Showing papers on "Critical speed published in 2006"

Dynamic Behavior and Stability of a Rotor Under Base Excitation

Abstract: The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.

Development of the active balancing device for high-speed spindle system using influence coefficients

Abstract: A high-speed spindle can be very sensitive to rotating mass unbalance which has harmful effect on many types of rotating machinery. Therefore, the balancing procedure is certainly needed to reduce vibration in all high-speed rotating systems. In this study, an active balancing program using influence coefficient method and an active balancing device of an electro-magnetic type with both simple and reliable structures were applied to the developed high-speed spindle system. A gain scheduling control using influence coefficients of the reference model was proved to be effective in balancing the spindle system although its characteristics were changed. The stability of reference influence coefficients was verified by experiments with frequency response functions. The active balancing experiment of the manufactured spindle system using an active balancing program and device was also performed efficiently during the operation. As a result, controlled unbalance responses after balancing work were below the vibration limit at all rotating speed ranges including critical speeds.

Vibration Suppression of a Flexible Shaft with a Simplified Bearingless Induction Motor Drive

Abstract: In this paper, new strategies of vibration suppression in flexible shaft of a motor with active and passive magnetic forces are presented. The shaft magnetic damping is originated from the principle of a bearingless motor having a radial magnetic force generation. The radial force is used for shaft vibration suppression in order to go through the first critical speed. Simplifications are described in suppression force system. Elimination of power source with self-excitation is proposed. Further elimination of sensors, controllers, and inverters is also proposed, although the effectiveness is limited.

Rain-wind induced vibrations - : phenomenology, mechanical modelling and numerical analysis

Abstract: The simultaneous appearance of rain and wind at cables of cable stayed bridges and hangars of arch bridges may induce varying oscillations with large amplitudes. These phenomena are identified as rain–wind induced vibrations. The paper presents a possible fluid-mechanical interpretation of rain–wind induced vibrations. Based on this interpretation a mechanical model is deduced, in order to enable numerical investigations. The complex system of nonlinear differential equations is analysed concerning the stability of solutions. Rain–wind induced vibrations exist only within a certain range of wind velocity. The lower limit of the critical velocity range is determined for various cable inclinations and angles of incidence. Furthermore, a fluid mechanical interpretation is given for the existence of the upper limit of critical velocity. The approximation of the upper limit velocities and the determination of the critical cable diameters can be derived from established fluid-mechanical correlations. The numerical investigations show that rain–wind induced oscillations occur on vertical cables, too. For the Faro–Falster Bridge, the numerical vibration analysis is carried out for the cables parallel and perpendicular to the wind direction. The analysis of the vibration frequencies is demonstrated for the Domitz Bridge.

Critical speed and limit cycles in the empty Y25-freight wagon

Abstract: In this research, an empty freight wagon with Y25 bogies have been modelled. Non-linear creep forces with spin moment between wheel and rail have been used, and also all impacts and friction forces have been modelled. Non-linear equations of motion and kinematical constraints have been solved in time domain, and limit cycles, saddle nodes, and critical speeds have been shown. Both primary and secondary hunting can be seen in the responses of the wagons. The relation between frequency of oscillations and speed can be seen, also, there are chaotic oscillations. Results show that stiffness in impacts affects calculation time and limit cycles.

Sliding thermoelastodynamic instability

Abstract: Numerous mechanisms can give rise to instabilities and vibrations in sliding systems. These can generally be characterized as either elastodynamic (e.g. brake squeal) or thermoelastic. The time-scales of these processes differ considerably, so it is usual to neglect coupling between them, i.e. to neglect thermal effects in elastodynamic analyses and to use the quasi-static approximation in thermoelastic analyses. In the present paper, we consider the potential coupling between them in the simplest possible contexta thermoelastodynamic layer sliding against a rigid plane and constrained to one-dimensional displacements. The results show that although the coupling is extremely weak, it has a destabilizing effect on the natural elastodynamic vibration of the layer at arbitrarily low sliding speeds. A numerical solution of the transient equations below the quasi-static critical speed shows that an initial disturbance grows exponentially until periods of separation develop, after which the system approaches as...

Kneading machine and kneading control method

Abstract: An object of the invention is to provide a mixer and a mixing control method that enable to keep the driving efficiency of a motor high, and to flexibly follow a predetermined rotation speed of a mixing rotor pair, which is varied depending on various applications of the mixing rotor pair. A fixed speed motor is rotated at a constant rotation speed, and a variable speed motor is variably rotated at an arbitrary rotation speed. A difference in rotation speed between the fixed speed motor and the variable speed motor is supplied to the mixing rotor pair as the rotation speed by operations of a sun gear, a planetary gear, an internal gear, and a gear retainer of a planetary gear transmission.

Frequency Analysis of a Rotating Cantilever Beam Using Assumed Mode Method with Coupling Effect

Abstract: A frequency response analysis for a rotating cantilever beam is presented in this study. The equations of motion are derived from Hamilton's principle. An assumed mode method is used for analyzing the vibration frequency characteristic. The equations are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of rotating angular speed are investigated through numerical study. With the coupling effect ignored, the analysis results are consistent with the results obtained by the conventional method. As the angular speed increases, the bending natural frequencies increase monotonically and the stretching natural frequencies decrease. With the coupling effect considered, when the angular speed increases up to a certain value, there exists the warping speed that is in relation with the slenderness ratio.

Hydrodynamic Fluid Film Bearings and Their Effect on the Stability of Rotating Machinery

Abstract: : The lecture introduces the basic principles of hydrodynamic lubrication and the fundamental equation of Classical Lubrication Theory. The analysis proceeds to derive the static and dynamic performance characteristics of short length cylindrical journal bearings, with application to the dynamic forced performance of a rigid rotor supported on plain bearings. In a radial bearing, the Sommerfeld number defines a relationship between the static load and the journal eccentricity within the bearing. This design parameter shows the static performance of the bearing as rotor speed increases. Rotordynamic force coefficients are introduced and their effect on the stability of a rotor-bearing system thoroughly discussed. Cross-coupled force coefficients are solely due to journal rotation, and the magnitude (and sign) of the cross-stiffness determines rotordynamic stability. The whirl frequency ratio (WFR) relates the whirl frequency of subsynchronous motion to a threshold speed of instability. The desired WFR is null; however, plain cylindrical bearings show a whirl ratio of just 0.50, limiting the operation of rotating machinery to shaft speeds below twice the system first critical speed. The analysis concludes with a review of practical (in use) journal bearing configurations with highlights on their major advantages and disadvantages, including remedies to reduce or entirely avoid subsynchronous whirl instability problems.

Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions

Abstract: Gas foil bearings (GFBs) satisfy the requirements for oil-free turbomachinery, i.e. simple construction and ensuring low drag friction and reliable high speed operation. However, GFBs have a limited load capacity and minimal damping, as well as frequency and amplitude dependent stiffness and damping characteristics. This paper provides experimental results of the rotordynamic performance of a small rotor supported on two bump-type GFBs of length and diameter equal to 38.10 mm. Coast down rotor responses from 25 krpm to rest are recorded for various imbalance conditions and increasing air feed pressures. The peak amplitudes of rotor synchronous motion at the system critical speed are not proportional to the imbalance introduced. Furthermore, for the largest imbalance, the test system shows subsynchronous motions from 20.5 krpm to 15 krpm with a whirl frequency at ∼ 50% of shaft speed. Rotor imbalance exacerbates the severity of subsynchronous motions, thus denoting a forced nonlinearity in the GFBs. The rotor dynamic analysis with calculated GFB force coefficients predicts a critical speed at 8.5 krpm, as in the experiments; and importantly enough, unstable operation in the same speed range as the test results for the largest imbalance. Predicted imbalance responses do not agree with the rotor measurements while crossing the critical speed, except for the lowest imbalance case. Gas pressurization through the bearings’ side ameliorates rotor subsynchronous motions and reduces the peak amplitudes at the critical speed. Post-test inspection reveal wear spots on the top foils and rotor surface.Copyright © 2006 by ASME

Finite Element Analysis of Thermoelastodynamic Instability Involving Frictional Heating

Abstract: A finite element method is used to solve the problem involving thermoelastodynamic instability (TEDI) in frictional sliding systems. The resulting matrix equation contains a complex eigenvalue that represents the exponential growth rate of temperature, displacement, and velocity fields. Compared to the thermoelastic instability (TEI) in which eigenmodes always decay with time when the sliding speed is below a critical value, numerical results from TEDI have shown that some of the modes always grow in the time domain at any sliding speed. As a result, when the inertial effect is considered, the phenomenon of hot spotting can actually occur at a sliding speed below the critical TEI threshold. The finite element method presented here has obvious advantages over analytical approaches and transient simulations of the problem in that the stabilities of the system can be determined for an arbitrary geometry without extensive computations associated with analytical expressions of the contact condition or numerical iterations in the time domain. DOI: 10.1115/1.2345412

Chaotic Vibration and Internal Resonance Phenomena in Rotor Systems

Abstract: Rotating machinery has effects of gyroscopic moments, but most of them are small. Then, many kinds of rotor systems satisfy the relation of I to (-1) type internal resonance approximately. In this paper, the dynamic characteristics of nonlinear phenomena, especially chaotic vibration, due to the 1 to (-1) type internal resonance at the major critical speed and twice the major critical speed are investigated. The following are clarified theoretically and experimentally: (a) the Hopf bifurcation and consecutive period doubling bifurcations possible route to chaos occur from harmonic resonance at the major critical speed and from subharmonic resonance at twice the major critical speed, (b) another chaotic vibration from the combination resonance occurs at twice the major critical speed. The results demonstrate that chaotic vibration may occur even in the rotor system with weak nonlinearity when the effect of the gyroscopic moment is small.

Modelling of floating-slab track with discontinuous slab part 1: response to oscillating moving loads

Abstract: This paper presents three different methods for modelling a track with discontinuous slab under oscillating moving loads. These are the FourierRepeating-unit method, the Periodic-Fourier method and the Modified-phase method. The first two methods, borrowed from the literature of periodic infinite structures, are accurate if careful consideration is taken when performing numerical integrations. The third method, not presented elsewhere before, is faster and simpler; it is only valid for velocities of moving loads lower than the critical velocity of the track, but this “velocity effect” is of no consequence for underground railways. Discontinuity of slab provides a parametric excitation for moving loads over floating-slab tracks. It is shown that in the frequency range of ground-borne vibration, more vibration propagates form such tracks at resonance frequencies of the slabs, compared with tracks with continuous slabs. It is found that the velocity effect is insignificant when calculating displacements of a typical floating-slab track under oscillating moving loads with velocities less than 100km/hr. However, a correction has to be made to account for the right phase between the input force and the output displacement.

Interface Instability under Forced Displacements

Abstract: By applying linear response theory and the Onsager principle, the power (per unit area) needed to make a planar interface move with velocity V is found to be equal to V2/ μ, μ a mobility coefficient. To verify such a law, we study a one dimensional model where the interface is the stationary solution of a non local evolution equation, called an instanton. We then assign a penalty functional to orbits which deviate from solutions of the evolution equation and study the optimal way to displace the instanton. We find that the minimal penalty has the expression V2/ μ only when V is small enough. Past a critical speed, there appear nucleations of the other phase ahead of the front, their number and location are identified in terms of the imposed speed.

Recent advances in the fundamental understanding of railway vehicle dynamics

Abstract: The topic of this article is the calculation of the critical speed for railway vehicles. It is emphasised that it is misleading to formulate the mathematical problem as a stability problem. It must correctly be formulated as a problem of existence of coexisting solutions to the full non-linear dynamical problem. The lowest speed at which there exist more solutions is the true critical speed, which corresponds well with the measured critical speed in road tests. A couple of examples show applications of the method to various dynamical models of railway vehicles. Freight wagons are treated in the end of the article because the dry friction damping with stick-slip and end stops in the suspensions demand the use of the newest numerical solvers and great care in their application to the dynamical problem in order to obtain reliable results.

Automotive composite driveshafts: investigation of the design variables effects

Abstract: Laminated composites, with their advantage of higher specific stiffness, gained substantiality in the field of torque carrying structures through many applications. Composite drive shafts offer the potential of lighter and longer life drive train with higher critical speed. In this study, finite element analysis performed to investigate the effects of fibers winding angle and layers stacking sequence on the critical speed, critical buckling torque and fatigue resistance. A configuration of a hybrid of one layer of carbon-epoxy (0o) and three layers of glass-epoxy (±45o, 90o) was used. The results show that, in changing carbon fibers winding angle from 0o to 90o, the loss in natural frequency is 44.5% and shifting from the best to the worst stacking sequence the DS loses 46.07% of its buckling strength, which gain the major concern over shear strength in DS design. The layers of ±45o angles are to be located far at inner side and that of cross-ply configuration located at top face with the 90o layer exposed to outside to increase the fatigue resistance, that the stacking sequence has an effect on fatigue properties.

Small Gas Turbine Engine Operating With High-Temperature Foil Bearings

Abstract: A 134 Newton thrust class, 120,000 rpm turbojet was redesigned to incorporate a high-temperature compliant foil bearing aft of the turbine rotor and a compliantly mounted ball bearing forward of the centrifugal compressor–cold section. Two rotor-bearing system configurations were evaluated, one for operation above the bending critical speed and one for rigid rotor operation. Required characteristics for the foil bearing and ball bearing equipped with compliant foil damper mount were determined through a series of design tradeoff studies evaluating critical speeds and system stability. Following the design studies, the necessary hardware was fabricated, the engine assembled and operation to full speed achieved. Engine speed, rotor vibrations, compressor discharge pressure, exhaust gas temperature, thrust and fuel consumption were all recorded for both a baseline fluid lubricated ball bearing supported engine and the new turbojet engine using the hybrid foil bearing support system. Issues related to high-speed operation above the bending critical speed are identified and recommendations offered. Engine test data show that approximately 10% less fuel is consumed by the hybrid foil bearing mount system than the baseline conventional design. It is also shown that the foil bearing life was longer than the ball bearing life even though the foil bearing operated in the exhaust gas stream at temperatures exceeding 800°C. The results of this program demonstrate the feasibility of developing a completely oil-free foil bearing gas turbine engine.Copyright © 2006 by ASME

Experimental Investigation Into the Effect of Fluid Viscosity on Instability of an Over-hung Flexible Rotor Partially Filled With Fluid

Abstract: The effect of fluid viscosity on the developing process of the instability in an over-hung flexible rotor partially filled with fluid, the dynamical behavior of the rotor system while the instability occurs, the unstable region of rotational speeds, and the whirl frequency of the rotor system in the unstable region of rotational speeds, are experimentally investigated in this paper. It is shown that when the rotational speed is just over the reduced first critical speed of the fluid-filled rotor system that is less than the first critical speed of empty rotor system, the unstable motion occurs. The rotor system in the unstable speed region does not whirl at either a constant rotational speed or the first critical speed of the empty rotor system, the whirl frequency of the rotor system in the unstable speed region, dominated by the fluid-filled ratio and weakly depending on the viscosity of fluid, linearly increases with the rotational speed. There exists a hysteresis range of rotational speeds at the upper bound of the unstable speed region, which is not caused by the rotor transient motion when passing through the unstable speed region. As the fluid viscosity increases, both the unstable speed region and the hysteresis region narrow. The influence of the fluid viscosity on the unstable speed region of a rotor filled with a high viscosity fluid must be considered. DOI: 10.1115/1.2166857

Method of controlling vehicle driving system and vehicle driving apparatus

Abstract: A method of controlling a vehicle driving system having differential gear including an input shaft, an outlet shaft and a reactionary shaft, a flywheel, an engine, the flywheel and the engine being interlocked with the input shaft, an output shaft interlocked with the outlet shaft, a first motor generator (MG) interlocked with the reactionary shaft and a second MG adapted to receive the output electric power of the first MG as input. If the indicated torque of the output shaft as indicated by the pedaled quantity of the accelerator pedal is T 2 and a torque of the reactionary shaft is Trd, while a power transmission efficiency from the input shaft to the reactionary shaft by way of the differential gear, a power transmission efficiency from the input shaft to the output shaft by way of the differential gear and a power transmission efficiency from the reactionary shaft to the output shaft by way of the first MG and the second MG are respectively ηmr, ηmo and ηe, a critical speed ratio of the differential gear, a rotational speed of the output shaft and that of the flywheel are respectively ec, N 2 and Nf, the torque Trd is determined by the relation of Trd =( ec −1 )× T 2 ηmr/[{ηmo −(η mr×ηe )}+{( ec×Nf/N 2 )×η mr×ηe}] and generation of electric power of the first MG is controlled so as to cause the reactionary shaft to produce the torque Trd.

“Frictionless” and “frictional” ThermoElastic Dynamic Instability (TEDI) of sliding contacts

Abstract: Recently, we found that a new form of coupled instability, named ThermoElastic Dynamic Instability (TEDI), can occur by interaction between frictional heating and the natural dynamic modes of sliding bodies. This is distinct from the classical dynamic instabilities (DI) which is produced by an interaction between the frictional forces at the sliding interface and the natural modes of vibration of the bodies if the friction coefficient is sufficiently high, and also from ThermoElastic Instability (TEI), which is due to the interaction of frictional heating and thermal expansion, leading for example to low pitched brake noise above some critical speed. This result was relative to an highly idealized system, comprising an elastic layer sliding over a rigid plane including both dynamic and thermoelastic effects, but neglecting shear waves at the interface due to frictional tractions (from which the denomination “frictionless TEDI”). We demonstrate here that including these shear waves destabilizes both the shear and dilatational vibration modes of the system at arbitrarily small friction coefficients and speeds, where DI and TEI are predicted to be stable. A detailed study of the new modes and transient simulations show that for low pressures and high speed, the system tends towards the results of the previous model (“ frictionless TEDI ”), i.e. the tendency to a state in which the layer bounces over the plane, with alternating periods of sliding contact and separation. In the case of low speeds and high pressures, viceversa, the system is dominated by the modes near the resonance of the shear and dilatational modes, with a resulting complex behaviour, but generally leading to stick-slip regimes, reducing the jumping mode of “ frictionless TEDI ”, because stick reduces or stops frictional heating production.