1、 SURFACE VEHICLE RECOMMENDED PRACTICE Modal Testing and Identification of Lower Order Tire Natural Frequencies of Radial Tires SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is enti
2、rely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invit
3、es your written comments and suggestions. Copyright 2005 SAE International 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 wr
4、itten permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-0790 Email: custsvcsae.org SAE WEB ADDRESS: http:/www.sae.org Issued 2005-10 J2710 ISSUED OCT2005 TABLE OF CONTENTS 1. Scope . 2 1.1 Rationale 2 2. References. 3
5、 2.1 Applicable Publications 3 3. Definitions. 3 3.1 Unloaded Tire and Associated Coordinate System. 3 3.2 Loaded Tire and Associated Coordinate System 4 3.3 Test 6 3.4 Test Program . 6 4. Nomenclature. 6 4.1 Natural Frequencies (Modes) of Radial Tires 6 4.2 Miscellaneous 7 5. Laboratory Quality Sys
6、tem Requirement. 7 6. Apparatus. 7 6.1 Loading Machine / Loading Fixture 7 6.2 Test Wheels . 8 6.3 Modal Test Vibratory Input Force (Excitation) . 8 6.4 Modal Test Vibratory Response Measurement . 10 6.5 Frequency Limits for Measurements and Analysis 10 6.6 Acceptable Methods of Data Acquistion 11 7
7、. Calibration 11 8. Preparation of Apparatus . 11 Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SAE J2710 Issued OCT2005 - 2 - 9. Selection and Preparation of Test Tires. 11 9.1 Selecting the Tires
8、 for Good Comparability . 11 9.2 Inflation Pressure . 12 9.3 Tire Preparation . 12 9.4 Sample Size . 12 10. Modal Test Procedure 12 10.1 General Guidelines 12 10.2 Reference Data 13 10.3 Modal Test Procedure for the Unloaded Tire 13 10.4 Modal Test Procedure for the Loaded Tire 21 11. Data Analysis
9、. 28 11.1 Frequency Analysis Device Capabilities 28 11.2 Identification of Resonances 28 12. Results to be Reported 28 13. Measurement Accuracy . 29 Appendix A 30 1. Scope This SAE Recommended Practice describes test methods for measuring and identifying the natural frequencies for the lower order m
10、odes of an inflated radial tire with a fixed spindle while expending modest effort and employing a minimum of test equipment. The methods apply to any size of radial tire so long as the test equipment is properly scaled to conduct the measurements for the intended test tire. Two types of boundary co
11、nditions are considered for the tire: unloaded and loaded against a flat surface. The test involves the performance and measurement of an input vibratory force (excitation) to the tire and the corresponding vibratory output (response). The data are suitable for use in determining parameters for road
12、 load models and for comparative evaluations of the measured properties in research and development. NOTE 1The focus of this standard is identification and reporting of the lower order natural frequencies of the tire using a simple test procedure. While higher order natural frequencies may be excite
13、d during these tests, the reliable identification of the associated mode shapes is not addressed in this document. NOTE 2Herein, road load models are models for predicting forces applied to the vehicle spindles during operation over irregular surfaces, paved or otherwise. Within the context of this
14、document, forces applied to the road or terrain surface are not considered. 1.1 Rationale This document was developed as part of a set of Recommended Practices intended to allow modelers to determine the parameters required by any of the common tire models for calculating spindle loads given the roa
15、d surface profile from a single set of experimental results, thus, eliminating duplicate testing. Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SAE J2710 Issued OCT2005 - 3 - 2. References 2.1 Appl
16、icable Publications The following publications form part of the specification to the extent specified herein. Unless otherwise indicated the latest revisions of all publications shall apply. 2.1.1 SAE PUBLICATIONS These are available from SAE at 400 Commonwealth Drive, Warrendale, PA 15096-0001; or
17、through the web sight www.sae.org. SAE J2047Tire Performance Terminology SAE J2429Free-Rolling Cornering Test for Truck and Bus Tires 2.1.2 OTHER PUBLICATIONS Available in wall chart form as #TTMP-7/95 from the Rubber Manufacturers Association, 1400 K St., N.W., Washington, DC 20005. OSHA Standard 1
18、910.177Servicing Multi-Piece and Single Piece Rim Wheels Available from American National Standards Institute, Global Engineering Documents, 15 Inverness Way, East Englewood, CO 80112. ISO Standard 17025General Requirements for the Competence of Testing and Calibration Laboratories 3. Definitions Th
19、e definitions that follow are of special meaning in this document and are either not contained in other Recommended Practices or are worded somewhat differently in this document. 3.1 Unloaded Tire and Associated Coordinate System The unloaded tire is defined as a tire/wheel assembly attached to a sp
20、indle, which is considered to be rigidly supported in both the Radial and Lateral directions. The wheel is locked to prevent rotation about the spindle. The tread is not in contact with any surface. The principal directions are defined in terms of a right-handed cylindrical coordinate system with it
21、s origin at the intersection of the spindle and the wheel plane. Three components are defined as follows and illustrated in Figure 1. 3.1.1 TANGENTIAL, T Tangential displacement is defined in terms of an angle measured about the lateral axis, the centerline of the spindle. It is positive clockwise w
22、hen looking in the positive lateral direction. The tangential component describes uniform torsional motion of the tread and belt acting as a ring. Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SAE
23、J2710 Issued OCT2005 - 4 - 3.1.2 LATERAL, L The lateral axis is directed along the centerline of the spindle. Its origin is in the wheel plane. The positive lateral direction is chosen such that the T-L-R system is a right handed coordinate system. 3.1.3 RADIAL, R The radial axis is directed outward
24、 from the centerline of the spindle in the wheel plane. It is positive moving away from the spindle. It has no preferred angular orientation, but the test engineer must define an orientation so that T has a definite reference. LRTSpindleWheel PlaneFIGURE 1CYLINDRICAL COORDINATE SYSTEM USED IN THE UN
25、LOADED CASE 3.2 Loaded Tire and Associated Coordinate System The loaded tire is defined as a tire/wheel assembly attached to a spindle, which is considered to be rigidly supported in both the Radial and Lateral directions. The wheel is locked to prevent rotation about the spindle. The tire is loaded
26、 in contact with the reaction (road) surface so as to produce a tire footprint. The footprint to road surface contact has a no-slip condition. The loaded tire has different natural frequencies and mode shapes than the unloaded tire due to the footprint constraint and the loss of symmetry. Its princi
27、pal directions are defined in terms of a right-handed Cartesian coordinate system with its origin at the intersection of the spindle and the wheel plane. The three axes are defined as follows and illustrated in Figure 2. Copyright SAE International Provided by IHS under license with SAENot for Resal
28、eNo reproduction or networking permitted without license from IHS-,-,-SAE J2710 Issued OCT2005 - 5 - X”Y”Z”SpindleFIGURE 2THE SAE PARALLEL COORDINATE SYSTEM USED IN THE LOADED CASE NOTEIn a practical sense it makes no difference which way the tire is mounted since the tire is not rotating. However,
29、for ease of discussion it was assumed that the tire is mounted as if it were on the right front of the vehicle, and as if it were going to move in the positive X” direction shown in Figure 2. 3.2.1 LONGITUDINAL, X” The longitudinal axis is parallel to the SAE XAxis as defined in J2047. It is positiv
30、e in the direction indicated in Figure 2. 3.2.2 LATERAL, Y” The lateral axis is parallel to the SAE YAxis as defined in J2047. Its positive sense is to the right as viewed in the direction of rolling. NOTEIn the case of a tire without inclination, as assumed in this document, Y” lies along the spind
31、le center line with a positive sense to the right. 3.2.3 VERTICAL, Z” The vertical axis is perpendicular to the road plane with a positive sense into the road surface. It is parallel to the SAE ZAxis as defined in J2047, but the origin of the vertical axis is at the center of the tire not at the roa
32、d surface. NOTE 1The tire is assumed to have no inclination in this document in which case Z” lies in the wheel plane. NOTE 2Steer motion is understood as a tire mode, which predominantly rotates the tire belt package about the Z”Axis. NOTE 3Mode shapes and nomenclature are further discussed in Sect
33、ion 4. Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SAE J2710 Issued OCT2005 - 6 - 3.3 Test A Test is execution of the procedure described in this document one time on one tire at a single set of
34、conditions. 3.4 Test Program A Test Program is a designed experiment involving a set of the tests described in this document.14. Nomenclature 4.1 Modes of Radial Tires In this document the modes of radial tires, loaded and unloaded, are categorized as shown in Figure 3. The modes of interest in this
35、 document have bold captions in Figure Figure 3. The mode shapes and natural frequencies associated with these modes of vibration are illustrated in Section 10 of this document. (See also SAE 860243.) NOTELower order mode shapes and their associated natural frequencies are characterized based on the
36、 dominant direction of motion of the tire belt package. Motion in the tire symmetry plane2(plane normal to the spindle) is referred to as in-plane motion (InP) while motion out of the symmetry plane is out-of-plane (OoP). InP RotationTorsion (Windup)InP TranslationRadial TranslationInP FlexibleBelt
37、ModesIn-Plane(InP)OoP RotationPitch RotationOoP TranslationLateral TranslationOoP FlexibleBelt ModesOut-of-Plane(OoP)Unloaded Tire ModesRollplpl1st LongitudinalMode1st VerticalModeHigher OrderInP ModesIn-plane(InP)Lateral Tilt(Camber)1st SteerModeHigher OrderOoP ModesOut-of-Plane(OoP)Loaded Tire Mod
38、esplFIGURE 3TIRE VIBRATION MODES 1There are many experimental possibilities: repeated tests of the same tire, tests of the same tire under multiple test conditions, tests of tires with different specifications (design details), application of this test as part of a series of different tests, etc. 2T
39、he tire symmetry plane is the R-T plane in the unloaded state and the X”-Z” plane in the loaded state. Copyright SAE International Provided by IHS under license with SAENot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SAE J2710 Issued OCT2005 - 7 - 4.2 Miscellaneous
40、 For information on items not defined in Section 3 of this document or illustrated within the figures of this section, please see SAE J2047. 5. Laboratory Quality System Requirement The laboratory performing the procedures specified in this document shall have a quality system either conforming to I
41、SO 17025 or which can be shown to be functionally equivalent to ISO 17025. The elements of such a system are assumed below and are not, therefore, specifically called out within this document. 6. Apparatus The required apparatus consists of a loading machine / loading fixture, test wheels, standard
42、modal test equipment and instrumentation (an instrumented impact hammer or shaker, accelerometers, power supplies/signal conditioners and analyzer either an integrated device or a data acquistion system coupled to a computer housing appropriate modal analysis software), and miniature light weight bl
43、ocks and adhesives for mounting modal test transducers on the tire. 6.1 Loading Machine / Loading Fixture The machine / fixture consists of a tire loading and positioning system, a measuring system, a flat surface simulated roadway, and the space housing the machine, which shall be maintained at 22
44、C 2 C. 6.1.1 LOADING AND POSITIONING SYSTEM The system shall maintain the tire with the wheel plane within 0.05 of perpendicular to the simulated roadway during all loading, a common machine specification when this document was drafted. Loading shall produce normal forces accurate to within 1.0% of
45、the test machines full-scale normal force range. The machines full-scale normal force range shall allow imposition of loads equivalent to at least the test requesters specified 100% load. During the loading process, the system must move the tire or the road surface; therefore, it cannot be rigid. It
46、 is assumed that during testing that appropriate system elements will lock the spindle to road surface distance and lock the hub in all six degrees-of-freedom. Machine resonances are a potential problem. They could lead to spurious natural frequencies appearing in the reported data. Ideally, all mac
47、hine resonances should be at frequencies well above the expected tire natural frequencies. However, this may not be possible.3Thus, it is recommended that the test machine be evaluated for modes while mounting a metal part simulating the mass and inertia of the tire/wheel assembly to be tested using
48、 the procedure described in this document.4This will identify machine resonances that could be a problem. 3Exact minimum machine resonant frequency recommendations are not made in this Recommended Practice. This was done for two reasons. First, this practice is applicable to all tires regardless of
49、size (wheelbarrow to earthmover) so a single answer is inappropriate. Second, evolving tire designs may alter the required frequencies. 4A disc with a thick outer edge can be used to produce the mass and inertia simulation. The required mass and inertia values can be determined by applying J2717 to the tire/wheel assembly that is to be tested. Copyright SAE International Provi
