Lateral Rotordynamic Analysis of a Large Alternator/Flywheel/Motor Train

2010 ◽  
Author(s):  
Jawad Chaudhry ◽  
Tim Dimond ◽  
Amir Younan ◽  
Paul Allaire
Keyword(s):  
Critical Speed ◽  
Operating Speed ◽  
Response Level ◽  
Critical Speeds ◽  
The Third ◽  
Unbalance Response ◽  
Speed Range ◽  
Stress Levels ◽  
Full Speed ◽  
Working Day

A large alternator/flywheel/motor train is employed as part of the power system for the ALCATOR C-MOD experiment at the MIT Plasma Fusion Center. The alternator is used to provide peak pulse power of 100 MW to the magnets employed in the fusion experiment. The flywheel diameter is 3.3m and the alternator is 1.8 m in diameter. After being driven up to full speed over a long period of time by a 1491 kW motor, the alternator is rapidly decelerated from approximately 1800 rpm to 1500 rpm during a 2 second interval. This sequence is repeated about six times per working day on average. A full lateral rotordynamic analysis of the including the rotors, fluid film bearings and unbalanced motor magnetic force was carried to assess the effects of rotor modifications in the alternator shaft bore. This paper provides a more detailed analysis of a complicated rotor train than is often performed for most rotors. Critical speeds, stability and unbalance response were evaluated to determine if lateral critical speeds might exist in the operating speed range in the existing or modified rotor train and if unbalance levels were within acceptable ranges. Critical speeds and rotor damping values determined for the rotor system with the existing and modified rotor. The first critical speed at 1069 rpm is an alternator mode below the operating speed range. The second critical speed is also an alternator mode but, at 1528 rpm, is in the rundown operating speed range. The third critical speed is a flywheel mode at 1538 rpm, also in the rundown operating speed range but well damped. The predicted highest rotor amplitude unbalance response level is at 1633 rpm, again in the operating speed range. Direct comparisons were made with measured bearing temperature values, with good agreement between calculations and measurements. Stress levels in the rotor were evaluated and found to be well below yield stress levels for the material for both original and modified rotors. Comparisons we carried out between standard vibration specifications and measured vibration levels which indicated that the third critical speed amplification factors were much higher than API standards indicate they should have been. Corrective actions to reduce unbalance were taken for the modified rotor.

Sensitivity of the Spool Rate on the Dynamic Response of the System

2021 ◽  
Author(s):  
Arnab Das ◽  
Praveen Iyappan ◽  
Srinivas Chinthapally ◽  
Avinash Kumar
Keyword(s):  
Natural Frequency ◽  
Critical Speed ◽  
System Response ◽  
Operating Speed ◽  
Static Structure ◽  
Critical Speeds ◽  
Structure Response ◽  
Full Speed ◽  
Major Factors ◽  
Engine Start

Abstract In rotodynamic systems, the rotor is spooled up from zero speed to its operating speed during the engine start. One of the considerations in design of rotating systems is the placement of rotor critical speed. It is vital to ensure that the rotor critical speeds are not close to the engine operating speed. However, it is not always possible to isolate all the frequencies above the operating speed. So, during the engine start to full speed, rotor system does travel through the mode. Therefore, to avoid a large system response, the rotor is spooled up quickly through the critical speed. In addition to the rotor critical speeds, the natural frequencies of the static structures may also get excited during the rotor spool up and spool down. The static structure response is one of the important considerations in designing a system for dynamic loading condition. It has been observed that the rotor spool rate affects the static structure response. This paper focuses on effect on system’s response under various spool rate. It has also been shown that the natural frequency of the system and damping in the system are two of the major factors towards sensitivity of system response with spool rate. Additionally, it has been observed that the presence of non-linearities shifts the peak response away from the natural frequency depending on the spool rate and spool direction.

Lund’s Contribution to Rotor Stability: The Indispensable and Fundamental Basis of Modern Compressor Design

2001 ◽  
Author(s):  
Edgar J. Gunter
Keyword(s):  
Critical Speed ◽  
Space Shuttle ◽  
Numerical Procedure ◽  
Complex Eigenvalue ◽  
Critical Speeds ◽  
Complex Roots ◽  
Full Speed ◽  
Order Of Magnitude ◽  
Excitation Mechanisms ◽  
Turbine Design

Abstract In the early design of compressors and turbines, it was of importance to locate the rotor critical speeds so as to insure that a turbo rotor would not be operating at a critical speed. As compressor and turbine design became more sophisticated, a more detailed analysis of the rotor damped critical speeds and rotor log decrements was necessary. With compressors and turbines operating at higher speeds, under high power levels, and at multiples of the first critical speed, the problem of stability or self-excited whirling is of paramount importance. The onset of self-excited motion may lead to large amplitudes of motion with possible destructions of the rotor or the inability of the compressor to operate at peak power levels. Encountering this phenomenon with a compressor on an off-shore oil platform can mean millions of dollars of lost production. Self-excited whirling can be caused by fluid-film bearings, seals, Alford-type cross-coupling forces, or internal shaft friction, to name a few of the excitation mechanisms. The problem of computing the approximate values of the rotor log decrement under full speed and loading conditions requires the solution of a complex eigenvalue problem. The computation of the rotor complex roots is an order of magnitude more difficult than the problem of undamped critical speed calculations. J. W. Lund presented the first practical numerical procedure for computing turbo-rotor log decrements. The mathematical transfer matrix method pioneered by Lund has allowed industry to develop and stabilize a vast array of rotating machinery leading to the savings to industry of millions of dollars. Without the procedures of Lund, for example, it would not have been possible to resolve stability problems encountered with both the hydrogen and oxygen space shuttle pumps. This paper briefly presents some of the attributes of the Lund stability procedure and its unique characteristics.

Experimental Evaluation of Multiplane-Multispeed Rotor Balancing Through Multiple Critical Speeds

1976 ◽  
Vol 98 (3) ◽  
pp. 988-998 ◽  
Author(s):  
J. M. Tessarzik ◽  
R. H. Badgley ◽  
D. P. Fleming
Keyword(s):  
Experimental Tests ◽  
Influence Coefficient ◽  
Critical Speeds ◽  
Vibration Data ◽  
Vibration Sensors ◽  
Flexible Rotors ◽  
Speed Range ◽  
Full Speed ◽  
Influence Coefficient Method ◽  
Rotor Balancing

Experimental tests have been conducted to further demonstrate the ability of the Influence Coefficient Method to achieve precise balance of flexible rotors of virtually any design for operation through virtually any speed range. Four distinct practical aspects of flexible-rotor balancing were investigated in the present work: (1) Balancing for operation through multiple bending critical speeds; (2) balancing of rotors mounted in both rigid and flexible bearing supports, the latter having significantly different stiffnesses in the horizontal and vertical directions so as to cause severe ellipticity in the vibration orbits; (3) balancing of rotors with various amounts of measured vibration response information (e.g., numbers of vibration data sets, and numbers and types of vibration sensors), and with different number of correction planes; (4) balancing of rotors with different (though arbitrary) initial unbalance configurations. Tests were made on a laboratory quality machine having a 122-cm (48-in.) long rotor weighing 50 kg (110 lb) and covering a speed range up to 18,000 rpm. The balancing method was found in every instance to be effective, practical, and economical, permitting safe rotor operation over the full speed range covering four rotor bending critical speeds.

scholarly journals Actively Controlled Bearing Dampers for Aircraft Engine Applications

1999 ◽  
Author(s):  
John M. Vance ◽  
Daniel Ying ◽  
Jorgen L. Nikolajsen
Keyword(s):  
Critical Speed ◽  
Aircraft Engine ◽  
Viscous Damping ◽  
Aircraft Engines ◽  
Equivalent Viscous Damping ◽  
Critical Speeds ◽  
Speed Range ◽  
Coulomb Type ◽  
Er Damper ◽  
San Andres

This paper describes some of the requirements for bearing dampers to be used in an aircraft engine and briefly discusses the pros and cons of various types of dampers that were considered as candidates for active control in aircraft engines. A disk type of electrorheological (ER) damper was chosen for further study and testing. The paper explains how and why the choice was made. For evaluating potential applications to aircraft engines, an experimental development engine (XTE-45) was used as an example for this study. Like most real aircraft engines, the XTE-45 ran through more than one critical speed in its operating speed range. There are some speeds where damping is desirable and other speeds where it is not. Thus, the concept of a damper with controllable forces appears attractive. The desired equivalent viscous damping at the critical speeds along with the available size envelope were two of the major criteria used for comparing the dampers. Most previous investigators have considered the ER damper to produce a purely Coulomb type of damping force and this was the assumption used by the present authors in this study. It is shown in a companion paper (Vance and San Andres, 1999), however, that a purely Coulomb type of friction cannot restrain the peak vibration amplitudes at rotordynamic critical speeds and that the equivalent viscous damping for rotordynamics is different from the value derived by previous investigators for planar vibration. Control laws for Coulomb damping are derived in Vance and San Andres, (1999) to achieve minimum rotor vibration amplitudes in a test rig while avoiding large bearing forces over a speed range that includes a critical speed. The type of control scheme required and its effectiveness was another criterion used for comparing the dampers in this paper.

Multilevel Optimization of the Geared Rotor-Bearing System for Multi-Objectives With Critical Speed Constraints

2004 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
W. B. Lu
Keyword(s):  
Critical Speed ◽  
Transmission Error ◽  
Mesh Stiffness ◽  
Error Response ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Unbalance Response ◽  
Multilevel Algorithm ◽  
Gear Mesh Stiffness ◽  
Bearing System

This paper presents the multi-objective optimization of a geared rotor-bearing system with the critical speeds constraints by using an efficient multilevel algorithm. The weight of each rotor shaft, the unbalance response, and the response due to the transmission error are minimized simultaneously under the critical speed constraints. The design variables are the inner radii of the shaft, the stiffness of bearings, and the gear mesh stiffness. The finite element method (FEM) is employed to analyze the dynamic characteristics and the method of feasible direction (MFD) is applied in the optimization of the single objective stage. Based on the sensitivity analysis that gear mesh stiffness has almost no influences on the critical speeds of the uncoupled modes of two shafts, an efficient multilevel algorithm composed of system and subsystem levels is developed. In the cycle of iteration, the minimization of the shaft weight is performed in the subsystem level with the critical speed constraints of only uncoupled modes of two shafts and the unbalance response and the transmission error response are reduced in the system level with the critical speed constraints of only coupled modes. It is indicated from the numerical results that the shaft weight, the unbalance response, and the transmission error response via the multilevel technique (ML) are all reduced much more than those via the weighting method (WM) and the goal programming method (GPM).

Lund’s Contribution to Rotor Stability: The Indispensable and Fundamental Basis of Modern Compressor Design

2003 ◽  
Vol 125 (4) ◽  
pp. 462-470 ◽  
Author(s):  
Edgar J. Gunter
Keyword(s):  
Critical Speed ◽  
Space Shuttle ◽  
Numerical Procedure ◽  
Complex Eigenvalue ◽  
Critical Speeds ◽  
Complex Roots ◽  
Full Speed ◽  
Order Of Magnitude ◽  
Excitation Mechanisms ◽  
Turbine Design

In the early design of compressors and turbines, it was of importance to locate the rotor critical speeds so as to insure that a turbo rotor would not be operating at a critical speed. As compressor and turbine design became more sophisticated, a more detailed analysis of the rotor damped critical speeds and rotor log decrements was necessary. With compressors and turbines operating at higher speeds, under high power levels, and at multiples of the first critical speed, the problem of stability or self-excited whirling is of paramount importance. The onset of self-excited motion may lead to large amplitudes of motion with possible destructions of the rotor or the inability of the compressor to operate at peak power levels. Encountering this phenomenon with a compressor on an off-shore oil platform can mean millions of dollars of lost production. Self-excited whirling can be caused by fluid-film bearings, seals, Alford-type cross-coupling forces, or internal shaft friction, to name a few of the excitation mechanisms. The problem of computing the approximate values of the rotor log decrement under full speed and loading conditions requires the solution of a complex eigenvalue problem. The computation of the rotor complex roots is an order of magnitude more difficult than the problem of undamped critical speed calculations. J. W. Lund presented the first practical numerical procedure for computing turbo-rotor log decrements. The mathematical transfer matrix method pioneered by Lund has allowed industry to develop and stabilize a vast array of rotating machinery leading to the savings to industry of millions of dollars. Without the procedures of Lund, for example, it would not have been possible to resolve stability problems encountered with both the hydrogen and oxygen space shuttle pumps. This paper briefly presents some of the attributes of the Lund stability procedure and its unique characteristics.

Prediction and Comparison of Critical Speeds and Potential Excitation Using In-House Developed Software for an Integrally Geared Centrifugal Air Compressor

2014 ◽  
Author(s):  
Mathew P. James ◽  
Pavan Kumar Reddy Pandillapalli ◽  
Swaminathan Gopalakrishnan
Keyword(s):  
Steady State ◽  
Computer Program ◽  
Critical Speed ◽  
Maximum Amplitude ◽  
Sound Intensity ◽  
Industrial Applications ◽  
Lateral Direction ◽  
Critical Speeds ◽  
Vibration Data ◽  
Unbalance Response

Integrally Geared Centrifugal Air Compressors (IGCAC) are becoming popular in many industrial applications. Development of such compressors requires in depth Rotordynamic Design and Analysis. To facilitate this, an in-house computer program based on transfer matrix method was developed using MATLAB® software. This computer program is capable of computing rotordynamic parameters such as static deflection, critical speed and interference diagram, and can output critical speed map, mode shape, unbalance response, orbit, for lateral direction. This software was used to analyze a two stage IGCAC with two impellers on a simply supported rotor running above second critical speed, driven by a two pole induction motor through a step-up gearbox. Undamped critical speed map, an output from the program was used to predict intended bearing stiffness for design. Using the above data and commercially available software DyRoBeS© a suitable bearing was designed. The speed dependent bearing characteristics, an output from DyRoBeS©, were used to determine damped unbalance response plot for a given residual unbalance. Corresponding to a maximum peak in unbalance response the damped critical speed and amplification factors (AF) were found out. The results from the newly developed software were compared with prediction from DyRoBeS©. It was found that critical speed was within 5% and AF was of the same order. Results from in-house software were comparable to that from DyRoBeS©. Based on the guidelines from API 684, the AF and separation margins were determined. A prototype IGCAC compressor as described above was built and tested. The testing included the collection of steady state, coast-up and coast-down data. Using the coast-up, coast-down data, a Bode plot was created. From this the critical speeds and AF’s were determined and compared with results from in-house software. It was found there was an error of less than 5% for the critical speed and around 5% for AF from the predicted results. For the same compressor a study on the potential excitation frequencies due to unbalance, impeller-diffuser and impeller-scroll tongue interactions were calculated. FFT of the steady state vibration data was deduced. It was found that the calculated frequency and measured frequency at maximum amplitude were aligning. Further noise measurements were recorded based on sound intensity as per guidelines in ISO 9614. The impeller-tongue interaction frequencies for stages were seen in the processed noise data. It was found that the predictions were in good agreement with the test results.

Rotordynamic Analysis of a Rotor-Disk System Including a Synchronously Reduced Modal Truncation Method

2013 ◽  
Author(s):  
Timothy Dimond ◽  
Jawad Chaudhry ◽  
Matthew Wagner ◽  
Feng He ◽  
Jianming Cao ◽  
...  
Keyword(s):  
Critical Speed ◽  
Mode Shapes ◽  
Complete Analysis ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Euler Beam ◽  
Critical Speeds ◽  
Unbalance Response ◽  
Rotor Bearing ◽  
Modal Truncation

There are many published works on rotordynamics which detail the types of analyses that are carried out: critical speeds, stability assessment, and forced response. The purpose of this paper is to present a more complete analysis of an existing, academic rotor/bearing model, taken from a textbook, more like it would be carried out in an industrial setting. The advantage is that all parameters of the rotor model are well known so that there are minimal uncertainties. However, some published papers on rotordynamics, as discussed in this work, present an incomplete analysis. For example, they may report the calculated critical speeds but leave out the critical speed plot and mode shapes in favor of the Campbell diagram. They may model a Bernoulli Euler beam model of the shaft and neglect the additional terms in the Timoshenko beam model. These papers may show some unbalance response plots for one disk in the model but not report on the amplification factor. This paper gives a much more complete rotordynamics analysis of this common rotor/bearing model than other works. The full undamped rotor analysis is presented, including critical speeds, critical speed map, and undamped mode shapes. The stability analysis presents the full set of eigenvalues including both forward and backward modes as well as the complex mode shapes. The differences between the Bernoulli Euler beam model and the full Timoshenko beam model are shown for this rotor. Full unbalance response plots, in the horizontal and vertical directions, are presented as well as the response along the semi-major axis. The unbalance response plots have calculated amplitudes, phase angles and amplification factors. In addition to the standard rotordynamic analyses, a synchronously reduced modal truncation method is presented. This method is better suited to automation, when compared to most truncation methods that require significant intervention by the analyst. The maximum error was on the order of 0.01%. It is hoped that future publications will present the more complete analysis shown for this rotor/bearing system.

Calculations and Experiments on the Unbalance Response of a Flexible Rotor

1967 ◽  
Vol 89 (4) ◽  
pp. 785-796 ◽  
Author(s):  
J. W. Lund ◽  
F. K. Orcutt
Keyword(s):  
Critical Speed ◽  
Distributed Parameter ◽  
Distributed Parameter System ◽  
Flexible Rotor ◽  
Parameter System ◽  
Damping Coefficients ◽  
The Third ◽  
Tilting Pad ◽  
Speed Range ◽  
Bearing System

The results of a combined analytical and experimental investigation of the unbalance vibrations of a rotor are presented. The analysis applies to a general rotor-bearing system in which the dynamic bearing forces are represented by four spring coefficients and four damping coefficients. The rotor can be represented as either a lumped or a distributed parameter system, and gyroscopic moments are included. In general, the unbalance whirl motion of the rotor will be elliptical. The analysis has been programmed for a digital computer to obtain results for comparison with the experimental data. The test rotor is a uniform, flexible shaft with heavy wheels mounted at the ends and in the middle. The rotor is supported in two silicone fluid-lubricated, tilting-pad bearings. The rotor amplitude caused by an induced unbalance has been measured over a speed range of 3000 to 24,000 rpm for three different rotor configurations, obtained by removing one or both end wheels. This speed range extends to or through the third critical speed for each of the rotor configurations. The results are compared with the theoretical values and, in general, the agreement is found to be good.

Zero (Or Low) Torsional Stiffness Couplings

1969 ◽  
Vol 11 (1) ◽  
pp. 76-87 ◽  
Author(s):  
C. W. Chapman
Keyword(s):  
The Other ◽  
Torsional Stiffness ◽  
Operating Speed ◽  
Critical Speeds ◽  
Operating Range ◽  
Rotating Systems ◽  
Speed Range ◽  
Coupling Stiffness

In many rotating systems shaft couplings of low torsional stiffness may bring dangerous one node critical speeds below the operating speed range. However, even soft couplings on multi-mass systems may allow higher node criticals to remain in the operating range. If two sections of a system be coupled by a coupling of zero stiffness torsional impulses cannot be transmitted from one section to the other, thus eliminating criticals. Coupling stiffness must be related to the torque transmitted, and experiments indicate that a stiffness/torque ratio below about 4 is almost as effective as zero stiffness.

Sign in / Sign up

Export Citation Format

Share Document