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Research Papers

Influence of Tensioner Dry Friction on the Vibration of Belt Drives With Belt Bending Stiffness

[+] Author and Article Information
Farong Zhu

Department of Mechanical Engineering, Scott Laboratory, The Ohio State University, 201 W. 19th Avenue, Columbus, OH 43210-1142

Robert G. Parker1

Department of Mechanical Engineering, Scott Laboratory, The Ohio State University, 201 W. 19th Avenue, Columbus, OH 43210-1142parker.242@osu.edu

1

Corresponding author.

J. Vib. Acoust 130(1), 011002 (Nov 12, 2007) (9 pages) doi:10.1115/1.2775510 History: Received September 08, 2006; Revised April 23, 2007; Published November 12, 2007

A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which reduces the dimension of the iteration matrices when employing the harmonic balance method. The Coulomb damping at the tensioner arm pivot mitigates the tensioner arm vibration but not necessarily the vibrations of other system components. The extent of the mitigation varies for different excitation frequency ranges. The critical amplitude of the dry friction torque beyond which the system operates with a locked arm is determined analytically. Superharmonic resonances are observed in the responses of the generalized span coordinates, but their amplitudes are small. The energy dissipation at the tensioner arm hub is discussed, and the stick-slip phenomena of the arm are reflected in the velocity reversals near the arm extreme location. Dependence of the span tension fluctuations on Coulomb torque is explored.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

A prototypical three-pulley serpentine belt system. The tildes on the physical quantities have been dropped for simplicity.

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Figure 2

The dry friction torque hc(t) (--) and its approximation hcs(t) (—)

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Figure 3

rms response of (a) the tensioner arm, (b) pulley 2, and (c) pulley 3 for various Coulomb torques for the parameters in Table 1: ∙∙∙∙ Qm=0, — Qm=0.1, -- Qm=1.5, -∙- Qm=5, 엯— locked arm

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Figure 4

rms response of transverse displacement averaged along each span varies with excitation frequency for the parameters in Table 1: ∙∙∙∙ Qm=0, — Qm=0.1, -- Qm=1.5, -∙- Qm=5, ⦵ locked arm

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Figure 5

Superharmonics are shown in (a) rms response and (b) spectra waterfall of the displacement amplitude a3 of the sin3πx component of span 1 for the parameters in Table 1. In (a), ∙∙∙∙ Qm=0, — Qm=0.1, -- Qm=0.5, -∙- Qm=1.5, 엯— locked arm; (b) Qm=0.5.

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Figure 6

rms response of (a) the tensioner arm, (b) pulley 2, and (c) pulley 3 with varying Coulomb torque for the parameters in Table 1: ∙∙∙∙ Ω=2.8, — Ω=3.3, -- Ω=5.7, -∙- Ω=6.3, 엯—Ω=8.0, ▵—Ω=8.7

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Figure 7

Energy dissipation varies with excitation frequency for the parameters in Table 1. — Qm=0.1; ∙∙∙∙ Qm=0.5; -- Qm=3; -∙- Qm=5.

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Figure 8

Energy dissipation varies with Coulomb torque for the parameters in Table 1. ν indicates the number of the velocity reversals near the arm extreme location in a half cycle for Ω=6.3; ∙∙∙∙ Ω=2.8, — Ω=3.3, -- Ω=5.7, -∙- Ω=6.3, 엯—Ω=8.0.

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Figure 9

Time history of θ̇t (--) and dry friction torque (—) for the parameters in Table 1 and Ω=6.3: (a) Qm=1.0, (b) Qm=3.5, (c) Qm=6.1, and (d) Qm=11

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Figure 10

Critical Coulomb torque varies with excitation frequency for different belt bending stiffness beyond which the tensioner arm is entirely locked for the parameters in Table 1: ∙∙∙∙ ε=0.01, -∙- ε=0.05, — ε=0.1, -- ε=0.2

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Figure 11

Maximum dynamic tension in each span varies with excitation frequency for the parameters in Table 1: ∙∙∙∙ Qm=0, — Qm=0.1, -- Qm=1.5, -∙- Qm=5

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