Application of high-speed camera measurements for determination of energy losses generated in a vibrating belt of CVT transmission

• Autorzy: Łatas Waldemar , Kot Adam

Identyfikatory

DOI

10.24425/bpasts.2023.146238

• Języki publikacji: EN

Abstrakty

EN

The paper presents a proposition of the theoretical-experimental method of determination of power losses in the transversely vibrating rubber V-belt of continuously variable transmission. The article comprises the results of experimental tests conducted on a special test stand with a complete scooter drivetrain powered by a small two-stroke internal combustion engine. Such a configuration allows ensuring real CVT working conditions. A high-speed camera was used for the contactless measurement of belt vibrations and time-lapse image analysis was performed in dedicated software. An axially moving Euler–Bernoulli beam was assumed as the mathematical model. Longitudinal vibrations and nonlinear effects were omitted. Additionally, it was assumed that the belt material behaves according to the Kelvin–Voigt rheological model. Analysis of the damped free vibrations of the cantilever beam, made of the belt segment, allowed to determine the equivalent bending damping coefficient. The CVT power losses, due to bending in the rubber transmission belt, were obtained for the fixed working conditions after numerical calculations. The proposed methodology is a new approach in this research area, which allows to obtain results impossible to achieve with other measurement methods.

Słowa kluczowe

EN

continuously variable transmission; moving beam vibrations; high-speed camera; power losses

PL

straty mocy; przekładnia bezstopniowa; kamera szybka; drgania belki sprężystej

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 5
• Strony: art. no. e146238
• Opis fizyczny: Bibliogr. 43 poz., rys., tab.

Twórcy

autor

Łatas Waldemar

• Department of Applied Mechanics and Biomechanics, Faculty of Mechanical Engineering, Cracow University of Technology, Poland

• https://orcid.org/0000-0002-2713-0740

autor

Kot Adam

• Department of Automotive Vehicles, Faculty of Mechanical Engineering, Cracow University of Technology, Poland

• https://orcid.org/0000-0002-3222-7520

Bibliografia

• [1] W. Kaczmarek, S. Borys, J. Panasiuk, M. Siwek, and P. Prusaczyk, “Experimental study of the vibrations of a roller shutter gripper,” Appl. Sci., vol. 12, no. 19, p. 9996, 2022, doi: 10.3390/app12199996.
• [2] F. Kuang, X. Zhou, J. Huang, H. Wang, and P. Zheng, “Machine-vision-based assessment of frictional vibration in water-lubricated rubber stern bearings,” Wear, vol. 426–427, pp. 760-769, 2019, doi: 10.1016/j.wear.2019.01.087.
• [3] C. Peng, C. Zeng, and Y. Wang, “Camera-based micro-vibration measurement for lightweight structure using an improved phase-based motion extraction,” IEEE Sens. J., vol. 20, no. 5, pp. 2590–2599, 2020, doi: 10.1109/JSEN.2019.2951128.
• [4] B. Bonsen, M. Steinbuch, and P.A. Veenhuizen, “CVT ratio control strategy optimization,” 2005 IEEE Vehicle Power and Propulsion Conference, 2005, doi: 10.1109/VPPC.2005.1554561.
• [5] R. Pfiffner, L. Guzzela, and C.H. Onder, “Fuel–optimal control of CVT powertrains,” Control Eng. Pract., vol. 11, no. 3, pp. 329–336, 2003, doi: 10.1016/S0967-0661(02)00219-8.
• [6] W. Grzegożek, M. Szczepka, and A. Kot, “The analysis of applying CVT gear ratio rate control for scooter efficiency improvement,” Asian J. Appl. Sci. Eng., vol. 6, no. 2, pp. 73–80, 2017.
• [7] A. Kot, W. Grzegożek, and W. Szczypiński-Sala, “The analysis of an influence of rubber V-belt physical properties on CVT efficiency,” IOP Conf. Ser.-Mat. Sci., vol. 421, no. 2, p. 022017, 2018, doi: 10.1088/1757-899X/421/2/022017.
• [8] G. Bhowmick, T. Sahoo, A. Bhat, G. Mathur, and D. Gambhir, “Approach for CO2 reductioning in India’s automotive sector,” SAE Int., vol. 28, p. 2388, 2019, doi: 10.4271/2019-28-2388.
• [9] T.C. Firbank, “Mechanics of the belt drive,” Int. J. Mech. Sci., vol. 12, no. 12, pp. 1053–1063, 1970, doi: 10.1016/0020-7403(70)90032-9.
• [10] M. Cammalleri, “A new approach to the design of speedtorque-controlled rubber V-belt Variator,” Proc. Inst. Mech. Eng. Part D-J. Automob. Eng., vol. 219, pp. 1413–1427, 2005, doi: 10.1243/095440705X35080.
• [11] G. Julió and J.-S. Plante, “An experimentally – validated model of rubber-belt CVT mechanic,” Mech. Mach. Theory, vol. 46, no. 8, pp. 1037–1053, 2011, doi: 10.1016/j.mechmachtheory.2011.04.001.
• [12] G.B. Gerbert, “Belt slip – a unified approach,” J. Mech. Design, vol. 118, no. 3, pp. 432–438, 1996, doi: 10.1115/1.2826904.
• [13] K. Kubas, “A two-dimensional discrete model for dynamic analysis of belt transmission with dry friction,” Arch. Mech. Eng., vol. 61, no. 4, pp. 571–593, 2014, doi: 10.2478/meceng-2014-0033.
• [14] H. Zhu, W. Zhu, and W. Fan, “Dynamic modeling, simulation and experiment of power transmission belt drives: A systematic review,” J. Sound Vib., vol. 491, no. 1, pp. 1–40, 2021, doi: 10.1016/j.jsv.2020.115759.
• [15] Z. Yu, Y. Cui, Q. Zhang, J. Liu, and Y. Qin, “Thermo-mechanical coupled analysis of V-belt drive system via absolute nodal coordinate formulation,” Mech. Mach. Theory, vol. 174, no. 1, p. 104906, 2022, doi: 10.1016/j.mechmachtheory.2022.104906.
• [16] I.V. Andrianov and W.T. Horrsen, “On the transversal vibrations of a conveyor belt: Applicability of simplified models,” J. Sound Vib., vol. 313, no. 3, pp. 822–829, 2008, doi: 10.1016/j.jsv.2007.11.053.
• [17] J. Ding and Q. Hu, “Equilibria and free vibration of a two-pulley belt-driven system with belt bending stiffness,” Math. Probl. Eng., p. 907627, 2014, doi: 10.1155/2014/907627.
• [18] E.-W. Chen, H. Lin, and N. Ferguson, “Experimental investigation of the transverse nonlinear vibration of an axially travelling belt,” J. Vibroeng., vol. 18, no. 8, pp. 4885–4900, 2016, doi: 10.21595/jve.2016.17341.
• [19] V. Ravindra, C. Padmanabhan, and C. Sujatha, “Static and free vibration studies on a pulley belt system with ground stiffness,” J. Braz. Soc. Mech. Sci., vol. 32, no. 1, pp. 61–70, 2010, doi: 10.1590/S1678-58782010000100009.
• [20] R. Zhang, X. Si, W. Yang, and N. Wang, “Analysis of resonance reliability for synchronous belt transmission with transverse vibration,” J. Vibroeng., vol. 16, no. 2, pp. 891–900, 2014.
• [21] L. Kong and R.G. Parker, “Steady mechanics of belt-pulley systems,” J. Appl. Mech., vol. 72, no. 1, pp. 25–34, 2005, doi: 10.1115/1.1827251.
• [22] H. Ding, C.W. Lim, and L.-Q. Chen, “Nonlinear vibration of a traveling belt with non-homogeneous boundaries,” J. Sound Vib., vol. 424, pp. 78–93, 2018, doi: 10.1016/j.jsv.2018.03.010.
• [23] M. Kim and J. Chung, “Dynamic analysis of a pulley-belt system with different pulley radii and support stiffness,” J. Mech. Sci. Technol., vol. 32, no. 12, pp. 5597–5613, 2018, doi: 10.1007/s12206-018-1106-8.
• [24] D. Schnürer and H.J. Holl, “Transversal vibrations of a toothed belt in linear drives during operation,” Proc. Appl. Math. Mech., vol. 20, no. 1, p. e202000026, 2021, doi: 10.1002/pamm.202000026.
• [25] J. Moon and J.A. Wickert, “Non-linear vibration of power transmission belts,” J. Sound Vib., vol. 200, no. 4, pp. 419–431, 1997, doi: 10.1006/jsvi.1996.0709.
• [26] W. Łatas, “Active vibration suppression of axially moving string via distributed force,” Vib. Phys. Syst., vol. 3, no. 2, pp. 2020215-1–2020215-8, 2020, doi: 10.21008/j.0860-6897.2020.2.15.
• [27] P. Lad and V. Kartik, “Stability transitions of an axially moving string subjected to a distributed follower force,” Proc. R. Soc. A., vol. 474, no. 2213, p. 20170779, 2018, doi: 10.1098/rspa.2017.0779.
• [28] F. Pellicano and F. Vestroni, “Nonlinear dynamics and bifurcations of an axially moving beam,” J. Vib. Acoust., vol. 122, pp. 21–30, 2000, doi: 10.1115/1.568433.
• [29] L.Q. Chen and X.D. Yang, “Stability in parametric resonance of axially moving viscoelastic beams with time-dependent speed,” J. Sound Vib., vol. 284, no. 3, pp. 879–891, 2005, doi: 10.1016/j.jsv.2004.07.024.
• [30] D. Karlicic, M. Cajic, S. Paunovi´c, and S. Adhikari, “Periodic response of a nonlinear axially moving beam with a nonlinear energy sink and piezoelectric attachment,” Int. J. Mech. Sci., vol. 195, 2021, doi: 10.1016/j.ijmecsci.2020.106230.
• [31] P.T. Pham and K.S. Hong, “Dynamic models of axially moving systems: A review,” Nonlinear Dyn., vol. 100, pp. 315–349, 2020, doi: 10.1007/s11071-020-05491-z.
• [32] H. Zhu, W.D. Zhu, and W. Fan, “Dynamic modeling, simulation and experiment of power transmission belt drives: A systematic review,” J. Sound Vib., vol. 491, 2021, doi: 10.1016/j.jsv.2020.115759.
• [33] L. Bertini, L. Carmignani, and F. Frendo, “Analytical model for the power losses in rubber V-belt continuously variable transmission (CVT),” Mech. Mach. Theory, vol. 78, pp. 289–306, 2014, doi: 10.1016/j.mechmachtheory.2014.03.016.
• [34] T.F. Chen and C.K. Sung, “Design considerations for improving transmission efficiency of rubber V-belt CVT,” Int. J. Vehicle Des., vol. 24, no. 4, pp. 320–333, 2000, doi: 10.1504/IJVD.2000.005195.
• [35] A. Kot and W. Łatas, “Experimental and theoretical investigation of CVT rubber belt vibrations,” Open Eng., vol. 11, pp. 1196–1206, 2021, doi: 10.1515/eng-2021-0121.
• [36] E.M. Mockensturm and J.P. Guo, “Nonlinear vibration of parametrically excited, viscoelastic, axially moving strings,” J. Appl. Mech., vol. 72, no. 3, pp. 374–380, 2005, doi: 10.1115/1.1827248.
• [37] IMSL® C Numerical Libraries, Visual Numerics, Inc.
• [38] Y. Hu, Y. Yan, L. Wang, and X. Qian, “Non-contact vbration monitoring of power transmission belts through electrostatic sensing,” IEEE Sens. J., vol. 16, no. 10, pp. 3541–3550, 2016, doi: 10.1109/JSEN.2016.2530159.
• [39] L. Manin and F. Besson, G. Michon, and R. Dufour, “Experimental investigation on the dynamic characteristics and transverse vibration instabilities of transmission belts,” 16ème Colloque Vibrations Chocs et Bruits, France, 2008.
• [40] A. Nabhan, M.R. El-Sharkawy, and A. Rashed, “Monitoring of belt-drive defects using the vibration signals and simulation models,” Int. J. Aerosp. Mech. Eng., vol. 13, no. 5, pp. 332–339, 2019, doi: 10.5281/zenodo.2702680.
• [41] W. Łatas and A. Kot, “Theoretical-experimental determination of CVT power losses due to rubber V-belt vibrations,” in A. Puchalski, B.E. Łazarz, F. Chaari, I. Komorska, R. Zimroz (Eds), Advances in Technical Diagnostics II. ICTD 2022. Applied Condition Monitoring, vol. 21. Springer, Cham., 2023, doi: 10.1007/978-3-031-31719-4_4.
• [42] L. Kong and R.G. Parker, “Approximate eigensolutions of axially moving beams with small flexural stiffness,” J. Sound Vib., vol. 276, pp. 459–469, 2004, doi: 10.1016/j.jsv.2003.11.027.
• [43] S. Garus et al., “Mechanical vibrations: recent trends and engineering applications,” Bull. Pol. Acad. Sci. Tech Sci., vol. 70, no. 1, pp. e140351, 2022, doi: 10.24425/bpasts.2022.140351.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).