Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs

Research output: Contribution to journalArticle

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Abstract

Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α = 0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights into the range of design parameters for squeeze-film dampers with retainer springs to ensure synchronous rotor response within a specified operating speed range.

Original languageEnglish
Pages (from-to)519-532
Number of pages14
JournalChaos, Solitons and Fractals
Volume39
Issue number2
DOIs
Publication statusPublished - 30 Jan 2009

Fingerprint

Damper
Rotor
Bifurcation
Range of data
Parameter Design
Exception
Rotating Machinery
Multiple Responses
Numerical Results
Decrease
Saddle-node Bifurcation
Hopf Bifurcation
Numerical Study
Hydrodynamics
Stiffness
Damping
Gravity
Initial conditions
Numerical Simulation

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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title = "Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs",
abstract = "Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α = 0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights into the range of design parameters for squeeze-film dampers with retainer springs to ensure synchronous rotor response within a specified operating speed range.",
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Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs. / Inayat-Hussain, Jawaid I.

In: Chaos, Solitons and Fractals, Vol. 39, No. 2, 30.01.2009, p. 519-532.

Research output: Contribution to journalArticle

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N2 - Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α = 0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights into the range of design parameters for squeeze-film dampers with retainer springs to ensure synchronous rotor response within a specified operating speed range.

AB - Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α = 0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights into the range of design parameters for squeeze-film dampers with retainer springs to ensure synchronous rotor response within a specified operating speed range.

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