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Dynamic analysis of a pulley–belt system with spring supports

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Abstract

In this paper, a new dynamic model for a pulley–belt system is proposed, in which the system considers not only the deflection of a belt but also the rigid-body motion of pulleys. This paper focuses on the effects of the rigid-body motion, which determines the dynamic characteristics of the pulley–belt system with spring supports. To this end, by using Hamilton’s principle, four linear governing equations of motion and eight boundary conditions are derived. The Galerkin method is used to discretize the equations of motion. The eigenvalue problems are solved to analyze the natural frequencies and mode shapes that are affected by the rigid-body motion of the system. The natural frequency loci veering and mode exchange are investigated for different moving velocities of the belt and various values of the spring constant. In addition, the beat phenomena in the upper and lower belts are also analyzed. Based on these analyses, we show that the natural frequency veering and beat phenomena are caused by a coupling effect between the rigid-body motion and belt deflection in the pulley–belt system.

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References

  1. Beikmann, R.S., Perkins, N.C.: Free vibration of serpentine belt drive. J. Vib. Acoust. Trans. ASME 118, 406–413 (1996)

    Article  Google Scholar 

  2. Beikmann, R.S., Perkins, N.C., Ulsoy, A.G.: Design and analysis of automotive serpentine belt drive systems for steady state performance. J. Mech. Des. 119, 162–168 (1997)

    Article  Google Scholar 

  3. Eliseev, V., Vetyukov, Y.: Effect of deformation in the dynamics of belt drive. Acta Mech. 223(8), 1657–1667 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kong, L., Parker, R.G.: Equilibrium and belt–pulley vibration coupling in serpentine belt drives. J. Appl. Mech. Trans. ASME 70, 739–750 (2003)

    Article  MATH  Google Scholar 

  5. Ding, H., Zu, J.W.: Steady-state responses of pulley–belt systems with a one-way clutch and belt bending stiffness. J. Vib. Acoust. Trans. ASME 136(041006), 1–14 (2014)

    Google Scholar 

  6. Ding, J., Hu, Q.: Equilibrium and free vibration of a two-pulley belt-driven system with belt bending stiffness. Math. Probl. Eng. 907627, 1–17 (2014)

    MathSciNet  Google Scholar 

  7. Mote, C.D., Wu, W.Z.: Vibration coupling in continuous belt and band systems. J. Sound Vib. 102, 1–9 (1985)

    Article  Google Scholar 

  8. Wang, K.W., Mote, C.D.: Vibration coupling analysis of band wheel mechanical systems. J. Sound Vib. 109, 237–258 (1986)

    Article  Google Scholar 

  9. Scurtu, P.R., Clark, M., Zu, J.W.: Coupled longitudinal and transverse vibration of automotive belts under longitudinal excitations using analog equation method. J. Vib. Control 18, 1336–1352 (2012)

    Article  Google Scholar 

  10. Kong, L., Parker, R.G.: Coupled belt–pulley vibration in serpentine drives with belt bending stiffness. J. Appl. Mech. Trans. ASME 71, 109–119 (2004)

    Article  MATH  Google Scholar 

  11. Hwang, S.J., Perkins, N.C., Ulsoy, A.G.: Rotational response and slip prediction of serpentine belt drive systems. J. Vib. Acoust. Trans. ASME 116, 71–78 (1994)

    Article  Google Scholar 

  12. Zhang, L., Zu, J.W.: Modal analysis of serpentine belt drive systems. J. Sound Vib. 222, 259–279 (1999)

    Article  Google Scholar 

  13. Zhang, L., Zu, J.W.: One-to-one auto-parametric resonance in serpentine belt drive systems. J. Sound Vib. 232, 783–806 (2000)

    Article  MATH  Google Scholar 

  14. Chowdhury, S., Yedavalli, R.K.: Dynamics of belt–pulley-shaft systems. Mech. Mech. Theory 98, 199–215 (2016)

    Article  Google Scholar 

  15. Parker, R.G.: Supercritical speed stability of the trivial equilibrium of an axially-moving string on an elastic foundation. J. Sound Vib. 221, 205–219 (1999)

    Article  MATH  Google Scholar 

  16. Perkins, N.C.: Linear dynamics of a translating string on an elastic foundation. J. Vib. Acoust. Trans. ASME 112, 2–7 (1990)

    Article  Google Scholar 

  17. Ravindra, V., Padmanabhan, C., Sujatha, C.: Static and free vibration studies on a pulley–belt system with ground stiffness. J. Braz. Soc. Mech. Sci. Eng. 32, 61–70 (2010)

    Article  Google Scholar 

  18. Kim, S.K., Lee, J.M.: Analysis of the non-linear vibration characteristics of a belt-driven system. J. Sound Vib. 223, 723–740 (1999)

    Article  Google Scholar 

  19. Ding, H.: Periodic responses of a pulley–belt system with one-way clutch under inertia excitation. J. Sound Vib. 353, 308–326 (2015)

    Article  Google Scholar 

  20. Pellicano, F., Vestroni, F.: Nonlinear dynamics and bifurcations of an axially moving beam. J. Vib. Acoust. Trans. ASME 122, 21–30 (2000)

    Article  Google Scholar 

  21. Chen, L.Q., Zu, J.W., Wu, J.: Steady-state response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. Acta Mech. 162(1–4), 143–155 (2003)

    Article  MATH  Google Scholar 

  22. Ding, H., Tan, X., Zhang, G.C., Chen, L.Q.: Equilibrium bifurcation of high-speed axially moving Timoshenko beams. Acta Mech. 227(10), 3001–3014 (2016)

    Article  MathSciNet  Google Scholar 

  23. Öz, H.R., Pakdemirli, M.: Vibration of an axially moving beam with time-dependent velocity. J. Sound Vib. 227, 239–257 (1999)

    Article  Google Scholar 

  24. Wang, L.H., Hu, Z.D., Zhong, Z., Ju, J.W.: Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length. Acta Mech. 214(3–4), 225–244 (2010)

    Article  MATH  Google Scholar 

  25. Mciver, D.B.: Hamilton’s principle for systems of changing mass. J. Eng. Math. 7, 249–261 (1973)

    Article  MATH  Google Scholar 

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Acknowledgements

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (No. 2011-0017408).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hanyang University, 55 Hanyangdaehak-ro, Sangnok-gu, Ansan, Gyeonggi-do, 15588, Republic of Korea

    Minsung Kim & Jintai Chung

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  1. Minsung Kim
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  2. Jintai Chung
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Correspondence to Jintai Chung.

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Kim, M., Chung, J. Dynamic analysis of a pulley–belt system with spring supports. Acta Mech 228, 3307–3328 (2017). https://doi.org/10.1007/s00707-017-1882-8

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  • DOI: https://doi.org/10.1007/s00707-017-1882-8

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