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Tire Dynamics Modeling Method Based on Rapid Test Method Dang Lu1, Lei Lu1, Haidong Wu1*, Wei Wang2 and Manyi Lv2

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Tire Dynamics Modeling Method Based on Rapid Test Method Dang Lu1, Lei Lu1, Haidong Wu1*, Wei Wang2 and Manyi Lv2 Lu et al. Chin. J. Mech. Eng. (2020) 33:85 https://doi.org/10.1186/s10033-020-00513-8 Chinese Journal of Mechanical Engineering ORIGINAL ARTICLE Open Access Tire Dynamics Modeling Method Based on Rapid Test Method Dang Lu1, Lei Lu1, Haidong Wu1*, Wei Wang2 and Manyi Lv2 Abstract Combined with the tire dynamics theoretical model, a rapid test method to obtain tire lateral and longitudinal both steady-state and transient characteristics only based on the tire quasi-steady-state test results is proposed. For steady state data extraction, the test time of the rapid test method is half that of the conventional test method. For transient tire characteristics the rapid test method omits the traditional tire test totally. At the mean time the accuracy of the two method is much closed. The rapid test method is explained theoretically and the test process is designed. The key parameters of tire are extracted and the comparison is made between rapid test and traditional test method. The result show that the identifcation accuracy based on the rapid test method is almost equal to the accuracy of the conventional one. Then, the heat generated during the rapid test method and that generated during the conven- tional test are calculated separately. The comparison shows that the heat generated during the rapid test is much smaller than the heat generated during the conventional test process. This benefts to the reduction of tire wear and the consistency of test results. Finally, it can be concluded that the fast test method can efciently, accurately and energy-efciently measure the steady-state and transient characteristics of the tire. Keywords: Tire dynamics modeling, Rapid test method, Tire steady-state and transient characteristics, Identifcation of tire characteristics parameters 1 Introduction method, the combined brake and side slip test method by Te tire is the only part of the vehicle that is in contact using the sweeping method of the outdoor trailer. Tey with the road surface. Studying the dynamic characteris- found that the mechanical properties of the tires are tics of the tire is the basis of vehicle dynamics [1]. Tire quite diferent at diferent loading and speeds. dynamics research is based on tire dynamics testing. Te Janowski [3] studied the test method of tire driving accuracy of the tire dynamics model depends to a large and braking in the winter environment. Te longitu- extent on the data quality of the tire modeling test. Te dinal force of the tire under diferent slip ratios was tire modeling test is infuenced by many factors, such as collected with the method loading diferent longitu- temperature and tire tread wear. Tese factors afect the dinal slip rate by the outdoor trailer. However, due to quality of the test data, so the consistency of the tire state the limitations of the test equipment and the uncon- and environmental state during the test must be ensured. trollability of environmental factors at that time, the However, diferent test methods will also make the tire reliability of the data was relatively poor. Sui et al. [4] state consistency diferent. studied and developed the tire mechanical character- Beauregard et al. [2] studied the linear brake test istic test rig. Tire cornering characteristics test and method, the steady-state test method, transient test longitudinal dynamics characteristics test were car- ried out using this test rig with the slip angle stepped steady state test methods. Pottinger et al. [5] measured *Correspondence: [email protected] 1 State Key Laboratory of Automotive Simulation and Control, Jilin the cornering characteristics of heavy truck tire dur- University, Changchun 130025, China ing free rolling by trailer test, at the same time, they Full list of author information is available at the end of the article also studied the infuence of tire infation pressure and © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Lu et al. Chin. J. Mech. Eng. (2020) 33:85 Page 2 of 10 tire surface properties on the mechanical properties steady-state characteristics and friction work are com- of tires. Liu et al. [6] analyzed the test methods of the pared with the results obtained by the conventional tests. non-steady state side slip characteristics of tires, and they also designed the steering and pure lateral motion test using the tire test rig. Sommerfeld et al. [7] pointed 2 Tire Longitudinal Transient Model out that tire constraints, unevenness and other fac- Te longitudinal characteristics of the tire include lon- tors have infuence on the vertical load control accu- gitudinal steady state characteristics and longitudinal racy of tire dynamics testing. By improving the design transient characteristics. In this paper, based on the lon- of the tire force and moments sensor, the infuence of gitudinal quasi-steady-state test results, the longitudinal the above factors on the test accuracy of the tire sen- relaxation length which represent the transient char- sor is reduced. Sui et al. [8] built a virtual tire testing acteristics of the tire is extracted. Te transient charac- platform through a fnite element method. Some spe- teristics extraction method is based on the longitudinal cial tire testing which can’t completed in conventional transient model of the tire. tire testing platform can be completed in the virtual tire testing platform. Tuononen et al. [9] used trailer equip- ment to measure the lateral stifness on ice and snow 2.1 Tire Longitudinal Transient Modeling by a new method. Li et al. [10] obtained the lateral Te longitudinal transient characteristics of the tire is relaxation length of the tire through the t method of the mainly caused by the elasticity of the tire carcass, which tire side angle step test. Te accuracy of the model is is refected by the hysteresis of the longitudinal force of verifed by comparing the relaxation lengths obtained the tire relative to the driving torque of the tire [12–16]. by the rate of stifness method and the slip angle step Te parameter refecting longitudinal transient charac- method. Qiu et al. [11] studied the diferent measure- teristics of the tire is the longitudinal relaxation length. ment methods to obtain tire relaxation length at difer- Te longitudinal transient model of the tire is shown in ent vertical loads. Figure 1 [14, 17, 18], where u is the longitudinal defor- In summary, steady-state modeling in tire dynamics mation of the carcass, u˙ is the longitudinal deformation studies is generally based on a quasi-steady-state test rate of the carcass, K is the longitudinal stifness of the method or the stepped steady state test method. Te carcass, C is the longitudinal damping of the tread, and Vx quasi-steady-state data of the tire contains not only the is the longitudinal speed of the tire, Vsx is the longitudinal steady-state characteristics but also the transient charac- slip speed of the tire. Ω is the tire rolling rotational veloc- teristics. Although the quasi-steady-state characteristic ity, and Re is the efective rolling radius of the tire. of the tire is approximately equivalent to the steady-state Assuming that the longitudinal force of the tire is Fx at characteristic, the test error will be inevitably introduced this time, based on the principle of force balance, Eq. (1) by directly using quasi-steady state data for steady-state can be obtained: modeling. Using the stepped steady state test method, F =−C · (V −˙u) = C · V , the tread wear is severe before and after tire testing, and x x sx F =−K · u. (1) the result data consistency is poor. Tire dynamics mod- x eling methods based on quasi-steady-state data to build Taking the derivative of second formula in Eq. (1) with tire transient model and extract steady state data are respect to time: rarely reported. Terefore, the rapid test method which is based on the quasi-steady-state test data of tires to extract steady-state data and transient parameters is a key technical research work to solve the modeling of tire dynamics test. Tis paper frst introduces the longitudinal transient model of the tire and the method of extracting the lon- gitudinal transient parameters from the quasi-steady state test results, and then introduces the lateral transient model without considering the turn-slip properties and the method of extracting the lateral transient parameters. Based on the above theory and method, a tire rapid quasi- steady-state test is designed, and the parameters of the transient characteristics and steady-state characteristics are extracted. Finally, the tire transient characteristics, Figure 1 Schematic diagram of longitudinal transient model Lu et al. Chin. J. Mech. Eng. (2020) 33:85 Page 3 of 10 F˙ the longitudinal force and the derivative of the longitu- u˙ =− x . K (2) dinal force versus time when the longitudinal slip ratio is zero, and the rolling speed of the tire.
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