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Research Papers

Self-Excited Vibration of a Flexibly Supported Shafting System Induced by Friction

[+] Author and Article Information
Wenyuan Qin

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: qinwenyuan@sjtu.edu.cn

Zhenguo Zhang

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zzgjtx@sjtu.edu.cn

Hui Qin

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: narlia525@sjtu.edu.cn

Zhiyi Zhang

State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University;
Collaborative Innovation Center
for Advanced Ship and Deep-Sea Exploration,
Dongchuan Road 800,
Shanghai 200240, China
e-mail: chychang@sjtu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 28, 2016; final manuscript received October 24, 2016; published online February 3, 2017. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 139(2), 021004 (Feb 03, 2017) (10 pages) Paper No: VIB-16-1272; doi: 10.1115/1.4035203 History: Received May 28, 2016; Revised October 24, 2016

Self-excited vibration of a flexibly supported shafting system in a gravity water tunnel was observed in the testing of friction of water-lubricated rubber bearings. The measured vibrations indicated that the self-excited vibration, characterized by a single-mode vibration modulated by the shaft speed, emerged at a specific speed and grew stronger as the shaft speed decreased, but it would cease at a very low-speed. To explain the mechanism of instability, a dynamic model of the system was built. The substructure synthesis method was employed to model the dynamics of the shafting system, which was divided into two subsystems: the flexible support and the shaft. Before the synthesis, natural frequencies and modes of the subsystems were computed by the finite element method. According to the modal parameters and connecting conditions, a synthesized model was built to take into account the friction between the shaft and the bearing. The fourth-order Runge–Kutta method was used to solve the dynamic equations, and the influences of physical parameters on vibration stability were analyzed. The results have shown that certain vibration modes of the flexible support tend to be unstable under the excitation of the friction. Both the simulation and experimental results have exhibited that the unstable modes are associated with the torsional vibration of the flexible support, which are in fact lightly damped and accordingly can be easily excited by the circumferential friction. Therefore, the coupling between the torsional vibration of the flexible support and the friction of the water-lubricated rubber bearing is the main factor leading to the vibration instability.

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Figures

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Fig. 1

Experimental setup

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Fig. 2

Photo of the stern support

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Fig. 3

Schematic of the stern support

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Fig. 4

Dynamic responses at the shaft speed 120 rpm: (a) dynamic reaction forces of the two horizontal swords (time domain) and (b) dynamic reaction forces (frequency domain)

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Fig. 5

Dynamic responses at the shaft speed 60 rpm: (a) dynamic reaction forces of the two horizontal swords (time domain) and (b) dynamic reaction forces (frequency domain)

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Fig. 6

Time–frequency representation of dynamic reaction force at the shaft speed 240 rpm

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Fig. 7

Time–frequency representation of dynamic reaction force at the shaft speed 90 rpm

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Fig. 8

Time–frequency representation of dynamic reaction force at the shaft speed 30 rpm

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Fig. 9

The finite element model: (a) structure–fluid coupled model and (b) the structure model

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Fig. 10

The first six modes of the stern support: (a) first 7.1 Hz, (b) second 30.0 Hz, (c) third 37.1 Hz, (d) fourth 80.0 Hz, (e) fifth 113.6 Hz, and (f) sixth 265.9 Hz

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Fig. 11

Simplified representation of the setup

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Fig. 12

Interface of the simplified system

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Fig. 13

Support substructure

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Fig. 14

Sketch of the bearing–shaft interaction

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Fig. 15

The shaking and picking points

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Fig. 16

Measured frequency response functions (FRFs) of the stern support

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Fig. 17

Case (1): (a) torsional vibration of shaft, (b) horizontal component of the friction, and (c) spectrum of the friction

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Fig. 18

Case (2): (a) torsional vibration of shaft, (b) horizontal component of the friction, and (c) spectrum of the friction

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Fig. 19

Case (3): (a) torsional vibration of shaft, (b) horizontal component of the friction, and (c) spectrum of the friction

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Fig. 20

Case (4): (a) torsional vibration of shaft, (b) horizontal component of the friction, and (c) spectrum of the friction

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Fig. 21

Case (5): (a) torsional vibration of shaft, (b) horizontal component of the friction, and (c) spectrum of the friction

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Fig. 22

Case (6): (a) torsional vibration of shaft, (b) horizontal component of the friction, and (c) spectrum of the friction

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