Showing papers on "Critical speed published in 1991"

Critical torque and speed of eddy current brake with widely separated soft iron poles

Abstract: A theoretical model ss derived for eddy current disc brakes with iron pole shoes with a wide spacing. The eddy current in the disc is not a simple periodic function allowing representation by sine functions. In the high speed region, the current distribution around the polo shoe occupies a limited zone width proportional to the air gap. The theory based on this effect leads to reasonably accurate values of the critical torque and speed compared with experimental data. The predicted air gap dependency of the critical values agrees better with experimental results than Rudenberg's theory.< >

Nonlinear free surface waves due to a ship moving near the critical speed in a shallow water

Abstract: This paper describes two methods of solution to the nonlinear free-surface waves generated by a ship moving steadily with the trancritical speed in a shallow water. As a mathematical model, a nonlinear initial/boundary-value problem is formulated within the scope of potential theory. One method is based on matched asymptotic expansion techniques and the Kadomtsev - Petviashvili equation is obtained as the leading-order solution for a slender ship. The other one is based on classical Hamilton's principle and the finite element method is implemented for numerical calculations. In order to examine the effect of the tank width on the wave field and resulting hydrodynamic for the Series 60 ship model with Cb = 0.8 by these two different methods. For wider tanks, the pressure distribution on the free surface, equivalent to the ship model, is treated. The results obtained by two different methods are compared each other and with experimental measurements available. Also discussed are the appearance of stem waves at the tank wall and the evolution of the crestline of diverging waves in the wide tank.

The effect of shear and rotary inertia of a rotor at its critical speeds

Abstract: This paper deals with the eigenfrequencies of flexural vibration of a homogeneous rotor model which includes shear, rotary inertia and the gyroscopic effect A formula for the critical speeds of this rotor has also been found It appears that the effect of these factors is smaller when the critical speed increases and the ratio of slenderness of a rotor decreases

Dynamic stability analysis of high speed axially moving bands with end curvatures

Abstract: It is shown that a pitch-fork bifurcation from the trivial equilibrium state will occur at the critical speed of a perfectly straight, axially moving band and the original trivial equilibrium configuration will become unstable. However, for bands with finite end curvatures. The equilibrium configuration will continuously change with increasing band speed, but will remain stable. Multiple equilibrium states will occur at sufficiently high band speed

Vibrations of a Rotating Shaft Containing a Transverse Crack. Vibrations at the Secondary Critical Speed.

Abstract: In order to develop a vibration monitoring system which detects a transverse crack in a rotating shaft system, it is necessary to clarify the vibration characteristics of a cracked shaft. In this paper, we investigated the influence of a crack on the resonance phenomena at the secondary critical speed where a natural frequency is equal to double the rotating speed. The followings are clarified: (a) when a crack appears in a horizontal rotating shaft, a whirling motion of the forward precession whose frequency is double the rotating speed appears, (b) the amplitude depends remarkably on the angular position of the unbalance relative to the crack, (c) this phenomenon is explained clearly if the spring characteristics are expressed by rotating nonlinearity.

Fuel feeding device for two-cycle internal combustion engine

Abstract: PURPOSE:To prevent overspeed without hindering the cooling ability and the lubricating ability of an engine when a detected result of the engine speed exceeds the predetermined value by controlling the fuel injection quantity from a fuel injection device provided in an intake passage so as to be increased CONSTITUTION:A solenoid type fuel injection valve 46 for injecting the lubricating oil mixed fuel is provided in an intake pipe 26 connected to an intake port 30 provided in a cylinder 12 The pressure-raised fuel is fed to the fuel injection valve 46 with a fuel pump 44, and while the pressure of the force-fed fuel is maintained at a certain value by a pressure controlling unit 48 The injection quantity of the fuel injection valve 46 is controlled by a control unit 58 for taking the speed signal N therein Namely, the detected speed N this time exceeds a preset critical speed N0 or not is judged, and when the detected speed N is less than the critical speed N0, the ordinary control operation is carried out, and when the detected speed N is more than the critical speed N0, the increase control operation is carried out

Analysis and Test of Multistage Pump “Wet” Critical Speeds

Abstract: The accurate prediction of the rotordynamic characteristics of centrifugal pumps is complicated by the presence of strong restoring and cross-coupling forces within annular sealing cavities such as wearing rings and thrust balancing devices. This so-called Lomakin Effect occurs when the sealing annulus shifts off-center, and can increase the first bending natural frequency of the pump rotor assembly by up to 200 percent. In addition, the lower natural frequencies may become critically damped, or in the other extreme unstable, relative to what would be expected if the rotor were run in air rather than in the pumped fluid. To properly account for this Lomakin Effect, a wet critical speed combined analysis and test approach is described. Examples are given to illustrate its effectiveness in product development and field trouble-shooting. Presented at the 35th STLE/ASME Tribology Conference In Fort Lauderdale, Florida October 16–19, 1989

Effect of shear on stability and nonlinear behavior of a rotating rod

Abstract: The nonlinear equations describing in-plane deformation of a rotating elastic rod, taking into account shear effect, are derived. It is shown that the critical rotation speed is determined from the linearized equation. The nonlinear equilibrium equations are solved numerically and the effect of shear on maximal deflection is studied.

Influence of impeller shroud forces on turbopump rotor dynamics

Abstract: The shrouded-impeller leakage path forces calculated by Childs (1987) have been analyzed to answer two questions. First, because of certain characteristics of the results of Childs, the forces could not be modeled with traditional approaches. Therefore, an approach has been devised to include the forces in conventional rotordynamic analyses. The forces were approximated by traditional stiffness, damping and inertia coefficients with the addition of whirl-frequency-dependent direct and cross-coupled stiffness terms. The forces were found to be well-modeled with this approach. Finally, the effect these forces had on a simple rotor-bearing system was analyzed, and, therefore, they, in addition to seal forces, were applied to a Jeffcott rotor. The traditional methods of dynamic system analysis were modified to incorporate the impeller forces and yielded results for the eigenproblem, frequency response, critical speed, transient response and an iterative technique for finding the frequency of free vibration as well as system stability. All results lead to the conclusion that the forces have little influence on natural frequency but can have appreciable effects on system stability. Specifically, at higher values of fluid swirl at the leakage path entrance, relative stability is reduced. The only unexpected response characteristics that occurred are attributed to the nonlinearity of the model.

Anisotropic stiffness effect on stability of a magnetically suspended momentum wheel

Abstract: This paper describes a method for designing the bearing stiffness and analyzing the damping characteristics of the whirling motion of a momentum wheel that is actively stabilized in the axial direction and passively supported in two orthogonal radial directions by magnetic force. A method for estimating the magnetic bearing stiffness is introduced, which uses magnetic circuit theory and numerical simulation technique. The equations of rotor motion include the effect of anisotropic stiffness of bearing. A solution to the equations of motion is obtained by applying the method of averaging, relating the relationship of the damping characteristics variation with angular speed to the anisotropy of stiffness. The limiting speed, where the damping factor is equal to null, increases by the quantity proportional to the difference of the bearing stiffness in two orthogonal directions perpendicular to the axis of rotation. The result was verified by the experiment with a single-axis controlled and magnetically suspended momentum wheel.

Analysis of aircraft engine blade subject to ice impact

Abstract: The ice impact on the engine blade made of layered composite is simulated. The ice piece is modeled as an equivalent spherical object and has the velocity opposite to that of the aircraft with direction parallel to the engine axis. Near the impact region and along the leading edge, the blade is assumed to be fully stressed and undergoes large deflection. A specified portion of the blade around the impact region is modeled. The effect of ice size and velocity on the average leading edge strain are investigated for a modified SR-2 model unswept composite propfan blade. Parametric studies are performed to study the response due to ice impact at various locations along the span. Also, the effects of engine speed on the strain and impact displacements are discussed. It is found that for a given engine speed, a critical ice speed exists that corresponds to the maximum strain and this critical speed increases with increase in the engine speed.

Dynamic modelling and analysis of a magnetically suspended flexible rotor

Abstract: A 12-state lumped-element model is presented for a flexible rotor supported by two attractive force electromagnetic journal bearings. The rotor is modeled as a rigid disk with radial mass unbalance mounted on a flexible, massless shaft with internal damping (Jeffcott rotor). The disk is offset axially from the midspan of the shaft. Bearing dynamics in each radial direction are modeled as a parallel combination of a negative (unstable) spring and a linear current-to-force actuator. The model includes translation and rotation of the rigid mass and the first and second bending models of the flexible shaft, and it simultaneously includes internal shaft damping, gyroscopic effects, and the unstable nature of the attractive force magnetic bearings. The model is used to analyze the dependence of the system transmission zeros and open-loop poles on system parameters. The dominant open-loop poles occur in stable/unstable pairs with bandwidth dependent on the ratios of bearing (unstable) stiffnesses to rotor mass and damping dependent on the shaft spin rate. The zeros occur in complex conjugate pairs with bandwidth dependent on the ratios of shaft stiffness to rotor mass and damping dependent on the shaft spin rate. Some of the transmission zeros are non-minimum phase when the spin rate exceeds the shaft critical speed. The transmission zeros and open-loop poles impact the design of magnetic bearing control systems. The minimum loop cross-over frequency of the closed-loop system is the speed of the unstable open-loop poles. For the supercritical shaft spin rates, the presence of non-minimum phase zeros limits the distribution rejection achievable at frequencies near or above the shaft critical speed. Since non-minimum phase transmission zeros can only be changed by changing the system inputs and/or outputs, closed-loop performance is limited for supercritical spin rates unless additional force or torque actuators are added.

Dual critical speed rotating machine - avoid overloading by actuating hydraulic presses that act as extra supports for one rotor bearing

Abstract: The machine has a rotor bearing resting on a foundation or against the stator`s casing. The rotor bearing`s support (6) has extra support elements (7) connected in an reaching a critical speed to suddenly alter the machine`s critical speed. The extra support elements are designed so that they cause a displacement in the critical speed by at least twice the minimum admissible resonace spacing. The support for the first rotor bearing has a lower spring constant than the support for the remaining rotor bearing (10). The extra support elements are hydraulic presses operated by valves. USE/ADVANTAGE - Avoids resonance in rotation machines and associated damage.

The Dawn of Machine Dynamics. The Balancing of Wheels and the Critical Speed of Rotating Shafts.

Abstract: When and how machine dynamics emerged from practical engineering issues is historically studied. The ever-increasing speed and power of steam engines in the mid-19th century energized the engineers to develop new techniques of balancing wheels, particularly those of steam locomotives, to obtain running stability at high speed. Vibration of slender shaftings placed along the ceiling of factories was another urgent problem to be solved. The concept of flexural critical speed of a rotating shaft was thereby introduced, resulting in the birth of a new disciplinary field known as "machine dynamics".

The Effects of Friction in Axial Splines on Rotor System Stability

Abstract: An in depth parametric evaluation of the effects of Coulomb friction in an axial spline joint on the stability of the rotor-bearing system was conducted through time transient integration of the equations of motion. Effects of: spin speed, friction coefficient, spline torque, external damping, imbalance and side load as well as asymmetric bearing stiffnesses were investigated.A subsynchronous instability is present at the bending critical speed when the spin speed is above this critical. The limit cycle orbit is circular, is proportional to the product of the friction coefficient and spline torque (μT), is inversely proportional to the external damping and is independent of spin speed.When imbalance is applied to the rotor, beating between the subsynchronous natural frequency and the synchronous (spin speed) frequency occurs. The subsynchronous component of the orbit is proportional to μT, while the synchronous component is proportional to the imbalance.When a static side load is applied, the unstable node at the center of the orbitally-stable limit cycle grows into an elliptical orbitally-unstable limit cycle, separating stable - from unstable regions of the phase plane. Below a threshold value of side load, the transient motion approaches one of two asymptotic solutions depending on the initial conditions: the larger stable limit cycle or a point at the center of the smaller unstable limit cycle. Beyond the threshold value of side load the rotor-bearing system is stable and all motions decay to a point.Asymmetry in the bearing stiffnesses reduces the size of the subsynchronous whirl orbit.Copyright © 1991 by ASME

A Beam Model for Tire Critical Speeds

Abstract: A brief review of tire critical speeds is given using the beam under tension as a physical model. In its most common form, this model visualizes the critical speed as that speed just sufficient to sustain a continuous sinusoidal bending wave in the tire tread band. A number of studies have been published modifying this concept by the introduction of material damping, centrifugal effects, and other characteristics, some of which aid in explaining the fact that the wave pattern observed experimentally is local and decays rapidly away from the contact patch. This paper presents a different view of the wave pattern needed for a critical speed to exist, namely that a naturally occurring local wave can arise independent of material damping and that as a practical fact, material damping may have little to do with the onset of the phenomenon. A discussion on the effect of tire design variables on critical speed is given based on the expressions derived here.

The Transient Response of a Journal in Plane Hydrodynamic Bearing with Flexible Damped Supports During Acceleration and Deceleration Periods

Abstract: This paper presents an assessment of the stability margin of plane hydrodynamic journal bearing systems mounted on flexible damped pedestals. The stability margin expressed in terms of critical speed (or critical mass) of journal are obtained using the conventional linearized theory. The assessment investigations are then carried out by delineating the motion of an accelerating or decelerating journal. This involves time marching solutions of the equations of motion of the journal and the bearing coupled with the Reynolds equation. It has been found that the motion of an accelerating or decelerating journal concurs with linearized theory in the stable region. However, at the accelerated speeds in the unstable region, the journal and bearing may either execute low amplitude limit cycles or become unstable. This work also furthers the ideas concerning the limiting speed as developed in an earlier work of the present authors.

Dynamic Characteristics and Stability Analysis of Space Shuttle Main Engine Oxygen Pump

Abstract: The dynamic characteristics of the Space Shuttle high pressure oxygen pump are presented. Experimental data is presented to show the vibration spectrum and response under actual engine operation and also in spin pit testing for balancing. The oxygen pump appears to be operating near a second critical speed and is sensitive to self excited aerodynamic cross coupling forces in the turbine and pump. An analysis is presented to show the improvement in pump stability by the application of turbulent flow seals, preburner seals, and pump shaft cross sectional modifications.

Elektrische maschine mit regelbarer drehzahl.

Abstract: The speed of a supercritically operated electric machine can be increased over a range between a first critical speed and a second critical speed. To this end, the shaft (11, 12) of the electric machine is elastically mounted on either side of the rotor (7). The flexural strength of the shaft (11, 12) between the rotor (7) and the second bearing (8) is substantially greater than in the region between the rotor (7) and the first bearing (9). As a result, the second critical speed shifts to higher speeds more readily than the first critical speed, and the difference between the first and the second critical speeds, and thus the maximum range over which the speed of the machine can be controlled, increases. The invention can be applied in supercritically operated, variable-speed electrical machines.

非線形ばね特性をもつ回転軸系の危険速度通過時の振動 : 1/3次分数調波振動の共振点

Abstract: Nonstationary vibration characteristic during acceleration through a critical speed of a 1/3-order subharmonic oscillation of forward precession is investigated. The following results are obtained: (1) Resonace curves exist separated from the zero-amplitude solution which is stable at any rotating speed ω. If there exists an initial disturbance, the solution jumps to the resonance curve and the subharmonic oscillation may occur. (2) The maximum amplitude depends not only on the angular acceleration A but also on the initial disturbance ΔP, the initial rotating speed ωs and the initial angular position, Ψ0, of the unbalance. And with respect to the initial angular position Ψ0, the maximum amplitudes vary periodicaly. (3) The amplitude may grow infinitely when the angular acceleration λ takes a value between two critical values λ1 and λ2. If the angular acceleration is outside of this range, the rotor can always pass the critical speed with a finite maximum amplitude. In addition, characteristics of 1/2- and 1/3-order subharmonic oscillations of backward precession are discussed briefly. From comparison of the results of all kinds of subharmonic oscilations, it becomes clear that the periodicity of the maximum amplitude for Ψ0 has strong relation to the periodicity of the spring characteristics around the equilibrium position.