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Research Papers

Suppression of Friction-Induced Bending Vibrations in a Flexible Disk Sliding in Contact With a Rigid Surface

[+] Author and Article Information
Boris Ryzhik

LuK GmbH & Co. oHG,
Industriestrasse 3,
Buehl 77815, Germany
e-mail: Boris.Ryzhik@schaeffler.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 5, 2012; final manuscript received August 19, 2013; published online October 3, 2013. Assoc. Editor: Philip Bayly.

J. Vib. Acoust 136(1), 011004 (Oct 03, 2013) (9 pages) Paper No: VIB-12-1340; doi: 10.1115/1.4025401 History: Received December 05, 2012; Revised August 19, 2013

The paper describes an instability mechanism in a friction unit comprising a rotating flexible annular disk pressed to a rigid surface on the whole outer circumference. It is shown that for such a system, sliding friction forces set up a feedback between the orthogonal bending eigenmodes of the disk with the same form but different angular orientation. Due to axisymmetry, these modes have the same eigenfrequency. The feedback between the vibration modes with the same frequency leads to appearance of the circulation terms in the equations of motion and to instability. As a measure to suppress squeal, special apertures in the disk are suggested. The goal is to detach the paired eigenfrequencies to stabilize the system. The positioning of the apertures is discussed. The instability mechanism is investigated on the simple analytical model. More detailed finite-element analysis confirms the analytical prediction about the influence of the friction and axisymmetry on the instability and enables to prove the measures against friction induced vibrations.

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Figures

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Fig. 1

Model of the system

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Fig. 2

Pair of eigenmodes with n = 0,m = 1: (a) one of these modes, (b) paired mode

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Fig. 3

Feedback between the paired eigenmodes: (a) eigenmode with n = 0,m = 1, (b) normal forces in contact, (c) tangential friction forces, (d) variation of tangential forces, and (e) paired mode

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Fig. 4

Q-R damped modal analysis: eigenfrequencies with positive real parts

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Fig. 5

Q-R damped modal analysis: influence of the friction coefficient μ

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Fig. 6

Q-R damped modal analysis: influence of the contact stiffness. Here, Ccb is the “basis” value of the contact stiffness used in calculations in Fig. 5.

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Fig. 7

Q-R damped modal analysis: influence of preload. Here, u0b is the basis value of the initial displacement used in calculations in Figs. 5 and 6.

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Fig. 10

Q-R damped modal analysis: influence of the disk radius Rs = 12(Rb+Ra). Here, Rsb is the basis radius used in calculations in Figs. 5 and 6.

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Fig. 8

Q-R damped modal analysis: influence of the disk thickness h. Here, hb is the basis thickness used in calculations in Figs. 5 and 6.

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Fig. 9

Q-R damped modal analysis: influence of the disk width b = rb - ra. Here, bb is the basis width used in calculations in Figs. 5 and 6.

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Fig. 11

Disk with two “symmetrical” apertures

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Fig. 12

Q-R damped modal analysis for the disk with two “symmetrical” apertures: eigenvalue with positive real part

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Fig. 13

Q-R damped modal analysis for the disk with two symmetrical apertures: eigenmode corresponding to eigenvalue with positive real part

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Fig. 14

Disk with two slightly “asymmetrical” apertures

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