Fortis_Design_Brief_Appendix_C_06_28_21.pdf

FORTIS 8-AXLE SNF RAILCAR

DESIGN DOCUMENTATION

APPENDIX C – VEHICLE DYNAMICS ANALYSIS

June 2021

Table of Contents List of Figures .............................................................................................................................................. iii

List of Tables .............................................................................................................................................. vii

Abbreviations .............................................................................................................................................. ix

Executive Summary ..................................................................................................................................... x

Summary of Simulation Results – 8-Axle SNF Railcar (1/3) ..................................................................... xi

1. Introduction

2. Description of the Car Model

3. Description of the Truck Model

4. Description of the Simulation Regimes

4.1 Non-Structural Static Analyses

4.1.1 Truck Twist Equalization (Section 4.2.1 in S-2043)

4.1.2 Car Body Twist Equalization (Section 4.2.2 in S-2043)

4.2 Dynamic Analyses

4.2.1 Twist & Roll Regime (Section 4.3.9.6 in S-2043)

4.2.2 Pitch & Bounce (Section 4.3.9.7 in S-2043)

4.2.3 Yaw & Sway (Section 4.3.9.8 in S-2043)

4.2.4 Dynamic Curving (Section 4.3.9.9 in S-2043)

4.2.5 Dynamic Curving with NAC STC Cask

4.2.6 Dynamic Curving with lower preload CCSB

4.2.7 Dynamic Curving Response with Carbody Flexible Modes

4.3 Perturbed Track Performance – Special Cases

4.3.1 Single Bump (Section 4.3.10.1 in S-2043)

4.3.2 Curving with Single Rail Perturbation (Section 4.3.10.2 in S-2043)

4.4 Unperturbed Track Performance

4.4.1 Hunting (Section 4.3.11.3 in S-2043)

4.4.2 Constant Curving

4.4.3 Curving with Various Lubrication Conditions

4.4.4 Limiting Spiral Negotiation (Section 4.3.11.6 in S-2043)

4.4.5 Turnouts and Crossovers (Section 4.3.11.7 in S-2043)

Cii DOE 8-Axle SNF Car – EEC Submittal – Appendix C

4.5 Ride Quality (Section 4.3.12 in S-2043)

4.6 Buff and Draft Curving (Section 4.3.13 in S-2043)

4.7 Braking Effects on Steering (Section 4.3.14 in S-2043)

4.8 Worn Component Simulations (Section 4.3.15 in S-2043)

4.8.1 Worn CCSB

4.8.2 Worn Center Plates

4.8.3 Worn Primary Pad

4.8.4 Worn Wedge with Contaminated Friction Surfaces

4.8.5 Worn Truck with Wedge Rise

4.8.6 Worn Truck with Broken Spring

5. Summary

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List of Figures Figure 1. 8-Axle SNF Railcar 2 Figure 2. Key Dimensions 3 Figure 3. VAMPIRE® Dynamic Model 3 Figure 4. Primary Suspension 8 Figure 5. Secondary Suspension 8 Figure 6. Track Model for Truck Twist Simulation 10 Figure 7. Min. Wheel Load under Truck Twist - Loaded Car 11 Figure 8. Min. Wheel Load under Truck Twist -Empty Car with Ballast 11 Figure 9. Track Model for Car Twist Simulation 12 Figure 10. Min. Wheel Load under Car Body Twist - Loaded Car 13 Figure 11. Min. Wheel Load under Car Body Twist – Empty Car with Ballast 13 Figure 12. AAR 2A Wheel Profile and AREA 136 lb. Rail Profile 14 Figure 13. Response of the Loaded SNF Railcar to Twist & Roll Input 15 Figure 14. Car Body Roll Angle in Twist & Roll (11 mph, loaded car) 15 Figure 15. Vertical Wheel Load Ratio in Twist & Roll (11 mph, loaded car) 16 Figure 16. Carbody & Bolster Lat. Displ. in Twist & Roll (11 mph, 39’ wavelength, loaded car) 16 Figure 17. Response of the Ballasted Car in Twist & Roll Regime 18 Figure 18. Car Body Roll in Twist & Roll Regime (60 mph, ballasted car) 18 Figure 19. Vertical Wheel Load Ratio in Twist & Roll (60 mph, ballasted car) 19 Figure 20. Carbody & Bolster Lat. Displ. in Twist & Roll (22 mph, 39’ wavelength, ballasted car) 19 Figure 21. Carbody & Bolster Lat. Displ. in Twist & Roll (60 mph, 39’ wavelength, ballasted car) 20 Figure 22. Response of Loaded Car in Pitch & Bounce Regime 22 Figure 23. Vertical Wheel Load Ratio in Pitch & Bounce (50 mph, loaded car) 22 Figure 24. Carbody Vertical Acceleration in Pitch & Bounce (50 mph, loaded car) 23 Figure 25. Vertical Wheel Load Ratio in Pitch & Bounce (70 mph, ballasted car) 24 Figure 26. Carbody Vert. Accel. in Pitch & Bounce (70 mph for 39’,60 mph for 35.8’, ballasted car) Figure 27. Close-up View of Carbody Vertical Acceleration in Pitch & Bounce (70 mph for 39’,60 mph for 35.8’, ballasted car) 25 Figure 28. Response of Ballasted Car in Pitch & Bounce Regime 26 Figure 29. Response of Loaded Car in Yaw & Sway Regime 27 Figure 30. Wheel L/V Ratio in Yaw & Sway (70 mph, loaded Car) 28 Figure 31. Truck Side L/V Ratio in Yaw & Sway (70 mph, loaded car) 28 Figure 32. Lateral Car Body Acceleration in Yaw & Sway (70 mph, loaded car) 29 Figure 33. Response of Car with Ballast in Yaw & Sway Regime 30 Figure 34. Wheel L/V Ratio in Yaw & Sway Regime (70 mph, ballasted car) 30 Figure 35. Wheel L/V Exceedance in Yaw & Sway (70 mph, 35.8’ wavelength, ballasted car) 31 Figure 36. Lateral & Vertical Forces in Yaw & Sway (70 mph, 35.8’ wavelength, ballasted car) 31 Figure 37. Leading Axle AOA in Yaw & Sway (70 mph, 35.8’ wavelength, ballasted car) 32 Figure 38. Truck Side L/V Ratio in Yaw & Sway (70 mph, ballasted car) 32

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Figure 39. Lateral Carbody Acceleration in Yaw & Sway (70 mph, ballasted car) 33 Figure 40. Perturbations for Dynamic Curving Regime 34 Figure 41. Response of Loaded Car in Dynamic Curving Regime 35 Figure 42. Wheel L/V Ratio in Dynamic Curving (12 mph, loaded car) 35 Figure 43. Wheel L/V Exceedance in Dynamic Curving (12 mph, 39’ wavelength, loaded car) 36 Figure 44. Lateral & Vertical Forces in Dynamic Curving (12 mph, 39’ wavelength, loaded car) 36 Figure 45. Leading Axle AOA in Dynamic Curving (12 mph, 39’ wavelength, loaded car) 37 Figure 46. Wheel L/V Exceedance in Dynamic Curving (12 mph, 35.8’ wavelength, loaded car) 37 Figure 47. Lateral & Vertical Forces in Dynamic Curving (12 mph, 35.8’ wavelength, loaded car) 38 Figure 48. Leading Axle AOA in Dynamic Curving (12 mph, 35.8’ wavelength, loaded car) 38 Figure 49. Truck Side L/V Ratio in Dynamic Curving (12 mph, loaded car) 39 Figure 50. Car Body Roll Angle in Dynamic Curving (12 mph, loaded car) 39 Figure 51. Response of Ballasted Car in Dynamic Curving Regime 40 Figure 52. Wheel L/V Ratio in Dynamic Curving (12 mph, ballasted car) 41 Figure 53. Truck Side L/V Ratio in Dynamic Curving (21 mph, ballasted car) 41 Figure 54. Wheel L/V Ratio for car loaded with NAC STC Cask in Dynamic Curving 44 Figure 55. Wheel Lat. Forces in Dyn. Curving (12 mph, 35.8’ wavelength, 3 lading types) 44 Figure 56. Wheel Vert. Forces in Dyn. Curving (12 mph, 35.8’ wavelength, 3 lading types) 45 Figure 57. CCSB Design Comparison in Dynamic Curving (loaded car) 46 Figure 58. CCSB Design Comparison (Dynamic Curving - Ballasted Car) 48 Figure 59. Response with Flexible Modes in Dyn. Curving (12 mph, 39’ wavelength, loaded car) 50 Figure 60. Response with Flexible Modes in Dyn. Curving (21 mph, 39’ wavelength, ballasted car) 50 Figure 61. Percent Vertical Wheel Load in Single Bump Regime (loaded car) 51 Figure 62. Vertical Wheel Load Ratio in Single Bump Regime (70 mph, loaded car) 52 Figure 63. Vertical Car Body Acceleration in Single Bump Regime (70 mph, loaded car) 52 Figure 64. Percent Vertical Wheel Load in Single Bump Regime (ballasted car) 53 Figure 65. Vertical Wheel Load Ratio in Single Bump Regime (70 mph, ballasted car) 54 Figure 66. Vertical Car Body Acceleration in Single Bump Regime (70 mph, ballasted car) 54 Figure 67. Response to Single Outside Rail Dip (12o curve, loaded car) 56 Figure 68. Response to Single Inside Rail Bump (12o curve, loaded car) 57 Figure 69. Response to Single Outside Rail Dip (12o curve, ballasted car) 58 Figure 70. Response to Single Inside Rail Bump (12o curve, ballasted car) 59 Figure 71. Carbody Lateral Acceleration in Hunting (70 mph, ballasted car) 60 Figure 72. RMS Car Body Lateral Acceleration in Hunting (loaded car) 61 Figure 73. RMS Car Body Lateral Acceleration in Hunting (ballasted car) 62 Figure 74. Wheel L/V Ratio Vs. Speed in Constant Curving (loaded car) 63 Figure 75. Wheel L/V Ratio in Constant Curving (loaded car) 64 Figure 76. Wheel L/V Ratio Vs. Speed in Constant Curving (ballasted car) 64 Figure 77. Wheel L/V Ratio in Constant Curving (ballasted car) 65 Figure 78. Hollow Wheel and Ground 136lb Rail Profiles 66 Figure 79. Effect of Lubrication on Curving (new profile, loaded car) 67

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Figure 80. Effect of Lubrication on Curving (worn profile, loaded car) 67 Figure 81. Wheelset Angle of Attack (12 mph, new profile, loaded car) 68 Figure 82. Effect of Lubrication on Curving (new profile, ballasted car) 69 Figure 83. Effect of Lubrication on Curving (worn profile, ballasted car) 69 Figure 84. Wheel L/V Ratio during Spiral Negotiation (loaded car) 70 Figure 85. Wheel L/V Ratio during Spiral Negotiation (ballasted car) 71 Figure 86. Track Curvature Model to Simulate # 7 Crossover 72 Figure 87. Truck Side L/V Ratio in Crossover (loaded car) 73 Figure 88. Truck Side L/V Ratio (#7 Turnout - loaded car) 73 Figure 89. Truck Side L/V Ratio (#7 Turnout, ballasted car) 74 Figure 90. Wheel L/V Ratio for Ride Quality Regime (loaded car) 75 Figure 91. Wheel L/V Ratio on Class 2 Track (loaded car) 76 Figure 92. Wheel L/V Ratio for Ride Quality Regime (ballasted car) 77 Figure 93. Free Body Diagram for Lateral Coupler Force 78 Figure 94. Wheel L/V Ratio (buff force, loaded car) 79 Figure 95. Wheel L/V Ratio (draft force, loaded car) 79 Figure 96. Wheel L/V Ratio (buff force, ballasted Car) 80 Figure 97. Wheel L/V Ratio (draft force, ballasted car) 80 Figure 98. Braking Force and Braking Torque for the Loaded Car 83 Figure 99. Primary Susp. Long. Displ. during Braking (22 mph, 12 deg. Curve, loaded car) 84 Figure 100. Primary Susp. Vert. Force during Braking (22 mph, 12 deg. curve, loaded car) 84 Figure 101. Wheel L/V Ratio during Braking (22 mph, 12 deg. curve, loaded car) 85 Figure 102. Wheel L/V Ratio during Braking (22 mph, 12 deg. curve, ballasted car) 85 Figure 103. Wheel L/V Ratio in Constant Curving for Worn CCSB (loaded car) 88 Figure 104. Wheel L/V Ratio in Dynamic Curving for Worn CCSB (loaded car) 88 Figure 105. Car Body RMS Lat. Acceleration in Hunting for worn CCSB (loaded car) 89 Figure 106. Car Body Roll Angle in Twist & Roll for worn CCSB (loaded car) 90 Figure 107. Wheel L/V Ratio in Constant Curving for Worn CP (loaded car) 91 Figure 108. Wheel L/V Ratio in Dynamic Curving for Worn CP (loaded car) 92 Figure 109. Wheel L/V Ratio in Constant Curving for Worn CP (ballasted car) 93 Figure 110. Wheel L/V Ratio in Dynamic Curving for Worn CP (ballasted car) 94 Figure 111. RMS Car Body Lateral Acceleration in Hunting for Worn CP (loaded car) 94 Figure 112. RMS Car Body Lateral Acceleration in Hunting for Worn CP (ballasted car) 95 Figure 113. RMS Car Body Lat. Accel. in Hunting for Worn Primary Pad (ballasted car) 96 Figure 114. Wheel L/V Ratio in Dynamic Curving for Worn Primary Pad (loaded car) 97 Figure 115. Wheel L/V Ratio in Dynamic Curving for Worn Primary Pad (ballasted car) 98 Figure 116. Wheel L/V Ratio in Dynamic Curving for Low Wedge Friction (loaded car) 99 Figure 117. Wheel L/V Ratio in Limiting Spiral for Low Wedge Friction (loaded car) 100 Figure 118. Maximum Roll Angle in Twist & Roll for Low Wedge Friction (loaded car) 101 Figure 119. Vertical Wheel Load in Pitch & Bounce for Low Wedge Friction (loaded car) 102 Figure 120. Secondary Spring Defl. in Pitch & Bounce, Low Wedge Friction (50 mph, loaded car) 102

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Figure 121. RMS Car Body Lat. Accel. in Hunting for Low Wedge Friction (ballasted car) 103 Figure 122. Wheel L/V Ratio in Dynamic Curving for Wedge Rise (loaded car) 105 Figure 123. Wheel L/V Ratio in Dynamic Curving for Wedge Rise (loaded car) 105 Figure 124. Wheel L/V Ratio in Dyn. Curving for Wedge Rise (close up view, loaded car) 106 Figure 125. Vertical Wheel Load Ratio in Dynamic Curving for Wedge Rise (12 mph, loaded car) 106 Figure 126. Wheel L/V Ratio in Limiting Spiral for Wedge Rise (loaded car) 107 Figure 127. Peak-to-Peak Roll Angle in Twist & Roll for Wedge Rise (loaded car) 108 Figure 128. Percent Wheel Load in Pitch & Bounce for Wedge Rise (loaded car) 109 Figure 129. RMS Lateral Acceleration in Hunting for Wedge Rise (ballasted car) 110 Figure 130. Missing Spring Locations in the Lead Truck 112 Figure 131. Wheel L/V Ratio in Dynamic Curving for Broken Spring (loaded car) 113 Figure 132. Car Body Roll Angle in Twist & Roll for Broken Spring (loaded car) 114 Figure 133. Percent Vert. Wheel Load in Pitch & Bounce for Broken Spring (loaded car) 115 Figure 134. Limiting Spiral Wheel L/V Ratio for Broken Spring (loaded car) 116

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List of Tables Table 1. Key Parameters of SNF Casks 4 Table 2. Weight and Inertia Parameters for Loaded Car 5 Table 3. Weight and Inertia Parameters for Empty Car with Ballast 5 Table 4. Rigid Bodies & Degrees of Freedom 6 Table 5. S-2043 Performance Criteria 9 Table 6. Twist & Roll Summary (loaded car) 17 Table 7. Twist & Roll Summary (ballasted car) 21 Table 8. Pitch & Bounce Summary (loaded car) 23 Table 9. Pitch & Bounce Summary (ballasted car) 26 Table 10. Yaw & Sway Summary (loaded car) 29 Table 11. Yaw & Sway Summary (ballasted car) 33 Table 12. Dynamic Curving Summary (loaded car) 40 Table 13. Dynamic Curving Summary (ballasted car) 42 Table 14. Model Details of the NAC STC Cask 43 Table 15. Summary for NAC STC Cask in Dynamic Curving 45 Table 16. Comparison of CCSB Designs in Dynamic Curving (loaded car) 47 Table 17. Comparison of CCSB Designs in Dynamic Curving (ballasted car) 48 Table 18. Modal Frequencies and Masses for Flexible Body Simulations 49 Table 19. Single Bump Summary (loaded car) 53 Table 20. Single Bump Summary (ballasted car) 55 Table 21. Summary for Single Rail Dip (loaded car) 56 Table 22. Summary for Single Rail Bump (loaded car) 57 Table 23. Summary for Single Rail Dip (ballasted car) 58 Table 24. Summary for Single Rail Bump (ballasted car) 59 Table 25. Hunting Simulation Summary (loaded car) 61 Table 26. Hunting Simulation Summary (ballasted car) 62 Table 27. Summary for Constant Curving 65 Table 28. Wheel/Rail Friction Coefficient 66 Table 29. Summary for Rail Lubrication (loaded car) 68 Table 30. Summary for Rail Lubrication (ballasted car) 70 Table 31. Summary for Spiral Negotiation 71 Table 32. Summary for Turnouts and Crossovers 74 Table 33. Ride Quality Summary (loaded car) 76 Table 34. Ride Quality Summary (ballasted car) 77 Table 35. Car Dimensions for Coupler Angle Calculation 78 Table 36. Buff Curving Summary (loaded car) 81 Table 37. Draft Curving Summary (loaded car) 81 Table 38. Buff Curving Summary (ballasted car) 82 Table 39. Draft Curving Summary (ballasted car) 82 Table 40. Summary for Braking Effect on Steering (loaded car) 86

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Table 41. Summary for Braking Effect on Steering (ballasted car) 86 Table 42. Worn Component Conditions 87 Table 43. Curving Summary for Worn CCSB (loaded car) 89 Table 44. Hunting and Twist & Roll Summary for Worn CCSB (loaded car) 90 Table 45. Curving Summary for Worn Center Plate (loaded car) 92 Table 46. Curving Summary for Worn Center Plate (ballasted car) 93 Table 47. Hunting Summary for Worn Center Plate 95 Table 48. Hunting Summary for Worn Primary Pad (ballasted car) 96 Table 49. Dynamic Curving Summary for Worn Primary Pad (loaded car) 97 Table 50. Dynamic Curving Summary for Worn Primary Pad (ballasted car) 98 Table 51. Dynamic Curving Summary for Low Wedge Friction (loaded car) 99 Table 52. Limiting Spiral Summary for Low Wedge Friction (loaded car) 100 Table 53. Twist & Roll Summary for Low Wedge Friction (loaded car) 101 Table 54. Pitch & Bounce Summary for Low Wedge Friction (loaded car) 103 Table 55. Hunting Summary for Low Friction Wedge (ballasted car) 104 Table 56. Dynamic Curving Summary for Wedge Rise (loaded car) 107 Table 57. Limiting Spiral Summary for Wedge Rise (loaded car) 108 Table 58. Twist & Roll Summary for Wedge Rise (loaded car) 109 Table 59. Pitch & Bounce Summary for Wedge Rise (loaded car) 110 Table 60. Hunting Summary for Wedge Rise (ballasted car) 111 Table 61. Dynamic Curving Summary for Broken Spring (39’ wavelength, loaded car) 113 Table 62. Dynamic Curving Summary for Broken Spring (35.8’ wavelength, loaded car) 114 Table 63. Twist & Roll Summary for Broken Spring (loaded car) 115 Table 64. Pitch & Bounce Summary for Broken Spring (Loaded Car) 115 Table 65. Limiting Spiral Summary for Broken Spring (loaded car) 116

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Abbreviations AAR Association of American Railroads

AOA Angle of Attack

CCSB Constant Contact Side Bearing

CG Center of Gravity

CP Center Plate

Displ. Displacement

DOE Department of Energy

DOF Degrees of Freedom

EEC Equipment Engineering Committee

FRA Federal Railroad Administration

HLRM High Level Radioactive Material

HLW High Level Radioactive Waste

L/V Ratio Ratio of Lateral Force to Vertical Force

MI Moment of Inertia

Max. Maximum

Min. Minimum mph Miles per Hour ms milli-second

MSRP Manual of Standards and Recommended Practices

RMS Root Mean Square

RTT Railroad Test Track

SA Sharma & Associates, Inc.

SNF Spent Nuclear Fuel

TTCI Transportation Technology Center, Inc.

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Executive Summary

The outcome of the initial concept study of an 8-axle railcar for transporting Spent Nuclear Fuel (SNF) and High Level radioactive Waste (HLW) casks was the selection of Amsted’s 125-ton Swing Motion® trucks for further evaluation in the detailed design phase.

Subsequently, Sharma & Associates, Inc. (SA) extended the concept and designed a SNF railcar with a flat deck, supported on two span bolsters. Each span bolster rests on two 125-ton Swing Motion® trucks. The car is 62’-10.5” long over pulling faces, with a span bolster center plate spacing of 49’-10”. The car was designed to transport any of the 17 SNF or HLW casks identified in the 12-axle Atlas railcar report.

This document summarizes the results of the vehicle dynamic analyses of the 8-axle SNF railcar with 4 Swing Motion® trucks to evaluate the trackworthiness performance requirements in S-2043. The secondary suspension uses an AAR standard spring group appropriate for 125-ton service. The primary suspension pads on the bearing adaptors between the side frame and axles allow the wheelsets to steer through curves. As required by the latest AAR Specification, 2A wheel profiles and AREMA 136 lb. rail profiles were used to model the wheel/rail contact geometry. The analyses were performed using VAMPIRE® software to evaluate the performance of the railcar for the simulation regimes specified in S- 2043. The loaded simulations were performed with the HI-Star 190XL, the heaviest cask with the highest center of gravity, and the unloaded simulations were performed with a ballast load on the deck of the car.

The results of the analyses are summarized in tables in the following three pages. The results suggest that the design largely meets the dynamic performance requirements of S-2043, with a few minor exceptions. On further review, it appears that the performance, even for the conditions with minor exceptions, is largely in line with the performance expected for the 12-axle Atlas railcar design that the DOE is testing.

Cxi

Summary of Simulation Results – 8-Axle SNF Railcar (1/3)

Regime S-2043 Section

Criteria for Assessment

Loading Condition

Simulation Value Atlas 12-Axle Cask

Car S-2043

Allowable Comment

Loaded 69 (3")/72 (2") 59 (3")/64.7 (2")

Empty w/ballast 56 (3")/65 (2") 56 (3")/62 (2")

Loaded 72 (3")/77 (2") 64 (3")/68 (2")

Empty w/ballast 66 (3")/72 (2") 62 (3")/68 (2")

Loaded 2.1 (39')/1.6 (35.8') 2.1 (39')/1.8 (38')

Empty w/ballast 1.9 (39')/1.8 (35.8') 1.8 (39')/1.6 (38')

Loaded 72 (39')/74 (35.8') 66 (39')/67 (38')

Empty w/ballast 67 (39')/67 (35.8') 63 (39')/64 (38')

Loaded 0.55 (39')/0.52 (35.8') 0.24 (39')/0.22 (38')

Empty w/ballast 0.54 (39')/0.56 (35.8') 0.19 (39')/0.19 (38')

Loaded 79 (39')/81 (35.8') 68 (39')/70 (38')

Empty w/ballast 25 (39')/38 (35.8') 61 (39')/62 (38')

Loaded 0.27 (39')/0.22 (35.8') 0.21 (39')/0.2 (38')

Empty w/ballast 1.1 (39')/0.7 (35.8') 0.34 (39')/0.35 (38')

Loaded 0.76 (39')/0.56 (35.8') 0.67 (39')/0.64 (38')

Empty w/ballast 0.22 (39')/0.19 (35.8') 0.5 (39')/0.42 (38')

Loaded 0.69 (39')/0.73(35.8') 0.59 (39')/0.57 (38')

Empty w/ballast 0.83 (39')/0.89 (35.8) 0.76 (39')/0.72 (38')

Loaded 0.42 (39')/0.46 (35.8') 0.3 (39')/0.3 (38')

Empty w/ballast 0.48 (39')/0.51 (35.8') 0.42 (39')/0.4 (38')

Loaded 0.83 (39')/0.86 (35.8') 0.88 (39')/0.9 (38')

Empty w/ballast 0.8 (39')/0.84 (35.8') 0.71 (39')/0.71 (38')

Loaded 0.4 (39')/0.44 (38.5') 0.37 (39')/0.38 (38')

Empty w/ballast 0.4 (39')/0.43 (38.5') 0.36 (39')/0.36 (38')

Loaded 2.5 (39')/2.1 (35.8') 1.2 (39')/1.5 (38')

Empty w/ballast 0.62 (39')/0.61 (35.8') 0.9 (39')/0.8 (38')

Loaded 78 71

Empty w/ballast 67 65

Loaded 0.33 0.22

Empty w/ballast 0.4 0.2

Loaded 0.7 (dip)/0.64 (bump) 0.79 (dip)/0.64 (bump)

Empty w/ballast 0.99 (dip)/0.85 (bump) 0.96 (dip)/0.91 (bump)

Loaded 0.4 (dip)/0.37 (bump) 0.38 (dip)/0.33 (bump)

Empty w/ballast 0.55 (dip)/0.5 (bump) 0.52 (dip)/0.49 (bump)

Loaded 5.2 (dip)/5.5 (bump) 4.5 (dip)/5 (bump)

Empty w/ballast 2.2 (dip)/2.2 (bump) 1.3 (dip)/2.2 (bump)

Loaded 0.29 0.25

Empty w/ballast 0.03 0.18

Loaded 0.19 0.64

Empty w/ballast 0.32 0.68

Loaded 0.1 0.36

Empty w/ballast 0.18 0.38

Truck Twist Equalization

4.2.1 Min. Vert. Load

40 (3-in)/ 60 (2-in)

Carbody Twist Equalization

4.2.2 Min. Vert. Load

40 (3-in)/ 60 (2-in)

Twist & Roll 4.3.9.6

Peak to peak carbody roll (deg)

Maximum roll angle for loaded car at 11 mph & for ballasted car at 60 mph

Min. Vert. Load

Peak to peak Lat.

Accn. (g)

1.3

Pitch & Bounce

4.3.9.7

Min. Vert. Load

25 Maximum vertical acceleration at 70 mph for the empty car with ballast exceed the limit

Max vert Accn.

(g)

0.9

Yaw & Sway 4.3.9.8

Peak to peak Lat.

Accn. (g)

1.3

For the 8-axle car with ballast, the peak wheel L/V Ratio occurs at 70mph.

Max. Wheel L/V 0.8

Max. Truck Side L/V

0.5

Dynamic Curving

(10 degree curve)

4.3.9.9

Max. Wheel L/V 0.8 For loaded 8-axle car, the peak value occurs at 12mph;

For ballast 8-axle car, the peak value occurs at 21mph.

Max. Truck Side L/V

0.5

Peak to peak carbody roll (deg)

Single Bump 4.3.10.1

Min. Vert. Load

Max vert Accn.

(g)

0.9

Curving with single rail perturbation (3" bump/dip)

4.3.10.2

Max. Wheel L/V 0.8

Max. Truck Side L/V

0.5

Peak to peak carbody roll (deg)

Hunting 4.3.11.3 Max. Lat. Accn.

(g) 0.75

The results is based on analytical track.

Constant Curving

(10 degree curve)

4.3.11.4

Max. Wheel L/V 0.8

Max. Truck Side L/V

0.5

Cxii

Summary of Simulation Results – 8-Axle SNF Railcar (2/3)

Regime

Section

Criteria for Assessment

Loading Condition

Simulation Value Atlas 12-Axle Cask

Car S-2043

Allowable Comment

Loaded 0.51 (case 4) 0.76 (case 4)

Empty w/ballast 0.57 (case 4) 0.75 (case 4)

Loaded 0.29 (case 4) 0.45 (case 4)

Empty w/ballast 0.35 (case 4) 0.47 (case 4)

Loaded 0.65 (case 2) 0.76 (case 2)

Empty w/ballast 0.72 (case 2) 0.78 (case 2)

Loaded 0.45 (case 2) 0.62 (case 2)

Empty w/ballast 0.47 (case 2) 0.61 (case 2)

Loaded 0.17 0.49

Empty w/ballast 0.34 0.66

Loaded 0.11 0.43

Empty w/ballast 0.15 0.39

Loaded 0.68 0.67

Empty w/ballast 0.69 0.74

Loaded 0.52 0.52

Empty w/ballast 0.46 0.5

Loaded 0.69 0.63

Empty w/ballast 0.77 0.73

Loaded 0.6 0.29

Empty w/ballast 0.74 0.62

Loaded 0.32 0.38

Empty w/ballast 0.34 0.7

Loaded 0.41 0.18

Empty w/ballast 0.54 0.54

Loaded 0.3 0.17

Empty w/ballast 0.55 0.31

Loaded 0.41(long) 0.6(like)

Empty w/ballast 0.57(long) 0.65(like)

Loaded 0.26(long) 0.39(like)

Empty w/ballast 0.38(long) 0.51(like)

Loaded 0.36(base) 0.6(base)

Empty w/ballast 0.54(base) 0.65(base)

Loaded 0.16(base) 0.39(base)

Empty w/ballast 0.24(base) 0.45(base)

Loaded 0.47 0.51

Empty w/ballast 0.52 0.55

Loaded 0.22 0.32

Empty w/ballast 0.26 0.36

Loaded 72 57

Empty w/ballast 87 29

Max. Truck Side L/V

(new wheel) 0.5

Max. Wheel L/V (worn wheel)

0.8

Max. Truck Side L/V

(worn wheel) 0.5

Limiting Spiral Negotiation

4.3.11.6

Max. Wheel L/V 0.8

Curving with Various

Lubrication Conditions

4.3.11.5

Max. Wheel L/V (new wheel)

0.8

Max. Truck Side L/V

0.5

Max. Truck Side L/V

0.5

Ride Quality 4.3.12

Max. Wheel L/V (Class 2)

0.8

Max. Wheel L/V (Class 3)

Max. Wheel L/V (Class 4)

Max. Wheel L/V (Class 5)

Max. Wheel L/V (Class 6)

Braking Effects on Steering (12 degree curve)

4.3.14

Max. Wheel L/V 0.8

Buff and Draft Curving

4.3.13

Max. Wheel L/V (Buff)

0.8

Turnouts and Crossovers

4.3.11.7

Max. Wheel L/V 0.8

Max. Truck Side L/V

0.5

Min. Vert. Load

Max. Truck Side L/V

(Buff) 0.5

Max. Wheel L/V (Draft)

0.5

Max. Truck Side L/V

(Draft) 0.8

Cxiii

Summary of Simulation Results – 8-Axle SNF Railcar (3/3)

Section

Criteria for Assessment

Loading Condition

Simulation Value Atlas 12-Axle Cask

Car S-2043

Allowable Comment

Constant Curving

Max. Wheel L/V Loaded 0.18 0.65 0.8

Max. Wheel L/V Loaded 0.8 (39')/0.84 (35.8') 1.16 0.8 Max. Truck Side

L/V Loaded 0.4 (39')/0.43 (35.8') 0.45 0.5

Hunting Max. Lat. acc (g) Loaded 0.2 0.26 0.75

Peak to peak carbody roll (deg)

Loaded 2.04 (39')/1.64 (35.8') 1.9 4

Min. Vert. Load

Loaded 72 (39')/72 (35.8') 68 25

Loaded 0.23 0.66

Empty w/ballast 0.36

Loaded 0.85 (39')/0.87 (35.8') 0.95

Empty w/ballast 0.82 (39')/0.85 (35.8') -

Loaded 0.41 (39')/0.44 (35.8') 0.37

Empty w/ballast 0.41 (39')/0.44 (35.8') -

Loaded 0.24 0.29

Empty w/ballast 0.02 -

4.3.15 Max. Lat. acc (g) Empty w/ballast 0.03 0.19 0.75

Max. Wheel L/V Loaded 0.97 (39')/0.88 (35.8') 0.87 0.8

Max. Truck Side L/V

Loaded 0.47 (39')/0.45 (35.8') 0.36 0.5

Limiting Spiral Max. Wheel L/V Loaded 0.17 0.5 0.8

Min. Vert. Load

Loaded 57 (39'')/70 (35.8') 66 25

Max. Vert. Accn.

(g)

Loaded 0.5 (39")/0.32 (35.8') 0.29 0.9

Peak to peak carbody roll (deg)

Loaded 3.36 (39')/1.77 (35.8') 2.2 4

Min. Vert. Load

Loaded 69 (39')/72 (35.8') 67 25

Hunting Max. Lat. acc (g) Empty w/ballast 0.07 - 0.75

Max. Wheel L/V Loaded 0.96 (39')/1.04 (35.8') - 0.8 Max. Truck Side

L/V Loaded 0.47 (39')/0.54 (35.8') - 0.5

Limiting Spiral Max. Wheel L/V Loaded 0.17 - 0.8

Min. Vert. Load

Loaded 29 (39'')/55 (35.8') - 25

Max. Vert. Accn.

(g)

Loaded 0.77 (39")/0.21 (35.8') - 0.9

Peak to peak carbody roll (deg)

Loaded 3.96 (39')/2.32 (35.8') - 4

Min. Vert. Load

Loaded 69 (39')/71 (35.8') - 25

Hunting Max. Lat. acc (g) Empty w/ballast 0.05 - 0.75

Max. Wheel L/V Loaded 0.92 (39')/0.95 (35.8') 0.9 0.8 Max. Truck Side

L/V Loaded 0.45 (39')/0.48 (35.8') 0.38 0.5

Limiting Spiral Max. Wheel L/V Loaded 0.17 0.5 0.8

Min. Vert. Load

Loaded 75 (39')/77 (35.8') 63 25

Max. Vert. Accn.

(g)

Loaded 0.28 (39')/0.23 (35.8') 0.21 0.9

Peak to peak carbody roll (deg)

Loaded 2.02 (39')/1.61 (35.8') 2.1 4

Min. Vert. Load

Loaded 73 (39')/71 (35.8') 67 25

Dynamic Curving

Max. Wheel L/V 0.8

Max. Truck Side L/V

0.5

Hunting

In Atlas report, only loaded car was simulated.

Regime W or n

C C

SB

4.3.15

In Sharma model, the worn CCSB has 70% of the stiffness and the preload of new CCSB.

In Atlas report, the CCSB has half the stiffness and half the preload of new

CCSB

Max. Lat. acc (g) 0.75

W or n C en te r Pl at e

Constant Curving

4.3.15

Max. Wheel L/V 0.8

Dynamic Curving

Twist & Roll

B ro ke n

Sp ri ng

Dynamic Curving

4.3.15

Worn Primary Pad Hunting

W ed ge R is e

Dynamic Curving

4.3.15 Pitch & Bounce

In Sharma model, one set D7&D6 spring was removed from the spring nest of the leading truck of the leading spanbolster to represent a broken or missing spring.

In Atlas report, one 1-96 spring was removed from the spring nest of the leading truck of the trailing span bolster.

Pitch & Bounce

Twist & Roll

4.3.15 Pitch & Bounce

Twist & Roll

Twist & Roll

D ec re as ed W ed ge

F ri ct io n

Dynamic Curving

In Sharma model, the wedge rised 1/2 inch to simulate the wedge worn condition.

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1. Introduction

Sharma & Associates, Inc. has designed an 8-axle SNF Railcar to transport Spent Nuclear Fuel (SNF) that complies with Association of American Railroads’ (AAR) Manual of Standard and Recommended Practices (MSRP) Standard S-2043, “Performance Specifications for Trains Used to Carry High-Level Radioactive Material (HLRM).”

The outcome of an initial concept study of an 8-axle railcar for transporting Spent Nuclear Fuel (SNF) and High-Level radioactive Waste (HLW) casks was the selection of Amsted’s 125-ton Swing Motion® trucks for further evaluation in the detailed design phase.

Subsequently, Sharma & Associates, Inc. (SA) extended the concept and designed a SNF railcar with a flat deck, supported on two span bolsters. Each span bolster rests on two 125-ton Swing Motion® trucks.

The dynamic performance of the designed car was evaluated using analysis regimes and the qualifying criteria specified in S-2043. Vehicle dynamics performance simulations were performed for the Hi-Star 190XL, the heaviest cask with the highest center of gravity and with a ballast load on the deck of an empty car. Confirmation of performance for an intermediate weight cask was also completed for selected cases.

This report describes the models and analyzes results of the vehicle dynamic simulations of the 8-axle SNF car, specifically in reference to S-2043 requirements. All modeling was performed using VAMPIRE® vehicle dynamics software, which is widely used in the railroad industry.

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2. Description of the Car Model

The SNF railcar, shown in Figure 1, is an 8-axle flat-deck railcar designed to transport any of the 17 Spent Nuclear Fuel (SNF) or High Level radioactive Waste (HLW) casks outlined in Table 1. The key dimensions of the car with a flat deck on four trucks are shown in Figure 2.

The cask and cradle system and mounting arrangements designed for the Atlas project, including all attachment points, have been incorporated into this design.

Figure 3 shows the VAMPIRE® wire frame model of the railcar with the 190XL cask and the end stops. The box shown in the top of the wire frame model represents the Hi-Star 190XL cask, cradle, end stops, and the platform deck. The truck assembly and span bolster models are also shown in the figure. Preliminary simulation runs of an empty car, with no ballast, predicted wheel L/V ratios higher than the S-2043 limit. Therefore, a configuration with the ballast load on the deck is modeled instead of an empty car. The 190XL cask, with the highest center of gravity (CG) among all the casks, was determined to provide the most extreme dynamic performance by the Atlas project team. The combined weight and inertia properties and effective CG of the loaded car with the Hi-Star 190XL cask are shown in Table 2. In this report, the empty car with the ballast is referred to as the “ballasted car” and the car with the Hi-Star 190XL containing the spent fuel is referred to as the “loaded car”.

Figure 1. 8-Axle SNF Railcar

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Figure 2. Key Dimensions

Figure 3. VAMPIRE® Dynamic Model

In addition, a loaded car with the NAC-STC cask is evaluated in the dynamic curving simulation regime. The weight and CG height of the car with this cask are approximately in the middle of the range between the ballasted car and the loaded car with Hi-Star 190XL cask.

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Table 1. Key Parameters of SNF Casks1

Manufacturer & Model

Length without Impact Limiters

(in.)

Length with

Impact Limiters

(in.)

Diameter without Impact Limiters

(in.)

Diameter with

Impact Limiters

(in.)

Empty Weight with

Impact Limiters (lb.)

Loaded Weight with Impact Limiters (lb.)

NAC International

NAC-STC 193.0 273.7 99.0 128.0 188,767-

194,560

241,664-254,589

NAC-UMS UTC 209.3 273.3 92.9 124.0 178,798 248,373-255,022

MAGNATRAN 214.0 322.0 110.0 128.0 208,000 312,000

Holtec International

HI-STAR 100 203.25 307.5 96.0 128.0 179,710 272,622-279,893

HI-STAR HB 128.0 230.8a 96.0 128.0 a b 187,200

HI-STAR 180 174.37 285.04 106.3 128.0 < 308,647 308,647

HI-STAR 60 158.94 274.37 75.75 128.0 a < 164,000 164,000

HI-STAR 190 SL 214.4688 339.5625 106.5 e 128 282,746 369,049-382,746 f

HI-STAR 190 XL 236.9688 362.0625 106.5 e 128 304,369 420,769 f

AREVA Transnuclear

MP187 201.5 308.0 92.5 126.75 190,200 265,100-271,300

MP197 208.0 281.25 91.5 122.0 176,710 265,100

MP197HB 210.25 271.25 97.75 126.0 179,000 303,600

TN-32Bc 184.0 261.0a 97.75 144.0 a d 263,000 a

TN-40 183.75 261.0 99.52 144.0 d 271,500

TN-40HT 183.75 260.9 101.0 144.0 d 242,343

TN-68 197.25 271.0 98.0 144.0 < 272,000 272,000

Energy Solutions

TS125 210.4 342.4 94.2 143.5 196,118 285,000

a) Estimated

b) HI-STAR HB transportation casks are already loaded so they would not be shipped empty

c) This is the TN-32B that DOE plans to use in the High Burnup Dry Storage Cask Research and Development Project, and ship from

North Anna Nuclear Power Plant. The TN-32B does not currently have a transport certificate of compliance. The dimensions and weight with impact limiters for the TN-32B are estimated.

d) TN-40 transportation casks are authorized for single use shipments and would not be shipped empty. TN-32B and TN-40HT transportation casks would be authorized for single use shipments and would not be shipped empty on an S-2043 cask car

e) Diameter is of cask body and does not include trunnions

f) Weights do not include the weights of any MPC spacers that may be required

1 Reference: Report # DE-NE0008390, “Design & Prototype Fabrication of Railcars for Transport of HLRM,” AREVA Federal Services LLC, Mar. 6, 2018

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Table 2. Weight and Inertia Parameters for Loaded Car

Component Center of Gravity2 (in.) Weight, lb.

Mass Moment of Inertia about Center of Gravity, (lb.-in.2)

X Y Z X Y Z

Platform Deck 0 0 48.6 72,550 9.7E7 2.43E9 2.5E9

Cask & Cradle 0 0 116.6 434,405 6.5E8 2.47E9 2.46E9

End Stop, Front 201.5 0 115.1 20,000 3.7E7 2.95E7 2.99E7

End Stop, Rear -201.5 0 115.1 20,000 3.7E7 2.95E7 2.99E7

Loaded Car 0 0 107.5 546,955 1.1E9 6.87E9 6.64E9

The ballast assembly is identical to the configuration used in the Atlas project. The ballast consists of two assemblies, each weighing 100,250 lb., located over the span bolsters on each end. The weight, inertia, and effective CG for the ballasted configuration are shown in Table 3.

Table 3. Weight and Inertia Parameters for Empty Car with Ballast

Center of Gravity (in.) Weight, lb.

Mass Moment of Inertia about Center of Gravity, (lb.-in.2)

X Y Z X Y Z

Platform Deck 0 0 48.6 72,550 9.7E7 2.43E9 2.5E9

Ballast, Front 215 0 73.0 100,250 8.34E7 1.05E8 1.61E8

Ballast, Rear -215 0 73.0 100,250 8.34E7 1.05E8 1.61E8

Ballasted Car 0 0 66.5 273,050 2.95E8 1.19E10 1.21E10

2 Distance from center of car for longitudinal, Centerline of Track for lateral and Top of Rail for vertical

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Table 4 lists the rigid bodies and the corresponding degrees of freedom (DOF). There are a total of 27 rigid bodies with 158 degrees of freedom in the dynamic model, including flexibility in the twist mode for the four transoms. This model is considered as the “base” model.

In addition, the response of a model with car flexibility in first bending and first torsional modes was analyzed in the dynamic curving regime and compared to the base model. The dynamic model with the car flexibilities has a total of 160 degrees of freedom with the increase in number of DOF for the car body from 6 to 8.

Similar to the approach taken with the Atlas project for the design of the 12-axle cask car, the full set of S-2043 simulations were performed with the ballast load and the HI-STAR 190XL cask configurations. For the simulation of the loaded car, the platform and the lading were considered one rigid body with the effective weight and CG modeled with the parameters shown for the loaded car in Table 2. Similarly, for the simulation of the ballasted car, the platform and the two ballast weights were considered one rigid body, modeled with the parameters in Table 3 for the ballasted car.

Table 4. Rigid Bodies & Degrees of Freedom

Body # Body Name # of DOF Weight in Lbs. Quantity per Car

M1 Cask and platform

6 546,955 (Loaded) 273,050 (Empty with ballast)

M2, M3, M15 and M16

Truck Bolster 6 2087 4

M4, M5, M6 and M7 and M17, M18, M19 and M20

Side Frame 6 1236 8

M8, M21 Span Bolster 6 12078 2 M9, M10, M22 and M23

Transom 7 817 4

M11 TO M14

M24 TO M27

Wheelset 5 3450 8

Total Number of degrees of freedom in the model: 158

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3. Description of the Truck Model

The SNF railcar model has four Amsted 125-ton Swing Motion® trucks. The model parameters for the truck, including the geometry, mass and inertia, stiffness and damping for the primary and secondary suspension, were based on the input provided to SA by Amsted.

A general description of the truck is given in the main Phase II report “8-Axle SNF Railcar Design” submittal. The primary suspension for the 125-ton truck was modeled with Adapter Plus® adapter pads with appropriate stiffness and damping characteristics provided by Amsted.

Figure 4 shows the VAMPIRE® wire frame model of the primary suspension with bump stops in the longitudinal, lateral, and vertical directions. The roll and yaw stiffness were also modeled at each location. Based on the design input from Amsted, the effect of car weight on the suspension parameters was incorporated.

The secondary suspension in Figure 5 shows the spring nest connecting the transom with the truck bolster. The spring nests were modeled with a large increase in stiffness to represent spring bottoming. The friction wedges, seated over the control coils, provide the damping for the connection. The side frame rocker seat is bolted to the transom in order to increase the warp stiffness of the Swing Motion® truck and prevent high speed truck hunting as described in Section 4 of the main report. This connection between the side frame and transom is modeled using bush elements shown in the figure and provides the lateral and longitudinal stiffness. The rocker arrangement provides the relative roll between the transom and side frame. The rocker arrangement was modeled using link elements in VAMPIRE®.

The truck bolster has a 16” diameter center bowl which is connected to the span bolster center plate using four vertical bump stops. The longitudinal and lateral connections between the truck bolster and span bolster were modeled with bump stops having 1/16” radial clearance. The truck bolster is also provided with two long travel constant contact side bearings (CCSB) with a preload of 6000 lb. The interface between the span bolster and the carbody was modeled using a 21.5” center bowl having a 1/16” radial clearance with the carbody center plate. A vertical clearance of 3/8” was modeled between the standard side bearing plates of span bolster and the car body centerplate. The longitudinal, lateral, and vertical connections between the span bolster and car body centerplate were also modeled with bump stops.

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Figure 4. Primary Suspension

Figure 5. Secondary Suspension

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4. Description of the Simulation Regimes

The dynamic analyses were performed using VAMPIRE® software to evaluate trackworthiness of the 8-axle SNF railcar for performance regimes listed in Section 4.3 of the AAR S-2043 Specification. Table 5 lists the performance criteria for the evaluation and the corresponding limiting values as given in Table 4.1 of the AAR S-2043 Standard. The output from VAMPIRE® simulations for the various performance regimes is compared to the limits specified in this table. The results presented were filtered with a 15 Hz low pass filter. The limiting values in the table from S-2043 are more stringent than the requirements in Chapter 11 of AAR M-1001 Standard for a railway freight car in interchange service.

Table 5. S-2043 Performance Criteria3

Criterion Limiting Value

Notes

Maximum car body roll angle (degrees) 4 Peak-to-Peak Maximum wheel L/V 0.8 Maximum truck side L/V 0.5 Minimum vertical wheel load (%) 25 Peak-to-Peak car body lateral acceleration (g) 1.3 Maximum car body lateral acceleration (g) 0.75 Lateral car body acceleration standard deviation (g)

0.13 Calculated over 1000 ft.

Maximum car body vertical acceleration (g) 0.9 Maximum vertical suspension deflection (%) 95 Maximum spring deflection as

% of spring travel. Suspension bottoming not allowed

4.1 Non-Structural Static Analyses

As required by Section 4.2 of S-2043, the results of truck twist and car body twist equalization evaluations are presented in this section.

4.1.1 Truck Twist Equalization (Section 4.2.1 in S-2043)

This requirement is to ensure adequate truck load equalization under statically applied track twist conditions. The standard requires that, with the railcar on level track, vertical wheel

3 Reference: Table 4.1 in AAR MSRP Standard S-2043

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In VAMPIRE®, the track was modeled with a dip or bump on one rail on tangent track for lowering or raising a wheel in the range from 0” to 3”. The truck has an axle spacing of 5’ 11”. The dip or bump spans a distance of 5 feet so that when one wheel of the truck is in the dip or on the top of the bump, other wheels are on the level track. The dip (bump) ramps down (up) over a distance of 2 feet and levels at the maximum amplitude for a foot and ramps up (back) down over 2 feet. The track model with a 3-inch dip on one rail is shown in Figure 6.

Figure 6. Track Model for Truck Twist Simulation

The simulations were run with the SNF railcar going over the bump at 1 mph, simulating the static condition. The runs were repeated by modeling a dip on one rail up to -3”. The resulting minimum wheel loads are plotted below for the entire range from -3” to +3”. Refer to Figure 7 for the loaded car and Figure 8 for the ballasted car. The limits for minimum vertical wheel load of 60% for 2” and 40% for 3” of track twist input are also plotted in these figures. The SNF railcar meets the requirements for truck wheel load equalization in this regime.

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Figure 7. Min. Wheel Load under Truck Twist - Loaded Car

Figure 8. Min. Wheel Load under Truck Twist -Empty Car with Ballast

4.1.2 Car Body Twist Equalization (Section 4.2.2 in S-2043)

This requirement is to determine wheel unloading during car body twist, as the car goes over a spiral. For this simulation regime, requirements from Section 4.2.2 in S-2043 are listed below:

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• Simulate a car being jacked up to 3” from underneath the wheels on one side of all trucks at one end of the car in 0.5” increments

• Analyze both the loaded car and empty car with ballast configurations

The track was modeled as a tangent section with a bump (or dip) on the left rail such that all wheels on one side of the span bolster were raised (or lowered). The distance between the last wheel of the lead span bolster and the first wheel of the trailing span bolster is 17’ 9”.

The track model was designed with a 15 feet long entry and exit ramp and 100 feet long section with a maximum cross level amplitude of 3”. The ramp length of 15 feet ensured that when one wheel of the lead span bolster was at the maximum amplitude of super elevation, the other wheels on one side of the trailing span bolster remained on the tangent track, thus creating the required track condition for this load case. The track model with the 3” dip on one rail is shown in Figure 9 for this simulation regime.

Figure 9. Track Model for Car Twist Simulation

The simulations were run at 1 mph as the loaded car went over the bump in the range of 0” to 3” in ½” increments. The runs were repeated with the loaded car going over the dip in the range of 0” to -3”. Figure 10 plots the minimum vertical wheel load at the wheels under both the leading and trailing span bolsters, as the loaded car went over the track bumps and dips. Figure 11 plots the results for the ballasted car. The car body response in both the loaded and ballasted conditions meets the S-2043 requirements for this regime.

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Figure 10. Min. Wheel Load under Car Body Twist - Loaded Car

Figure 11. Min. Wheel Load under Car Body Twist – Empty Car with Ballast

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4.2 Dynamic Analyses

For all the simulation regimes, wheels with the AAR 2A profile and AREA 136-lb profile rail with 1:40 cant were used (Figure 12). The wheel/rail interface coefficient of friction was 0.5 as required by AAR S-2043 and AAR M-1001 Chapter XI.

Figure 12. AAR 2A Wheel Profile and AREA 136 lb. Rail Profile

4.2.1 Twist & Roll Regime (Section 4.3.9.6 in S-2043)

A tangent track with ten staggered cross level perturbations of ¾” maximum amplitude and wavelength of 39’ was modeled as required by the S-2043 Standard. The simulations were performed from 5 to 70 mph at 5 mph increments. Finer increments of 2 mph were used near the resonant speed. The simulations were repeated for a perturbation wavelength of 35.8’, which is the distance between the centers of the span bolsters in the SNF car. The results of the analysis in terms of the peak-to-peak car body roll angle for the loaded car are plotted in Figure 13. The maximum roll angle of 2o at 11 mph is less than the limiting value of 4o.

The time history plots of the car body roll angle and ratio of the vertical dynamic wheel load to the static wheel load are shown in Figure 14 and Figure 15 , respectively. The results for the twist and roll response for the loaded car summarized in Table 6 shows all the parameters are below the S-2043 limits.

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Figure 13. Response of the Loaded SNF Railcar to Twist & Roll Input

Figure 14. Car Body Roll Angle in Twist & Roll (11 mph, loaded car)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 10 20 30 40 50 60 70

Ro ll an gl e (d eg

Speed (mph)

39' wavelength

35.8' wavelength limit

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Figure 15. Vertical Wheel Load Ratio in Twist & Roll (11 mph, loaded car)

The roll angle plotted in Figure 13 shows that the resonance occurs at 11 mph. To find out if this resonance mode is a lower or upper center roll, the lateral displacements of the car body, span bolster and the truck bolster at the respective CG are plotted for the 39’ wavelength perturbation in Figure 16. Since the lateral displacements of the span bolster and the truck bolster are successively less than that of the car body, the mode the loaded car experiences is lower center roll resonance.

Figure 16. Carbody & Bolster Lat. Displ. in Twist & Roll (11 mph, 39’ wavelength, loaded car)

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Table 6. Twist & Roll Summary (loaded car)

Parameters Values S-2043 Limit

Perturbation wavelength 39-feet 35.8-feet

Peak to peak carbody roll, deg. 2.05 1.64 4

Maximum Wheel L/V 0.07 0.08 0.8

Max Truck Side L/V 0.06 0.06 0.5

Min Vert. wheel load, % 72 74 25

Peak to peak Car body lateral g 0.55 0.52 1.3

Max Car body lateral g 0.28 0.27 0.75

Maximum carbody vertical (g) 0.06 0.07 0.9

Maximum vertical suspension deflection (%) 77 78 95

For the car with ballast, the dynamic performance results are plotted in Figure 17 to Figure

19. As seen from Figure 17, there are two resonance peaks for the ballasted car, one at 22 mph, and another at 60 mph for the 39’ wavelength perturbations. For the 35.8’ wavelength case, the two peaks occur at 15 mph and 55 mph, respectively.

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Figure 17. Response of the Ballasted Car in Twist & Roll Regime

Figure 18. Car Body Roll in Twist & Roll Regime (60 mph, ballasted car)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 10 20 30 40 50 60 70

Ro ll an gl e (d eg

Speed (mph)

39' wavelength

35.8' wavelength limit

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Figure 19. Vertical Wheel Load Ratio in Twist & Roll (60 mph, ballasted car)

The lateral displacements for the first roll resonance of the ballasted car at 22 mph are shown in Figure 20. The vehicle response is similar to the loaded car discussed previously (Figure 16). The mode of resonance for the ballasted car is a lower center roll since the carbody lateral displacement is greater than the span bolster and truck bolster displacements.

Figure 20. Carbody & Bolster Lat. Displ. in Twist & Roll (22 mph, 39’ wavelength, ballasted car)

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The response of the ballasted car when the second resonance peak occurs at 60 mph is shown in Figure 21. The truck lateral displacement is higher than the span bolster and car body lateral displacements. At this speed, the car body lateral displacement is the lowest.

This indicates that the resonant mode at 60 mph is an upper center roll for the ballasted car.

Figure 21. Carbody & Bolster Lat. Displ. in Twist & Roll (60 mph, 39’ wavelength, The results for the car with ballast for the Twist & Roll regime are summarized in Table 7.

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Table 7. Twist & Roll Summary (ballasted car)

Perturbation Wavelength 39-feet 35.8-feet

Peak to peak carbody roll, deg. 1.91 1.83 4

Maximum Wheel L/V 0.26 0.13 0.8

Max Truck Side L/V 0.16 0.1 0.5

Min Vert. wheel load, % 67 67 25

Peak to peak Car body lateral g 0.54 0.56 1.3

Max Car body lateral g 0.28 0.29 0.75

Maximum carbody vertical (g) 0.08 0.08 0.9

Maximum vertical suspension deflection (%) 48 48 95

As seen from Table 6 and Table 7 the predicted values from the simulations in the Twist & Roll regime meet the S-2043 criteria for both the loaded and ballasted cars.

4.2.2 Pitch & Bounce (Section 4.3.9.7 in S-2043)

A tangent track with 10 parallel joints with maximum of ¾” vertical amplitude and spaced at 39’ interval was used for the pitch and bounce simulations. A similar track with wavelength of 35.8’, the distance between span bolster centers, was also modeled as required by S- 2043. Simulations were run from 10 mph to 70 mph at 5 mph increments for both the loaded and ballasted car configurations.

A plot of the vertical wheel load as a percentage of static wheel load is shown in Figure 22.

The loaded car meets the minimum vertical load of 25% as required by S-2043 for the entire speed range.

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Figure 22. Response of Loaded Car in Pitch & Bounce Regime

The time history plot of the vertical wheel load as a ratio of the static wheel load is shown in Figure 23 for both perturbation wavelengths (39’ and 35.8’) for the loaded SNF railcar. For both wavelengths, the vertical wheel load ratio is well above the limit of 0.25.

Figure 23. Vertical Wheel Load Ratio in Pitch & Bounce (50 mph, loaded car)

0%

20%

40%

60%

80%

100%

0 10 20 30 40 50 60 70

Ve r2 ca l w he el lo ad

(P er ce nt

ta 2c

Speed (mph)

39' wavelength

35.8' wavelength

Limit

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In Figure 24, the time history of vertical acceleration for this scenario is shown. In VAMPIRE® axes system, positive acceleration acts downward. The maximum vertical acceleration of 0.27g for the 39’ wavelength perturbation is well below the S-2043 limit of 0.9g.

Figure 24. Carbody Vertical Acceleration in Pitch & Bounce (50 mph, loaded car)

Table 8 shows that the loaded car meets the specification requirements in the Pitch & Bounce regime.

Table 8. Pitch & Bounce Summary (loaded car)

Parameters Values S-2043 Limit

Perturbation Wavelength 39-feet 35.8-feet

Peak to peak carbody roll, deg. 0.001 0.002 4

Maximum Wheel L/V 0.004 0.004 0.8

Max Truck Side L/V 0.004 0.004 0.5

Min Vert. wheel load, % 79 81 25

Peak to peak Car body lateral g 0.0013 0.0015 1.3

Max Car body…