Abstract
The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete–continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the firing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Furthermore, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numerical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pulley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foundation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.
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References
Ulsoy, A.G., Whitsell, J.E., Hooven, M.D.: Design of belt-tensioner systems for dynamic stability. J. Vib. Acoust. 107, 282–290 (1985)
Chen, L.Q.: Analysis and control of transverse vibrations of axially moving strings. Appl. Mech. Rev. 58, 91–116 (2005)
Marynowski, K., Kapitaniak, T.: Dynamics of axially moving continua. Int. J. Mech. Sci. 81, 26–41 (2014)
Chen, L.Q., Yang, X.D.: Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models. Int. J. Solids Struct. 42, 37–50 (2005)
Chen, L.Q., Yang, X.D.: Stability in parametric resonance of an axially moving viscoelastic beam with time-dependent velocity. J. Sound Vib. 284, 879–891 (2005)
Mote, C.D., Wu, W.Z.: Vibration coupling in continuous belt and band systems. J. Sound Vib. 102, 1–9 (1985)
Michon, G., Manin, L., Parker, R.G., et al.: Duffing oscillator with parametric excitation: analytical and experimental investigation on a belt-pulley system. J. Comput. Nonlinear Dyn. 3, 031001 (2008)
Zhang, L., Zu, J.W.: One-to-one auto-parametric resonance in serpentine belt drive systems. J. Sound Vib. 232, 783–806 (2000)
Ding, H., Chen, L.Q.: Approximate and numerical analysis of nonlinear forced vibration of axially moving viscoelastic beams. Acta Mech. Sin. 27, 426–437 (2011)
Yao, M.H., Zhang, W., Zu, J.W.: Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt. J. Sound Vib. 331, 2624–2653 (2012)
Özhan, B.B., Pakdemirli, M.: A general solution procedure for the forced vibrations of a system with cubic nonlinearities: three-to-one internal resonances with external excitation. J. Sound Vib. 329, 2603–2615 (2010)
Sze, K.Y., Chen, S.H., Huang, J.L.: The incremental harmonic balance method for nonlinear vibration of axially moving beams. J. Sound Vib. 281, 611–626 (2005)
Yan, Q.Y., Ding, H., Chen, L.Q.: Periodic responses and chaos behaviors of an axially accelerating viscoelastic Timoshenko beam. Nonlinear Dyn. 78, 1577–1591 (2014)
Ding, H., Zhang, G.C., Chen, L.Q., et al.: Forced vibrations of supercritically transporting viscoelastic beams. ASME J. Vib. Acoust. 134, 051007 (2012)
Yang, X.D., Zhang, W.: Nonlinear dynamics of axially moving beam with coupled longitudinal-transversal vibrations. Nonlinear Dyn. 78, 2547–2556 (2014)
Ding, H., Zu, W.J.: Periodic and chaotic responses of an axially accelerating viscoelastic beam under two-frequency excitations. Int. J. Appl. Mech. 5, 1350019 (2013)
Yan, Q.Y., Ding, H., Chen, L.Q.: Nonlinear dynamics of an axially moving viscoelastic Timoshenko beam under parametric and external excitations. Appl. Math. Mech. (Engl. Ed.) (2015). doi:10.1007/s10483-015-1960-7
Vernay, P., Ferraris, G., Delbez, A., et al.: Transient behaviour of a sprag-type over-running clutch: an experimental study. J. Sound Vib. 248, 567–572 (2001)
Lewicki, D.G., DeSmidt, H., Smith, E.C., et al.: Dynamics of a dual-clutch gearbox system: analysis and experimental validation. J. Am. Helicopter Soc. 58, 17–28 (2013)
Leamy, M.J., Wasfy, T.M.: Transient and steady-state dynamic finite element modeling of belt-drives. ASME J. Dyn. Syst. Meas. Control 124, 575–581 (2002)
Zhu, F., Parker, R.G.: Non-linear dynamics of a one-way clutch in belt-pulley systems. J. Sound Vib. 279, 285–308 (2005)
Zhu, F., Parker, R.G.: Perturbation analysis of a clearance-type nonlinear system. J. Sound Vib. 292, 969–979 (2006)
Mockensturm, E.M., Balaji, R.: Piece-wise linear dynamic systems with one-way clutches. ASME J. Vib. Acoust. 127, 475–482 (2005)
Cheon, G.J.: Nonlinear behavior analysis of spur gear pairs with a one-way clutch. J. Sound Vib. 304, 18–30 (2007)
Zhu, F., Parker, R.G.: Piece-wise linear dynamic analysis of serpentine belt drives with a one-way clutch. Proc. Inst. Mech. Eng. Part C 222, 1165 (2008)
Ding, H., Zu, W.J.: Effect of one-way clutch on the nonlinear vibration of belt-driven systems with a continuous belt model. J. Sound Vib. 332, 6472–6487 (2013)
Ding, H., Zu, W.J.: Steady-state responses of pulley-belt systems with a one-way clutch and belt bending stiffness. ASME J. Vib. Acoust. 136, 041006 (2014)
Ding, H., Li, D.P.: Static and dynamic behaviors of belt-drive dynamical systems with a one-way clutch. Nonlinear Dyn. 78, 1553–1575 (2014)
Beikmann, R.S., Perkins, N.C., Ulsoy, A.G.: Free vibration of serpentine belt drive systems. ASME J. Vib. Acoust. 118, 406–413 (1996)
Li, X.J., Chen, L.Q.: Modal analysis of coupled vibration of belt drive systems. Appl. Math. Mech. (Engl. Ed.) 29, 9–13 (2008)
Ke, L.L., Wang, Y.S., Yang, J., et al.: Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mech. Sin. 30, 516–525 (2014)
Yang, Y., Ding, H., Chen, L.Q.: Dynamic response to a moving load of a Timoshenko beam resting on a nonlinear viscoelastic foundation. Acta Mech. Sin. 29, 718–727 (2013)
Chen, L.Q., Zhang, Y.L.: Multi-scale analysis on nonlinear gyroscopic systems with multi-degree-of-freedoms. J. Sound Vib. 333, 4711–4723 (2014)
Zhang, J.R., Rachid, A., Zhang, Y.: Attitude control for part actuator failure of agile small satellite. Acta Mech. Sin. 24, 463–468 (2008)
Leamy, M.J.: On a perturbation method for the analysis of unsteady belt-drive operation. ASME J. Appl. Mech. 72, 570–580 (2005)
Čepon, G., Boltezar, M.: Dynamics of a belt-drive system using a linear complementarity problem for the belt-pulley contact description. J. Sound Vib. 319, 1019–1035 (2009)
Chen, L.Q., Jiang, W.A.: A piezoelectric energy harvester based on internal resonance. Acta Mech. Sin. 31, 223–228 (2015)
Yang, S.P., Li, S.H., Lu, Y.J.: Investigation on dynamical interaction between a heavy vehicle and road pavement. Veh. Syst. Dyn. 48, 923–944 (2010)
Acknowledgments
The project was supported by the State Key Program of the National Natural Science Foundation of China (Grant 11232009) and the National Natural Science Foundation of China (Grants 11372171, 11422214).
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Ding, H. Steady-state responses of a belt-drive dynamical system under dual excitations. Acta Mech. Sin. 32, 156–169 (2016). https://doi.org/10.1007/s10409-015-0510-x
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DOI: https://doi.org/10.1007/s10409-015-0510-x