Showing papers on "Critical speed published in 1985"

Forces on Centrifugal Pump Impellers

Abstract: Forces are exerted on a centrifugal pump impeller, due to the asymmetry of the flow caused by the volute of diffuser, and to the motion of the center of the impeller whenever the shaft whirls. Recent work in the measurement of these forces as a function of the whirl speed to shaft speed ratio, and the influence of the volute, is reviewed. These forces may be decomposed into a steady force, a static stiffness matrix, a damping matrix and an inertia matrix. It is shown that for centrifugal pumps of the moderate specific speed typical of boiler feed stages, there is a region of potential shaft vibration excitation from the hydrodynamic forces if the operating speed is well above the first flexural critical speed.

Investigation of the Steady-State Response of a Dual-Rotor System With Inter-Shaft Squeeze Film Damper

Abstract: This paper presents an analysis of the steady-state unbalance response of a dual-rotor gas turbine engine with a flexible intershaft squeeze film damper using a simplified transfer matrix method. The simplified transfer matrix method is convenient for the evaluation of the critical speed and response of the rotor system with various supports, shaft coupling, intershaft bearing, etc.The steady-state unbalance response of the rotor system is calculated for different shaft rotation speeds. The damping effects of an intershaft squeeze film damper with different radial clearances under various levels of rotor unbalance are investigated.Copyright © 1985 by ASME

Thermal Effect on the Transverse Vibration of High-Speed Rotating Anisotropic Disk

Abstract: An attempt has been made to consider the thermal effect on the transverse vibration of a high-speed rotating disk in a steady-state heat conduction. The material of the disk, in this case, is assumed to be thermomechanically anisotropic. The present attempt is made with an objective to provide some theoretical studies on the problem that may serve as a base from which more detailed investigations with regard to the usage of composite material may be attempted to gain new andneeded design information regarding turbine disks and thereby to reduce the chances of turbine failure. In this connection a new critical speed of disk rotation has been obtained and consequently this critical speed is found to depend on central temperature, thermomechanical anisotropy, and so forth. 19 references.

Critical Speed Analysis Of An Eight-Stage Centrifugal Pump

Abstract: Kenneth E. Atkins is a Project Engineer A critical speed and unbalance response analysis of an with Engineering Incoreight-stage centrifugal pump was performed, considering the ~orated, and has in perfomvariation of stiffness and damping coefficients with speed for l ing lateral and torsional critical speeds, both the oil film bearings and the fluid seals (interstage, neck rotor stability and the evaluation ring and balance piston). The rotor response to unbalance was of structural problems using fipredicted and compared to measured test stand data, utilizing nite element He has been four different methods to estimate the fluid seal effects. The tively in field troubleshooting of comparison showed that correlation was best when using the a wide Variety of rotord~namicsl structurlatest finite length seal procedures. The wide variation in predictand piping vibrations. He has a ES. ed critical speeds and response amplitudes indicates the need degree in Engineering Science from Tiit+ for additional research in this area, to define the exact stiffness ty University and is a registered professional engineer in the and damping values for fluid film seals, State of Texas. James D. Tison is a Project Engineer with Engineering Dynamics, lncorporated. He is active in solving major industrial vibration problems in the power and petrochemical industries, utilizing field measurement and computer rnodeling techniques. He has developed and applied computer codes in the areas of torsional and lateral critical speeds, lateral instabilities, balancing, reciprocating equipment, crankshaft and frame loading and structural vibration. He has B.S. and M.E. degrees in Mechanical Engineering from the University of Florida. He is a member of ASME and Pi Tau Sigma. J. C. (Buddy) Wachel is President of Engineering Dynamics, Incorporated, an independent engineering consulting fim. He has over25 years of experience in the field of vibration analysis and has solved vibration problems worldwide. He has published over 30 technical papers in rotordynamics, piping vibrations and acoustics. He holds B.S. and MS. degrees in Mechanical Engineering from the University of Texas. He is a member of ASME, PI Tau Sigma and Tau Beta Pi and is a registered professional engineer in the State of Texas. INTRODUCTION The importance of analyzing the lateral critical speed of rotating equipment in the design stage is well known. The cost of downtime and maintenance caused by high lateral vibration in rotating equipment far exceeds the cost of a careful rotordynamic analysis. Although the state-of-the-art of lateral critical speed analysis has progressed greatly in the last few decades, the challenge of accurate simulation of pump rotor response and stability is the subject of a continuing research effort. Pump rotordynamics are dependent on a greater number of design variables than are many other types of rotating equipment. Besides the journal bearing and shaft characteristics, the dynamic characteristics of the seals and the impellerdiffuser interaction can have significant effects on the critical speed location, rotor unbalance sensitivity, and rotor stability. Unfortunately, the accuracy of computations of stiffness and damping properties for seals and impeller effects is questionable even when all the state-of-the-art capabilities are included. The high pressure turbo-pumps of the space shuttle main engine are a prime example of the difficulty in accurately modelling seal effects [I]. For modelling purposes, seals can be treated as bearings in the sense that direct and cross-coupled stiffness and damping properties can be calculated based on the seal's hydrostatic and hydrodynamic properties. Seal clearances, geometry, pressure drop, fluid properties, inlet swirl, surface roughness and shaft speed are all important in these calculations. Since the pressure drop across seals increases approximately with the square of the pump speed, the seal stiffness also increases with the square of the speed. This increasing stiff~ess effect is often thought of as a "negative" mass effect, which is usually referred to as the "Lomakin effect or the "Lomakin mass" [2]. In some cases the 60 PROCEEDINGS O F THE SECOND INTERNATIONAL PUMP SYMPOSIUM theoretical Lomakin mass or stiffness effect can be of sufficient magnitude to prevent the critical speed of the rotor from ever being coincident with the synchronous speed. Adequate experimental data exist today to document that the analytical procedures used for simulating the rotor response and stability of compressors and turbines are sufficiently accurate to predict critical speeds and potential instabilities from the design information. This analysis is not available for pumps, however-especially for pumps which use grooved seals, labyrinth seals, or screw type seals with several leads. The accurate prediction of the stiffness and damping properties of seals for different geometries and operating conditions is a subject of ongoing research [3,4,5]. The basic theories presented by Black [6] have been modified to account for finite length seals, inlet swirl, surface roughness, and other important parameters. However, a universally accepted procedure to accurately predict seal properties is not available for all the types of seals that are in use today. This is particularly true for grooved seals. If the seal effects are not correctly modelled, calculated critical speeds can be significantly different from actual critical speeds. The rotordynamic analysis of an eight-stage centrifugal pump which utilized serrated (grooved) seals is discussed. Using the corrections for serrated seals as suggested by Black and Cochrane [7], the first critical speed was calculated to be above the running speed of 3550 rprn. When the shop acceptance tests were made on the pump, peak vibration responses occuring at as low as 1500 rpm were measured. The calculated critical speed of the pump varied from 1700 to 6000 rpm, depending upon which theory was used to develop the seal stiffness and damping coefficients. This example illustrates the need for additional research in this area. CRITICAL SPEED ANALYSIS Critical Speed Map-No Seal Effects The first step in a rotordynamic analysis of a pump is to model the basic rotor, using the lumped parameter techniques. A sketch of the rotor with the location of the seals and bearings is given in Figure 1. Even though the bearings and seals add considerable cross-coupling and damping, the authors have found that it is still desirable to generate an undamped critical speed map to establish the range of the undamped (dry) critical speeds. Figure 1. Pump Rotor Model Showing Locations of All Eleven Effective Bearings. After the undamped critical speed map is developed, the bearings are analyzed to calculate the stiffness and damping characteristics over the entire speed range of operation. The bearing stiffness and damping characteristics can be simulated by using eight coefficients representing the direct and crosscoupled stiffness and damping terms for the specific values of oil viscosity, speed, diameter and length of bearing, clearance, and load (Sommerfeld number). Generally, bearing properties are calculated at small speed increments from the minimum to the maximum speed. These values are used when the forced vibration response analysis is performed so that accurate predictions of the critical speeds can be obtained. Bearing characteristics that are assumed to be independent of speed should not be used, since this can result in incorrect predictions of the critical speeds. The major axis bearing stiffness curves (K,, and K,,) are usually plotted on the undamped critical speed map, so that the location of the pump critical speeds for no seals (or extremely worn seals) can be estimated. The journal bearings for the eightstage pump were five-shoe load-between-pad pivotted shoe bearings. The assembled clearance range analyzed was five to eight mils diametrical for a preload value of 0.2. The critical speed map for the "dry rotor" model. i.e.. no supports considered at the seals, is shown in Figure 2. The first four undamped lateral critical speeds are plotted versus the bearing support stiffness. Horizontal and vertical journal bearing stiffness curves (K,, and K,,) for both the minimum and the maximum assembled clearances are also shown. Intersections between the bearing stiffness curves and the mode curves represent undamped critical speeds. These intersections are circled in Figure 2. Note that the "Mode 1" curve is fairly flat in the region where the intersections occur. The first two lateral mode shapes were then calculated for a nominal bearing stiffness of 500.000 lbiin and are shown in Figures 3 and 4. DRY ROTOR NO SEALS

Automatic balancer (Pendulum balancer)

Abstract: This paper is concerned with theoretical and experimental investigations on the dynamic behavior and the stability of an automatic balancer using centrifugal pendulums. It is found that the unbalance of the rotor can be completely corrected only if the pivots of the pendulums are on the center of the shaft. A violent self-excited vibration occurs when the speed of the shaft is nearly equal to the sum of the critical speed of the rotor and the natural frequency of the pendulum. To verify the theoretical results experiments are carried out.

Method and apparatus for laser beam cutting

Abstract: PURPOSE:To make possible the cutting to a sharp angled shape and to make uniform the roughness of a cut surface by detecting the moving speed of a laser beam relative to a work, changing over the laser from continuous output to pulse output and controlling the pulse frequency. CONSTITUTION:An arithmetic control unit 13 calculates the relative moving speed of the laser beam 3 with respect to the work 1 in accordance with the speed change in the X-, Y-directions of a processing table 10 detected by a speed detector 12 in the stage of cutting. The laser output is changed over from the continuous output to the pulse output by a laser output control means 14 and the pulse frequency is controlled when the processing speed drops to the critical speed or below in the angular part of the cutting shape. The cutting to the sharp angle shape is thus made possible and the roughness of the cut surface is made uniform.

A Method of High Speed Structural Analysis Using a Personal Computer : Comparison with the Transfer Matrix Method

Abstract: This paper suggests a rational method of structural analysis which executes the connection process in series through a recurrent form, using a cantilever with a lumped mass and lumped moments of inertia at the tip as a fundamental element, and applies the boundary conditions at the left hand end of a system at the beginning of computation. When applied to calculating the critical speeds of axially symmetric rotating machines, the present method demands much less CPU time than the transfer matrix method and so it is found very suitable for structural analysis using a personal computer.

Forced vibrations of elastic shallow shell due to the moving mass

Abstract: This paper discusses the forced vibrations of the elastic shallow shell due to the moving mass by means of the variational method. In the text mentioned above a series of problems such as the forced vibrations, resonance conditions and critical speed and so forth.

Modern rotor balancing - Emerging technologies

Abstract: Modern balancing methods for flexible and rigid rotors are explored. Rigid rotor balancing is performed at several hundred rpm, well below the first bending mode of the shaft. High speed balancing is necessary when the nominal rotational speed is higher than the first bending mode. Both methods introduce weights which will produce rotor responses at given speeds that will be exactly out of phase with the responses of an unbalanced rotor. Modal balancing seeks to add weights which will leave other rotor modes unaffected. Also, influence coefficients can be determined by trial and error addition of weights and recording of their effects on vibration at speeds of interest. The latter method is useful for balancing rotors at other than critical speeds and for performing unified balancing beginning with the first critical speed. Finally, low-speed flexible balancing permits low-speed tests and adjustments of rotor assemblies which will not be accessible when operating in their high-speed functional configuration. The method was developed for the high pressure liquid oxygen turbopumps for the Shuttle.

Cavitation warning device of warships and other vessels

Abstract: PURPOSE:To give warning to a steersman to the basis of judgment that propeller cavitation is being generated in case propeller rotational speed exceeds critical rotational speed for generation of propeller cavitation by checking whether or not rotational speed of a propeller during navigation exceeds said critical speed at real time. CONSTITUTION:Rotational speed 2 of a propeller detected by means of a rotation-counter 1 fitted to a propeller shaft and vessel speed 4 detected by means of a log 3 are digitally converted by S/D conversion device 5 and inputted to an operation device 6. The operation circuit 6 has a chart or a formula of calculation to find a critical rotational speed for generation of propeller cavitation. For example, in the formula of calculation by Dr. Nakajima, by previously inputting coefficient, determined by the shape of a hull and characteristics of a propeller, as data, propeller cavitation nc can be easily found when a speed (v) and rotational speed (n) of propeller during navigation are obtained. Then, calculation of n/nc is performed at all times during navigation and a warning is given by means of a warning device 7 when n/nc exceeds a certain value.

Rotor-to-stator rub vibration in centrifugal compressor

Abstract: One example of excessive vibration encountered during loading of a centrifugal compressor train (H type compressor with HP casing) is discussed. An investigation was made of the effects of the dynamic load on the bearing stiffness and the rotor-bearing system critical speed. The high vibration occurred at a "threshold load," but the machine didn't run smoothly due to rubs even when it had passed through the threshold load. The acquisition and discussion of the data taken in the field as well as a description of the case history which utilizes background information to identify the malfunction conditions is presented. The analysis shows that the failures, including full reverse precession rub and exact one half subharmonic vibration, were caused by the oversize bearings and displacement of the rotor center due to foundation deformation and misalignment between gear shafts, etc. The corrective actions taken to alleviate excessive vibration and the problems which remain to be solved are also presented.