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1、400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web: www.sae.org SAE TECHNICAL PAPER SERIES 2006-01-1559 Force and Moment Characteristics of Two Space-Saver Tires L. D. Metz Metz Engineering and Racing 2006 SAE World Congress Detroit, Michigan April 3
2、-6, 2006 Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87 The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAEs peer review process under the supervision of the session organizer. This process requires a minimum of three (3) reviews by indust
3、ry experts. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests
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5、vicesae.org ISSN 0148-7191 Copyright 2006 SAE International Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the p
6、aper if it is published in SAE Transactions. Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract to Secretary, Engineering Meetings Board, SAE. Printed in USA Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87
7、2006-01-1559 Force and Moment Characteristics of Two Space-Saver Tires L. D. Metz Metz Engineering and Racing Copyright 2006 SAE International ABSTRACT Many modern vehicles utilize so-called “space-saver” spare tires. Such tires are not fitted to the vehicle and driven on until a tire problem has ar
8、isen with a service tire, and are limited in the mileage and speed at which they can operate. They also may have quite different characteristics (rolling radius, tread pattern, contact patch width and length, aspect ratio, stiffnesses, self- aligning torques, etc.) than the service tires with which
9、the vehicle is equipped. As such, they have the potential for presenting significantly different handling signatures to the driver when they are fitted In the present work, we present force and moment char- acteristics for two disparate space-saver spare tires. The tires were tested at the T.I.R.F.
10、(TIre Research Facility), Calspan Corporation, Buffalo, NY. Using the data ob- tained from the experimental tire test program, under- steer gradients (UG) were calculated for two vehicles typical of those that would employ each respective tire (sports car, passenger car). INTRODUCTION Because of pac
11、kaging, cost and other considerations, space-saver spare tires are commonly supplied on many modern passenger cars. This is particularly true with sports cars, which often have quite limited trunk space. Both the tire and the rim on which it is mounted differ considerably from the service tires on t
12、he vehicle. Be- cause of these differences, analyses of the characteris- tics of such a tire and the associated vehicle behavior resulting from its use are important 4. TEST PROGRAM Two different space-save spare tires were dynamically tested on the T.I.R.F. (TIre Research Facility) machine at Calsp
13、an Corporation, 4455 Genesee Street, Buffalo, NY 14225. The facility uses a flat-track test machine equipped to record and control variables of interest dur- ing testing. Figure One below shows an overview photo- graph of the T.I.R.F. test apparatus. The apparatus has been widely used and validated
14、by numerous groups, manufacturers and other interested parties for over 30 years 8. Figure One: Calspan T.I.R.F Tire Test Machine TIRE 1083-5: The first tire tested was a Firestone “Tem- porary Use Only” T125/70-D14, designated as Tire 1083-5 during testing. This type of tire is quite common on nume
15、rous production cars, and was mounted on a steel space-saver rim specifically designed for such a tire. The Firestone tire used for testing came from a mid- size U.S. passenger car four-door sedan. The tire, rim and tread pattern are shown in Figures Two and Three: Figure Two: Tire 1083-5 Mounted on
16、 Rim Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87 The tire was tested by measuring its sideforce Fy vs. slip angle and self-aligning torque Mz vs. slip angle charac- teristics for nine combinations of camber or inclination angle and vertical load Fz. Figure Three: Tire 1083-5 Tread Pattern
17、The slip angles measured were swept through the range = 8 o at a steer sweep rate of 5.5o/sec. The sweep rate and T.I.R.F. belt speed were chosen so that tran- sient tire behavior and relaxation characteristics were minimized 1,3. The standard SAE axis system was employed 2 when preparing the presen
18、tation of results. Tire pressure was monitored and held constant during the testing at the recommended inflation pressure of 60 psi. The roadway surface used on the T.I.R.F. machine was 120 grit 3Mite from 3M Corporation, simulating typi- cal pavement aggressiveness but likely more tractive than any
19、thing except new, sharp, brushed concrete 9. Thus, ultimate friction measurements were overesti- mated during testing. TIRE 1083-4: The second tire tested was a Vredestein “Space Master” 165/70-16, a type typically used only in a few sports car type vehicles, designated as Tire 1083- 4 during testin
20、g. This tire and rim combination, for ex- ample, was supplied as the emergency tire on a 1998 Porsche 993 Carrera 4 cabriolet vehicle. The tire, rim and tread pattern are shown in Figures Four and Five: Figure Four: Tire 1083-4 Mounted on Rim Figure Five: Tire 1083-4 Tread Pattern The Vredestein tir
21、e is unique in that, in its uninflated state, the sidewall folds in upon itself, as shown in Fig- ures Six and Seven below. This tire was also inflated to its recommended inflation pressure, in this case 36 psi. Figure Six: Tire 1083-4 in Uninflated Stated Author:Gilligan-SID:1178-GUID:20758466-141.
22、213.232.87 Figure Seven: Tire 1083-4 in Inflated State Identical test procedures were used for both Tire 1083-4 and Tire 1083-5. A 10-minute warm-up run and two con- ditioning sweeps were performed prior to actual data measurements. Following warm-up and conditioning, each tire was held at constant
23、vertical load Fz and cam- ber angle combinations while the slip angle sweep was performed. Each tire was tested over a test matrix con- sisting of three different vertical loads (Fz) and three dif- ferent camber angles (), as shown below: Fz values: 600, 950, 1,300 lbf values: 0 o, -1o, -2o RESULTS
24、Results of the tire tests are shown in the Appendix, Fig- ures A.1 A.12. Each of the 12 figures shows results for the three vertical loads noted above: 600, 950 & 1,300 lbf. Tire 1083-5 had a rated vertical load capacity of Fz = 1,390 lbf and a recommended inflation pressure of 60 psi. Tire 1083-4 w
25、as rated at Fz = 1,400 lbf with a rec- ommended inflation pressure of 36 psi. Both tires were tested at their respective recommended inflation pres- sures, as noted above, and at no other pressures. T.I.R.F. machine belt speed was set to the equivalent of a 45 mph vehicle forward speed. Figures A.1
26、A. 6 show test results of sideforce Fy vs. slip angle and self- aligning torque Mz vs. slip angle for tire 1083-4. Figures A.7 A. 12 show corresponding data for tire 1083-5. Despite their fundamentally different appearance and construction, both tires exhibited very similar character- istics. The sp
27、ace-saver tire characteristics, however, were quite different from those exhibited by the service tires of one of their corresponding vehicles. In that case, the differences give rise to changes in vehicle handling as discussed below. VEHICLE DYNAMICS CONSIDERATIONS UNDERSTEER GRADIENT A commonly us
28、ed steady- state vehicle handling metric is the Understeer Gradient (UG). UG information can be extracted from measured skidpad data, and is given by the derivative or slope of the Steer wheel angle (SWA) vs. lateral acceleration curve 10,11, i.e.: gda d UG y deg , = Eq (1) Passenger cars equipped w
29、ith O.E. tires are generally understeer throughout most of their reachable lateral acceleration limit. Rear wheel drive (RWD) vehicles with sufficient power can exhibit final oversteer because of the power consumption needed to overcome slip angle drag at high ay-values and the associated friction c
30、ircle. Understeer front wheel drive (FWD) cars will increase their UG near the lateral acceleration limit for similar rea- sons. Vehicles with four wheel drive (4WD) may exhibit either behavior near tire saturation limits, depending on the torque split between front and rear axles. As an alternative
31、 to a skidpad test, UG can be directly calculated in the linear region of car and tire behavior (ay-values Cf. With the exemplar Porsche 993, +UG with service tires is achieved by fitting the car with larger rear tires and rims to counter the rear weight bias. Use of cornering stiffness coefficients
32、 to calculate the UG implicitly implies that the car is being driven in the linear range of cornering behavior (ay 0.4g or so). Behavior near the cornering limit could be expected to be similar, though the UG would be expected to be even worse for the rear space-saver tire position due to in- creasi
33、ng thrust requirements at higher slip angles. Example Handling Behavior: Chevrolet Lumina: Con- sider Tire 1083-5 (Firestone) mounted at either the front or rear axle of a Chevrolet Lumina. The service tires for such a car (depending on manufacturer and inflation pressure po) typically have a corner
34、ing stiffness in the range of Cf Cr 125 lbf/deg. The fore/aft weight distri- bution of the car is 65/35 with a curb weight of 3,200 lbf . With service tires, the UG according to Eq (2) is given by: g UG deg 84 . 3 1252 )35 . 0 65 . 0 (200, 3 = = Eq (7) Author:Gilligan-SID:1178-GUID:20758466-141.213.
35、232.87 In this case, unlike the Porsche 993, the cornering stiff- ness coefficient of the space-saver spare tire is ap- proximately the same as the cornering stiffness coeffi- cients of the service tires. Under such conditions, we expect little change in the UG gradient, regardless of the mounting l
36、ocation of the space-saver tire. SELF-ALIGNING TORQUE - The location of the peak of the self-aligning torque vs. slip angle curve is a useful feedback mechanism to alert the driver to impending tire saturation. The magnitude and rate of falloff of this curve also serve a similar purpose, although po
37、wer assisted steering can mask magnitude differences. When the steering “goes light,” i.e., the tire passes the slip angle where self-aligning torque peaks, the driver senses that the tire is about to be saturated or, at the very least, is entering the nonlinear region of operation. The shapes and m
38、agnitudes of the self-aligning curves for both space-saver tires are similar to those for service tires. Thus, the feedback mechanism alerting a driver to impending saturation is (relatively) invariant with respect to tire wear, vertical load or inflation pressure for the tires tested. Prudence also
39、 dictates that a vehicle fitted with a space-saver tire not be driven energetically! CONCLUSION The two space-saver spare tires tested have character- istics which are remarkably similar given their completely different design and construction philosophies. The ef- fect that installation of one of t
40、he tires would have on vehicle handling depends on how closely the tire charac- teristics match those of the service tire being replaced. ACKNOWLEDGMENTS The Author would like to acknowledge Messrs. George A. Tapia and David Gentz at Calspan Corporation for their help in organizing and conducting th
41、e tests de- scribed above. REFERENCES 1. Weber, R. & Persche, H.-G., “Frequency Response of Tires Slip Angle and Lateral Force, SAE Paper No. 760030 (1977). 2. _, “Vehicle Dynamics Terminology,” SAE Recommended Practice J670e also see SAE J2047, Figure One, p. 11 (latest version). 3. Wallentowitz, H
42、., Khn, P. & Holdmann, P., “Dy- namic Properties of Tires Testing and Simulation,” SAE Paper No. 1999-01-0790 (1999). 4. Allen, R. W., et al., “The Effect of Tire Characteris- tics on Vehicle Handling and Stability,” SAE Paper No. 2000-01-0698 (2000). 5. Allen, R. W., et al., “Tire Modeling Requirem
43、ents for Vehicle Dynamics Simulations,” SAE Paper No. 950312 (1995). 6. Xia, X. & Willis, J. N., “The Effects of Tire Cornering Stiffness on Vehicle Linear Handling Performance,” SAE Paper No. 950313 (1995). 7. McNorton, T. & Wheeler, F., “Camber and Toe Ef- fect on SBFA Heavy Truck Steering Axle Ti
44、re Wear,” SAE Paper No. 922485 (1992). 8. Schuring, D. J., “Experimental Validation of the Cal- span Tire Research Facility,” Calspan Report No. ZM-5269-K, 12.21.1973. 9. Baker, J. S., Traffic Accident Investigation Manual, The Traffic Institute, Northwestern University, Evanston, IL, ISBN 0-912642-
45、01-7, p. 210, Exhibit 9- 5 (1975). 10. Milliken, W. F., Jr. & Milliken, D. L., Race Car Vehi- cle Dynamics, Society of Automotive Engineers, 400 Commonwealth Drive, Warrendale, PA 15096.0001, ISBN 1-56091-526-9, pp. 224-225, 5.17.1 (1995). 11. _, “Vehicle Dynamics Terminology,” Op. Cit., Definition
46、9.4.7 (latest version). 12. Bundorf, R. T., “The Effect of Vehicle Design Pa- rameters on Characteristic Speed and Understeer,” SAE Paper No. 670078 (1967). 13. Bundorf, R. T. & Leffert, R. L., “The Cornering Com- pliance Concept for Description of Directional Con- trol Properties,” General Motors P
47、ublication No. 2771 (1967, 1973). 14. _, “Vehicle Dynamics Terminology,” Op. Cit., Definition 7.5.1 (latest version). CONTACT Inquiries should be directed to Dr. L. Daniel Metz, Metz Engineering and Racing, 1108 West William Street, Champaign, IL 61821.4507, (01) 217.351.6070 (voice + fax), INDYDOCU
48、IUC.EDU. Author:Gilligan-SID:1178-GUID:20758466-141.213.232.87 -1500 -1000 -500 0 500 1000 1500 -10-50510 Slip Angle, degrees Lateral force Fy, lbf Figure A.1: Tire 1083-4, 0o camber -1500 -1000 -500 0 500 1000 1500 -10-50510 Slip Angle, degrees Lateral Force Fy, lbf Figure A.2: Tire 1083-4, -1o cam
49、ber -1500 -1000 -500 0 500 1000 1500 -10-50510 Slip Angle, degrees Lateral Force Fy, lbf Figure A.3: Tire 1083-4, -2o camber -150 -100 -50 0 50 100 150 -10-50510 Slip Angle, degrees Self-Aligning Torque, ft-lbf Figure A.4: Tire 1083-4, 0o camber -150 -100 -50 0 50 100 150 -10-50510 Slip Angle, degrees Self-Aligning Torque, ft-lbf Figure A.5: Tire 1083-4, -1o camber -150 -100 -50 0 50 100 150 -10-50510 Slip Angle, degrees Self-Aligning Torque, ft-lbf Figure A.6: Tire 1083-4, -2o camber Author:
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