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.

Interrogating the Lead-up to a Critical Speed in Rotordynamics

2021 ◽  
pp. 1-18
Author(s):  
Lawrie Virgin
Keyword(s):  
Critical Speed ◽  
Stress Test ◽  
Equations Of Motion ◽  
Rotating Shaft ◽  
Small Perturbations ◽  
New Approach ◽  
Naturally Occurring ◽  
Jeffcott Rotor ◽  
Random Disturbances ◽  
Rotor Model

Abstract This paper presents a new approach to predicting an incipient critical speed in a rotating shaft. Based on the classical governing equations of motion for an eccentric mass on a flexible shaft (the Jeffcott rotor model), the approach is centered on examining the behavior of small perturbations or random disturbances to infer the approach of a critical speed (resonance). Such disturbances, that may be based on intentional probing, or simply the result of naturally occurring fluctuations, cause small transients. It is the changing nature of these transients (as characterized by their associated eigenvalues) that is used to assess the proximity to a critical speed. In this paper the material developed is based on analysis, but generating the data from simulations or experiments will be the next step. The approach is a kind of stress-test, conceptually not dissimilar to structural health monitoring and damage detection, but here directed toward the lead-up to resonance.

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.

Influence of Acceleration on the Critical Speed of a Jeffcott Rotor

1981 ◽  
Vol 103 (1) ◽  
pp. 108-113 ◽  
Author(s):  
H. L. Hassenpflug ◽  
R. D. Flack ◽  
E. J. Gunter
Keyword(s):  
Numerical Integration ◽  
Critical Speed ◽  
Equations Of Motion ◽  
Beat Frequency ◽  
Angular Acceleration ◽  
Amplitude Response ◽  
Peak Response ◽  
High Acceleration ◽  
Jeffcott Rotor ◽  
Theoretical Predictions

The effects of angular acceleration on a Jeffcott rotor have been examined both theoretically and experimentally. The equations of motion were solved via numerical integration. The rotor’s response to unbalance was predicted for a number of cases of acceleration and damping. Both amplitude and phase responses were studied. In addition, techniques were developed for identifying system damping from data taken during accelerated runs. The results of the analysis indicate that for high acceleration rates the amplitude response at the critical speed may be reduced by a factor of four or more. The speed at which the peak response occurs can also be shifted by 20 percent or more. Experimentally, a small lightly damped rotor (ζ = 0.0088) was run for several acceleration rates. The peak responses typically agree within 6 percent of theoretical predictions. Also, a beat frequency was observed both theoretically and experimentally after the rotor had passed through the critical speed.

Dynamics of a hydropower generator subjected to unbalanced magnetic pull

2011 ◽  
Vol 225 (9) ◽  
pp. 2076-2088 ◽  
Author(s):  
Y Calleecharan ◽  
J-O Aidanpää
Keyword(s):  
Periodic Motion ◽  
Critical Speed ◽  
Radial Component ◽  
Electrical Machines ◽  
External Forcing ◽  
New Model ◽  
Unbalanced Magnetic Pull ◽  
Wide Range ◽  
Jeffcott Rotor ◽  
Rotor Model

Eccentricity leading to unbalanced magnetic pull (UMP) in electrical machines is a significant concern in industry. The UMP is known to be composed of two components: a radial component and a tangential one. Models that are used in industry tend to include the radial component alone. In this article, a Jeffcott rotor model together with a new UMP model that incorporates both radial and tangential UMP constituents is studied for an industrial hydropower generator. Characterizing the UMP as springs permits the model to inherit UMP stiffness contribution. Interesting dynamics are observed with the new model for a wide range of external forcing frequencies. It is shown firstly that the new UMP model is sensitive to forcing frequency in the rotor movements. Secondly, it is found that this sensitivity to forcing frequency increases with decreasing rotor system stiffness. Moreover, quasi-periodic motion in the rotor displacements is observed and it is noted that the rotor does not need to be forced by frequencies above its critical speed for this less desirable motion to occur. Thus, it becomes interesting to be able to account for the UMP stiffness contribution in order to curb machine malfunction which might result from these UMP forces.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

scholarly journals Seismic Assessment of 10-Story Building Using Tuned Mass Damper

2020 ◽  
Author(s):  
Mohammad Aghajani Delavar
Keyword(s):  
Frequency Tuning ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Tuned Mass Dampers ◽  
Earthquake Excitation ◽  
Optimum Parameters ◽  
Seismic Records ◽  
Structural Responses ◽  
Lateral Displacements ◽  
Shear Building

In this paper, optimum parameters of Tuned Mass Dampers (TMD) are considered to control the responses of 10-story shear building under harmonic loading and 22 set of seismic records of FEMA-P695. The criterion used to obtain the optimum parameters is to select mass ratio, the frequency (tuning) and damping ratio that would result in smallest lateral displacements. State-space equations of motion are presented to compute the structural responses by developing a MATLAB file. A 10-story shear building is presented as a case study to assess the effects of TMDs on the multi-story structures. The results indicate that using TMD can reduce structural responses up to the average 20% under earthquake excitation and up to 90% under harmonic loadings. TMDs are not always effective under any type of ground motion; therefore, being aware of the given location is significant to design TMDs properly.

scholarly journals Dynamical analysis of hollow-shaft dual-rotor system with circular cracks

2020 ◽  
pp. 146134842094828
Author(s):  
Yang Yongfeng ◽  
Wang Jianjun ◽  
Wang Yanlin ◽  
Fu Chao ◽  
Zheng Qingyang ◽  
...  
Keyword(s):  
Critical Speed ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Circular Crack ◽  
Rotor System ◽  
Resonance Phenomenon ◽  
Dynamical Analysis ◽  
Dynamical Response ◽  
Critical Speeds ◽  
Hollow Shaft

In this paper, we considered a dual-rotor system with crack in shaft. The influence of circular crack in hollow shaft on dynamical response was studied. The equations of motion of 12 elements dual-rotor system model were derived. Harmonic balance method was employed to solve the equations. The critical speed and sub-critical speed responses were investigated. It was found that the circular crack in hollow shaft had greater influence on the first-backward critical speed than the first-forward critical speed. Owing to the influence of crack, the vibration peaks occurred at the 1/2, 1/3 and 1/4 critical speeds of the rotor system, along with a reduction in sub-critical speeds and critical speeds. The deeper crack away from the bearing affected the rotor more significantly. The whirling orbits, the time-domain responses and the spectra were obtained to show the super-harmonic resonance phenomenon in hollow-shaft cracked rotor system.

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 On the Role of Nonsynchronous Rotating Damping in Rotordynamics

2000 ◽  
Vol 6 (6) ◽  
pp. 467-475 ◽  
Author(s):  
Giancarlo Genta ◽  
Eugenio Brusa
Keyword(s):  
General Model ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
System Parameters ◽  
Spin Speed ◽  
Rotating Systems ◽  
Jeffcott Rotor ◽  
The Stability ◽  
Rotor Model

Nonsynchronous rotating damping, i.e. energy dissipations occurring in elements rotating at a speed different from the spin speed of a rotor, can have substantial effects on the dynamic behaviour and above all on the stability of rotating systems.The free whirling and unbalance response for systems with nonsynchronous damping are studied using Jeffcott rotor model. The system parameters affecting stability are identified and the threshold of instability is computed. A general model for a multi-degrees of freedom model for a general isotropic machine is then presented. The possibility of synthesizing nonsynchronous rotating and nonrotating damping using rotor- and stator-fixed active dampers is then discussed for the general case of rotors with many degrees of freedom.

Application of the POD Method for Cracked Rotors

2017 ◽  
Author(s):  
Ayesha Al Mehairi ◽  
Mohammad A. AL-Shudeifat ◽  
Shadi Balawi ◽  
Adnan S. Saeed
Keyword(s):  
Covariance Matrices ◽  
Cracked Rotor ◽  
Force Vector ◽  
Highly Sensitive ◽  
Jeffcott Rotor ◽  
Unbalance Force ◽  
Proper Orthogonal ◽  
Integration Response ◽  
Cracked Rotor System ◽  
Rotor Model

The application of the proper orthogonal decomposition (POD) method to the vibration response of a cracked Jeffcott rotor model is investigated here. The covariance matrices of horizontal and vertical whirl amplitudes are formulated based on the numerical integration response and the experimental whirl response, respectively, for the considered cracked rotor system. Accordingly, the POD is directly applied to the obtained covariance matrices of the numerical and experimental whirl amplitudes where the proper orthogonal values (POVs) and the proper orthogonal modes (POMs) are obtained for various crack depths, unbalance force vector angles and rotational speeds. It is observed that both POVs and their corresponding POMs are highly sensitive to the appearance of the crack and the unbalance angle changes at the neighborhoods of the critical. The sensitivity zones of the POVs and POMs to the crack propagation coincide with the unstable zones of the cracked system obtained by Floquets theory.

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