The Analytical Imbalance Response of Jeffcott Rotor During Acceleration

2000 ◽  
Vol 123 (2) ◽  
pp. 299-302 ◽  
Author(s):  
Shiyu Zhou ◽  
Jianjun Shi
Keyword(s):  
Natural Frequency ◽  
Initial Condition ◽  
Constant Acceleration ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Jeffcott Rotor ◽  
Physical Insight

Since many rotor systems normally operate above their critical speeds, the problem of accelerating the machine through its critical speeds without excessive vibration draws increasing attention. This paper provides an analytical imbalance response of the Jeffcott rotor under constant acceleration. The response consists of three parts: transient vibration due to the initial condition of the rotor, “synchronous” vibration, and suddenly occurring vibration at the damped natural frequency. This solution provides physical insight to the vibration of the rotor during acceleration.

Nonlinear Flutter Response of Tilting 4 Pad Bearings-Rotor System

2011 ◽  
Author(s):  
Jiayang Ying ◽  
Yinghou Jiao ◽  
Zhaobo Chen ◽  
R. Gordon Kirk
Keyword(s):  
Transient Vibration ◽  
Oil Film ◽  
Rotor Systems ◽  
Tilting Pad ◽  
Jeffcott Rotor ◽  
Rotor Bearing ◽  
Nonlinear Transient ◽  
Rotor Center ◽  
Design Speed ◽  
Tilting Pad Journal Bearing

Nonlinear analysis is increasingly applied in the dynamics analysis of rotor bearing systems. The use of tilting-pad bearings is now a standard feature of many types of rotor systems. The concern for oil film excitation of the rotor lowest natural frequency is eliminated by the use of the tilting pad journal bearings. For new higher speed or larger low speed applications, the possibility of the pad flutter instability still remains and most commonly used design tools do not consider the pad inertia as a standard feature. In this paper, taking the Jeffcott rotor supported by two 4 pad bearings as an example, the influence of pad inertia and journal diameter were studied. The influence of shaft diameter and pad inertia was determined by the transient response of a simple rotor-bearing system operating over a wide design speed range. The tilting pad journal bearing oil-film force was calculated by a database method. The resulting nonlinear transient vibration is discussed using bifurcation diagrams, orbits, frequency spectrum plots, phase trajectories, and Poincare maps. The results directly show that journal diameter and pad inertia greatly influence the nonlinear vibrations of the journal and rotor center.

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Linear Theory ◽  
Lateral Force ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Rotating Disks ◽  
Critical Speeds ◽  
Applied Forces ◽  
Thin Disks

Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.

PI Control of HSFDs for Active Control of Rotor-Bearing Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 658-667 ◽  
Author(s):  
J. P. Hathout ◽  
A. El-Shafei
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Closed Loop ◽  
Rotating Machinery ◽  
Loop System ◽  
Pi Control ◽  
Closed Loop System ◽  
Transient Vibration ◽  
Critical Speeds ◽  
Rotor Bearing

This paper describes the proportional integral (PI) control of hybrid squeeze film dampers (HSFDS) for active control of rotor vibrations. Recently it was shown that the automatically controlled HSFD based on feedback of rotor speed can be a very efficient device for active control of rotor vibration when passing through critical speeds. Although considerable effort has been put into the study of steady-state vibration control, there are few methods in the literature applicable to transient vibration control of rotor-bearing systems. Rotating machinery may experience dangerously high dynamic loading due to the sudden mass unbalance that could be associated with blade loss. Transient run-up and coast down through critical speeds when starting up or shutting down rotating machinery induces excessive bearing loads at criticals. In this paper, PI control is proposed as a regulator for the HSFD system to attenuate transient vibration for both sudden unbalance and transient runup through critical speeds. A complete mathematical model of this closed-loop system is simulated on a digital computer. Results show an overall enhanced behavior for the closed-loop rotor system. Gain scheduling of both the integral gain and the reference input is incorporated into the closed-loop system with the PI regulator and results in an enhanced behavior of the controlled system.

Coupling of Rotor-Gear-Casing Vibrations During Extreme Operating Events

1992 ◽  
Vol 114 (4) ◽  
pp. 464-471 ◽  
Author(s):  
F. K. Choy ◽  
J. Padovan ◽  
Y. F. Ruan
Keyword(s):  
Element Model ◽  
Operating Conditions ◽  
Transient Vibration ◽  
Rotor Systems ◽  
Power Plant Equipment ◽  
Modal Synthesis ◽  
Operating Environments ◽  
Rotor Bearing ◽  
The Matrix ◽  
Plant Equipment

During extreme operating environments (i.e., seismic events, base motion-induced vibrations, etc.), the coupled vibrations developed between the rotors, bearings, gears and enclosing structure of gear-driven rotating equipment can be quite substantial. Generally, such large vibrational amplitudes may lead to failures in both the rotor-gearing system and/or the casing structure. This paper simulates the dynamic behavior of rotor-bearing-gear system resulting from motion of the enclosed structure. The modal synthesis approach is used in this study to synthesize the dynamics of the rotor systems with the vibrations of their casing structure in modal coordinates. Modal characteristics of the rotor-bearing-gear systems are evaluated using the matrix transfer technique, while the modal parameters for the casing structure are developed through a finite element model using NASTRAN. The modal accelerations calculated are integrated through a numerical algorithm to generate modal transient vibration analysis. Vibration results are examined in both time and frequency domains to develop representations for the coupled dynamics generated during extreme operating conditions. Typical three-rotor bull gear-driven power plant equipment (compressors, pumps, etc.) is used as an example to demonstrate the procedure developed.

Vibration of Bending-Torsion Coupled Resonance in a Rotor

2013 ◽  
Author(s):  
Hiroyuki Fujiwara ◽  
Tadashi Tsuji ◽  
Osami Matsushita
Keyword(s):  
Numerical Simulations ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Rotational Speed ◽  
Coupling Effect ◽  
The Other ◽  
Resonance Phenomenon ◽  
Horizontal Direction ◽  
Bending Vibration ◽  
Rotor Systems

In certain rotor systems, bending-torsion coupled resonance occurs when the rotational speed Ω (= 2π Ωrps) is equal to the sum/difference of the bending natural frequency ωb (= 2π fb) and torsional natural frequency ωθ(= 2πfθ). This coupling effect is due to an unbalance in the rotor. In order to clarify this phenomenon, an equation was derived for the motion of the bending-torsion coupled 2 DOF system, and this coupled resonance was verified by numerical simulations. In stability analyses of an undamped model, unstable rotational speed ranges were found to exist at about Ωrps = fb + fθ. The conditions for stability were also derived from an analysis of a damped model. In rotational simulations, bending-torsion coupled resonance vibration was found to occur at Ωrps = fb − fθ and fb + fθ. In addition, confirmation of this resonance phenomenon was shown by an experiment. When the rotor was excited in the horizontal direction at bending natural frequency, large torsional vibration appeared. On the other hand, when the rotor was excited by torsion at torsional natural frequency, large bending vibration appeared. Therefore, bending-torsion coupled resonance was confirmed.

scholarly journals Dynamics of a rotor system coupled with water-lubricated rubber bearings

2018 ◽  
Vol 232 (23) ◽  
pp. 4263-4277 ◽  
Author(s):  
YF Shi ◽  
M Li ◽  
GH Zhu ◽  
Y Yu
Keyword(s):  
Elastic Deformation ◽  
Dynamic Characteristics ◽  
Hydrodynamic Lubrication ◽  
Dynamic Performance ◽  
Elastohydrodynamic Lubrication ◽  
Rotor System ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Mass Unbalance ◽  
Rubber Bearings

Dynamic behaviour is significantly important in the design of large rotor systems supported on water-lubricated rubber bearings. In this study, the mathematical model of elastohydrodynamic lubrication of the bearing is established based on the theory of hydrodynamic lubrication after considering the elastic deformation of rubber, and the dynamic characteristics of water-lubricated rubber bearings are analysed under small perturbation conditions according to the load increment method and the finite difference method. Next, the differential equation of rotor systems coupled with the water-lubricated rubber bearing is deduced using Lagrange’s approach, and its critical speeds, stability, and unbalanced responses are analysed in detail. The numerical results show that several parameters, such as the eccentricity, length–diameter ratio, and clearance of bearing and the rotating speed of the rotor, have a great impact on the dynamic performance of water-lubricated rubber bearings, and this influence cannot be ignored, especially in the case of large eccentricity ratios. The dynamic characteristics of rotor systems guided by water-lubricated rubber bearings reveal that the critical speeds are much lower than the ones under the rigid supports because of the elastic deformation, and they also indicate that the rotor system supported on water-lubricated rubber bearings has a weaker stability. In addition, the steady-state responses of the rotor system are analysed when the mass unbalance of the propeller exists, and the effect of the thickness of the rubber liner is also considered.

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.

Internal Resonance Phenomena of the Jeffcott Rotor With Nonlinear Spring Characteristics

2004 ◽  
Vol 126 (4) ◽  
pp. 476-484 ◽  
Author(s):  
Yukio Ishida ◽  
Tsuyoshi Inoue
Keyword(s):  
Internal Resonance ◽  
Critical Speed ◽  
Nonlinear Phenomena ◽  
Nonlinear Analyses ◽  
Rotor Systems ◽  
Gyroscopic Moment ◽  
Resonance Phenomena ◽  
Jeffcott Rotor ◽  
The One ◽  
Two Degree Of Freedom

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>0 and that of a backward-whirling mode pb<0 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. Furthermore in many practical rotating machines, the effect of gyroscopic moments are relatively small. Therefore, the one-to-one internal resonance relationship holds approximately between forward and backward natural frequencies in such machinery. 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 a small gyroscopic moment. 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 that the usage of the Jeffcott rotor in nonlinear analyses of rotor systems may induce incorrect results.

A Design Technique for a Magnetic Bearing-Rotor in a Turbo Blower Considering Critical Speeds

2012 ◽  
Vol 569 ◽  
pp. 564-567
Author(s):  
Hoon Hyung Jung ◽  
Seung Hee Kang ◽  
Bang Hyun Cho ◽  
Chae Sil Kim
Keyword(s):  
Element Model ◽  
Magnetic Bearing ◽  
Design Technique ◽  
Loop Control ◽  
Critical Speeds ◽  
Rotor Systems ◽  
Turbo Blower ◽  
Bearing Stiffness ◽  
Control Forces ◽  
Stiffness And Damping

This paper introduces a rotor design technique for a turbo blower supported by magnetic bearings that considers the critical speeds of the rotor. An important factor for rotor critical speeds is the stiffness of its bearings. The magnetic bearing acts as a negative spring, called the position stiffness prior to operation, and rotor systems are initially unstable until the stiffness (current stiffness) and damping in the active control rotating system are determined using closed loop control forces. This paper describes a finite element model for the rotor, derives the stiffness equations for the magnetic bearing, and defines the total magnetic bearing stiffness including the position stiffness and current stiffness. Finally, the magnetic bearing stiffness that avoids the rotor critical speeds is chosen.

On the Problem of Spiralling in BTA Deep-Hole Machining

1994 ◽  
Vol 116 (2) ◽  
pp. 161-165 ◽  
Author(s):  
Y. B. Gessesse ◽  
V. N. Latinovic ◽  
M. O. M. Osman
Keyword(s):  
Natural Frequency ◽  
Experimental Approach ◽  
Deep Hole ◽  
Boring Bar ◽  
Critical Speeds ◽  
Standard Position ◽  
Boring Tool ◽  
Hole Machining

The phenomenon of spiralling or helical multi-lobe formation in holes, produced by the BTA (Boring and Trepanning Association) machining, is experimentally investigated for the solid boring tool. The causes leading to spiralling are deduced from this investigation. The experimental approach pursued in exploring the problem involved the running of the machine, at analytically predicted critical speeds and observing the reoccurrence of the phenomenon. It has been established that sprialling is caused by defectiveness of the tool (radial oversize of the circle-land with respect to the leading pad around the circumference) and the coincidence of the lateral natural frequency of the boring bar-tool asssembly, with five cycles per revoution of the tool, relative to the workpiece. It has also been established that spiralling occurs only in five lobes for the commercially available BTA-solid tool and is a consequence of the standard position of the circle-land, relative to the leading pad. The trials are repeated a number of times with various workpiece materials, to assert validity of the observations.

Sign in / Sign up

Export Citation Format

Share Document