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Nonsynchronous vibrations of rotor system induced by oil-block inside the rotating drum

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Abstract

Lubrication oil in a rotor system guarantees the rotating components working smoothly and protects the system from being damaged due to friction. A volume of lubrication oil, however, sometimes leaks into the inner cavity of shaft and drums of rotor system and forms an oil-block during rotating operation. The oil-block usually induces abnormal vibration of the rotating machine, which is often observed in practical cases, such as in aero-engine. The work in this paper studies the nonsynchronous vibration (NSV) induced by an oil-block in a rotating drum of a Jeffcott rotor system, which consists of a shaft, a drum and two supporting isotropic bearings. The additional effect due to an oil-block rotating on the inner wall of the drum is included into rotor system differential equations considering the Coriolis acceleration and friction interaction between the oil-block and the drum. Numerical simulations are carried out under two rotating speeds conditions: a lower one and a higher one than the first critical rotor speed, which are defined as rigid rotor case and flexible rotor case. Numerical results states the transverse vibrations by bifurcation diagrams, shaft center trajectories, frequency spectra and Poincare diagrams, which reveal multi-periodic, quasi-periodic and other complex motions due to the existing of oil-block. The internal friction coefficient and mass of the oil-block are found to have a significant effect on the generation and development of NSV. As the oil-block case is very common in practice, the investigation of NSV caused by oil-block in rotor system would benefit the understanding of complex phenomena and contribute to fault detection and diagnosis of rotating machine.

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Abbreviations

\( \user2{a}_{C} = (\textit{\"{x}},\;\textit{\"{y}}) \) :

Absolute acceleration of geometry center C of the drum (m/s2)

a Coriolis :

Coriolis acceleration (m/s2)

a r :

Relative acceleration (m/s2)

B :

Position of the oil-block

C :

Geometry center of the drum

C :

Damping matrix of the rotor system

c ij (i, j = 1, 2):

Equivalent viscous damping coefficients of the rotor system (N s/m)

F n , F f :

Normal force and tangential force applied on the oil-block (N)

F ox , F oy :

Forces induced by the oil-block in x- and y-directions (N)

J :

Gyroscopic matrix of the rotor system

J d :

Transverse moment of inertia of the oil drum

J p :

Polar moment of inertia of the oil drum

K :

Stiffness matrix of the rotor system

k ij (i, j = 1, 2):

Stiffness coefficients of the rotor system (N/m)

l BC :

Length of BC, i.e., radius of the inner drum (m)

n BC :

Unit vector from B to C

M :

Mass matrix of the rotor system

m :

Lumped mass of the oil drum and the steel disc (kg)

m e :

Eccentric masses of the drum and the steel disc (kg)

m oil :

Mass of the oil-block (kg)

O :

Rotating center of the disc

Oxyz :

Fixed coordinate system along the bearings’ centerline and its origin at the drum

P x (t), P y (t):

The external exciting force vectors in x- and y-directions

r :

Eccentric rotating radii of the drum and the steel disc (m)

t :

Time (s)

u 1, u 2 :

Generalized displacement vectors

\( \user2{v}_{{BB^{'} }} \) :

Relative velocity of the oil-block at B to its convected point B′ (m/s)

x, y :

Displacements of the center of the drum (m)

Ω:

Rotating angular speed of the rotor (rad/s or Hz)

α :

Angle from OC to the tangential (friction) direction at B (rad)

β :

Angle from the tangential (friction) direction to the vertical axis y (rad)

θ x , θ y :

Rotating angle displacements of the drum in y- and x-directions (rad)

ϕ = ωt :

Rotating angle from the horizontal axis x to OC (rad)

ϕ 1 :

The initial phases of the drum unbalances (rad)

μ :

Coefficient of dynamic friction between the oil-block and disc

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Acknowledgments

This work is supported by National Basic Research Program of China (No. 2012CB026000), and Natural Science Foundation of China (Grant No. 51175070).

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Authors and Affiliations

  1. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Qingkai Han & Jingyu Zhai

  2. Key Laboratory of Health Maintenance for Mechanical Equipment of Hunan Province, Hunan University of Science and Technology, Xiangtan, 411201, People’s Republic of China

    Qingkai Han

  3. College of Bullet Train Application and Maintenance Engineering & College of Mechanical Engineering, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Meiling Wang

  4. College of Mechanical Engineering, Dalian Jiaotong University, Dalian, 116028, People’s Republic of China

    Tianmin Guan

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  1. Qingkai Han
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Correspondence to Qingkai Han.

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Han, Q., Zhai, J., Wang, M. et al. Nonsynchronous vibrations of rotor system induced by oil-block inside the rotating drum. Meccanica 49, 2335–2357 (2014). https://doi.org/10.1007/s11012-014-0003-1

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  • DOI: https://doi.org/10.1007/s11012-014-0003-1

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