0 HE 18.5 U M T A-M A-06-0025-83- 1 .A3 7 DOT-TSC-UMTA-83-31 no. DOT- TSC- UMTA- Stability and Curving 83-31 US. Department Performance of of Transportation Urban Mass Transportation Conventional and Advanced Administration Rail Transit Vehicles D. N. Wormley J. K. Hedrick M. L. Nagurka Massachusetts Institute of Technology Department of Mechanical Engineering Cambridge MA 02139 January 1984 Final Report This document is available to the public through the National Technical Information Service, Springfield, Virginia 22161. UMTA Technical Assistance Program NOTICE This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Govern- ment assumes no liability for its contents or use thereof. NOTICE The United States Government does not endorse prod- ucts or manufacturers . Trade or manufacturers' names appear herein solely because they are con- sidered essential to the object of this report. Technical Report Documentation Page i$.Sr Government No. AiJ 1. Report No. 2. Accession No. 3. Recipient s Catalog /\o, UMTA-MA- 06-0 025-83-10 dot- TSC- 4. Title and Subtitle 5. Report Date STABILITY AND CURVING PERFORMANCE OF CONVENTIONAL January 1984 AND ADVANCED RAIL TRANSIT VEHICLES. 6. Performing Orgonizotion Code DTS-76 -m 8. Performing Orgonizotion Report No. 7. Author's) I OF DOT-TSC-UMTA-83-31 D.N. Wormley, J.K. Hedrick, M.L. Nagurka • 'ORTATJON 9. Performing Name and Addr#Sf 10. Work Unit No. (TRAIS) Organization JUN 1 i i ]%4 UM377/R3691 Massachusetts Institute of Technology* Grant No. Department of Mechanical Engineering 11. Contract or library DTRS 57-80C-00152 Cambridge, Massachusetts 02139 j 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Final Report U.S. Department of Transportation Jan. 1981 - Nov. 1982 Urban Mass Transportation Administration Office of Technical Assistance 14. Sponsoring Agency Code URT-11 Washington DC 20590 15. Supplementary Notes U.S. Department of Transportation Research and Special Programs Administration *Under Contract to: Transportation Systems Center Cambridge MA 02142 16. Abstract Analytical studies are presented which compare the curving performance and speed capability of conventional rail transit trucks with self steering (cross-braced) and forced steering (linkages between carbody and wheelsets) radial trucks. Truck curving performance is measured in terms of the work performed by the wheel/rail friction forces in the contact zone during curve negotiation. The contact work is used as an indication of wheel and rail wear rates as well as the additional power required to negotiate curves. Truck speed capability is expressed in terms of the maximum operating speed before lateral instability or hunting occurs. The studies are based upon a generalized computational model which is capable of representing conventional and innovative trucks that are currently being considered for implementation. The stability analysis utilizes a linear model while the curving analysis includes the essential nonlinearities associated with wheel/rail profile geometry, wheel/rail friction force saturation and suspension stiffnesses. In addition, the curving analysis includes an accurate description of two-point wheel/ rail contact which can occur with common wheel profiles during flanging. Results of the study indicate that for curves greater than 5°, forced steering trucks can offer substantial performance improvements in comparison to well designed conventional trucks in terms of work performed during curve negotiation. Also comparison of a new AAR 1/20 wheel profile with a modified Heumann (single point contact) profile indicates that the latter profile can offer substantial performance improvements in terms of reduced work during curve negotiation. 17. Kay Words 18. Distribution Statement Rail Vehicles DOCUMENT IS AVAILABLE TO THE PUBLIC H N I C A L Rail Trucks THROUGH THE N AT I ON A L TEC INFORMATION SERVICE, SPRINGFIELD, Radial Trucks VIRGINIA 22161 Forced Steering Trucks 21. No. of Pages 22. Pnc® 19. Security Clossif. (of this report) 20. Security Classif. (of this page) Unclassified Unclassified 348 Form DOT F 1700.7 (8-72) Reproduction of completed page authorized 1 FACTORS CONVERSION TIT TIT it r tit TIT TIT TIT 1 inches METRIC § e J E E E EE i0J®«-2 2 I </> u E £ -a «/> ® © © ® 2 1 a | © © © © 2 6 * c sill 3 3 3 3 O 8 — — © © © ff cr ® 2 - g M W H M7 £ •9 S o ao © o o « 2 u LU <D co o r** k/> if) o o o o zts © CL © -a «. N2 & $ -C — "0 © O C k — 3 3 3 3 2 © — J3 © © != ? 2 9 3 © 3 c © ® 7 7 7 7 0 « - g v> w * w <o ^ u a o-oo < Z. i— ~ u Q.crai. 11 . PREFACE In support of the Office of Rail and Construction Technology of the Urban Mass Transportation Administration (UMTA) , the Transportation Systems Center is conducting analytical and experimental studies to relate transit truck de- sign characteristics to wheel rail forces and wheel rail wear ratio. The results of these studies are expected to provide rail transit systems with options for reducing the wheel-rail wear rates while maintaining or improving equipment performance. In the past decade, there have been significant efforts toward developing steerable truck configurations employing direct connections between axles and supplemental linkages connecting the axles to the carbody. These new configur- ations aid in steering while maintaining the speed capability of the truck design. Under contracts DOT-TSC-1739 and DOT-TSC-1740 with the Budd Company and with the Urban Transportation Development Corporation, design studies have been conducted for the retrofit of existing trucks to linkage-steered config- urat ions Under an earlier contract with the U.S. Department of Transportation, Office of University Research (DOT-03-70052), the Department of Mechanical Engineering of Massachusetts Institute of Technology had conducted studies of the performance limits of conventional and self-steering trucks for intercity passenger applica- tion. This study used curve negotiation criteria in which both flange contact and wheel slip were prevented. Such a study is unrealistic for the sharp curves typical of transit application. The study described in this document extends the previous analyses to in- clude regions of significant flange contact for sharper curve radii. Also iii considered is the performance achievable with forced steering mechanizations employing truck to carbody linkages. The work was performed under contract to the Transportation Systems Center in support of the Urban Mass Transportation Administration. The authors would like to thank Dr. Herbert Weinstock for many productive discussions on the work in progress and his careful review and comments on this report. IV TABLE OF CONTENTS Chapter Page 1. INTRODUCTION i-1 1.1 Background 1-1 1.2 Study Objectives and Scope 1-2 2. STUDY METHODOLOGY 2-1 2.1 Performance Criteria 2-1 2.1.1 Lateral Stability 2-1 2.1.2 Curve Negotiation 2-2 2.2 Truck Configuration 2-6 2.2.1 Conventional Truck 2-6 2.2.2 Self- Steering Radial Truck 2-8 2.2.3 Forced Steering Radial Truck 2-14 2.2.4 Generic Truck Model 2-20 2.3 Linear Stability Model 2-24 2.3.1 Numerical Methods 2-24 2.4 Steady State Curving Model 2-25 2.5 Baseline Rail and Vehicle Parameters 2-26 3. STABILITY OF CONVENTIONAL, SELF-STEERED AND FORCED-STEERED RADIAL TRUCKS 3-1 3.1 Introduction 3-1 3.2 Stability of Conventional Trucks 3-5 3.3 Stability of Self- Steered Radial Trucks 3-11 3.4 Stability of Forced-Steered Radial Trucks 3-20 4. CURVING PERFORMANCE OF CONVENTIONAL, SELF -STEERED. AND FORCED- STEERED RADIAL TRUCKS i-1 4.1 Introduction 4-1 4.2 Curving Performance of Conventional Trucks 4-10 4.3 Curving Performance of Self-Steered Radial Trucks 4-37 4.4 Curving Performance of Forced-Steered Radial Trucks 4-43 4.5 Effect of Wneelset Misalignment on Curving Performance 4-5 7 v 2 TABLE OF CONTENTS (CONTINUED) Chapter Page 5. STABILITY/CURVING PERFORMANCE TRADEOFF 5-1 5.1 Introduction 5-1 5.2 Parametric Tradeoff Studies 5-6 5.3 Comparative Performance of Conventional, Self-Steered and Forced-Steered Trucks 5-16 6. SUMMARY AND CONCLUSIONS 6-1 APPENDIX A: DERIVATION OF CURVATURE STEERING GAIN AND INTERAXLE BENDING STIFFNESS FOR THREE FORCED-STEERING TRUCK PROTOTYPES A-l A.l The S Truck Prototype A-2 A. 2 The L Truck Prototype A-8 A. 3 The U Truck Prototype A-15 APPENDIX B: DERIVATION OF CURVATURE STEERING GAIN B-l APPENDIX C: LINEARIZED EQUATIONS FOR THE 6 DOF STABILITY MODEL (CONVENTIONAL TRUCK) C-l C.l Conventional Truck Model C-l C.2 Wheel/Rail Geometry C-l C.3 Wheel/Rail Forces and Moments C-4 C.4 Suspensions C-7 C.4.1 Primary Suspension C-7 C.4. Secondary Suspension C-7 C.5 Equations of Motion C-9 APPENDIX D: DERIVATION OF ADDITIONAL TERMS DUE TO STEERING LINKAGES... D-l APPENDIX E: LINEARIZED EQUATIONS FOR THE 15 DOF STABILITY MODEL (CONVENTIONAL TRUCK) E-l APPENDIX F: STEADY- STATE CURVING EQUATIONS FOR A SINGLE WHEELSET F-l F.l Single Wheelset Model F-l vi F.1.1 Coordinate Systems, F-l F.1.2 Wheel/Rail Profile Geometry F-2 F.1.3 Wheelset Equilibrium Conditions F-9 F. 1.3.1 Single-Point Contact F-12 F.1.3. 2 Two-Point Contact F-18 F.1.4 Numerical Methods F-23 F. 1.4.1 Single-Point Contact F-23 F.1.4. 2 Two-Point Contact F-24 APPENDIX G: NONLINEAR CREEP FORCE MODEL G-l APPENDIX H: STEADY-STATE CURVING FORMULATION FOR HALF-CARBODY MODEL H-l H.l Half-Carbody Model H-l H.1.1 Degrees of Freedom H-l H.1.2 Primary Suspension H-5 H.l.