Elimination of Unstable Ranges of Rotors Utilizing Discontinuous Spring Characteristics: An Asymmetrical Shaft System, an Asymmetrical Rotor System, and a Rotor System With Liquid

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Yukio Ishida ◽  
Jun Liu
Keyword(s):  
Active Vibration Control ◽  
Rotor System ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Simple Method ◽  
Rotor Systems ◽  
Shaft System ◽  
Speed Range ◽  
Active Vibration ◽  
Unstable Vibration

Unstable vibration occurs in the vicinities of the major critical speeds of asymmetrical shaft and rotor systems. It occurs also in a wide rotational speed range higher than the major critical speed of a shaft with a hollow disk partially filled with liquid. The occurrence of the unstable vibrations is a serious problem because the amplitude increases exponentially, and finally, the system is destroyed. The active vibration control can suppress unstable vibrations but the method is generally complicated and costly. No simple effective method to suppress unstable vibrations has been developed yet. In the previous paper, the authors proposed a simple method by utilizing discontinuous spring characteristics, which can suppress steady-state resonances. This paper shows that this method is also effective to suppress unstable vibrations. By using this method, the unstable vibrations can be changed into almost periodic motions, and the amplitudes are suppressed to the desired small level even in an unstable range. The validity of the proposed method is also verified by experiments.

Hybrid Active Vibration Control of Rotorbearing Systems Using Piezoelectric Actuators

1993 ◽  
Vol 115 (1) ◽  
pp. 111-119 ◽  
Author(s):  
A. B. Palazzolo ◽  
S. Jagannathan ◽  
A. F. Kascak ◽  
G. T. Montague ◽  
L. J. Kiraly
Keyword(s):  
Vibration Control ◽  
Search Algorithm ◽  
Active Vibration Control ◽  
Piezoelectric Actuators ◽  
Operating Speed ◽  
Speed Range ◽  
Active Vibration ◽  
Linear Fit ◽  
Hybrid Interface ◽  
Grid Search Algorithm

The vibrations of a flexible rotor are controlled using piezoelectric actuators. The controller includes active analog components and a hybrid interface with a digital computer. The computer utilizes a grid search algorithm to select feedback gains that minimize a vibration norm at a specific operating speed. These gains are then downloaded as active stiffnesses and dampings with a linear fit throughout the operating speed range to obtain a very effective vibration control.

Internal Resonance of the Jeffcott Rotor With Nonlinear Spring Characteristics

2001 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Almost Periodic ◽  
Periodic Motions ◽  
Nonlinear Analyses ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Jeffcott Rotor ◽  
Two Degree Of Freedom

Abstract The Jeffcott rotor is a two-degree-of-freedom linear model with a disk at the midspan of a massless elastic shaft. This model executing lateral whirling motions has been widely used in the linear analyses of rotor vibrations. In the Jeffcott rotor, the natural frequency of a forward whirling mode pf and that of a backward whirling mode pb have the relation of internal resonance pf : pb = 1 : (−1). Recently, many researchers analyzed nonlinear phenomena by using the Jeffcott rotor with nonlinear elements. However, they did not take this internal resonance relationship into account. While, in many cases of the practical rotating machinery, such a relationship holds apprximately due to small gyroscopic moment. In this paper, nonlinear phenomena in the vicinity of the major critical speed and the rotational speeds of twice and three times the major critical speed are investigated in the Jeffcott rotor and rotor systems with small gyroscopic moment. Especially, the influences of internal resonance on the nonlinear resonances are studied in detail. The following were clarified theoretically and experimentally: (a) the shape of resonance curves becomes far more complex than that of a single resonance, (b) almost-periodic motions occur, (c) these phenomena are influenced remarkably by the asymmetrical nonlinearity and gyroscopic moment, and (d) the internal resonance phenomena are strongly influenced by the degree of the discrepancies among critical speeds. The results teach us the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incrrect results.

Vibration Control and Unbalance Estimation of a Nonlinear Rotor System Using Disturbance Observer

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Jun Liu ◽  
Yukio Ishida ◽  
Yusuke Yoshimura
Keyword(s):  
Vibration Control ◽  
Disturbance Observer ◽  
Control Method ◽  
Rotor System ◽  
Control Force ◽  
Rotor Systems ◽  
Parameter Variations ◽  
Speed Range ◽  
Disturbance Term ◽  
Nonlinear Rotor System

In rotating machinery, rotor unbalance causes many resonances at critical speeds corresponding to different modes. In this paper, a vibration control method for rotor systems utilizing disturbance observer is proposed. The nonlinear terms, unbalance, parameter variations, and uncertain terms of a rotor system are lumped into a disturbance term, and this term is canceled by using disturbance observer. As a result, the vibrations are suppressed to small amplitudes all over the rotational speed range. Simultaneously, unbalance of the first mode is estimated from the information of control force of disturbance observer. Moreover, the effects of parameter errors of the control system are also investigated. The validity of the proposed method is verified through numerical simulations and experiments.

Period-1 to Period-8 Motions in a Nonlinear Jeffcott Rotor System

2020 ◽  
Author(s):  
Yeyin Xu ◽  
Albert C.J. Luo
Keyword(s):  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Mapping Method ◽  
Rotor System ◽  
Period Doubling Bifurcation ◽  
Periodic Motions ◽  
Bifurcation Tree ◽  
Rotor Systems ◽  
Period 2 ◽  
Jeffcott Rotor

Abstract In this paper, a bifurcation tree of period-1 to period-8 motions in a nonlinear Jeffcott rotor system is obtained through the discrete mapping method. The bifurcations and stability of periodic motions on the bifurcation tree are discussed. The quasi-periodic motions on the bifurcation tree are caused by two (2) Neimark bifurcations of period-1 motions, one (1) Neimark bifurcation of period-2 motions and four (4) Neimark bifurcations of period-4 motions. The specific quasi-periodic motions are mainly based on the skeleton of the corresponding periodic motions. One stable and one unstable period-doubling bifurcations exist for the period-1, period-2 and period-4 motions. The unstable period-doubling bifurcation is from an unstable period-m motion to an unstable period-2m motion, and the unstable period-m motion becomes stable. Such an unstable period-doubling bifurcation is the 3rd source pitchfork bifurcation. Periodic motions on the bifurcation tree are simulated numerically, and the corresponding harmonic amplitudes and phases are presented for harmonic effects on periodic motions in the nonlinear Jeffcott rotor system. Such a study gives a complete picture of periodic and quasi-periodic motions in the nonlinear Jeffcott rotor system in the specific parameter range. One can follow the similar procedure to work out the other bifurcation trees in the nonlinear Jeffcott rotor systems.

Active vibration control of rotor-bearing system by virtual dynamic absorber

2019 ◽  
Vol 86 (3) ◽  
pp. 30901
Author(s):  
Behnam Monjezi ◽  
Hamidreza Heidari
Keyword(s):  
Transient Response ◽  
Control Method ◽  
Active Vibration Control ◽  
Resonance State ◽  
Rotor System ◽  
Manufacturing Defects ◽  
Resonance Frequencies ◽  
Active Vibration ◽  
Dynamic Absorber ◽  
Rotor Dynamic

The main sources of the vibration in rotor dynamic systems are unbalanced masses and manufacturing defects of bearings used in the rotor system. In this study, magnetic absorber as a new method brings the rotor system out of resonance state by applying a dynamic absorber system force and creating two new natural frequencies. This study virtually reconstructed magnetic absorber controller software as a combined active and passive dynamic absorber to reduce vibration amplitude, efficiently. In this approach, combined routes are defined for the rotor frequency response, so that the optimal values of the parameters of dynamic absorber system are calculated using H∞ method and maximum damping for frequencies lower and higher than resonance frequencies, respectively. The results confirm that transient response overshoot is less, and transient response attenuation is more in maximum damping method. Hence, the controller system easily recognizes initial overshoots and determines the parameters of the dynamic absorber system in accordance with maximum damping state if it is struck at any rotor frequency and any rotation angle. It is also observed that for all rotor rotation frequencies, the system overshoot reduces in comparison with H∞ method by using this control method.

Period-1 Motion to Chaos in a Nonlinear Flexible Rotor System

2020 ◽  
Vol 30 (05) ◽  
pp. 2050077 ◽  
Author(s):  
Yeyin Xu ◽  
Zhaobo Chen ◽  
Albert C. J. Luo
Keyword(s):  
Period Doubling ◽  
Rotor System ◽  
Harmonic Amplitude ◽  
Flexible Rotor ◽  
Periodic Motions ◽  
Bifurcation Tree ◽  
Rotor Systems ◽  
Saddle Node ◽  
Jeffcott Rotor ◽  
And Control

In this paper, a bifurcation tree of period-1 motion to chaos in a flexible nonlinear rotor system is presented through period-1 to period-8 motions. Stable and unstable periodic motions on the bifurcation tree in the flexible rotor system are achieved semi-analytically, and the corresponding stability and bifurcation of the periodic motions are analyzed by eigenvalue analysis. On the bifurcation tree, the appearance and vanishing of jumping phenomena of periodic motions are generated by saddle-node bifurcations, and quasi-periodic motions are induced by Neimark bifurcations. Period-doubling bifurcations of periodic motions are for developing cascaded bifurcation trees, however, the birth of new periodic motions are based on the saddle-node bifurcation. For a better understanding of periodic motions on the bifurcation tree, nonlinear harmonic amplitude characteristics of periodic motions are presented. Numerical simulations of periodic motions are performed for the verification of semi-analytical predictions. From such a study, nonlinear Jeffcott rotor possesses complex periodic motions. Such results can help one detect and control complex motions in rotor systems for industry.

Sign in / Sign up

Export Citation Format

Share Document