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Nonlinear dynamic response of a rub-impact rod fastening rotor considering nonlinear contact characteristic

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Abstract

The nonlinear dynamic characteristics of a rub-impact rod fastening rotor have been investigated in this paper. A model of the rod fastening rotor bearing system under rub-impact condition is proposed considering nonlinear contact characteristic between disks, nonlinear oil-film force, unbalance mass, etc. The equation of motion of the system has been derived by D’Alembert principle. The contact effects between disks are modeled as a flexural spring with nonlinear stiffness. The dynamic equations of motion are solved using fourth-order Runge–Kutta method. Bifurcation diagram, vibration waveform, frequency spectrum, shaft orbit and Poincaré map are used to illustrate the rich diversity of the system response with complicated dynamics. The studies indicate that it is unsuitable to take the rod fastening rotor as an integral rotor in analyzing the rub-impact dynamic response of the system. The subharmonic periodic motion, multiple periodic motion, quasi-periodic motion and chaotic motion are observed in this study. Larger radial stiffness of stator will simplify the system motion and make the oil whirl weaker or even disappear at a certain rotating speed. The corresponding results can provide the guidance for the fault diagnosis of a rub-impact rod fastening rotor; meanwhile, the study may contribute to the further understanding of the nonlinear dynamic characteristics of a rub-impact rod fastening rotor.

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Abbreviations

c :

Radial clearance of bearing

\(\mu \) :

Oil viscosity

L :

Bearing length

R :

Bearing radius

\(\delta \) :

Sommerfeld correction coefficient

h :

Thickness of oil-film

p :

Dimensionless pressure of oil-film

\(F_{x}, F_{y}\) :

Nonlinear oil-film force in x direction and y direction

\(f_{x}, f_{y}\) :

Dimensionless nonlinear film force in x direction and y direction

\(P_{T}, P_{N}\) :

Impact force in radial and tangential direction

\(P_{x} \quad P_{y}\) :

Impact force in x direction and y direction

\(\eta \) :

Friction coefficient

\(r_{0}\) :

Initial clearance

\(k_{c}\) :

Radial stiffness of stator

\(F_{cx}, F_{cy}\) :

Restoring force of contact layer in x direction and y direction

\(m_{\mathrm{b1}}, m_{\mathrm{b2}}\) :

Lumped mass of bearings

\(m_{1}, m_{2}\) :

Lumped mass of disks

\(e_{1}, e_{2}\) :

Eccentric distance of disks

\(\varphi \) :

Angle between initial deflection and unbalance mass

k :

Shaft stiffness

\(k_{1}\) :

Linear contact stiffness

\(k_{1}^\prime \) :

Nonlinear contact stiffness

\(c_{1}\) :

Damping of bearing

\(c_{2}\) :

Damping of disk

\(c_{3}\) :

Damping of contact layer

\(x_{i}, y_{i}\,(i=1,2)\) :

Displacements of disks in x direction and y direction

\(x_{bi}, y_{bi}\,(i=1,2)\) :

Displacements of bearings in x direction and y direction

\(\omega \) :

Rotating speed

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Acknowledgments

This work is supported by the Construction Project Special Funds of Beijing China (No. ZDZH20141005401), National Natural Science Foundation of China (No. 51575180) and the Fundamental Research Funds for the Central Universities (No. 2015XS79).

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Authors and Affiliations

  1. School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing, 102206, China

    Liang Hu, Yibing Liu, Li Zhao & Chao Zhou

  2. Beijing Energy Investment Holding Co., Ltd., Beijing, 10002, China

    Li Zhao

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  1. Liang Hu
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Correspondence to Yibing Liu.

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Hu, L., Liu, Y., Zhao, L. et al. Nonlinear dynamic response of a rub-impact rod fastening rotor considering nonlinear contact characteristic. Arch Appl Mech 86, 1869–1886 (2016). https://doi.org/10.1007/s00419-016-1152-6

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  • DOI: https://doi.org/10.1007/s00419-016-1152-6

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