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Research Papers

Investigation of the Stability of a Squeak Test Apparatus Based on an Analytical and Finite Element Models

[+] Author and Article Information
Gil Jun Lee

Department of Mechanical and
Materials Engineering,
College of Engineering and Applied Science,
University of Cincinnati,
584D Rhodes Hall, 2600 Clifton Avenue,
Cincinnati, OH 45221
e-mail: leeg4@mail.uc.edu

Jay Kim

Fellow ASME
Department of Mechanical and
Materials Engineering,
College of Engineering and Applied Science,
University of Cincinnati,
589 Rhodes Hall, 2600 Clifton Avenue,
Cincinnati, OH 45221
e-mail: jay.kim@uc.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 5, 2017; final manuscript received December 12, 2017; published online February 9, 2018. Assoc. Editor: Philippe Velex.

J. Vib. Acoust 140(3), 031011 (Feb 09, 2018) (12 pages) Paper No: VIB-17-1240; doi: 10.1115/1.4038945 History: Received June 05, 2017; Revised December 12, 2017

Squeak is an unwanted, annoying noise generated by self-excited, friction-induced vibration. A unique squeak test apparatus that can generate squeak noises consistently was developed by modifying and employing a sprag-slip mechanism. Such an apparatus enables building database that accurately ranks squeak propensity of material pairs and will be highly useful for noise, vibration, and harshness (NVH) engineers and vehicle interior designers. An analytical model of the apparatus was developed to identify instability conditions that induce unstable, large-amplitude vibration, therefore squeak noises. A finite element model was established and studied in this work to refine the design of the apparatus and better understand underlying phenomena of the squeak generation. Complex eigenvalue analysis (CEA) was used to study the instability of the system and results show that the instability occurs by the coalescence of two modes, which makes the effective damping of one of the coalesced modes negative. The instability condition from the CEA shows good agreement with the results obtained from the analytical model. Furthermore, dynamic transient analysis (DTA) was performed to investigate the stability of the system and confirm the instability conditions identified from the CEA. The effects of main design parameters on the stability were investigated by DTA. The results obtained from the actual tests show that the test apparatus consistently generates unstable vibration of a very large amplitude, indicating generation of squeak noises.

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Figures

Grahic Jump Location
Fig. 2

A finite element model of the squeak test apparatus shown in Fig. 1(a). N, V, and θa are the applied normal force at the top end of the bent beam, the velocity of the rigid surface at the bottom, and the angle of attack, respectively; l1 and l2 are the length of the beam segments.

Grahic Jump Location
Fig. 1

(a) Experimental setup of the squeak test apparatus (cross section of the bent beam: 15 mm × 1 mm), (b) its analytical model (k: stiffness of the linear spring, ξo: initial compression, ξ: dynamic displacement of spring from initial compression, ξs: free length of the linear spring, K: stiffness of the torsional spring, l: length of a rigid bar, θa: angle of attack, θ: dynamic variation of angle, θT: total angle, Fn: normal force, Ft =μFn: friction force), and (c) Euler–Bernoulli beam model of the bent beam of the squeak test apparatus

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Fig. 7

Comparison of the instability region identified from the analytical and FEM model of the squeak test apparatus in terms of the kinetic coefficient of friction (μ) and the angle of attack (θa)

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Fig. 3

Complex eigenvalues of the FEM model of the squeak test apparatus with three different values of the kinetic coefficient of friction (μ) when θa = 8 deg, N = 10 N, and V = 2 mm/s

Grahic Jump Location
Fig. 4

The evolution of the eigenvalues with respect to the kinetic coefficient of friction (μ): (a) mode 7 and 8 and (b) mode 13 and 14

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Fig. 5

The mode shapes of the test apparatus with μ = 0.2: (a) mode 7 and (b) mode 8

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Fig. 6

Eigenvalues of the FEM model of the MSSM with four different values of the angle of attack (θa)

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Fig. 12

(a) The acceleration time history of the tip of the bent beam of the squeak test apparatus, which is numerically obtained and (b) its frequency spectrum with respect to the applied normal force N when μ = 0.2, θa = 8 deg, and V = 2 mm/s

Grahic Jump Location
Fig. 8

(a) The acceleration time history of the tip of the bent beam of the squeak test apparatus, which is numerically obtained and (b) its frequency spectrum with respect to the friction coefficient μ when θa = 8 deg, N = 10 N, and V = 2 mm/s

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Fig. 13

Experimental setup of the squeak test apparatus for material pair testing

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Fig. 9

(a) The acceleration time history of the tip of the bent beam of the squeak test apparatus, which is numerically obtained and (b) its frequency spectrum with respect to the angle of attack θa when μ = 0.2, N = 10 N, and V = 2 mm/s

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Fig. 14

Experimentally measured time histories from aluminum–aluminum pair: (a) acceleration and (b) sound pressure

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Fig. 15

Experimentally measured time histories from aluminum–polymer pair: (a) acceleration and (b) sound pressure

Grahic Jump Location
Fig. 10

(a) Relative velocity of the tip of the beam of the squeak test apparatus to the rigid surface at the bottom, which is numerically obtained, (b) zoom-in of the relative velocity, (c) contact force between the tip of the beam of the squeak test apparatus to the rigid surface at the bottom, which is numerically obtained, and (d) zoom-in of the contact force of the unstable system when μ = 0.2, N = 10 N, and V = 2 mm/s. ((1): stick, (2): slip, and (3) separation-slip).

Grahic Jump Location
Fig. 11

(a) The acceleration time history of the tip of the bent beam of the squeak test apparatus, which is numerically obtained and (b) its frequency spectrum with respect to the velocity of the rigid surface V when μ = 0.2, θa = 8 deg, and N = 10 N

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