Reducing Lateral Vibration of a Rotor Passing Through Critical Speeds by Phase Modulating

2003 ◽  
Vol 125 (3) ◽  
pp. 766-771 ◽  
Author(s):  
S.-M. Wang ◽  
Q.-S. Lu ◽  
E. H. Twizell
Keyword(s):  
Vibration Amplitude ◽  
Critical Speed ◽  
Lateral Vibration ◽  
Constant Acceleration ◽  
Unbalanced Rotor ◽  
Acceleration Rate ◽  
Modulated Phase ◽  
Response Phase ◽  
Theoretical And Numerical Analysis ◽  
Rotor Model

A method is presented to reduce the lateral vibration amplitude of an unbalanced rotor accelerating or decelerating through its critical speed, by means of modulating the response phase with varying acceleration rate. Theoretical and numerical analysis on the amplitude and the phase characteristics of lateral vibration of a rotor model are made. Numerical results show that when the rotor passes through its critical speed with a modulated phase, the response amplitude can be reduced by 20% or so, compared with the nonmodulated (constant) acceleration case.

The Limited-Torque Acceleration Through Critical Speed Phenomenon in Rotating Machinery

2012 ◽  
Author(s):  
Anand Srinivasan ◽  
Trent W. Thurston
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Drive Train ◽  
Transient Solution ◽  
Acceleration Rate ◽  
Jeffcott Rotor ◽  
Full Speed ◽  
Lateral Displacements ◽  
Design Speed ◽  
Rotor Model

Rotor-bearing systems of modern day turbomachinery are generally designed to operate at speeds well above the lateral critical speed(s). Acceleration from rest to design speed of turbomachines is usually accomplished by a driver such as a motor or a turbine. The driver provides the torque required to bring the drive-train to full speed. If the torque delivered by the driver is less than the torque demanded by the driven machine, the drive-train stalls at a speed below running speed. If this speed coincides with a lateral critical speed of the turbomachine, the amplitude of vibration may increase to levels high enough to trip the machine. In extreme cases, damage due to rubs from vibration excursions may occur on the rotating components. Such a phenomenon is referred to as a limited-torque-acceleration of rotors through the critical speed. A theoretical analysis of this phenomenon requires a time-transient solution of the lateral equations of motion, with the acceleration rate determined from the torque equation. In this paper, the acceleration of the Jeffcott rotor model with a variable torque input has been studied, and the time-transient response of the shaft lateral displacements has been presented. Data recorded from a turbomachine that incurs vibration excursions during limited-torque acceleration through critical speed has also been presented. The importance of fast acceleration rates through critical speeds for rotating equipment has been stressed in this paper.

Experimental Researches on Reducing the Critical Acceleration That Induces Sustainable Rotor Rubbing

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Wang Shimin ◽  
Zhang Xingye
Keyword(s):  
Phase Modulation ◽  
Vibration Amplitude ◽  
Critical Speed ◽  
Maximum Amplitude ◽  
Modulation Method ◽  
Constant Acceleration ◽  
Critical Acceleration ◽  
Driving System ◽  
Pass Through ◽  
Experimental Researches

When an imbalanced rotor is sped up to pass through the critical speed with a constant acceleration, sustainable rubbing can be induced if the maximum vibration amplitude of the rotor exceeds the gap. This is the so-called stiffness increase or stiffening phenomenon. The maximum vibration amplitude is dependent on the magnitude of the rotor’s acceleration: the smaller the acceleration, the larger the maximum amplitude. Thus, there exists a critical acceleration: for accelerations smaller than the critical one, the sustainable rubbing will be induced. To prevent such unwanted rubbing, the rotor acceleration or the gap must be large enough. Since the acceleration is limited by the power/torque of driving system while large gap decreases the efficiency of some rotating machines, smaller driving power and higher efficiency have to be content with the second best. In this paper, the phase modulation method is applied to reduce the critical acceleration, and experiments are conducted on a setup designed to test the phase of the imbalanced force. The method is to operate the rotor with a scheduled, not continuously increased speed: when accelerated to a given speed, the rotor is decelerated to an assigned speed, and then accelerated again. Numerical and experimental results show that the critical acceleration is reduced about 50% by this technique. A prerequisite for this method is that the rotor’s speed is controllable.

Extension of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions

1980 ◽  
Vol 102 (1) ◽  
pp. 122-129 ◽  
Author(s):  
M. S. Darlow ◽  
B. T. Murphy ◽  
J. A. Elder ◽  
G. N. Sandor
Keyword(s):  
Transfer Matrix ◽  
Cross Sections ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Critical Speed ◽  
Axial Direction ◽  
Matrix Analysis ◽  
Beam Elements ◽  
Conical Section ◽  
Rotor Model

The transfer matrix method for rotordynamic analysis (alternately known as the HMP or LMP method) has enjoyed wide popularity due to its flexibility and ease of application. A number of computer programs are generally available which use this method in various forms to perform undamped critical speed, unbalance response, damped critical speed and stability analyses. For all of these analyses, the assembly of the transfer matrices from the rotor model is essentially the same. In all cases, the rotor model must be composed entirely of cylindrical beam elements. There are two situations when this limitation is not desirable. The first situation is when the rotor being modelled has one or more sections whose cross sections vary continually in the axial direction. The most common of these sections is the conical section. Presently, a conical section must be modelled as a series of “steps” of cylindrical sections. This adversely affects both the simplicity and accuracy of the rotor model. The second situation when current transfer matrix techniques are not accurate is when the rotor being modelled has one or more sections that do not behave as beam elements. The most common example is a trunnion which behaves as a plate. This paper describes the analytical basis and the method of application for direct representation of conical sections and trunnions for a transfer matrix analysis. Analytical results are currently being generated to demonstrate the need for and advantages of these modelling procedures.

scholarly journals Active Elastic Support/Dry Friction Damper with Piezoelectric Ceramic Actuator

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Liao Mingfu ◽  
Song Mingbo ◽  
Wang Siji
Keyword(s):  
Dry Friction ◽  
Piezoelectric Ceramic ◽  
Vibration Amplitude ◽  
Critical Speed ◽  
Rotor System ◽  
Elastic Support ◽  
Basic Operation ◽  
Friction Damper ◽  
Rotor Vibration ◽  
Active Damper

The basic operation principle of elastic support/dry friction damper in rotor system was introduced and the unbalance response of the rotor with elastic support/dry friction damper was analyzed theoretically. Based on the previous structure using an electromagnet as actuator, an active elastic support/dry friction damper using piezoelectric ceramic actuator was designed and its effectiveness of reducing rotor vibration when rotor traverses its critical speed and blade-out event happened was experimentally verified. The experimental results show that the active elastic support/dry friction damper with piezoelectric ceramic actuator can significantly reduce vibration in rotor system; the vibration amplitude of the rotor in critical speed region decreased more than 2 times, and the active damper can protect the rotor when a blade-out event happened, so the rotor can traverse the critical speed and shut down smoothly. In addition, the structure is much simpler than the previous, the weight was reduced by half and the power consumption was only 5 W.

Efficiency of Balancing by Liquid-Type Automatic Balancing Devices

2014 ◽  
Vol 1040 ◽  
pp. 858-863 ◽  
Author(s):  
Evgeny N. Pashkov ◽  
Nikita Martyushev ◽  
Andrey V. Ponomarev
Keyword(s):  
Vibration Amplitude ◽  
Rotor Speed ◽  
Mathematical Research ◽  
Rotor Vibration ◽  
Liquid Type ◽  
Automatic Balancing ◽  
Rotor Model

The article focuses on modelling the behaviour of a liquid-type automatic balancing device. To perform mathematical research the rotor model is used that contains a ring functioning as a vessel coupled to the rigid shaft being rotatable on bearings. Data on the influence of various factors on balancing accuracy are presented. The obtained modeling results indicate that the vibration amplitude at supercritical frequencies will decrease proportionally to the increase in the parameters of a liquid autobalancer. The performed calculation also reveals that the more the parameters of a liquid autobalancing device, the higher the efficiency of balancing. Provided the condition of the liquid sufficiency in the ring is satisfied, the independence of the rotor vibration amplitude from the mass of the liquid in the vessel is achieved. Critical rotor speed does not depend on the volume of the liquid in the ring if the condition of its sufficiency is met.

Deceleration of an Unbalanced Rotor Through a Critical Speed

1967 ◽  
Vol 89 (4) ◽  
pp. 582-585
Author(s):  
W. K. Bodger
Keyword(s):  
Critical Speed ◽  
Degree Of Freedom ◽  
Bending Stress ◽  
Rotor Speed ◽  
Single Degree Of Freedom ◽  
Closed Solution ◽  
Rotor Shaft ◽  
Single Degree ◽  
Unbalanced Rotor ◽  
Maximum Increment

The problem of a single-degree-of-freedom rotor decelerating slowly through its critica speed is solved by an energy approach; a closed solution is obtained. A small discontinuous downward jump of rotor speed across the critical speed is shown to be required, either with or without damping in the system. The maximum increment of deflection, hence bending stress, in the rotor shaft is shown to be small, provided the rotor is carefully balanced and/or the system is sufficiently damped.

Numerical Analysis of Coupled Lateral and Torsional Vibrations of a Vertical Unbalanced Rotor

2010 ◽  
Vol 20-23 ◽  
pp. 352-357
Author(s):  
Xue Li An ◽  
Dong Xiang Jiang ◽  
Ming Hao Zhao ◽  
Chao Liu
Keyword(s):  
Torsional Vibration ◽  
Coupling Effect ◽  
Torsional Vibrations ◽  
Lateral Vibration ◽  
Transient Vibration ◽  
Coupled Vibrations ◽  
Lateral Vibrations ◽  
Vertical Rotor ◽  
Unbalanced Rotor ◽  
Mass Eccentricity

A model for the coupled lateral and torsional vibrations of a vertical unbalanced rotor is developed. The equation of motion is obtained using Lagrangian dynamics without considering the external actuating forces and torque. The equation showed coupling and nonlinear interaction between the rotor lateral and torsional vibrations. Most of the earlier work on coupled vibrations has been done for the horizontal rotor model. The coupled vibrations for a vertical rotor have not been reported in the past. An attempt is made to reveal dynamic characteristics of vertical rotor. The results of the simulation showed the coupled between torsional and lateral vibrations is induced by mass eccentricity. Coupled vibrations have appeared in the start period of the vibration. After a transient vibration process, the vibrations are not coupling. The lateral vibration becomes equal amplitude with shafting speed. And the torsional vibration keeps on attenuating until it stops. When the vibration is coupled, the coupling effect on which torsional vibration to lateral vibration is evident. But there’s no coupling effect on the lateral to the torsional. It is also shown that for some operational parameters, the controlling action may excite large lateral vibrations due to coupling with the torsional motion.

scholarly journals Reducing Lateral Vibrations of a Rotor Passing Through Critical Speeds by Acceleration Scheduling

1997 ◽  
Author(s):  
Knox T. Millsaps ◽  
Gregory L. Reed
Keyword(s):  
Critical Speed ◽  
Vibrational Energy ◽  
Lumped Parameter Model ◽  
Integration Scheme ◽  
Lateral Vibrations ◽  
Acceleration Rate ◽  
Lumped Parameter ◽  
Numerical Integration Scheme ◽  
Single Disk ◽  
Acceleration And Deceleration

A method is presented for reducing the lateral response of an imbalanced rotor accelerating or decelerating through its first lateral bending critical speed by using a variable acceleration rate. A lumped parameter model along with a numerical integration scheme is used to simulate the response of a simply supported, single disk rotor during fast acceleration and deceleration through critical speed. The results indicate that the maximum response and/or the total vibrational energy of a rotor passing through the critical speed can be reduced significantly by using a variable acceleration schedule. That is, reducing the acceleration rate after the nominal critical speed is passed. These predictions were verified experimentally for a single disk rotor.

Measures to Reduce the Lateral Vibration of the Tail Car in a High Speed Train

1996 ◽  
Vol 210 (2) ◽  
pp. 87-93 ◽  
Author(s):  
H Fujimoto ◽  
M Miyamoto
Keyword(s):  
Vibration Amplitude ◽  
High Speed ◽  
Vibration Mode ◽  
Simulation Analysis ◽  
Lateral Vibration ◽  
High Speed Train ◽  
Aerodynamic Forces ◽  
Vibration Data ◽  
Tunnel Section ◽  
Train Vibration

From the vibration data obtained simultaneously on several cars in the same Shinkansen train, it was observed that the vibration amplitude of the tail car is greater than those of the other cars in a train. The authors' analysis arrived at the conclusion that the vibration mode of a train has a tendency for the tail car to vibrate more than the others, when the carbody hunting characteristics of a train for the yawing mode are likely to emerge, and when aerodynamic forces work in a tunnel section. Referring to those results, by simulation analysis etc., it was found that two longitudinal dampers installed parallel between the car ends (Fig. 1) with their forces depending on the angular velocity between cars, are effective in decreasing the train vibration including the tail car's vibration. Then, the prototype of the longitudinal dampers between the cars for Shinkansen was designed by obtaining the proper damping coefficient through simulation. The effectiveness of the installed damper was verified when it was tested up to 310 km/h in the Shinkansen train.

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