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Research Papers

A Computational Investigation of the Disk-Housing Impacts of Accelerating Rotors Supported by Hydrodynamic Bearings

[+] Author and Article Information
Jaroslav Zapoměl1

Department of Mechanics, VSB-Technical University of Ostrava, 17 Listopadu 15, Ostrava - Poruba, 70833 Czech Republicjaroslav.zapomel@vsb.cz

Petr Ferfecki

Center of Advanced Innovation Technologies Structural Integrity and Materials Design, VSB-Technical University of Ostrava, 17 Listopadu 15, Ostrava - Poruba, 70833 Czech Republicpetr.ferfecki@vsb.cz

1

Corresponding author.

J. Appl. Mech 78(2), 021001 (Nov 04, 2010) (13 pages) doi:10.1115/1.4002527 History: Received July 07, 2009; Revised February 12, 2010; Posted September 09, 2010; Published November 04, 2010; Online November 04, 2010

As the radial clearance between disks and the casing of rotating machines is usually very narrow, excessive lateral vibration of accelerating rotors passing critical speeds can produce impacts between the disks and the housing. The computer modeling method is an important tool for investigating such events. In the developed procedure, the shaft is flexible and the disks are absolutely rigid. The hydrodynamic bearings and the impacts are implemented in the mathematical model by means of nonlinear force couplings. Most of the publications and computer codes from the field of rotor dynamics are referred only in the case when the rotor turns at a constant angular speed and in simple cases of disk-housing impacts. Moreover, if the disks turning at variable speed are investigated, the resulting form of the equations of motion derived by different authors slightly differs and the differences depend on the method used for their derivation. Therefore, particular emphasis in this article is given to the derivation of the motion equations of a continuous rotor turning with variable revolutions to explain the mentioned differences, to develop a computer algorithm enabling the investigation of cases when impacts between an arbitrary number of disks and the stationary part take place, and to analyze the mutual interaction between the impacts and the fluid film bearings. The Hertz theory is applied to determine the contact forces. Calculation of the hydrodynamic forces acting on the bearings is based on solving the Reynolds equation and taking cavitation into account. Lagrange equations of the second kind and the principle of virtual work are used to derive equations of motion. The Runge–Kutta method with an adaptive time step is applied for their solution. The applicability of the developed procedure was tested by computer simulations. The results show that it can be used for the modeling of complex rotor systems and that the short computational time enables carrying out calculations for a number of design and operation parameters.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Frames of reference of the disk

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Figure 2

Frames of reference of the disk and definition of the angular position of the rotor

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Figure 3

Rotation angles defining the spherical motion of the disk

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Figure 4

Components of the inertia moment acting on the disk

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Figure 5

Decomposition of the inertia moment into the y′, ξ, and x∗ directions

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Figure 6

Magnitude of the disk inertia moment in the x∗ direction

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Figure 8

Coordinate system referred to the hydrodynamic bearing

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Figure 9

Scheme of the investigated rotor system

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Figure 10

The Campbell diagram

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Figure 11

Normal mode referred to natural frequency of 550.3 rad/s and speed of rotation of 400 rad/s

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Figure 12

Dependence of the maximum real part of the system eigenvalues on the rotor speed

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Figure 13

Steady state orbit of the rotor journal center in bearing B1 (speed 400 rad/s)

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Figure 14

Steady state orbit of the rotor journal center in bearing B2 (speed 400 rad/s)

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Figure 15

Trajectory of the center of disk D1 (speed 800 rad/s)

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Figure 16

Trajectory of the center of disk D3 (speed 800 rad/s)

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Figure 17

Trajectory of the rotor journal center in bearing B1 (speed 800 rad/s)

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Figure 18

Trajectory of the rotor journal center in bearing B2 (speed 800 rad/s)

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Figure 19

Trajectory of the rotor journal center in bearing B2 (speed 800 rad/s) in detail

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Figure 20

Time history of the horizontal displacement of the disk D2 center

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Figure 21

Time history of the vertical displacement of the disk D2 center

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Figure 22

Time history of the impact force acting on disk D1 in the horizontal direction

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Figure 23

Time history of the impact force acting on disk D1 in the vertical direction

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Figure 24

Time history of the impact force acting on disk D3 in the horizontal direction

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Figure 25

Time history of the impact force acting on disk D3 in the vertical direction

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Figure 26

Time history of the impact force acting on disk D3 in the horizontal direction in detail

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Figure 27

Time history of the indentation of disk D1 in the horizontal direction

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Figure 28

Time history of the indentation of disk D1 in the vertical direction

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Figure 29

Normal component of the contact force-indentation relationship

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