Showing papers on "Critical speed published in 1994"

Dynamically stable magnetic suspension/bearing system

Abstract: A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium. However, owing to the limitations imposed by Earnshaw's Theorem, the magnetic bearing systems to be described do not possess a stable equilibrium at zero rotational speed. Therefore, mechanical stabilizers are provided, in each case, to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. The magnetic forces exerted by these elements, when taken together, levitate the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations. At the same time, this equilibrium is made stable against displacements of the rotating object from its equilibrium position by using combinations of elements that possess force derivatives of such magnitudes and signs that they can satisfy the conditions required for a rotating body to be stably supported by a magnetic bearing system over a finite range of those displacements.

Optimal driving strategies for a train journey with speed limits

Abstract: How should a vehicle he driven to minimise fuel consumption? In this paper we consider the case where a train is to be driven along a straight, level track, but where speed limits may apply over parts of the track. The journey is to be completed within a specified time using as little fuel as possible.For a journey without speed limits, the optimal driving strategy typically requires full power, speed holding, coasting and full braking, in that order. The holding speed and braking speed can be determined from the vehicle characteristics and the time available to complete the journey. If the vehicle has discrete control settings, the holding phase should be approximated by alternate coast and power phases between two critical speeds.For a journey with speed limits, a similar strategy applies. For each given journey time there is a unique holding speed. On intervals of track where the speed limit is below the desired holding speed, the speed must be held at the limit. If braking is necessary on an interval, the speed at which braking commences is determined in part by the holding speed for the interval. For vehicles with discrete control, speed-holding is approximated by alternate coast and power phases between two critical speeds, or between a lower critical speed and the speed limit.

Parametric resonances at subcritical speeds in discs with rotating frictional loads

Abstract: This paper is concerned with the parametric resonances in a stationary classical annular disc when excited by a rotating mass-spring-damper system together with a frictional follower load. An analysis by the method of multiple scales is performed to reveal the existence of instabilities associated with subcritical parametric resonances, and other instabilities of the backward waves in modes with nodal diameters. The latter are shown to be driven by friction and not to be dependent upon the rotational speed. A state-space analysis, with truncated modes, is used to investigate the effect of varying the friction, stiffness, mass and damping prameters in a series of simulated problems. The results obtained from the state-space eigenvalue method tend to support the conclusions of the multiple scales analysis.

Does a critical speed for railroad vehicles exist

Abstract: The author discusses the definition and existence of a critical speed for the onset of hunting of railroad vehicles. First the field test situation is described. It is argued that the important problem is the determination of the forces and accelerations in the vehicle and the rails, which may be large even when the vehicle does not hunt. Next the author discusses the relevance of the critical speed in railway engineering. It is desirable to know the speed below which a vehicle will not hunt, since hunting is always connected with large wheel-rail forces. Next the modelling of railroad vehicles is discussed and the nonlinear aspects are emphasized. The author explains why it is necessary to reformulate the mathematical problem for calculation of the critical speed due to the nonlinear character of the modelling. It is suggested that another critical speed be defined for a railroad vehicle. It can be calculated without great effort using a well functioning simulation program. It yields a "global" criterion for the onset of hunting, in contrast to the linear stability criterion, which is still commonly used. The linear eigenvalue problem yields a bifurcation point, which in general will not be the lowest parameter value for existence of oscillating solutions in a nonlinear dynamical system. The author suggests the use of a "nonlinear critical speed" as an acceptance criterion for railroad vehicles. >

Nonlinear Vibrations and Chaos in Rotordynamics

Abstract: In turbomachinery, nonlinearity appears in restoring forces or damping forces due to various causes, such as clearances in bearings, squeeze film dampers, oil films in journal bearings, magnetic forces, seals, frictions and stiffening effect in elongation of a shaft center line. As a result, various kinds of nonlinear phenomena occur. For example, it is known that subharmonic oscillations, summed - and - differential harmonic oscillations, chaotic motions, jump phenomena, and limit cycles occur in rotor systems. In this review article, characteristics of these nonlinear phenomena are outlined and literature on these phenomena is introduced.

Axial instability of rotating rods revisited

Abstract: For strain sufficiently small such that Hooke's Law is valid, it is shown that only a linear model for axial deformation of rotating rods can be derived. As discussed in the literature, this linear model exhibits an instability when the angular speed reaches a certain critical value. However, unless this linear model is valid for large strain, it is impossible to determine whether this instability really exists; because, as the angular speed is increased, the strain becomes large well short of the critical speed. Next, axial deformation of rotating rods is analyzed using two strain energy functions to model non-linear elastic behavior. The first of these functions is the usual quadratic strain energy function augmented with a cubic term. With this model it is shown that no instability exists if the non-linearity is stiffening (i.e. if the coefficient of the cubic term is positive), although the strain can become large. If the non-linearity is of the softening variety, then the critical angular speed drops as the degree of softening increases. Still, the strains are large enough that, except for rubber-like materials, a non-linear elastic model is not likely to be appropriate. The second strain energy function is based on the square of the logarithmic strain and yields a softening model. It quite accurately models the behavior of certain rubber rods which exhibit the instability within the validated range of elongation.

Flexural Instabilities in Axially Moving Bands

Abstract: Flexural instabilities in moving bands under harmonic tension fluctuation are The. investigated discretized equations of flexural motion represent a periodically perturbed linear gyroscopic system. Explicit conditions for the onset ofinstability are established employing the method of averaging. The effects due todamping, mean band speed, and the band compliance on the band stability are discussed. The present analysis is adequate in the design of moving bands where it is necessary to avoid critical speed ranges.

Stabilization of high-speed railway vehicles.

Abstract: SUMMARY The problems of critical speeds of railway vehicles with dry friction units determination are discussed. A new approach is used which extends the field of application of dynamic response linear analysis methods to vital nonlinear multibody systems. The special features concerning the influence of dry friction forces in the body supports on the trucks and parameters of horizontal constraints of wheelsets and truck frames on critical speed are indicated. It is shown that a significant rising of railway vehicle critical speeds can be reached by changing the structure of constraints between the body and the trucks.

The numerical bifurcation method of nonlinear lateral stability analysis of a locomotive

Abstract: SUMMARY This paper gives a model of twenty-seven degrees of freedom for a six-axle locomotive with three-axle bogies, sets up the numerical bifurcation method as the method of nonlinear lateral stability analysis of a locomotive, and derives criteria of stabillity analysis. This paper makes a point that the subcritical Hopf bifurcation speed Vn and the derailing speed Vd must be obtained in order to describe a complete picture of the lateral stability of a locomotive. However, the critical speed Ve is not the most important index of locomotive stability. At the end of this paper, the diesel locomotive DF9 has been analyzed for nonlinear lateral stability. To solve the locomotive equations of motion about nonlinear lateral stability, the paper gives preference to Newmark's predictor-corrector integration scheme as an integration algorithm, and sets up the numerical integration programs using FORTRAN language. At the same time, the aftertreatment programs have been set up. Nonlinear geometry, changing conta...

Magnetic bearing controlling method and device

Abstract: PURPOSE:To obtain a magnetic bearing controlling method and a device thereof, wherein proof stress of the magnetic bearing is improved by decreasing resonance amplitude of unbalance vibration of revolution synchronization, and also decreasing electric current to flow in the electromagnetic coil of the magnetic bearing. CONSTITUTION:Rotation synchronous components Xn, Yn multiplied by proportional coefficient delta given by coefficient multipliers 23X 23Y are added to outputs of control circuits 4X, 4Y. The purpose is to increase the spring constant, accordingly the resonance point is shifted in the higher direction. Vibration can be decreased by shifting the resonance point to the higher revolutions in the revolution range just before the resonance point. Taking of the coerfficient is the method for restraining the resonance amplitude, and is effective only in critical speed passing. After the critical speed is passed to a considevable entent, this methol is no more needed, but the control of only ABS is desired. Accordingly, when the values of the proportional coefficient alpha, beta are selected according to the revolution range, the most-effective control wherein controlled electric current is minimum in the whole revolution range is made possible.

Critical Speed Estimation for Aircraft Tires

Abstract: This paper introduces a semi‐analytic finite element technique for predicting standing wave motions (critical speed phenomena) in pneumatic tires. A general formulation is presented which encompasses inflation and rotation of the tire as well as vibratory motions superimposed upon the inflated and rotating state. The use of sinusoidal basis functions for the circumferential variation of each displacement component reduces the finite element model to two dimensions and improves solution accuracy for higher‐frequency modes. Under suitable assumptions, the harmonic components uncouple, and the three‐dimensional problem may be solved as a sequence of smaller two‐dimensional analyses. The proposed technique provides improved accuracy over three‐dimensional analysis at a small fraction of the cost and modeling effort.

Theoretical investigations into the dynamical properties of railway tracks using a continuous beam model on elastic foundation

Abstract: The development in railway vehicle technology requires adequate dynamical analyses to ensure accurate and reliable information on the expected loading conditions of the vehicle components in the period of design This paper takes an attempt to formulate an exact mechanical and mathematical description of the wheel track system The wheel is considered as a rigid disk, while the track is modelled by an Euler-Bernoulli beam on damped elastic foundation The connection of the wheel and the track is realized by the linear Hertzian spring and damper Stability considerations, critical speed determina-tion and solution of the boundary value problem will be carried out Also the complex eigenfrequencies will be pointed out

Active Vibration Control of Rotating Machinery With a Hybrid Piezo-Hydraulic Actuator System

Abstract: An integrated, compact piezo-hydraulic actuator system for active vibration was designed and developed with a primary application for gas turbine aircraft engines. Copper tube was chosen as the transmission line material for ease of assembly. Liquid plastic which meets incompressibility and low viscosity requirements was adjusted to provide optimal actuator performance. Variants of the liquid plastic have been prepared with desired properties between −40°F and 400° F. The effectiveness of this hybrid actuator for active vibration control (AVC) was demonstrated for suppressing critical speed vibration through two critical speeds for various levels of intentionally placed imbalance. A high accuracy closed loop simulation which combines both finite element and state space methods was applied for the closed loop unbalance response simulation with/without AVC. Good correlation between the simulation and test results was achieved.Copyright © 1994 by ASME

Handling Characteristics of Four-Wheel-Steering Vehicles

Abstract: A linear analysis of four-wheel-sceering(4WS) vehicles is presented. Using the classical two degree-of-freedom "bicycle model" of the vehicle, comparisons of steady-state and transient responses are made between 4WS and FWS(front-wheel steering) vehicles. In addition, understeer coefficient and characteristic or critical speed are discussed. The findings indicate that maneuverability is increased at low speeds and stability is improved at high speeds in 4WS vehicles.

Speed Control of a Hybrid Transducer-type Ultrasonic Motor

Abstract: A hybrid transducer-type ultrasonic motor serves a high controllability, since the driving force can be controlled independently of the friction controlling component. The torsional vibration velocity has a direct effect on the speed, while the longitudinal vibration controls the traction transmission through friction. We can change the speed smoothly, if we vary the torsional vibration velocity, with the longitudinal vibration being maintained at the optimum value.This paper presents an experimental study of a speed control system for a hybrid transducer-type ultrasonic motor. First, we utilize an optical rotary encoder to measure the speed of the rotor, and it is feedbacked to the excitation magnitude of the torsional vibration. Stability and transient responses of the speed are improved. Second, we point out that the speed has a linear relation to the current of the torsional port. Then, by monitoring the current, a feedback system can be built without any auxiliary encoders.

Design, construction, and testing of a five active axes magnetic bearing system

Abstract: A high speed electric spindle based on active electromagnetic suspension technology has been designed, built, and tested. The main goal of the research work was the construction of a highly modular unit which can be used for teaching and research purposes. The design of the electromechanical components and of the control unit is described in detail, together with the characterization tests performed on the various subsystems. A description of the preliminary tests on the unit, conducted at speeds not in excess of the first deformation critical speed of the rotor, concludes the work.

Feed drive arrangement for machine tool table etc. - has leadscrew supported in rotatable nuts of crossbeams which are driven along bed guideways at half table speed by auxiliary leadscrew and which raise critical speed of leadscrew

Abstract: The table (10) has linear ball bearing units (8) running on guideways (6), and is driven along the bed by a leadscrew (2) supported in end bearings and engaging with a recirculating ball nut (3) fixed to the table. Also running on the guideways (6) are two crossbeams (13,14) connected by a bar (15) and having rotatably mounted recirculating ball nuts (4,5) in engagement with the leadscrew (2). Driven at half speed by a timing belt from the leadscrew (2) is an auxiliary leadscrew (16) of the same pitch and in engagement with a nut (24) fixed to the crossbeam (13) nearest the feed drive motor (23). Since the crossbeam nuts (4,5) are rotatably mounted the position of the beams along the bed is determined only by the rotation of the auxiliary leadscrew. Corresponding to the movement of the table (10) the crossbeams move at half speed to maintain optimum support of the leadscrew. USE/ADVANTAGE - Feed drive arrangement for machine tool table etc. raises critical speed of leadscrew and minimises vibration, esp. in high speed drives. System alignment is easily maintained.

A Study on the Whirling Critical Speeds of Marine Propeller Shafts

Abstract: In this paper the modelling procedure and analysis technique for the prediction of accurate critical speeds of marine propeller shafts are suggested. As a solution method the transfer matrix method is employed to calculate the critical speeds, which are correspond to natural frequencies of the shaft in lateral vibration, and whirling responses. Furthermore, in order to check the validity of the simple prediction formulae, such as Jasper's formula and Panagopulos's formula, numerical calculations were performed. From the numerical results it was found that the critical speed of the propeller shaft is sensitive to the position and the supporting conditions of journal bearings.

Alternative Approach to Estimation of Critical Cornering Speed

Abstract: An alternative approach to the estimation of the critical cornering speed of large combination vehicles is presented. Existing techniques are based on analytical models subject to a series of simplifying assumptions, and do not explicitly consider grades and other three‐dimensional roadway features of the real problem. One result of this study indicates that these simplified models may overestimate critical cornering speed by as much as 50%. The proposed technique combines detailed simulation of the dynamics of the motion of large combination vehicles through a three‐dimensional roadway, with a Monte Carlo sampling of possible vehicle configurations and component mechanical properties to produce databases for statistical analysis. This approach is applied to the study of critical cornering speed at freeway‐to‐freeway connectors. Databases for several samples of vehicles are generated, and a series of regression models that predict critical cornering speed is created. Results indicate that these regression...

Multifunction stop end for railway train

Abstract: The utility model relates to a multifunction stop end for a railway train, which is suitable for the tail of a railway marshalling yard and all places where the problem of slide of railway trains exists and has the functions of speed reduction, shutting-down and anti-slide for trains. The utility model is composed of an oil cylinder, a piston, a pressure valve, a speed valve, a return one-way valve, an unlocking part and a sealing cover. The utility model has the function of speed discrimination, or has critical speed. When the speed of a train is lower than the critical speed, the stop end does not perform the braking action, such as when the train is pulled out or passes through at high speed.

Unbalance response attenuation of a flexible rotor suspended by magnetic bearings with open loop control

Abstract: To reduce unbalance response of a flexible rotor suspended by electromagnetic bearings, two methods have mainly been investigated. One is the method of increasing damping of the mechanical system ; the other is the method of cancelling out unbalances. For the former method, PID control is generally used. Although PID control is very effective for reducing resonance vibration, in other ranges of rotational speed it yields little effect. On the other hand, with the latter method of open loop control, it is expected that unbalance response is greatly attenuated in all ranges of rotational speed. In this paper, we combine PID control and open loop control with a variable gain against rotational speed. PID control is needed to stabilize the rotor system and open loop control is used to reduce unbalance response. From calculated and experimental results, we find that the above method has greater capability of suppressing vibration of a flexible rotor than does ordinary PID control.

Forced Oscillations of a Continuous Rotor with Nonlinear Spring Characteristcs. Vertical Shaft with Geometric Nonlinearity.

Abstract: Nonlinear forced oscillations of a vertical continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft has geometric stiffening nonlinearity due to the extension of the shaft center line. The possibility of the occurrence of nonlinear forced oscillations at various subcritical speeds and the shapes of resonance curves at the major critical speeds and at some subcritical speeds are investigated. Consequently, the following is clarified : (a) the shape of resonance curves at the major critical speed becomes a hard-spring type, and (b) among various kinds of nonlinear forced oscillations, only some special kinds of summed-and-differential harmonic oscillations have possibility of occurrence.

Tensioning Effect on Rotating Disk Vibration

Abstract: Distributed tensioning in a wide range is usually applied to a tipped saw. This distributed tensioning effect was studied analytically and experimentally using normal and tensioned disks. The following conclusions were reached. (1) Residual stress due to tensioning was measured. Residual stress distribution could be calculated in terms of Gaussian-type isotropic additional stress. (2) Natural frequency change due to tensioning treatment was calculated by means of the energy method and was in good agreement with measured frequencies. (3) A backward-traveling wave of the two-nodal-diameter mode determined the critical rotating speed, and the rotating speed domain above this critical point was unstable. This phenomenon was confirmed by transfer function measurement. (4) The tensioning effect increased natural frequencies and expanded the stable domain.

Investigations on the Vibrational Behaviour of Gas Turbogenerator Units at the First Start-up: Aims and Methodology. Case Histories on 120 MW Units

Abstract: The paper illustrates methods and results of an investigation on the dynamic behaviour of gas turbine units, about which there was no previous operation experience in the Company. Deep insight into the dynamic response was gained. Vibration problems were early detected and their solution could be promptly devised by the manufacturers.

Right and Left-Hand Natural Modes of Industrial Rotating Machines. Model Study

Abstract: The rotors of rotating machines are guided by links. The matrixes representing links are, in general, not symmetrical. Right and left-hand natural modes differ. Left-hand modes are particularly used to define modal unbalances.