Showing papers on "Critical speed published in 1982"

Nonlinear Stability and Tracking of Rail Passenger Trucks

Abstract: An analysis of a rail passenger truck which includes nonlinear wheel/rail geometry and creep forces is formulated for determining truck stability and response to rail alignment irregularities. Digital simulation studies using the analysis have illustrated the large amplitude flange to flange response which occurs in operation of a truck below critical speed on a track with significant alignment irregularity, of a truck near critical speed and excited by irregularities and of a truck operated obove critical speed. The variations in temporal waveform, probability density and power spectral density of vehicle motions for these conditions are described. The influence of vehicle suspension parameters and wheel/rail geometry on truck stability and tracking ability is discussed and related to operating conditions.

Experiments on the Stability and Response of a Flexible Rotor in Three Types of Journal Bearings

Abstract: Three sets of bearings were tested on a three-mass flexible rotor: axial-groove, pressure-dam and preloaded three-lobe, and the instability thresholds and unbalance responses were determined. The pressure-dam bearings were designed for maximum rigid rotor stability; the three-lobe bearings had preload factors of approximately 0.75. Rotor first and second critical speeds were observed at 2550 and 9800 rpm, respectively. The instability thresholds and unbalance responses at the first critical speed for the axial-groove and three-lobe bearings were found to be strongly dependent on the load orientation. Maximum stability limits of 6550, 7400 and 10 400 rpm were found for the axial-groove, pressure-dam, and three-lobe bearings, respectively. Thus, the preloaded three-lobe bearings were the only set that allowed this particular rotor to operate above the second critical speed. The experimental data were also compared to theoretical predictions. Differences in instability thresholds of up to 37 percent were rea...

Vibration diagnosis method for rotary machine

Abstract: A vibration diagnosis method for a rotary machine is disclosed. The presence or absence of a self-excited vibration is determined by checking if a rotating speed is in a rotating speed range which allows the occurrence of the self-excited vibration, if an amplitude of a frequency component corresponding to a first order critical speed is larger than a predetermined level, and if phases at characteristic points of vibration signals change among cycles.

Nonlinear Forced Oscillations of a Rotating Shaft Carrying an Unsymmetrical Rotor at the Major Critical Speed

Abstract: This paper deals with the motion of an unsymmetrical rotor possessing nonlinear spring characteristics, due to the angular clearance of a singlerow deep groove ball bearing, in the vicinity of the major critical speed. When this system is operated near the major critical speed, no unstable vibration occurs, but we obtain peculiar resonance curves of hard spring type which have three stable amplitudes at most against the rotating speed. The resonance curves are classified into two types. They are the cases where the jump phenomenon appears once or twice during deceleration of the rotating speed. It is clarified that the type of the resonance curve depends on the angular position of rotor unbalance.

Design and Evaluation of Trucks for High-Speed Wheel/Rail Application

Abstract: Increasing requirements of ride quality and speed demand an optimal design of high speed trucks.

Detecting method for unbalance distribution of elastic rotor

Abstract: PURPOSE:To precisely detect unbalance distribution, by a method wherein a support condition on a support position and a support rigidity in a support part which turns an elastic rotor is caused to vary, and the elastic rotor is caused to turn under different support conditions. CONSTITUTION:A pair of bearings 2 (bearings which support the opposite ends), which rotatably supports an elastic rotor 1, and a pair of bearings 3, which support at another position, are constituted so that they can individually and freely move vertically. Firstly, the bearings 2 at the opposite ends are raised to support the elastic rotor 1 and the other bearings 3 are lowered to be brought into a nonsupporting state. With this the elastic rotor 1 is caused to turn at a rotation speed to measure and analyze a unbalance weight against a critical speed mode in the elastic rotor 1. Then, the bearings 2 are lowered and the bearings 3 are raised to measure and analyze a unbalance weight against a critical speed mode in the elastic rotor 1. Like this, the elastic rotor is caused to turn under different conditions, and this permits the precise detection of a unbalance distribution.

Critical Speed of Rotor in a Liquid

Abstract: Analytical results on the fundamental critical speed of a shaft in a viscous fluid are presented. When the fluid is set in motion by the shaft whirling, dynamic forces imposed by the fluid on the shaft are obtained by solving the two-dimensional Navier -Stokes equations under appropriate boundary conditions and on the assumption of small amplitude of the whirling motion. Added mass coefficients of the fluid and viscous damping coefficients are determined using these dynamic forces, and accordingly the equations of whirling motion of the shaft are derived. The critical speed of the shaft are found by solving these equations of whirl motion. In this analysis, configurations of the shaft are assumed to be a uniform elastic beam or a diskattached elastic beam, whose both ends are simply supported by bearings. For the latter case, an experimental study was made in order to confirm the analytical results. From this study, it was revealed that the critical speed decreases for large viscosity of the fluid, and when the fluid fills an annulus between the shaft and a cylindrical wall, the critical speed decreases for small annular gap width.

Comment on "Estimation of Flutter Boundary from Random Responses Due to Turbulence at Subcritical Speeds"

Abstract: T are two comments which need to be made with regard to a statement made by Drs. Matsuzaki and Ando. They stated that, "It is evident that this estimation technique of the flutter boundary is quite effective even for the signals which contain more than two degrees of freedom, as is seen [in their plot of stability parameter, frequency, and coefficients vs dynamic pressure for the three mode analysis ] where the data at the lowest third and fourth pressure should be neglected." It is only evident when all of the data have been collected and the critical speed is known before the analysis is done. For the three-mode case presented, the first three points indicated flutter would occur just above 0.6 kg/cm. If the first three points were the only information that the engineer had, and this would be a normal sequence of events, then the test would have to be halted. What is not indicated in the paper is a procedure for determining when data can safely be omitted when all the data has not been obtained. Second, subcritical analysis of flight test data is not only carried out to allow for extrapolation of test data to determine the critical speed, but also to allow for analytical/experimental data comparison throughout the flight envelope instead of just at the critical speed. It would have been of interest to see a comparison of the method applied to a numerical model of wind tunnel model/test and the experimental model/test data for both the twoand three-mode cases. Because there are differences between the results obtained for the two-mode analysis and the three-mode analysis of the same experimental data, a numerical example of a three-mode case would seem to be in order.

Determination of Ball Bearing Dynamic Stiffness

Abstract: The dynamic radial stiffness characteristics of rolling element bearings are currently determined by analytical methods that have not been experimentally verified. These bearing data are vital to rotating machinery design integrity because accurate critical speeds and rotor stability predictions are highly dependent on the bearing stiffness. A tester was designed capable of controlling the bearing axial preload, speed, and rotor unbalance. The rotor and support structures were constructed to permit critical speeds that are predominantly determined by a 57 mm test bearing. A curve of calculated critical speed versus stiffness was used to determine the actual bearing stiffness from the empirical data. The results of extensive testing are used to verify analytical predictions, increase confidence in existing bearing computer programs, and to serve as a data base for efforts to correct these programs.

Overspeed safety device

Abstract: In a pneumatically powered rotating grinding machine there is provided a safety unit (13) comprising a speed governor and an overspeed release mechanism the purpose of which is to ensure a predetermined maximum speed. For safety reasons, the motor speed must never exceed a certain critical speed level which is determined by the mechanical strength of the working tool attached to the machine. When choosing a working tool to be attached to the machine the maximum speed mark of the machine is decisive. By having a portion of the safety unit exposed through an aperture (57) in the tool housing (10) and having the maximum speed mark (52) of the safety unit (13) located at the exposed portion, the maximum speed mark of the machine will always be the same as that of the safety unit (13). The suggested overspeed safety device avoids the risk involved in the event that a machine carrying a certain maximum speed mark might be erroneously fitted with a safety unit (13) intended for a higher maximum speed.

Critical Speed in Centrifugal Pumps

Abstract: In high pressure centrifugal pumps the magnitude of the critical speed is strongly affected by the presence of liquid in the close clearance spaces of sealing rings and throttle bushings. The stiffening and damping effect resulting from the non-axisymmetric pressure drop across such gaps is often large compared with the elastic stiffness of the shaft. In many cases it raises the critical speed far above the “dry” value, and in some cases it eliminates the critical speed altogether. As a consequence, design specifications based on shaft critical speeds, calculated disregarding the effects of the fluid, become quite meaningless. In this paper simplified equations are derived for the calculation of the effect of the fluid gap. The results have been verified by measurements on a test pump. Sample calculations for a typical multistage boiler feed pump are included as illustration.Copyright © 1982 by ASME

Abnormal vibration controller for rotary object

Abstract: PURPOSE:To control and excessive vibration of a rotary object so that its rotational speed can be shifted in a higher speed range over the critical speed, by forcing a vibration suppressor wheel to touch the rotary object set on a thrust magnetic bearing when its rotational speed reaches a certain specific level. CONSTITUTION:When any abnormal vibration is generated to a rotary object 4, and the output from a rotational speed detector 12 increases beyond the level which is set in a standard voltage source 14, a comparator 13 shall be set in ON status, causing the current source 15 to supply a solenoid 16 with a current. Accordingly, the solenoid 16 forces a wheel fixing frame 18 to touch the face of groove 11 provided on the periphery of the rotary object 4 so as to suppress any excessive vibration of the rotary object 4 during its rotational motion.

Optimal Design of Squeeze Film Supports for Flexible Rotors

Abstract: Assuming central preloading operation below the second bending critical speed and full film lubrication, this paper presents a theoretical model which allows one, with minimum computation, to design squeeze film damped rotors under conditions of high unbalance loading. Closed form expressions are derived for the maximum vibration amplitudes pertaining to optimally damped conditions. The resulting vibration amplitude and transmissibility data of design interest are presented for a wide range of practical operating conditions on a single chart. It can be seen that for a given rotor, the lighter the bearing the more easily one can satisfy design constraints relating to allowable rotor vibration levels and lubricant supply pressure requirements. The data presented are shown to be applicable to a wide variety of rotors, and a recommended procedure for optimal design is outlined.Copyright © 1982 by ASME

The balancing of flexible rotating shafts which have 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.

Method of controlling operation of fan

Abstract: PURPOSE:To enable to operate a fan safely, quietly and at a high efficiency, by eliminating occurrence of resonance by controlling operation of the fan such that it is operated at a speed higher than the critical speed range in case that the speed of the fan is raised near to or has reached the critical speed. CONSTITUTION:Under the operational condition (shown by an arrow III in the drawing) in which a control frequency signal F (higher than a lower limit frequency Fa of a critical frequency range Fx) is given from a converter 3 so as to operate a motor 1 at a higher speed jumping over a low speed range Nm lower than the critical speed Nx, the control frequency signal F applied from the converter 3 to a frequency discriminator 4 is varied from a low frequency range Fm toward a critical frequency range Fx. Here, an arithmetic mechanism in the frequency discriminator 4 is operated to control an inverter 5 such that the motor 1 is operated at a particular frequency within a high frequency range Fn jumping over the critical frequency range Fx. With such an arrangement, it is enabled to eliminate occurrence of resonance of the fan and to operate the fan safely, quietly and at a high efficiency.

Shaft dynamics in the rotors of large centrifugal fans

Abstract: 1. A realistic way of improving the viability of the rotor in a centrifugal fan is to reduce the amount of metal, particularly in the shaft, whose mass exceeds half the mass of the rotor. The critical speed of the rotor should not thereby be reduced. 2. Hollow and other types of light two-bearing shaft have natural frequencies 15–20% lower for the same diameters in relation to solid shafts (for the usual masses of the fans). 3. A light single-bearing shaft under the same conditions has a natural frequency virtually equal to that of a solid shaft. 4. If the outside diameter of a hollow shaft is 6–8% larger than that of a solid one and the wall thickness is 8% of the outside diameter, the natural frequency of the hollow shaft should be not lower than that of the solid one. 5. The mass of the rotor as a whole with a single-bearing hollow shaft is reduced by 35–40%, while that of a rotor with a two-bearing hollow shaft having the same natural frequency as a solid one is reduced by up to 25%, which substantially improves the reliability and working life of the bearings. 6. One obtains reliable and viable hollow shafts with welded bearing rings if the technological requirements are met. 7. In calculating the critical speed of a two-bearing shaft in a centrifugal fan, there is only a very small correction from the gyroscopic effect, which may be taken as a certain safety margin only for rotors where the fan proper is off center. This correction is 9–11% for a single-bearing shaft.

Unstable Vibrations of an Unsymmetrical Shaft at the Secondary Critical Speed due to Ball Bearings

Abstract: It is clarified theoretically and experimentally that, when an unsymmetrical shaft is supported by single-row deep groove ball bearings, an unstable vibration with frequency +2ω (ω : rotating speed of a shaft) appears at the secondary critical speed due to the coexistence of a stationary directional difference and a rotating directional difference of stiffness. The stationary directional difference is due to the directional difference of support condition by means of a single-row deep groove ball bearing which has angular clearance, and the rotating directional difference is due to the flatness of the shaft. The width of this unstable region depends on the assembly of the system. No unstable vibration appears at the secondary critical speed in the system where an unsymmetrical shaft is supported by self-aligning double-row ball bearings and in an unsymmetrical rotor system.

Flexible shaft whirl induced by dry friction and its stability

Abstract: This paper is devoted to the study of the whirling phenomena of flexible rotors due to dry friction. The mechanical model used here is a two-degree-of-freedom system in which the rubbing plane is not coincident with the rotating plane of the lumped mass. The characteristic equation of whirl speeds is derived and the whirling modes are obtained. The dynamic stability of each admissible whirling motion is also discussed. The results show that the whirl speeds are always higher than the critical speed of the shaft.

Evaluation of unstable probability of rotors having stiffness errors of asymmetry

Abstract: The bending stiffness of a shaft in a two pole generator and so on is regarded as a random variable, thus the amplitude and the stability of a rotor system are statistically analyzed to seek the influence of the error of the bending stiffness on the system, That is, the variance of amplitude of the rotor and the mode function due to the error are obtained. The probability of unstable vibration of the rotor system is predicted and compared with the results of the simulation of Monte Carlo method. The variation of the amplitude of the rotor appears remarkable near the critical speed of the symmetrical rotor and a half of that speed. The probability of unstable vibration is in good agreement with results of the simulation, so the statistical analysis serves as a reference in designing or producing a rotary machine.