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Research Papers

Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness

[+] Author and Article Information
Hu Ding

Shanghai Institute of Applied Mathematics
and Mechanics,
Shanghai Key Laboratory of
Mechanics in Energy Engineering,
Shanghai University,
Shanghai 200072, China
e-mail: dinghu3@shu.edu.cn

Jean W. Zu

Mem. ASME
Department of Mechanical &
Industrial Engineering,
University of Toronto,
Toronto, ON M5S 3G8, Canada
e-mail: zu@mie.utoronto.ca

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 25, 2013; final manuscript received April 15, 2014; published online April 29, 2014. Assoc. Editor: Weidong Zhu.

J. Vib. Acoust 136(4), 041006 (Apr 29, 2014) (14 pages) Paper No: VIB-13-1092; doi: 10.1115/1.4027456 History: Received March 25, 2013; Revised April 15, 2014

A nonlinear hybrid discrete-continuous dynamic model is established to analyze the steady-state response of a pulley-belt system with a one-way clutch and belt bending stiffness. For the first time, the translating belt spans in pulley-belt systems coupled with one-way clutches are modeled as axially moving viscoelastic beams. Moreover, the model considers the rotations of the driving pulley, the driven pulley, and the accessory. The differential quadrature and integral quadrature methods are developed for space discretization of the nonlinear integropartial-differential equations in the dynamic model. Furthermore, the four-stage Runge–Kutta algorithm is employed for time discretization of the nonlinear piecewise ordinary differential equations. The time series are numerically calculated for the driven pulley, the accessory, and the translating belt spans. Based on the time series, the fast Fourier transform is used for obtaining the natural frequencies of the nonlinear vibration. The torque-transmitting directional behavior of the one-way clutch is revealed by the steady-state of the clutch torque in the primary resonances. The frequency-response curves of the translating belt, the driven pulley, and the accessory show that the one-way clutch reduces the resonance of the pulley-belt system. Furthermore, the belt cross section's aspect ratio significantly affects the dynamic response.

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Figures

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Fig. 1

Pulley-belt system with two pulleys and a one-way clutch

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Fig. 2

The time histories and frequencies of the free vibration of the pulley-belt system

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Fig. 3

The frequencies of the free vibration of the pulley-belt system versus the belt speed

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Fig. 4

The dynamic response of the clutch torque of the pulley-belt system

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Fig. 5

The sweep frequency-response of the prototypical pulley-belt system with one-way clutch

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Fig. 6

The sweep frequency of the prototypical pulley-belt system to compare the steady-state response with and without one-way clutch

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Fig. 7

The convergence study for the numerical simulations

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Fig. 8

The steady-state response for the different aspect ratios of the belt's cross section

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Fig. 10

The steady-state response for the different initial static tensions of the belt

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Fig. 11

The steady-state response for the different viscous damping coefficients

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Fig. 9

The steady-state response for the different Young's moduli of the belt

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Fig. 12

The steady-state response for the different stiffnesses of wrap spring

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Fig. 13

The steady-state response for the different damping coefficients of the wrap spring

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Fig. 14

The steady-state response for the different rotational inertia of the driven pulley

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Fig. 15

The steady-state response for the different rotational inertia of the accessory

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Fig. 16

The steady-state response for the different friction coefficients of the rotational angle

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Fig. 17

The steady-state response for the different amplitudes of the excitation frequency

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Fig. 18

The steady-state response for the different preloads of the driven pulley

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