Measurement of stiffness and damping coefficient of rubber tractor tires using dynamic cleat test based on point contact model
Keywords:
ride vibration, rubber tractor tire, stiffness, damping coefficient, cleat test, point contact modelAbstract
The ride vibration of a tractor is affected mostly by the stiffness and damping coefficient of the seat suspension, cabin suspension, cabin rubber mounts, and rubber tires. However, in the case of rubber tractor tires, the stiffnesses and damping coefficients have not been researched adequately thus far, and it is not simple to measure these characteristics. In this study, a method for measuring and analyzing the stiffnesses and damping coefficients of rubber tractor tires, which were the input parameters for the tractor ride vibration simulation, was proposed. The cleat test, proposed in this study, did not require separate and complicated test equipment, unlike the conventional methods. The test was conducted simply by measuring acceleration under the driving conditions of the vehicle without detaching tires from the vehicle body or setting up additional test equipment. Based on the ground-vertical acceleration data obtained, the stiffness was calculated using the logarithmic decrement method, and the damping coefficient was calculated using least squares exponential curve fitting. The result of the cleat test indicated that the front tires had stiffnesses of 486.08-570.69 kN/m and damping coefficients of 4.02-4.52 kN·s/m; the rear tires had stiffnesses of 409.42-483.79 kN/m and damping coefficients of 2.21-2.67 kN·s/m. During the test, 40 mm height cleats were installed on the track and the speed of the tractor was set to 7 and 10 km/h, which were the most common speeds during the operation. This study is meaningful in that it has presented a new method that improves the practicality of results, reduces cost, and simplifies the test process for measuring the stiffnesses and damping coefficients of rubber tractor tires. Keywords: ride vibration, rubber tractor tire, stiffness, damping coefficient, cleat test, point contact model DOI: 10.25165/j.ijabe.20211401.5799 Citation: Yoo H, Oh J, Chung W-J, Han H-W, Kim J-T, Park Y-J, et al. Measurement of stiffness and damping coefficient of rubber tractor tires using dynamic cleat test based on point contact model. Int J Agric & Biol Eng, 2021; 14(1): 157–164.References
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[2] Choi K, Oh J, Ahn D, Park Y J, Park S U, Kim H S. Experimental study of the dynamic characteristics of rubber mounts for agricultural tractor cabin. J Biosyst Eng, 2018; 43(4): 255–262.
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[8] Lines J A, Murphy K. The radial damping of agricultural tractor tyres. J Terramech, 1991; 28(2-3): 229–241.
[9] Cuong D M, Zhu S, Ngoc N T. Study on the variation characteristics of vertical equivalent damping ratio of tire–soil system using semi-empirical model. J Terramech, 2014; 51: 67–80.
[10] Zheng E, Zhong X, Zhu R, Xue J, Cui S, Gao H, et al. Investigation into the vibration characteristics of agricultural wheeled tractor-implement system with hydro-pneumatic suspension on the front axle. Journal of Terramechanics, 2019; 186: 14–33.
[11] Witzel P. The Hohenheim tyre model: A validated approach for the simulation of high volume tyres – Part I: Model structure and parameterization. Journal of Terramech, 2018; 75: 3–14.
[12] Captain K M, Boghani A B, Wormley D N. Analytical tire models for dynamic vehicle simulation. Vehicle System Dynamics, 1979; 8(1): 1–32.
[13] Inman D J. Engineering Vibration, 4th ed. Upper Saddle River, NJ, USA: Prentice Hall Inc., 2013; pp.21–26, 58–61.
[14] ASTM D5992-96. Standard guide for dynamic testing of vulcanized rubber and rubber-like materials using vibratory methods. West Conshohocken, PA, USA: American Society for Testing and Materials International, 2018. doi: 10.1520/D5992-96R18.
[15] Diani J, Fayolle B, Filormini P. A review on the Mullins effect. European Polymer Journal, 2009; 45(3): 601–612.
[16] Amin A F M S, Lion A, Sekita S, Okui Y. Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification. Int J Plast, 2006; 22(9): 1610–1657.
[17] Brinkmann C. Experimental investigations on tractor tire vibration properties. Doctoral dissertation. Stuttgart, Baden-Württemberg, Germany: University of Stuttgart, 2017; 178p.
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[19] Nang N V, Matsuo T, Koumoto T, Inaba S. Static and dynamic vertical properties of agricultural tires. Bulletin of the Faculty of Agriculture-Saga University (Japan), 2009; 94: 37–49.
[20] Bernard J, Vanderploeg M, Jane R. Tire models for the determination of vehicle structural loads. Vehicle System Dynamics, 1981; 10(2-3): 168–173.
[21] Crolla D A, Horton D N L, Stayner R M. Effect of tyre modelling on tractor ride vibration predictions. J Agr Eng Res, 1990; 47: 55–77.
[22] Lines J A. The suspension characteristics of agricultural tractor tyres. Doctoral dissertation. Cranfield, Bedfordshire, England, UK: Silsoe College, Cranfield Institute of Technology, 1991; 128p.
[2] Choi K, Oh J, Ahn D, Park Y J, Park S U, Kim H S. Experimental study of the dynamic characteristics of rubber mounts for agricultural tractor cabin. J Biosyst Eng, 2018; 43(4): 255–262.
[3] Kim B S, Hong D P, Chi C H. An experimental study on the measurement of radial directional natural frequency in a passenger car tire roboting under the load. Trans the Kor Soc Mech Eng A, 1996; 20(1): 1–13. (in Korean).
[4] Sleeper R K, Dreher R C. Tire stiffness and damping determined from static and free-vibration tests. NASA Technical Paper 1671, 1980; L-13500.
[5] Kising A, Göhlich H. Ackerschlepper-Reifendynamik Teil 2: Dynamische Federungs-und Dämpfungswerte (Tractor tyre dynamics part 2: Dynamic spring rate and damping values). Grundlagen der Landtechnik, 1988; 38(4): 101–106. (in German)
[6] Lines J A, Young N A. A machine for measuring the suspension characteristics of agricultural tyres. J Terramech, 1989; 26(3-4): 201–210.
[7] Lines J A, Murphy K. The stiffness of agricultural tractor tyres. J Terramech, 1991; 28(1): 49–64.
[8] Lines J A, Murphy K. The radial damping of agricultural tractor tyres. J Terramech, 1991; 28(2-3): 229–241.
[9] Cuong D M, Zhu S, Ngoc N T. Study on the variation characteristics of vertical equivalent damping ratio of tire–soil system using semi-empirical model. J Terramech, 2014; 51: 67–80.
[10] Zheng E, Zhong X, Zhu R, Xue J, Cui S, Gao H, et al. Investigation into the vibration characteristics of agricultural wheeled tractor-implement system with hydro-pneumatic suspension on the front axle. Journal of Terramechanics, 2019; 186: 14–33.
[11] Witzel P. The Hohenheim tyre model: A validated approach for the simulation of high volume tyres – Part I: Model structure and parameterization. Journal of Terramech, 2018; 75: 3–14.
[12] Captain K M, Boghani A B, Wormley D N. Analytical tire models for dynamic vehicle simulation. Vehicle System Dynamics, 1979; 8(1): 1–32.
[13] Inman D J. Engineering Vibration, 4th ed. Upper Saddle River, NJ, USA: Prentice Hall Inc., 2013; pp.21–26, 58–61.
[14] ASTM D5992-96. Standard guide for dynamic testing of vulcanized rubber and rubber-like materials using vibratory methods. West Conshohocken, PA, USA: American Society for Testing and Materials International, 2018. doi: 10.1520/D5992-96R18.
[15] Diani J, Fayolle B, Filormini P. A review on the Mullins effect. European Polymer Journal, 2009; 45(3): 601–612.
[16] Amin A F M S, Lion A, Sekita S, Okui Y. Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification. Int J Plast, 2006; 22(9): 1610–1657.
[17] Brinkmann C. Experimental investigations on tractor tire vibration properties. Doctoral dissertation. Stuttgart, Baden-Württemberg, Germany: University of Stuttgart, 2017; 178p.
[18] MATLAB. Signal Processing Toolbox. Ver. R2019b Update 1 (9.7.0.1216025). Natick, MA, USA: Mathworks Inc, 1984.
[19] Nang N V, Matsuo T, Koumoto T, Inaba S. Static and dynamic vertical properties of agricultural tires. Bulletin of the Faculty of Agriculture-Saga University (Japan), 2009; 94: 37–49.
[20] Bernard J, Vanderploeg M, Jane R. Tire models for the determination of vehicle structural loads. Vehicle System Dynamics, 1981; 10(2-3): 168–173.
[21] Crolla D A, Horton D N L, Stayner R M. Effect of tyre modelling on tractor ride vibration predictions. J Agr Eng Res, 1990; 47: 55–77.
[22] Lines J A. The suspension characteristics of agricultural tractor tyres. Doctoral dissertation. Cranfield, Bedfordshire, England, UK: Silsoe College, Cranfield Institute of Technology, 1991; 128p.
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Published
2021-02-10
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Yoo, H., Oh, J., Chung, W.-J., Han, H.-W., Kim, J.-T., Park, Y.-J., & Park, Y. (2021). Measurement of stiffness and damping coefficient of rubber tractor tires using dynamic cleat test based on point contact model. International Journal of Agricultural and Biological Engineering, 14(1), 157–164. Retrieved from https://ijabe.migration.pkpps03.publicknowledgeproject.org/index.php/ijabe/article/view/5799
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Power and Machinery Systems
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