CP i ! NASA Conference Publication 2264 2264 , c.1 Proceedings of a workshop held at Langley Research Center Hampton, Virginia September 7-9, 1982 TECH LIBRARY KAFB. NM Modeling Compiled b::, John A. Tanner Langley Research Center Hampton, Virginia Proceedings of a workshop held at Langley Research Center Hampton, Virginia September 7-9, 1982 National Aeronautics and Space Administration Scisntlfic and Technical lntomatlon Branch 1983 .~ ____.,.. _-- .--_ L ..--.--.- PREFACE The papers included herein were presented at the NASA Tire Modeling Workshop held at Langley Research Center, September 7-9, 1982. The workshop was organized into six sessions dealing with finite element developments, applications to tire dynamic problems, solution techniques for tire contact problems, experimental data, tire thermal studies, and current design practices. Discussion periods at the end of each session allowed the participants to describe their own work or problem areas and to make recommendations for future directions of tire modeling research. The objective of the workshop was to provide a forum for the interchange of information among tire analysts and to establish goals and objectives for future research programs in this area. Hence.the various conclusions and recommendations suggested by the workshop participants are expected to provide guidance for tire modeling studies within NASA and, to some extent, the tire industry for the next several years. Special recognition is due Ms. Connie 0. Featherston for her planning, coordination, and execution of the various administrative tasks associated with the workshop. The use of trade names or names of manufacturers in this report does not constitute an official endorsement of such products or manufacturers, either expressed or implied, by the National Aeronautics and Space Administration. John A. Tanner Langley Research Center iii I: CONTENTS PREFACE.................................iii ATTENDEES................................vii FINITE ELEMENT MODELING AND ANALYSIS OF TIRES . 1 Ahmed K. Noor and C. M. Andersen FINITE ELEMENT METHODS FOR NONLINEAR ELASTOSTATIC PROBLEMS IN RUBBER ELASTICITY . 39 J. T. Oden, E. B. Becker, T. H. Miller, T. Endo, and E. B. Pires APPLICATION OF TIRE DYNAMICS TO AIRCRAFT LANDING GEAR DESIGNANALYSIS............................ 71 Raymond J. Black A TIRE CONTACT SOLUTION TECHNIQUE . 95 John T. Tielking ANALYTICAL AND EXPERIMENTAL STUDY OF A STANDING TORUS WITHNORMALLOADS...........................123 Michael J. Mack, Jr., Daniel E. Hill, and Joseph R. Baumgarten EXPERIMENTAL AND FINITE ELEMENT STUDY OF A STANDING TORUS UNDER NORMAL AND TANGENTIAL LOADS. 141 Donald R. Flugrad and Bruce A. Miller OVERVIEW OF NASA TIRE EXPERIMENTAL PROGRAMS. 163 John A. Tanner ADHESION TESTING OF AIRCRAFT TIRES . 175 Stephen N. Bobo HEAT GENERATION IN AIRCRAFT TIRES . 193 Samuel K. Clark RESULTS FROM RECENT NASA TIRE THERMAL STUDIES . 211 John L. McCarty SUMMARYOF SESSION DISCUSSIONS . 223 John A. Tanner BIBLIOGRAPHY . ...225 V ATTENDEES Carl M. Andersen William F. Conley Senior Research Associate in Math Goodyear Aerospace Corporation and Computer Science Wheel and Brake Engineering College of William and Mary D693 B-2 Williamsburg, VA 23185 1210 Massillon Road Akron, OH 44315 Joseph R. Baumgarten Iowa State University Robert H. Daugherty Department of Mechanical Engineering NASA Langley Research Center 209 Mechanical Engineering Mail Stop 497 Ames, IA 50011 Hampton, VA 23665 Ian Beaty Jozef DeEskinazi Cranfield Institute of Technology The General Tire and Rubber Company Cranfield, Bedford One General Street United Kingdom MK43 OAL Akron, OH 44329 Raymond J. Black James E. Evans Bendix Aircraft Brake and Strut General Dynamics/Fort Worth Division Division 3520 W. Westmoor Street Mail Zone 2646 P.O. Box 10 P.O. Box 748 South Bend, IN 46624 Fort Worth, TX 76013 Stephen N. Bobo Edwin L. Fasanella Department of Transportation Kentron International Incorporated Transportation Systems Center NASA Langley Research Center Kendall Square Mail Stop 495 Cambridge, MA 02142 Hampton, VA 23665 Michael F. Card Connie 0. Featherston NASA Langley Research Center NASA Langley Research Center Mail Stop 244 Mail Stop 497 Hampton, VA 23665 Hampton, VA 23665 Mathew K. Chakko Denis J. Feld B. F. Goodrich Company Goodyear Aerospace Corporation Research and Development Center Research and Development - 9921 Brecksville Road Operations Brecksville, OH 44141 1210 Massillon Road Department 150-G2 Samuel K. Clark Akron, OH 44315 Department of Applied Mechanics and Engineering Science Donald R. Flugrad 1121 G. G. Brown Lab Iowa State University Beal and Hayward Streets Department of Mechanical Engineering University of Michigan 209 Mechanical Engineering Ann Arbor, MI, 48109 Ames, IA 50011 vii Jerry B. Gehringer Trafford J. W. Leland The Goodyear Tire and Rubber Company NASA Langley Research Center 1144 E. Market Street Mail Stop 497 Department 461B Hampton, VA 23665 Akron, OH 44316 Daniel I. Livingston Robert C. Goetz Goodyear Aerospace NASA Langley Research Center 142 Goodyear Boulevard Mail Stop 118 Akron, OH 44316 Hampton, VA 23665 Spencer D. Lucas Robert J. Hayduk Dunlop Tire and Rubber Corporation NASA Langley Research Center P.O. Box 1109 Mail Stop 495 Buffalo, NY 14240 Hampton, VA 23665 John R. Luchini Etienne Jankovich Cooper Tire and Rubber Company Battelle Columbus Laboratories Lima and Western Avenues 505 King Avenue Findlay, OH 45840 Columbus, OH 43201 Bill Macy Ben-Gang Kao McDonnell Aircraft Company Ford Motor Company P.O. Box 516 Structural Analysis Department St. Louis, MO 63166 ECC 218 20000 Rotunda Drive Stan Mays Dearborn, MI 48121 B. F. Goodrich Tire Company 500 South Main Street Subhotosh Khan Department 6143 E. I. Du Pont De Nemours Incorporated Building 10E Textile Research Laboratory Akron, OH 44318 Chestnut Run Wilmington, DE 19898 John L. McCarty NASA Langley Research Center Richard L. Kirk Mail Stop 497 Goodyear Aerospace Corporation Hampton, VA 23665 Wheel and Brake Engineering D693 B-2 Marc C. McReynolds 1210 Massillon Road McDonnell-Douglas Corporation Akron, OH 44315 Douglas Aircraft Company 3855 Lakewood Boulevard Werner W. Klingbeil Long Beach, CA 90846 Corporate Research Center Uniroyal Incorporated Chet Miller World Headquarters R-l-2 E. I. Du Pont De Nemours Incorp- Middlebury, CT 06749 orated Du Pont Experimental Station Lin-E. Kung Building 304 Room C217 Purdue University Wilmington, DE 19898 Ray W. Herrick Laboratories West Lafayette, IN 47907 viii Ahmed K. Noor Shimoga K. Srinath George Washington University Boeing Commercial Airplane Company Joint Institute for Advancement P.O. Box 3707 of Flight Sciences Mail stop 47-03 Mail Stop 246 Seattle, WA 98124 Langley Research Center Hampton, VA 23665 James A. Susko Cooper Tire and Rubber Company J. Tinsley Oden Box 550 The University of Texas Findlay, OH 45840 TICOM - ASE-EM Department Austin, TX 78712 Farhad Tabaddor B. F. Goodrich Company John J. Parker 500 South Main Street Cooper Tire and Rubber Company Akron, OH 44318 Lima and Western Avenues Findlay, OH 45840 John A. Tanner NASA Langley Research Center Peter Popper Mail Stop 497 E. I. Du Pont De Nemours Incorporated Hampton, VA 23665 Du Pont Experimental Station Building 304 Room C217 Robert L. Taylor Wilmington, DE 19898 721 Davis Hall University of California Marion G. Pottinger Department of Civil Engineering B. F. Goodrich Berkley, CA 94720 Research and Development Center 9921 Brecksville Road Robert G. Thomson Brecksville, OH 44141 NASA Langley Research Center Mail Stop 495 Gerald R. Potts Hampton, VA 23665 GM1 Engineering and Management Institute John T. Tielking 1700 W. Third Avenue Texas A&M University Flint, MI 48502 Civil Engineering Department College Station, TX 77843 Wim J. Schaffers E. I. Du Pont De Nemours Incorporated M. J. Trinko Du Pont Experimental Station Department 460G Building 304 Room C217 Goodyear Tire and Rubber Company Wilmington, DE 19898 Akron, OH 44316 Leonard Segel William A. Vogler Highway Safety Research Institute Kentron International Incorporated University of Michigan NASA Langley Research Center Huron Parkway and Baxter Road Mail Stop 497 Ann Arbor, MI 48109 Hampton, VA 23665 Kevin L. Smith M. Susan Williams AFWAL/FIEMA NASA Langley Research Center Wright-Patterson AFB, OH 45433 Mail Stop 495 Hampton, VA 23665 ix - Doug L. Wilson S2105 Scientific Research Laboratory Ford Motor Company 20000 Rotunda Drive Dearborn, MI 48121 Christopher Winkler Highway Safety Research Institute University of Michigan Huron Parkway and Baxter Road Ann Arbor, MI 48109 Thomas J. Yager NASA Langley Research Center Mail Stop 497 Hampton, VA 23665 X FINITE ELEMENT MODELING AND ANALYSIS OF TIRES Ahmed K. Noor Joint Institute for Advancement of Flight Sciences George Washington University and C. M. Andersen College of William and Mary Abstract Although the problem of tire modeling and analysis has been a subject of continuing concern for the tire industry, to date no simple and general tire model exists for predicting the response of the tire under various loading conditions. Much of the recent progress in finite element technology has not been exploited for tire modeling and analysis. The present paper focuses on this issue. Specifically, the paper reviews some of the recent advances in finite element technology which have high potential for application to tire modeling problems. It also identifies the analysis and modeling needs for tires. The topics covered include: 1) reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment