Research Papers

Vibration Analysis of the Flexible Connecting Rod With the Breathing Crack in a Slider-Crank Mechanism

[+] Author and Article Information
Yan-Shin Shih

Department of Mechanical Engineering,
Chung Yuan Christian University,
Chung-Li 32023, Taiwan
e-mail: ysshih@cycu.edu.tw

Chen-Yuan Chung

Department of Mechanical and Aerospace
Case Western Reserve University,
Cleveland, OH 44106
e-mail: zhen-yuan@alu.cycu.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 4, 2012; final manuscript received March 12, 2013; published online June 19, 2013. Assoc. Editor: Corina Sandu.

J. Vib. Acoust 135(6), 061009 (Jun 19, 2013) (9 pages) Paper No: VIB-12-1306; doi: 10.1115/1.4024053 History: Received November 04, 2012; Revised March 12, 2013

This paper investigates the dynamic response of the cracked and flexible connecting rod in a slider-crank mechanism. Using Euler–Bernoulli beam theory to model the connecting rod without a crack, the governing equation and boundary conditions of the rod's transverse vibration are derived through Hamilton's principle. The moving boundary constraint of the joint between the connecting rod and the slider is considered. After transforming variables and applying the Galerkin method, the governing equation without a crack is reduced to a time-dependent differential equation. After this, the stiffness without a crack is replaced by the stiffness with a crack in the equation. Then, the Runge–Kutta numerical method is applied to solve the transient amplitude of the cracked connecting rod. In addition, the breathing crack model is applied to discuss the behavior of vibration. The influence of cracks with different crack depths on natural frequencies and amplitudes is also discussed. The results of the proposed method agree with the experimental and numerical results available in the literature.

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Fig. 1

Slider-crank mechanism with a flexible cracked (x = l/2) connecting rod under undeformed configuration

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Fig. 2

Geometry of the rectangular cross-section with straight edge crack

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Fig. 3

Slider-crank mechanism with a flexible cracked (x = l/2) connecting rod under deformed configuration

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Fig. 4

The dimensionless transverse natural frequency ratio versus the crack depth ratio and comparison with Chondros et al. [16,22]

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Fig. 5

Transient transverse amplitudes of the first and second modes compared with those of Fung [7]

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Fig. 6

Transient transverse amplitude of the second mode g2(τ) compared with that of Jou [5]

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Fig. 7

Comparison among the uncracked, open, and breathing crack models of transverse amplitude g1(τ) at Ω = 0.2266

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Fig. 8

Comparison among the uncracked, open, and breathing crack models of transverse amplitude g2(τ) at Ω = 0.2266

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Fig. 9

Transient transverse amplitude g1(τ) for the breathing crack model with different crack depth ratios at Ω = 0.2

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Fig. 10

Transient transverse amplitude g2(τ) for the breathing crack model with different crack depth ratios at Ω = 0.2




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