Subharmonic and Chaotic Motions of a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor With Active Control

2002 ◽  
Vol 124 (2) ◽  
pp. 198-208 ◽  
Author(s):  
Chieh-Li Chen ◽  
Her-Terng Yau ◽  
Yunhua Li
Keyword(s):  
Lyapunov Exponent ◽  
Active Control ◽  
Chaotic Motion ◽  
Numerical Results ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Maximum Lyapunov Exponent ◽  
Rigid Rotor ◽  
Squeeze Film Damper

The hybrid squeeze-film damper bearing with active control is proposed in this paper. The pressure distribution and the dynamics of a rigid rotor supported by such bearing are studied. A PD (proportional-plus-derivative) controller is used to stabilize the rotor-bearing system. Numerical results show that, due to the nonlinear factors of oil film force, the trajectory of the rotor demonstrates a complex dynamics with rotational speed ratio s. Poincare´ maps, bifurcation diagrams, and power spectra are used to analyze the behavior of the rotor trajectory in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent and fractal dimension concepts are used to determine if the system is in a state of chaotic motion. Numerical results show that the maximum Lyapunov exponent of this system is positive and the dimension of the rotor trajectory is fractal at the nondimensional speed ratio s=3.0, which indicate that the rotor trajectory is chaotic under such operation condition. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain is applied to control this system. It is shown that the rotor trajectory will leave chaotic motion to periodic motion in the steady state under control action.

Time Transient Analysis of Horizontal Rigid Rotor Supported With O-Ring Sealed Squeeze Film Damper

2013 ◽  
Author(s):  
Saeid Dousti ◽  
Timothy W. Dimond ◽  
Paul E. Allaire ◽  
Houston E. Wood
Keyword(s):  
Transient Analysis ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Numerical Data ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers

This study addresses the nonlinear dynamic behavior of O-ring seals as the retaining spring in squeeze film dampers (SFDs). An analytical model is developed to predict the restoring and hysteresis forces of elastomer O-rings based on experimental and numerical data. This model takes into account the temperature softening and excitation frequency hardening effects in O-rings as well as the installation conditions in the form of radial and vertical preloads, σ and γ, respectively. Long bearing assumption is adopted for the solution of Reynolds equation. The equations of motion of horizontal unbalanced rigid rotor are derived, and a dimensional analysis is conducted on them. The numerical results substantiates the synchronizing effects of bearing parameter, B and vertical preload, γ, and the asynchronizing effects of O-ring parameter, O and radial preload, σ. It is shown that the variation of temperature and rotational speed as operating conditions influence the rotor response significantly.

Subharmonic, Quasi-Periodic and Chaotic Motions of a Rigid Rotor Supported by an Eccentric Squeeze Film Damper

1993 ◽  
Vol 207 (6) ◽  
pp. 383-392 ◽  
Author(s):  
J Y Zhao ◽  
E J Hahn
Keyword(s):  
Reynolds Equation ◽  
Power Spectra ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Eccentricity Ratio ◽  
Jump Phenomenon ◽  
Chaotic Motions ◽  
Squeeze Film Damper ◽  
Static Eccentricity

This paper analyses the complexity of the unbalance response possible with a simple rigid rotor supported by an eccentric squeeze film damper. The damper forces are obtained from the ‘π’ film short bearing approximation to the Reynolds equation and a fourth-order Runge-Kutta integration is used to evaluate the rotor response. Poincaré maps, rotor trajectories, bifurcation diagrams and power spectra are used to elucidate and to illustrate the diversity of the system behaviour. It is shown that for a large unbalance and static eccentricity ratio, the system can exhibit undesirable jump phenomenon and subharmonic, quasi-periodic and even chaotic motions, which limit the operating conditions at which dampers should be used.

Gear Dynamics Analysis With Turbulent Journal Bearings Mounted Hybrid Squeeze Film Damper—Chaos and Active Control Analysis

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Cai-Wan Chang-Jian
Keyword(s):  
Chaotic Motion ◽  
Journal Bearing ◽  
Complex Dynamics ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Maximum Lyapunov Exponent ◽  
Control Analysis ◽  
Bifurcation Diagrams ◽  
Squeeze Film Damper ◽  
Chaotic Vibrations

The hybrid squeeze film damper mounted turbulent journal bearing–gear system is proposed in this paper. The nonlinear dynamics of a gear pair supported by such bearing is studied. Numerical results show that, due to the nonlinear factors of lubricant film force, the trajectory of the pinion demonstrates a complex dynamics with dimensionless unbalance parameters. Poincaré maps and bifurcation diagrams are used to analyze the behavior of the pinion trajectory in the horizontal direction. The maximum Lyapunov exponent is used to determine if the system is in a state of chaotic motion. In order to avoid the nonsynchronous chaotic vibrations, an increased proportional gain kp = 0.1 is applied to control this system. It is shown that the pinion trajectory will leave chaotic motion to periodic motion in the steady state under control action.

Nonlinear Dynamic Study on Effects of Rub-Impact Caused by Oil-Rupture in a Multi-Shafts Turbine With a Squeeze Film Damper

2014 ◽  
Author(s):  
T. N. Shiau ◽  
C. R. Wang ◽  
D. S. Liu ◽  
W. C. Hsu ◽  
T. H. Young
Keyword(s):  
Dynamic Behavior ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Rotor System ◽  
Squeeze Film ◽  
Speed Ratio ◽  
Frequency Spectra ◽  
Squeeze Film Damper ◽  
Assumed Mode Method ◽  
Nonlinear Dynamic Behavior

An investigation is carried out the analysis of nonlinear dynamic behavior on effects of rub-impact caused by oil-rupture in a multi-shafts turbine system with a squeeze film damper. Main components of a multi-shafts turbine system includes an outer shaft, an inner shaft, an impeller shaft, ball bearings and a squeeze film damper. In the squeeze film damper, oil forces can be derived from the short bearing approximation and cavitated film assumption. The system equations of motion are formulated by the global assumed mode method (GAMM) and Lagrange’s approach. The nonlinear behavior of a multi-shafts turbine system which includes the trajectories in time domain, frequency spectra, Poincaré maps, and bifurcation diagrams are investigated. Numerical results show that large vibration amplitude is observed in steady state at rotating speed ratio adjacent to the first natural frequency when there is no squeeze film damper. The nonlinear dynamic behavior of a multi-shafts turbine system goes in its way into aperiodic motion due to oil-rupture and it is unlike the usual way (1T = >2T = >4T = >8T etc) as compared to one shaft rotor system. The typical routes of bifurcation to aperiodic motion are observed in a multi-shafts turbine rotor system and they suddenly turn into aperiodic motion from the periodic motion without any transition. Consequently, the increasing of geometric or oil parameters such as clearance or lubricant viscosity will improve the performance of SFD bearing.

Experiment and analysis on chaotic characteristics vibration mill with variable rotational speed

2021 ◽  
pp. 2150052
Author(s):  
Xiaolan Yang ◽  
Yuan Gao ◽  
Minping Jia
Keyword(s):  
Chaotic Motion ◽  
Average Particle Size ◽  
Engineering Application ◽  
Operating Conditions ◽  
Average Particle ◽  
Maximum Lyapunov Exponent ◽  
Motor Speed ◽  
Low Efficiency ◽  
Motion Characteristics ◽  
Vibration Mill

In an attempt to improve the current low efficiency and high consumption situation of vibration mills, this paper analyses the chaotic motion characteristics of the system and the movement of vibration mill. The complex stiffness-dispersion coupling of the system is also studied, so as to investigate the effect of the system’s chaotic motion characteristics on the efficiency improvement and energy consumption reduction. Based on the ADAMS software, this paper establishes a simplified vibration mill mechanical model, analyzes the singularity and stability of the system, and determines the critical speed at which the vibration motor becomes chaotic according to the bifurcation diagram. Then the chaotic state of the grinding machine with sinusoidal variation in its motor speed is studied based on the Poincaré principle, singular attractor and maximum Lyapunov exponent. Lastly, a 200[Formula: see text]h vibration test on diamond powder with an average particle size of 10 [Formula: see text]m was carried out. Test results under the two operating conditions of variable and constant speeds are compared and analyzed. Our results show that with variable speed the vibration mill achieved higher grinding efficiency but smaller particle grain size. The research elaborated in this paper provides a valuable reference for the engineering application of the chaotic characteristics of vibration mill.

Active Control Algorithms for the Control of Rotor Vibrations Using HSFDs

2000 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Active Control ◽  
Gain Scheduling ◽  
Rotating Machinery ◽  
Squeeze Film ◽  
Control Algorithms ◽  
Critical Stage ◽  
Squeeze Film Damper ◽  
Active Vibration

The Hybrid Squeeze Film Damper (HSFD) has proven itself to be an effective controlling device of vibration in rotating machinery. The critical stage in the development of the HSFD as an active vibration suppressant, is the development of the control algorithms for active control of rotor vibrations. This paper summarizes, evaluates and compares the control algorithms for HSFD supported rotors. Quantitative as well as qualitative measures of the effectiveness of the control algorithms are presented. The study includes the PID-type controllers, LQR, gain scheduling, adaptive and bang-bang controllers. The adaptive, gain scheduling and nonlinear proportional controllers, have proved to be quite effective in the active control of HSFD supported rotors, with impressive results.

Eccentric Operation and Blade-Loss Simulation of a Rigid Rotor Supported by an Improved Squeeze Film Damper

1995 ◽  
Vol 117 (3) ◽  
pp. 490-497 ◽  
Author(s):  
J. Y. Zhao ◽  
E. J. Hahn
Keyword(s):  
Outer Ring ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Cavitation Model ◽  
Squeeze Film Damper ◽  
Constant Stiffness ◽  
Flexible Support ◽  
Squeeze Film Dampers ◽  
Stiffness And Damping ◽  
Blade Loss

This paper outlines an improved squeeze film damper which reduces significantly the dependence of the stiffness of conventional squeeze film dampers on the vibration amplitudes. This improved damper consists of a conventional squeeze film damper with a flexibility supported outer ring. This secondary flexible support is considered to be massless, and to have a constant stiffness and damping. Assuming the short bearing approximation and the ‘π’ film cavitation model, the performances of this damper in preventing bistable operation and sub-synchronous and nonsynchronous motions are theoretically demonstrated for a rigid rotor supported on a squeeze film damper. Blade-loss simulations are carried out numerically.

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