Showing papers on "Critical speed published in 1984"

A new approach to finite element modelling of flexible rotors

Abstract: A 3‐dimensional formalism adapted to critical speed and stability analysis of rotating machinery is presented. Gyroscopic effects are properly taken into account in the expression of the kinetic energy through a proper kinematic description which takes account of the local changes of angular velocity induced by the deformation. Two approaches are suggested according to the respective stiffness and geometric properties of the rotating and fixed parts: the rotating frame approach and the inertial frame approach. In both cases, an axisymmetric finite element modelling of the rotor is proposed which takes into account the 3‐dimensional nature of the system while keeping the number of degrees of freedom to a reasonable level. In order to perform the stability analysis, a preliminary reduction of the system is achieved using the component mode method. Critical speeds are calculated next either by the classical sweeping procedure or by a direct method when the restrictive conditions of its applicability are met. The concepts proposed are then applied to an example in order to demonstrate their adequacy.

The Vibrational Behaviour of a Rotating Shaft Containing a Transverse Crack

Abstract: Frequently cracks in turbine rotors were found. Nevertheless, until now it is not really known, how cracks can be recognized early enough so that large consecutive damage can be prevented.

A Nonlinear Analysis of the Generic Types of Loss of Stability of the Steady State Motion of a Tractor-Semitrailer∗

Abstract: SUMMARY All different types of loss of stability which occur generically for a tractor semitrailer vehicle are studied when varying two parameters namely the speed V of the vehicle and the position d of the center of mass of the trailer. For a fixed value of d and varying V it turns out that only two cases either a divergence or a Hopf bifurcation can occur typically. By means of a nonlinear analysis the post-bifurcation behavior for both cases is treated showing that it is critical in both cases. This latter result means that the system is an imperfection sensitive one for which the calculation only of the linear stability limit, does not have very much practical meaning, because small perturbations of the system (changes of parameters) can lead to a drastic reduction of the critical speed. Our paper furthermore indicates how a nonlinear investigation of stability problems in vehicle dynamics with no restriction to the number of degrees of freedom of the system can be done in a straight forward manner.

Rotor dynamics of turbo‐machinery

Abstract: THESE notes are concerned with the lateral vibration of the rotor and the influence that other machine components have on that vibration. When investigating the dynamical behaviour of a turbo‐machine, the following elements are typically of interest:

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

Abstract: SUMMARY The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values. It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesi...

Large-Scale Advanced Prop-Fan (LAP) blade design

Abstract: This report covers the design analysis of a very thin, highly swept, propeller blade to be used in the Large-Scale Advanced Prop-Fan (LAP) test program. The report includes: design requirements and goals, a description of the blade configuration which meets requirements, a description of the analytical methods utilized/developed to demonstrate compliance with the requirements, and the results of these analyses. The methods described include: finite element modeling, predicted aerodynamic loads and their application to the blade, steady state and vibratory response analyses, blade resonant frequencies and mode shapes, bird impact analysis, and predictions of stalled and unstalled flutter phenomena. Summarized results include deflections, retention loads, stress/strength comparisons, foreign object damage resistance, resonant frequencies and critical speed margins, resonant vibratory mode shapes, calculated boundaries of stalled and unstalled flutter, and aerodynamic and acoustic performance calculations.

Balancing flexible rotating shafts with an initial bend

Abstract: The synchronous whirl of a rotating, flexible shaft induced by an initial bend is similar, though slightly different, than that induced by a pure mass unbalance. The differences are due to differences in the forcing effects produced by these phenomena. A discussion of the problems associated with balancing bent, flexible shafts is presented. Experimental results are reported for a long, flexible shaft which demonstrate the effects of initial bend at speeds up to and beyond the fourth critical speed. Included are the results of a series of very successful balancing tests.

Influence of rotor-bar stiffness on the critical speed of an induction motor with an aluminium squirrel cage

Abstract: Most authors, dealing with electromagnetically induced vibrational phenomena in rotating machines, consider the mechanical parameters (spring constant, damping coefficient) to be known. In the paper we will show that the generally made approximations for the calculation of these mechanical parameters are no longer acceptable when considering aluminium rotors. Therefore a more accurate method has been worked out taking into account the rotor-cage stiffness. The results are then compared with experimentally obtained values. These experiments have been made using the modal analysis method.

Vibration Control of Rotating Shaft with Self-optimizing Support System

Abstract: This paper proposes a new design concept of a self-optimizing support system for a rotating shaft. The purpose of this support system is to provide the self-tuning for the support stiffness such that the vibration of a rotating shaft usually occurs at the near antiresonance with changes of a rotating speed. The optimal tuning values of support stiffness are obtained by the on-line estimations of rotating angular velocities of a rotating shaft. The effect of the self-optimizing support system is proved by the tests of nonstationary responses for a fundamental rotor-shaft system.

Real Time Vibration Control of Rotating Circular Plates by Temperature Control and System Identification

Abstract: A system for real-time control of the transverse vibration of a rotating circular plate, based on a thermal stressing technique and dynamic system identification, is presented in this paper. In this method the plate natural frequency spectrum is modified through the purposeful introduction of thermal membrane stresses. The critical speed is maximized. In effect vibration is controlled through real-time control of the plate design. Evaluations with computer simulation and experimental measurements on a thin circular plate verify the system capability to control transverse vibration in a changing thermal environment.

Vibrations of a Rotating Shaft with Rotating Nonlinear Restoring Forces at the Major Critical Speed

Abstract: This paper deals theoretically and experimentally with a nonlinear forced oscillation at a major critical speed in a rotating shaft which is initially bent. When an unsymmetrical shaft carrying a disc or a round shaft (a shaft with circular cross section) carrying an unsymmetrical rotor has an initial bend, and when it is supported by singlerow deep groove ball bearings having angular clearances, its nonlinear spring characteristic fluctuates with rotation of the shaft due to the initial bend. In such a rotating shaft system, there appears a nonlinear restoring force rotating with the shaft. The resonance curves at the major critical speed in this system are more complicated in shape than those in a straight shaft system and their shapes vary with the angular position of the rotor unbalance.

Formation of Standing Waves in Radial Tires

Abstract: Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel‐reinforced tire wall also has a higher density p...

Bearing abnormal vibration preventive device

Abstract: PURPOSE:To shorten the time of holding the speed for awaiting the rise of oil temp. at the time of starting by judging quantitatively if a journal bearing is stable, comparing the result with the critical speed for bearing stable operation, and thereby holding the bearing speed in stabilized range. CONSTITUTION:The bearing oiling temp. TL, revolutional speed omega, bearing oil- film temp. TF and bearing metal temp. TM are sensed to calculate the lubricant viscosity mu and bearing surface pressure P. On the other hand, the rotary shaft radius r, bearing radial clearance C, rotary shaft static deflection delta, rotary shaft critical speed omegac, viscosity mu and bearing surface pressure P are determined to calculate Sommarfeldt's number So, oil-film spring constant betaij, and oil-film damping factor gammaij. Therefrom the stability critical speed omegag is calculated, which is compared with the current revolving speed omega. If the revolving speed is higher than the stable speed, it is judged to be in unstable range, and the exhaust chamber degree-of-vacuum control 40 and oiling temp. control 41 are put in effect to return to the stable range. Thereby the time with oil temp. stand-by speed can be shortened.

Critical speed of centrifugal pumps

Abstract: Until recently, critical speed calculations of centrifugal pumps were made without considering the rotor dynamic effects of close clearance running fits. Publications in the last few years have made it clear that these effects must be considered in order to make the computations relevant to pump operation. This paper is a review of methods available for calculating critical speeds of pumps including rotor dynamic effects.

Combined bearing and variable speed viscous coupling

Abstract: A combined variable speed viscous coupling and bearing includes a rolling element bearing that supports a driven member for relative rotation on a powered member. A viscous grease interposed and sealed with respect to the rolling elements of the bearing acts as a variable speed drive, frictionally retarding the rolling of the rolling elements when the powered member turns below a certain critical speed, thus causing the driven member to turn with the powered member in a one-to-one relationship. Above the predetermined critical speed, the rolling elements roll sufficiently through the viscous material to allow the powered member to overrun the driven member. In a preferred embodiment, the invention is disclosed as a variable speed drive for the cooling fan of a vehicle alternator.

Car speed controller

Abstract: PURPOSE:To prevent a car from going up beyond a critical speed, by installing a series of such devices as capable of detecting a car speed, setting the specified car speed and detecting the specified engine speed in a controller. CONSTITUTION:A car speed control circuit consists of an F-V(S) circuit 51, an F-V(N) circuit 53, each of comparators 52, 54 and 55, an AND gate 56 and an OR gate 57. A car speed increases, thereby entering a critical speed range, and when the output of the F-V(S) circuit 51 exceeds the specified value, an output terminal Y of the OR gate 57 comes to an H level, causing a control element 27 to come into a conductive state. The output of a generator coil 21 is bypassed by the control element 27. When an engine speed reaches to a critical level, an output terminal A of a third comparator 55 comes to the H level as well whereby an output terminal X of the AND gate 56 also comes to the H level so that car speed control operates. With this constitution, a car is in no case reached to more than the critical speed.

Method of hydraulically controlling speed change in automatic transmission for vehicle

Abstract: PURPOSE: To prevent the occurrence of speed change shock by controlling the supply of oil pressure to a frictional engaging element for selecting a rotary element so that the change ratio of rotational speed in the rotary element during the speed change in a transmission follows up a desired value. CONSTITUTION: A speed change gear 22 is constituted from a labyniyo type planet gear mechanism 36 in which a front sun gear 44 is connected to an input shaft 20 through a kick-down drum 52 and a front clutch 24. Oil pressure is supplied to a kick-down servo piston 30 such that the change ratio in rotational speed of the kick-down drum during speed change follows up that in a desired rotational speed. Thus, satisfactory speed change is achieved without excessive speed change shock and slip of a frictional engaging element. COPYRIGHT: (C)1986,JPO&Japio

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

Abstract: SUMMARY A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated. Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only. This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity. The influence of some geometrical factors typical of the wheel-rail contact,...

Stability of Rotors in Bearings

Abstract: A rotor is said to be unstable when the shaft orbit increases with time, without apparent limit. Instability begins when the rotor speed exceeds a so-called “threshold” speed. Stable operation usually resumes when the speed is again decreased below this threshold speed. Unstable whirl motions can cause mechanical problems such as rubbing between journal and bearing, seal rubbing, and blade/stator rub contacts, and may result in substantial machine damage. Unstable motions can also themselves introduce additional dynamic forces within the bearing which stabilize the whirling at a limiting whirl radius. Such whirl motions are called “bounded” instabilities.

Optimum design of rotating machines with overhung weight. part 1: formulation of optimum problems

Abstract: Regarding rotating machines with overhung weight as a system with one shaft and one rigid body, the extreme value problems of the static natural frequencies, forward and backward critical speeds under constant volume of the shaft are formulated by using the matrix method by which the spring constants of the axial symmetric structure are directly calculated. In this case, the shaft of a rotating machine consists of some uniform beams which are connected in series with one another. Besides the length, inside and outside diameters of every beam that is an element of the shaft, the distance between shaft/rigid body connection point and center of gravity of the rigid body is used as a design variable.

Real time vibration control of rotating circular plates by temperature control and system identification

Abstract: A system for real-time control of the transverse vibration of a rotating circular plate, based on a thermal stressing technique and dynamic system identification, is presented in this paper. In this method the plate natural frequency spectrum is modified through the purposeful introduction of thermal membrane stresses. The critical speed is maximized. In effect vibration is controlled through real-time control of the plate design. Evaluations with computer simulation and experimental measurements on a thin circular plate verify the system capability to control transverse vibration in a changing thermal environment.

An improved sootblower apparatus for use in a boiler and method of operating the same

Abstract: A sootblower of the long retracting variety including a drive system (16) which simultaneously rotates the lance tube (12) as it is inserted and withdrawn from the boiler. A variable speed drive is employed to modulate the rotational speed of the lance tube in accordance with the projected distance of the lance tube such that the lance tube is driven faster at intermediate lance tube projected distances thereby optimizing the cycle time of the sootblower. The modulated rotational speed of the lance tube is maintained at all projected distances below the critical speed which varies as a function of projected distance and the sootblower type. By driving the lance tube at certain projected distances at a rotational speed above the critical speed for other projected distances, the translational speed is increased and cycle time reductions are realized as compared with the prior art wherein the lance tube is driven at a constant speed below the minimum critical speed. The lance tube speed may be varied upon retraction and operated at constant speed for insertion or vice-versa or the speed may be varied both on insertion and retraction, as the cleaning requirements of a particular application requires.

Supression of Rotor Instability

Abstract: The following principles are effective for increasing the stable operating speed range of a rotor: a. raise the lowest, critical speed of the system b. increase the external system damping The first requirement can be achieved by increasing the bearing radial stiffness or the bending stiffness of the rotor, or both. The second requirement can be met by using a bearing or support type which inherently contains more non-rotating velocity damping. It should be noted that the increase of any damping which rotates with the shaft itself has a stabilizing effect below the bending critical speed, and a destabilizing effect above the bending critical speed.