Showing papers on "Critical speed published in 2009"

Diagnosis of Induction Machines' Rotor Faults in Time-Varying Conditions

Abstract: Motor current signature analysis is the reference method for the diagnosis of induction machines' rotor faults; however, in time-varying conditions, it fails as slip and speed vary, and, thus, sideband components are spread in a bandwidth that is proportional to the variation. Variable speed drive applications are common in the aerospace, appliance, railway, and automotive industries and also in electric generators for wind turbines. In this paper, a simple and effective method is presented that allows the diagnosis of rotor faults for induction machine drives in time-varying conditions. It is tailored to direct rotor flux field-oriented controlled drives, where the control system provides suitable signals that are exploited for the demodulation to a constant frequency of time-varying signatures related to the rotor faults. Simulations and experiments are reported to validate the proposed method on a critical speed transient.

Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

Abstract: We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

Particle capture in binary solidification

Abstract: We examine the interaction of a spherical foreign particle with a propagating solidification front in a binary alloy. Depending on the material properties and the speed of the front, the particle may be pushed ahead of the front, or engulfed and incorporated into the solid phase. We apply numerical boundary integral and continuation methods to determine the critical speed for particle capture, as a function of the system parameters. We reconcile the differing predictions of previous theoretical works, and show that many typical systems may obey a new scaling of the critical speed, as obtained here. We show that due to constitutional undercooling, the presence of solute decreases particle speeds by an order of magnitude below those for a single-component system. We briefly consider the case of spherical bubbles, where thermocapillary and solutocapillary effects play a large role.

Rotordynamics of 120 $\thinspace$ 000 r/min 15 kW Ultra High Speed Motor

Abstract: This paper introduces a rotor with shrink fit and analyzes its rotordynamics by 3-D FEA. An ultra high speed motor prototype is manufactured for fuel cells at the rating of 15 kW, 120000 r/min. First, the stability of the rotor structure with shrink fit is evaluated in non-loading and loading condition (120 000 r/min, 210degC). And then the 3-D rotordynamics analysis and Campbell diagram considering shrink fit are examined for the critical speed of rotor. The analysis shows that the critical speed of the rotor is higher when the rotor is shrink fitted than when the rotor is not shrink fitted. The analysis also shows the increase of shaft stiffness when the rotor is shrink fitted.

Blade Tip Clearance Flow and Compressor Nonsynchronous Vibrations: The Jet Core Feedback Theory as the Coupling Mechanism

Abstract: This paper investigates the role of tip clearance flow in the occurrence of nonsynchronous vibrations (NSVs) observed in the first axial rotor of a high-speed high-pressure compressor in an aeroengine. NSV is an aeroelastic phenomenon where the rotor blades vibrate at nonintegral multiples of the shaft rotational frequencies in operating regimes where classical flutter is not known to occur. A physical mechanism to explain the NSV phenomenon is proposed based on the blade tip trailing edge impinging jetlike flow, and a novel theory based on the acoustic feedback in the jet potential core. The theory suggests that the critical jet velocity, which brings a jet impinging on a rigid structure to resonance, is reduced to the velocities observed in the blade tip secondary flow when the jet impinges on a flexible structure. The feedback mechanism is then an acoustic wave traveling backward in the jet potential core, and this is experimentally demonstrated. A model is proposed to predict the critical tip speed at which NSV can occur. The model also addresses several unexplained phenomena, or missing links, which are essential to connect tip clearance flow unsteadiness to NSV. These are the pressure level, the pitch-based reduced frequency, and the observed step changes in blade vibration and mode shape. The model is verified using two different rotors that exhibited NSV.

Soft EHL Simulations of U-Cup and Step Hydraulic Rod Seals

Abstract: A numerical soft elastohydrodynamic lubrication model of a reciprocating hydraulic seal has been used to simulate the performance of a U-cup seal and a step seal in a conventional actuator. The model consists of coupled steady state fluid mechanics, deformation mechanics, contact mechanics, and thermal analyses, with an iterative computational procedure. The results indicate that for a given seal roughness and stroke length there is a critical rod speed above which the seal will not leak. The critical speed is dependent on both seal roughness and sealed pressure.

Imbalance Vibration Suppression of a Supercritical Shaft via an Automatic Balancing Device

Abstract: This research explores the use of automatic balancing (AB) devices or "autobalancers" for imbalance vibration suppression of flexible shafts operating at supercritical speeds. Essentially an autobalancer is a passive device consisting of several freely moving eccentric masses or balancer balls free to roll within a circular track mounted on a rotor that is to be balanced. At certain speeds, the stable equilibrium positions of the balls are such that they reduce or cancel the rotor imbalance. This "automatic balancing" phenomenon occurs as a result of the nonlinear dynamic interactions between the balancer balls and the rotor transverse vibration. Thus, autobalancer devices can passively compensate for unknown imbalance without the need for a control system and are able to naturally adjust for changing imbalance conditions. Autobalancers are currently utilized for imbalance correction in some single plane rotor applications such as computer hard-disk drives, CD-ROM drives, machine tools and energy storage flywheels. While autobalancers can effectively compensate for imbalance of planar, disk-type, rigid rotors, the use of autobalancing devices for nonplanar and flexible shafts with multiple modes of vibration has not been fully considered. This study explores the dynamics and stability of an imbalanced flexible shaft-disk system equipped with a dual-ball automatic balancing device. The system is analyzed by solving a coupled set of nonlinear equations to determine the fixed-point equilibrium conditions in rotating coordinates, and stability is assessed via eigenvalue analysis of the perturbed system about each equilibrium configuration. It is determined that regions of stable automatic balancing occur at supercritical shaft speeds between each flexible mode. Additionally the effects of bearing support stiffness, axial mounting offset between the imbalance and autobalancer planes, and ball/track viscous damping are explored. This investigation develops a new, efficient, analysis method for calculating the fixed-point equilibrium configurations of the flexible shaft-AB system. Finally, a new effective force ratio parameter is identified, which governs the equilibrium behavior of flexible shaft/AB systems with noncollocated autobalancer and imbalance planes. This analysis yields valuable insights for balancing of flexible rotor systems operating at supercritical speeds.

Synchronous Response to Rotor Imbalance Using a Damped Gas Bearing

Abstract: One type of test performed for evaluating bearings for application into turbomachinery is the synchronous bearing response to rotor imbalance. This paper presents rotordynamic tests on a rotor system using a 70 mm diameter damped gas bearing reaching ultra-high speeds of 50,000 rpm. The main objective of the study was to experimentally evaluate the ability of the damped gas bearing to withstand large rotor excursions and provide adequate damping through critical speed transitions. Two critical speeds were excited through varying amounts and configurations of rotor imbalance while measuring the synchronous rotordynamic response at two different axial locations. The results indicated a well-damped rotor system and demonstrated the ability of the gas bearing to safely withstand rotor vibration levels while subjected to severe imbalance loading. Also, a waterfall plot was used to verify ultra-high-speed stability of the rotor system throughout the speed range of the test vehicle. In addition to the experimental tests, a rotordynamic computer model was developed for the rotor-bearing system. Using the amplitude/ frequency dependent stiffness and damping coefficients for the ball bearing support and the damped gas-bearing support, a pseudononlinear rotordynamic response to imbalance was performed and compared with the experiments.

Scaling and dynamics of washboard roads.

Abstract: Granular surfaces subjected to forces due to rolling wheels develop ripples above a critical speed. The resulting pattern, known as washboard or corrugated road, is common on dry unpaved roads. We investigated this phenomenon theoretically and experimentally using laboratory-scale apparatus and beds of dry sand. A thick layer of sand on a circular track was forced by a rolling wheel on an arm whose weight and moment of inertia could be varied. We compared the ripples made by the rolling wheel to those made using a simple inclined plow blade. We investigated the dependence of the critical speed on various parameters and described a scaling argument that leads to a dimensionless ratio, analogous to the hydrodynamic Froude number, which controls the instability. This represents the crossover between conservative dynamic forces and dissipative static forces. Above onset wheel-driven ripples move in the direction of motion of the wheel, but plow-driven ripples move in the reverse direction for a narrow range of Froude numbers.

Transfer matrix for rotor coupler with parallel misalignment

Abstract: A transfer matrix for shafts coupler with parallel misalignment (offset) was derived. The responses of a rotor system composed of flexible shafts, unbalanced disks, elastic supports and shafts coupler with misalignment were then investigated. Through the derivation, the boundary shears induced by a rotating shaft were first discovered to be coupled in two perpendicular directions. These coupling shears might reduce the first critical speed up to 50% in the free-free case. The studies showed that the shafts coupler altered the rotor’s critical speeds and the misalignment played as an external load resulting through the whole driven shaft. The combined effects of disk unbalance and shaft misalignment showed that the misalignment predominated the response in most of the rotation speeds, but the unbalance could become significant at high speed. The whirling orbits before and after the misalignment were illustrated as well, and numerical results showed that the two ends of the misalignment whirled asynchronously as the rotation fell into some regions.

Vibration Control and Unbalance Estimation of a Nonlinear Rotor System Using Disturbance Observer

Abstract: In rotating machinery, rotor unbalance causes many resonances at critical speeds corresponding to different modes. In this paper, a vibration control method for rotor systems utilizing disturbance observer is proposed. The nonlinear terms, unbalance, parameter variations, and uncertain terms of a rotor system are lumped into a disturbance term, and this term is canceled by using disturbance observer. As a result, the vibrations are suppressed to small amplitudes all over the rotational speed range. Simultaneously, unbalance of the first mode is estimated from the information of control force of disturbance observer. Moreover, the effects of parameter errors of the control system are also investigated. The validity of the proposed method is verified through numerical simulations and experiment.

Display control device and display control method

Abstract: PROBLEM TO BE SOLVED: To provide a display control device that allows a flexible and high-speed scroll operation while minimizing the load of reading huge amount of data, with a sense of distance SOLUTION: The display control device is provided with: an acquisition means 34 for acquiring data configuring predetermined information; a detection means 34 for detecting the scroll speed; a generation means 34 for calculating a moving speed when a frame is displayed, for each frame, based on the scroll speed, and for generating moving speed information based on the result; a determination means 34 for, based on the generated moving speed information and a predetermined visual recognition critical speed, determining whether the moving speed of the frame exceeds a visual recognition critical speed; and a display control means 34 for, when the moving speed of the frame does not exceed the visual recognition critical speed, controlling the acquisition means 34 to acquire the data configuring the predetermined information of the item, and for controlling the display to display the predetermined information when the frame is displayed on the display, and for, when the moving speed of the frame exceeds the visual recognition critical speed, controlling the display to display the predetermined image when the frame of the item is displayed on the display COPYRIGHT: (C)2011,JPO&INPIT

Magnetic Bearing Application by Time Delay Control

Abstract: In this paper a magnetic bearing system is designed for the suppression of rotor vibration. Magnetic bearing is able to support the shaft without mechanical contacts, and it is also able to control the rotational vibration. Magnetic bearing is composed of position sensors, a digital controller, actuating amplifiers, and electromagnets. In order to control the vibration of a magnetic bearing system effectively, Time Delay Control (TDC) is utilized. It proposes the design skill of an optimal controller when the system has the uncertainty, i.e. it has a difficulty in extracting the exact mathematical expressions, as well as it has external disturbances. The observer with the position information is utilized as a feedback signal for regulating the rotor whirling motion. Simulation is performed first to check the validation of the proposed controller in suppressing the rotor whirling. Experiments are followed to guarantee its usefulness in the rotor rig with a magnetic actuator. The vibrating suppression is co...

High-frequency ultrasonic elliptical vibration cutting device

Abstract: The invention discloses a high frequency ultrasound elliptic vibration cutting device which comprises an ultrasound vibration unit and a casing unit. The ultrasound vibration unit is arranged in the casing unit. The casing unit comprises a base, A cover plate, B cover plate and an upper cover plate. The ultrasound vibration unit comprises an amplitude transformer, a vibrating body, A excitation source, B excitation source and C excitation source. The amplitude transformer is installed on the vibrating body. The end part of the amplitude transformer is provided with a cutting tool. The A excitation source and the B excitation source are arranged in parallel way and are adhered on the lateral side of the vibrating body. The C excitation source is installed on the lower part of the vibrating body. The A excitation source and the B excitation source form the driving power in horizontal direction. The C excitation source forms the driving power in vertical direction. The phase separation between two mutually vertical high frequency vibrations is applied for compounding an elliptic vibration at the point of the cutting tool. Thus, the processing surface roughness is lowered effectively. The cutting device works at the high vibration frequency of 100 kHz-200 kHz, so that the vibration chipping critical speed of the cutting tool is improved, and the processing efficiency is improved obviously. The amplitude transformer is adopted to be inserted in the vibration body, so that the installation is easy, and the practicality of the ultrasound elliptic vibration cutting can be promoted.

Active Control of Rotor Vibrations by Two Feedforward Control Algorithms

Abstract: Resonance vibrations (critical speeds) play a significant role in rotor vibration control. Active vibration control methods for rotors are studied to develop solutions to enhance machines' dynamic b ehavior, durability, and operating range. This paper reports rotor vibration attenuation with a supplementary electromagnetic actuator located outside the rotor bearing span. Feedback and feedforward control system design are shown, and comparative experiments on two active vibration control methods for mass unbalance compensation are reported. The methods compared are adaptive FIR filter with the least mean squares (LMS) algorithm and convergent control (CC) method with a frequency-domain adaptation algorithm. The methods were experimentally validated on the rotor test rig (rotor weight 2.7 kg, length 560 mm, and first critical speed about 50 Hz). The feedback system provided wideband damping in the sub- and supercritical regions. The feedforward systems attenuated vibratory responses at the speed of rotation and its harmonic. The attenuation achieved was about 20 dB depending on the rotor speed. Also, discrete-time CC algerithm is shown to have a feedback equivalent circuit. The significance of feedback control lies in making the system phase-characteristics sufficiently smooth for feedforward control methods. Then, feedforward algorithms provided a good vibration damping performance over the operating range. CC was found to be a more effective and simpler algorithm for the purpose than the adaptive FIR filter with the LMS algorithm. The equivalent feedback circuit derived for CC, and systems similar to CC, facilitates their stabil ty and robustness analysis.

Comparison of Tilting-Pad Journal Bearing Dynamic Full Coefficient and Reduced Order Models Using Modal Analysis

Abstract: There is significant disagreement concerning the frequency response of tilting pad journal bearings (TPJBs) due to non-synchronous excitations. Two linear models for the frequency dependence of TPJBs have been proposed. The first model, the full-coefficient or KC model, considers Np tilting pads and rotor motions for Np + 2 degrees of freedom. Dynamic reduction of the KC model results in eight frequency-dependent stiffness and damping coefficients. The second model, based on results from bearing system identification experiments, yields twelve frequency-independent stiffness, damping, and mass (KCM) coefficients. Experimental data has been presented to support both models. There are major differences in the two approaches. The analysis in this paper takes a new approach of considering the pad dynamics explicitly in a state-space modal analysis. TPJB shaft and bearing pad stiffness and damping coefficients are calculated using a well known laminar, isothermal analysis and a pad assembly method. The TPJB rotor and pad full system eigenvalues and eigenvectors are then evaluated using state-space methods, with rotor and bearing pad inertias included explicitly in the model. The full bearing coefficient results are also non-synchronously reduced to the 8 stiffness and damping coefficients are and expressed as shaft complex impedances. The system identification method is then applied to these complex impedances, and the state space modal analysis is applied to the resulting KCM model. The damping ratios, natural frequencies, and mode shapes from the two bearing representations are compared. Two example TPJBs are examined in detail. The analysis indicated that four underdamped modes, two forward and two backward, dominate the rotor response over excitation frequencies from 0 to running speed. The full coefficient, non-synchronously reduced model predicts additional critically damped or overdamped modes due to the additional degrees of freedom as compared to the identified KCM model. The KCM model results in natural frequencies that are 63–65 percent higher than the full coefficient model. The difference in modal damping ratio estimates depend on the TPJB considered, with KCM being 7–17 percent higher than the full coefficient model. The full coefficient model also indicates that the bearing pads contribute significantly to the underdamped modes. The results indicate that the system identification method results in a reduced order model of TPBJ dynamic behavior. Additionally, the differences in the modal calculated system natural frequency and modal damping have potential implications for rotordynamic analyses of flexible rotors, such as critical speed and stability analyses.Copyright © 2009 by ASME

Vibration Suppression of Rotating Machinery Utilizing an Automatic Ball Balancer and Discontinuous Spring Characteristics

Abstract: Automatic ball balancer is a balancing device where two balls inside a hollow rotor move to optimal rest positions automatically to eliminate unbalance. As a result, vibrations are suppressed to the zero amplitude in the rotational speed range higher than the major critical speed. However, it has the following defects. The amplitude of vibration increases in the rotational speed range lower than the major critical speed. In addition, almost periodic motions with large amplitude occur in the vicinity of the major critical speed due to the rolling of balls inside the rotor. Because of these defects, an automatic ball balancer has not been used widely. This paper proposes the vibration suppression method utilizing the discontinuous spring characteristics together with an automatic ball balancer to overcome these defects and to suppress vibration. The validity of the proposed method is confirmed theoretically, numerically, and experimentally. The results show that amplitude of vibration can be suppressed to a small amplitude in the vicinity of the major critical speed and the zero amplitude in the range higher than the major critical speed.

A novel design for a gas-inducing impeller at the lowest critical speed

Abstract: To disperse the unreacted overhead gas phase into the liquid in an agitated reactor without gas outlet, a gas-inducing impeller is usually employed. To determine the lowest critical rotating speed, the gas-induction mechanism was reconsidered by constituting a mechanical energy conservation equation between the gas inlet orifice in the gas phase and the gas outlet orifice in the liquid phase under a certain rotational speed. According to this model, the critical speed of the gas-inducing impeller could be basically determined by the submersion depth and the radial position of the gas outlet, and a novel design was proposed by introduction of six short pipes stretched radially from the axis of the impeller. The final design of the gas-inducing impeller was obtained by an optimal combination of the gas-inducing pipes, the blades of the impeller and the baffle dimension.

Mathematical analysis of rotor shaft displacements in asynchronous machines; a critical speed or just a rotation of the orbit axis?

Abstract: This paper presents a mathematical analysis of rotor shaft displacements in asynchronous machines caused by different types of rotor eccentricity. Based on a simplified rotor model, the theoretical coherence between electromagnetic, rotor dynamic, and the specific characteristics of sleeve bearings is shown. The orbits of the rotor mass and the shaft journal are mathematically described for each kind of eccentricity and the shaft displacement with respect to two virtual fixed sensors is derived. Based on this theoretical description and on a numerical example, the paper shows that focusing in a theoretical rotor dynamic analysis only on the calculated amplitudes in direction of two fixed sensor positions, may lead to wrong conclusions concerning the evaluation of resonances. The aim of this paper is, based on a simplified rotor model, to show the mathematical coherence concerning typical rotor eccentricities in asynchronous machines and to demonstrate the necessity to focus not only on the amplitudes relative to two fixed sensor positions, but to also consider the semi-major axis of the calculated orbit and its angular position. The aim of the paper is not to replace a detailed finite element rotor dynamic analysis by a simplified analytical rotor model for predicting the real shaft vibrations. The intension is to prepare the basis for adopting the conclusions, derived from a simplified analytical model, into a more detailed rotor dynamic model – e.g. a finite element rotor dynamic model – and therefore to derive a more precise theoretical analysis of the real shaft displacements.

The Critical Speed of Slipper Bearings in Axial Piston Swash Plate Type Pumps and Motors

Abstract: A stationary model is adopted to determine the critical condition for which the slipper moves away from the swashplate in an axial piston machine. The aim of the analysis is to find the critical speed, i.e. the value of the machine speed for which the slipper moves away from the swashplate; usually this condition may determine bad operating behaviour of the machine, although a retainer plate is used to maintain the slipper sufficiently near to the swashplate. The influences of the pressure transition in the cylinder, the swashplate angle and the radial clearance between piston and cylinder on the critical speed are depicted. Successively, the role of the position of the point of application of the resultant force due to the slipper-retaining plate contact is analyzed.Copyright © 2009 by ASME