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Research Papers

Coupled Lateral and Torsional Nonlinear Transient Rotor–Bearing System Analysis With Applications

[+] Author and Article Information
Jianming Cao

Rotor Bearing Solutions International,
3277 Arbor Trace,
Charlottesville, VA 22911
e-mail: jianming.cao@rotorsolution.com

Paul Allaire

Rotor Bearing Solutions International,
3277 Arbor Trace,
Charlottesville, VA 22911
e-mail: paul.allaire@rotorsolution.com

Timothy Dimond

Rotor Bearing Solutions International,
3277 Arbor Trace,
Charlottesville, VA 22911
e-mail: tim.dimond@rotorsolution.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 7, 2014; final manuscript received April 28, 2015; published online June 24, 2015. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(9), 091011 (Sep 01, 2015) (9 pages) Paper No: DS-14-1463; doi: 10.1115/1.4030612 History: Received November 07, 2014; Revised April 28, 2015; Online June 24, 2015

This paper provides a time transient method for solving coupled lateral and torsional analysis of a flexible rotor–bearing system including gyroscopic effects, nonlinear short journal bearings, nonlinear short squeeze film dampers (SFDs), and external nonlinear forces/torques. The rotor is modeled as linear, and the supporting components, including bearings and dampers, are modeled as nonlinear. An implicit Runge–Kutta method is developed to solve the nonlinear equations of motion with nonconstant operating speed since the unbalance force and the gyroscopic effect are related to both the rotational speed and the acceleration. The developed method is compared with a previous torsional analysis first to verify the nonlinear transient solver. Then the coupled lateral and torsional analysis of an example flexible three-disk rotor, perhaps representing a compressor, with nonlinear bearings and nonlinear dampers driven by a synchronous motor is approached. The acceleration effects on lateral and torsional amplitudes of vibration are presented in the analysis. The developed method can be used to study the rotor motion with nonconstant rotational speed such as during startup, shutdown, going through critical speeds, blade loss force, or other sudden loading.

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References

Figures

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Fig. 1

12DOF element and coordinates

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Fig. 2

Cross section of bearing and damper

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Fig. 3

Transient analysis flow chart

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Fig. 4

Synchronous motor driven system [19]

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Fig. 5

Torque–speed curves [19]

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Fig. 6

Motor startup response

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Fig. 7

Shaft vibratory torque response

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Fig. 8

Three-disk flexible rotor model

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Fig. 9

Undamped critical speed map

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Fig. 10

Frequency interference diagram

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Fig. 11

Bearing dynamic coefficients

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Fig. 12

Speeds of nodes 1 and 13 with linearized bearing

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Fig. 13

Center disk torque with linearized bearing

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Fig. 14

Center disk response with linearized bearing

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Fig. 15

Center disk speed of nonlinear system

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Fig. 16

Nodal torque at center disk (node 13)

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Fig. 17

Shaft displacement in left bearing

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Fig. 18

Bearing displacement in left SFD

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Fig. 19

Left bearing force and fast Fourier transform (FFT)

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Fig. 20

Shaft displacement and FFT in left bearing

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Fig. 21

Left SFD force and FFT

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Fig. 22

Bearing displacement and FFT in left SFD

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