Showing papers on "Critical speed published in 2002"

Effects of rotational direction and rotation-to-revolution speed ratio in planetary ball milling

Abstract: The rotational direction of a pot in a planetary ball mill and its speed ratio against revolution of a disk were studied in terms of their effects on the specific impact energy of balls calculated from the simulation on the basis of the Discrete Element Method (DEM) and structural change of talc during milling. The specific impact energy of balls is measured as a significantly large value, and the structure of talc is transferred into an amorphous state quickly when the mill pot is rotated in the counter direction against the revolution. In both rotation–revolution relationships, the specific impact energy increases with an increase in the rotation-to-revolution speed ratio in the initial stage and then falls around the critical speed ratio, which can be calculated by the balance equation based on the centrifugal forces acting on a ball due to the combination of the rotation and revolution. The highest value in the specific impact energy of balls during milling can be achieved effectively around this critical speed. This critical speed would, therefore, be a key condition in milling for designing suitable and optimum mechanical milling performance.

Nonlinear effects in the response of a floating ice plate to a moving load

Abstract: The steady response of an infinite unbroken floating ice sheet to a moving load is considered. It is assumed that the ice sheet is supported below by water of finite uniform depth. For a concentrated line load, earlier studies based on the linearization of the problem have shown that there are two critical' load speeds near which the steady deflection is unbounded. These two speeds are the speed c 0 of gravity waves on shallow water and the minimum phase speed c min . Since deflections cannot become infinite as the load speed approaches a critical speed, Nevel (1970) suggested nonlinear effects, dissipation or inhomogeneity of the ice, as possible explanations. The present study is restricted to the effects of nonlinearity when the load speed is close to c min . A weakly nonlinear analysis, based on dynamical systems theory and on normal forms, is performed. The difference between the critical speed c min and the load speed U is taken as the bifurcation parameter. The resulting normal form reduces at leading order to a forced nonlinear Schrodinger equation, which can be integrated exactly. It is shown that the water depth plays a role in the effects of nonlinearity. For large enough water depths, ice deflections in the form of solitary waves exist for all speeds up to (and including) c min . For small enough water depths, steady bounded deflections exist only for speeds up to U * , with U * < c min . The weakly nonlinear results are validated by comparison with numerical results based on the full governing equations. The model is validated by comparison with experimental results in Antarctica (deep water) and in a lake in Japan (relatively shallow water). Finally, nonlinear effects are compared with dissipation effects. Our main conclusion is that nonlinear effects play a role in the response of a floating ice plate to a load moving at a speed slightly smaller than c min . In deep water, they are a possible explanation for the persistence of bounded ice deflections for load speeds up to c min . In shallow water, there seems to be an apparent contradiction, since bounded ice deflections have been observed for speeds up to c min while the theoretical results predict bounded ice deflection only for speeds up to U * < c min . But in practice the value of U * is so close to the value of c min that it is difficult to distinguish between these two values.

Coupled, forced response of an axially moving strip with internal resonance

Abstract: In this paper, the forced response of a non-linear axially moving strip with coupled transverse and longitudinal motions is studied. In particular, the response of the system is examined in the neighborhood of a 3 : 1 internal resonance between the first two transverse modes. The equations of motion are derived using the Hamilton's Principle and discretized by the Galerkin's method. First, with the longitudinal motion neglected, the forced transverse response is investigated by applying the method of multiple scales to assess the effects of speed and the internal resonance. In general, the speed is shown to affect each mode differently. The internal resonance results in the constant solutions having transition to instability of both a saddle-node type and a Hopf bifurcation. In the region where the Hopf bifurcation occurs, steady-state periodic motion does not exist. Instead the stable motion is amplitude- and phase-modulated. When the coupled system with longitudinal motion is examined with internal resonance, results reveal that the modulated motions disappear. Thus, the presence of the longitudinal motion has a stabilizing effect on the transverse modes in the Hopf bifurcation region. The second longitudinal mode is shown to drift due primarily to a direct excitation of the first transverse mode. Effects of the longitudinal motion on the transverse response are shown to be significant for speeds both away from and close to the critical speed.

Method and apparatus for varying the critical speed of a shaft

Abstract: A system is provided for changing the critical speed of a shaft that includes: a first shaft supported for relative rotational movement with respect to a stationary structure, a forward bearing disposed at the forward end of the shaft, an aft bearing disposed at the aft end of the shaft, at least one active bearing disposed between the forward bearing and the aft bearing, and means for changing the support stiffness of the active bearing.

A Passive Magnetic Bearing Flywheel

Abstract: A 100 percent passive magnetic bearing flywheel rig employing no active control components was designed, constructed, and tested. The suspension clothe rotor was provided by two sets of radial permanent magnetic bearings operating in the repulsive mode. The axial support was provided by jewel bearings on both ends of the rotor. The rig was successfully operated to speeds of 5500 rpm, which is 65 percent above the first critical speed of 3336 rpm. Operation was not continued beyond this point because of the excessive noise generated by the air impeller and because of inadequate containment in case of failure. Radial and axial stiffnesses of the permanent magnetic bearings were experimentally measured and then compared to finite element results. The natural damping of the rotor was measured and a damping coefficient was calculated.

Effect of lateral linear stiffness on nonlinear characteristics of hunting motion of a railway wheelset

Abstract: Railway wheelset experiences the problem of hunting above a critical speed, which is a kind of self-excited oscillation. At the critical speed, it is known that the system undergoes a subcritical Hopf bifurcation. Therefore, for clarifying the nonlinear characteristics of hunting it is very important to detect, for example, the nonlinear forces in the wheelset due to the creep forces acting between the wheels and rails, and the nonlinear component of the resorting forces by the suspensions. However, it is impossible to determine each force quantitatively. In the present paper, it is first shown, by using the center manifold theory and the method of normal form, that the nonlinear characteristics of the bifurcation in a wheelset model with two degrees of freedom are governed by a single parameter, hence each nonlinear force need not be detected when examining the nonlinear characteristics. Also, a method of determining the governing parameter from experimentally observed radiuses of the unstable limit cycle is proposed. Next, we experimentally investigate the variation of the parameter due to the presence of linear spring suspensions in the lateral direction and discuss the variation of the nonlinear characteristics of the hunting motion, which depends on the lateral stiffness. As a result, the improvement of the stability of the wheelset against the disturbance by the linear spring suspensions is clarified.

Optimization of the Lateral Stability of Rail Vehicles

Abstract: Summary The lateral stability of a rail vehicle is optimized using a combination of multibody dynamics, sequential quadratic programming, and a genetic algorithm. Several steps are taken to validate this integrated approach and to show its effectiveness. First, a hand-derived solution to a 17 degree of freedom linear rail vehicle model is compared to the simulation results from the A'GEM multibody dynamics software. Second, the calculation of the ‘critical speed’ (above which a rail vehicle response becomes unstable) using sequential quadratic programming is validated for a specific example. In the process, the existence of sharply-discontinuous ‘cliffs’ in the plots of critical speed versus suspension stiffnesses are identified. These cliffs, which are due to switching of the least-damped mode in the system, greatly hinder the application of gradient-based optimization methods. Two methods that do not require gradient information, a genetic algorithm and the Nelder-Mead's Simplex algorithm, are used to o...

Transient thermoelastic analysis of disk brake using the fast fourier transform and finite element method

Abstract: This article introduces a finite element method that combines the fast Fourier transform technique and a conventional finite element method as a computational technique for investigating a thermomechanical problem. The conventional finite element formulation is very inefficient in the analysis of a three-dimensional disk brake model of a rotating axisymmetric disk subjected to a nonaxisymmetric transient heat flux condition due to frictional contact with asymmetric pads fixed in space. Because the proposed technique reduces the three-dimensional disk brake mathematics to two dimensions, is an extreme time saver, and costs less, we can solve the transient thermoelastic problem and the thermoelastic instability. As a result of the study we present some analyses on temperature distributions and displacement distributions in a disk brake system at a low speed and on the hot spots at a high speed above critical speed.

Critical Speed Control of a Solar Car

Abstract: The World Solar Challenge is a 3000 km race for solar powered cars across the Australian continent from Darwin to Adelaide. Each car is powered by a panel of photovoltaic cells which convert sunlight into electrical power. The power can be used directly to drive the car or stored in a battery for later use. Previous papers (P. Howlett, P. Pudney, T. Tarnopolskaya, and D. Gates, IMA Journal of Mathematics Applied in Business and Industry vol. 8, pp. 59-81, 1997; P.G. Howlett and P.J. Pudney, Dynamics of Continuous, Discrete and Impulsive Systems vol. 4, pp. 553-567, 1998) using a simplified model of the battery, have shown that the optimal strategy is essentially a speedholding strategy. In this paper, with a more realistic model of the battery, we show that the optimal driving strategy is a critical speed strategy. For an optimal journey with no beginning and no ending the solar car must always travel at the critical speed. For an optimal journey of finite length the speed must be close to the critical speed for most of the journey. The critical speed depends on the solar power and will normally vary slowly with time.

Experimental Study on the Vibration of an Overhung Rotor with a Propagating Transverse Crack

Abstract: This paper presents an experimental study on the dynamic response of an overhung rotor with a propagating transverse crack The effects of a propagating transverse crack and side load on the dynamic response of an overhung rotor are investigated in order to identify vibration signatures of a propagating crack in rotating shafts Startup and steady state vibration signatures were analyzed and presented in the form of Bode plots, Frequency Spectrum Cascades, Frequency Spectrum Waterfalls and orbits The startup results showed that crack reduces the critical speed and increases the vibration amplitude of the rotor system It also excites 2X vibration in the startup vibration signatures The steady state results showed that the propagating crack produces changes in vibration amplitudes of 1X and 2X vibration harmonics and excites 3X harmonic just before fracture During crack propagation, 1X amplitude may increase or decrease depending on the location of the crack and the direction of vibration measurement while 2X amplitude always increases The steady state vibration signal of a propagating crack also produces a two-loop orbit

Vibration Instability in Rolling Mills: Modeling and Experimental Results

Abstract: Models for the occurrence of the vibrational instability during rolling known as third octave chatter are presented and discussed. An analysis of rolling mill chatter was performed for the purpose of identifying characteristics of the vibrations and to determine any dependency on the rolling schedule. In particular, a stability criterion for the critical rolling speed is used to predict the maximum rolling speed without chatter instability on schedules from a 5 stand tandem mill rolling thin steel product. The results correlate well with measurements of critical speed occurring on the mill using a vibration monitor: This research provides significant insights into the chatter phenomena and has been used to investigate control methods for suppression of the instability.

Critical and flutter speeds of optical disks

Abstract: Critical speeds and aerodynamic flutter instability of various optical disks are experimentally studied in this paper. The two nodal diameter modes of ASMO and CD/DVD disks have the lowest critical speeds at 3800 and 6900 rpm, respectively, where the backward natural frequency vanishes. As the rotational speed increases, aeroelastic disk flutter is observed. Experiments using ASMO disks show that the three nodal diameter mode causes flutter instability at 8750 rpm. At the flutter speed, the vibration amplitude of the flutter mode grows dramatically. The natural frequencies of multiple vibration modes remain almost constant in the post-flutter region, which is called frequency lock-on. CD/DVD disks do not experience flutter up to 14,000 rpm.

Active Control of the Running Behaviour of a Railway Vehicle: Stability and Curving Performances

Abstract: The paper deals with the application of active control to high speed trains. To this end, an innovative controlled electro-mechanical device was designed to substitute traditional yaw dampers currently in use. The main components of this system are a brushless motor, with gear and spindle, used to apply a longitudinal force between the carbody and the bogie, and a velocity transducer used to measure the yaw vibrations of the bogie. Different control strategies are developed for tangent track running, where the objective is to increase the critical speed, and for curve negotiation, where the goal is to reduce the maximum values of track shift forces. The paper also reports about the results of a mathematical model of the actively controlled vehicle. These results, together with those coming from line tests, show that the proposed active control strategy allows significant improvements in vehicle performances both in tangent track and in curve.

Effect of Temperature on Thermoelastic Instability in Thin Disks

Abstract: A model of a thin annular plate sliding against an elastic foundation was developed and used to study thermoelastic instability (TEI) in clutches. The analysis examines the stability of the quasi-steady state solution of the governing equations by considering non-axisymmetric perturbations. The results indicate that above critical values of temperature and sliding speed the response of the plate becomes unstable and exhibits large deformations. Two mechanisms account for this behavior: thermal buckling and bending. It is shown that a conservative approximation of the stability boundaries can be constructed by computing only two points on the stability curve. The boundary between stable and unstable behavior depends on the material properties, geometry, and boundary conditions. The model was used to conduct a parametric study which indicates that stability of the sliding system can be improved by reducing the sliding speed, decreasing the modulus of elasticity of the plate, increasing the thermal conductivity, or increasing the thickness. In addition, for a range of sliding speeds, increasing the stiffness of the friction material improves the stability of the system. For speeds outside this range, increasing the stiffness makes the system less stable.

Exact Analysis of Dynamic Sliding Indentation at any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space

Abstract: plane-strain study of steady sliding by a smooth rigid indentor at any constant speed on a class of orthotropic or transversely isotropic half-spaces is performed. Exact solutions for the full displacement fields are constructed, and applied to the case of the generic parabolic indentor. The closed-form results obtained confirm previous observations that physically acceptable solutions arise for sliding speeds below the Rayleigh speed, for a single critical transonic speed, and for all supersonic speeds. Continuity of contact zone traction is lost for the latter two cases. Calculations for five representative materials indicate that contact zone width achieves minimum values at high, but not critical, subsonic sliding speeds. A key feature of the analysis is the factorization that gives, despite anisotropy, solution expressions that are rather simple in form. In particular, a compact function of the Rayleigh-type emerges that leads to a simple exact formula for the Rayleigh speed itself. ©2002 ASME

Nonlinear investigation of the possibility to exceed the critical speed by a load on a string

Abstract: The paper is devoted to the investigation of a possibility of overcoming the critical speed by a moving concentrated load on a string. It is known that exceeding the critical speed is impossible in the framework of the linear statement for this problem. The general geometrically nonlinear statement for the problem is suggested. It allows one to take into account the coupling between transversal and longitudinal waves and the contact friction between the string and the load. It is shown that solutions corresponding to the case in which the load tries to overcome the critical speed are essentially nonlinear. The conception of critical speed for the case of nonlinear waveguide is discussed. It is shown that overcoming the critical speed is impossible in the system without friction. The speed of the load can reach and exceed the value of the critical speed for an unstrained string, but the solution remains subcritical. The case of decelerating load is also considered. Taking into account the contact friction between the string and the load explains that exceeding the critical speed can be possible. The nature of the wave resistance force exerting on the load from the string is discussed.

Sensitivity Analysis and Optimization of Undamped Rotor Critical Speeds to Supports Stiffness

Abstract: This paper introduced a new approach that employed the assumed-modes method and the receptance method, to the sensitivity analysis and the optimization of rotor-bearing systems. First, the frequency equation in terms of receptances was derived. The natural frequencies and the critical speeds for a typical rotor system were then illustrated. Beginning with the receptance equation, the authors, for the first time, derived a sensitivity matrix and employed it into an optimization process. The topographical method in conjunction with the variable metric method followed for the optimal solution. In the solution process, the sensitivity matrix provided important information for search direction. Examples of critical speeds adjustment via supports change in an optimal sense were illustrated. Numerical results showed that the approach was very efficient and the solutions were very accurate. This approach, in addition, provided such valuable information as which supports dominated specific critical speeds. The developed approach proved to be very helpful to rotor engineers in both rotor modification and rotor design.

The Role of High Performance Foil Bearings in an Advanced, Oil-Free, Integral Permanent Magnet Motor Driven, High-Speed Turbo-Compressor Operating Above the First Bending Critical Speed

Abstract: The demand for high power density, reliable, low maintenance, oil-free turbomachinery imposes significant demands on the bearing system. The full benefits of high speed, permanent magnet driven machines, for example are realized at speeds exceeding the capabilities of rolling element bearings. The high speeds, and a desire for oil-free operation also make conventional liquid lubricated bearings an undesirable alternative. The modern, oil-free foil bearing provides an excellent alternative, providing low power loss, adequate damping for supercritical operation, tolerance of elevated temperatures and long life. In this paper, the application of modern foil bearings to a high speed, oil-free turbo-compressor is discussed. In this demanding application, foil bearings support a 24 pound, multi-component rotor operating at 70,000 RPM with a bending critical speed of approximately 43,000 RPM. Stable and reliable operation over the full speed range has been demonstrated. This application also required low bearing start-up torque for compatibility with the constant torque characteristic of the integral permanent magnet motor. This work discusses the rotor bearing system design, the development program approach, and the results of testing to date. Data for both a turbine driven configuration, as well as a high speed integral motor driven configuration are presented.Copyright © 2002 by ASME

Braking control system for a washing machine

Abstract: An inner tub of a washing machine is rapidly braked during a portion of a deceleration phase following an extraction phase of an overall spin cycle. A controller establishes the braking operation over a critical speed band or resonant frequency zone during which excessive vibrations would be developed. The critical speed band is preferably determined based on one or more signals received from speed, load, and/or out-of-balance sensors.

An experimental investigation into vapor dispersion and solid suspension in boiling stirred tank reactors

Abstract: Power consumption, gas hold-up, critical impeller speed for just complete off-bottom solid suspension and minimum impeller speed for ultimately homogeneous solid suspension were measured in boiling water using a 0.2 m i.d. stirred tank reactor with three four-pitched blade downflow turbines. Water and three different size glass beads were used as the liquid and solid phases, respectively. At higher vapor generation rates nucleation occurred at the heater, whereas at low vapor generation rates vapor was mainly generated from the impellers instead of the heater. At higher vapor generation rates, the boiling-to-nonboiling mechanical power ratio and the gas hold-up decreased and increased uniformly with increasing impeller rotational speed, respectively. At lower vapor generation rates, however, boiling-to-nonboiling mechanical power ratio exhibited a minimum and gas hold-up went through a maximum with varying impeller rotational speed. The changes in the nucleation site and solid suspension with impeller speed were responsible for these hydrodynamic behaviors. An empirical correlation for the Reynolds number corresponding to the minimum power consumption ratio or corresponding to the maximum gas hold-up in boiling liquids was developed using the present experimental data. The critical impeller speed for just complete off-bottom solid suspension and minimum impeller speed for ultimately homogeneous solid suspension in boiling systems were higher than those in gas-sparging systems. On the whole, the solid suspension in the boiling systems was poor as compared with that in the gas-sparging systems. Empirical correlations for critical impeller speed for just complete off-bottom solid suspension and minimum impeller speed for ultimately homogeneous solid suspension in boiling slurry stirred tank reactors were proposed.