (worst case) on concrete ties only (wood tie cracking is not a problem and as such is not considered herein), the calculated P 1 forces are slightly above the Lower Cracking Level but well below the Upper Cracking Level. Noting that the concrete ties are currently not cracking under the AEM7 equipment being operated at 125 mph on the Northeast Corridor, the calculated P 1 forces were normalized to and compared with the AEM7 force levels. Assuming that the AEM7 is below the lower cracking force threshold by at least a 5% margin, a conservative assumption, the actual track condition on the Northeast Corridor can be calculated to correspond to corresponding P 1 force level. This resulted in a track condition value α = 0.0024. Based on this parameter the percentage cracking levels and corresponding maximum operating speeds can be calculated for the different equipment in light of the concrete cracking
issue. The results are presented in Table 12 which shows the percentage of P 1 cracking level, defined here to be the percentage of calculated P 1 compared to level of load needed for concrete tie cracking. Also presented are the operating speeds of the different equipment types required to avoid the risk of tie cracking. Note, if the percentage is less than 100% or the speed is shown to be 150 mph, the P 1 force level is within acceptable cracking levels. Table 12. Concrete Tie Cracking Potential No. Trainset Fuel Allowable Speed Percentage P 1 Crack Cracking Avoidance Speed * 1 A-1 EL 150 99% 150 2 A-2 FF 125 92% 125 3 B-1 EL 150 102% 145 4 B-2 FF 125 110% 102 5 C1 EL 150 97% 150 6 C2 FF 125 97% 125 7 D-1 FF 125 97% 125 8 D-2 FF 125 109% 104 9 D-3 FF 125 102% 120 * Based on lower cracking threshold As can be seen from Table 12, four of the nine trainsets, require some degree of speed reduction to insure that no tie cracking damage can occur. Note: the units that generated the highest P 1 forces require a speed reduction based on the calculated P 2 force. The other five trainsets generated force levels, both P 1 and P 2, within acceptable levels. Application of Results to the Final Selection of Equipment As can be seen from the previous section, the results of the dynamic analyses show that some of the designs would require some level of speed reduction to meet the limits set for track damage. Most designs met the requirements of track loading and as such did not require any speed reduction below the specified limits of 150 (electric) and 125 (non-electric). Using these results, and the process of calculating the P 1 and P 2, criteria, Amtrak developed a go/no-go criteria for evaluation of the High Speed Trainset proposals. This process was the method used
to get only compliant proposals that would not accelerate the rate of change to the track structure on the Northeast Corridor. References: 1. Jenkins, H. H., Stephenson, J. E., Clayton, G. A., Morland, G. W. and Lyon, D., The Effect of Track and Vehicle Parameters on Wheel/Rail Vertical Dynamic Forces, Railway Engineering Journal, January 1974. 2. Ahlbeck, D. R., An Investigation of Impact Loads Due to Wheel Flats and Rail Joints, American Society of Mechanical Engineers, 80-WA/RT-1, 1980. 3. Dean, F. E., Harrison, H. D., Prause, R. H. and Tuten, J. M., Investigation of the Effects of Tie Pad Stiffness on the Impact Loading of Concrete Ties on the Northeast Corridor, Federal Railroad Administration Report FRA/ORD-83/05, April, 1983. 4. Ahlbeck, D. R., Tuten, J. M., Hadden, J. A., and Harrison, H. D., Development of Safety Criteria for Evaluating Concrete Tie Track in the Northeast Corridor; Volume 1. Remedial Projects Assessment, Federal Railroad Administration Report FRA/ORD-86/08.1, June 1986. 5. Ahlbeck, D. R., Tuten, J. M., Hadden, J. A., and Harrison, H. D., Development of Safety Criteria for Evaluating Concrete Tie Track in the Northeast Corridor; Volume 2. Track Safety Evaluation, Federal Railroad Administration Report FRA/ORD-86/08.2, June 1986.