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    List of figures: Title Page no.

    Fig. 3.1 Skewed rollers & cage 4

    Fig.3.2 Scoring of roller ends 4

    Fig. 3.3 Flaking of rollers & race 4

    Fig. 3.4 Bending of cage 4

    Fig. 3.5 Pitting of ball 4

    Fig. 3.6 Indentation in race 4

    Fig. 4.1 Levitating plate 5

    Fig. 4.2 Levitating ball 5

    Fig. 4.3 Levitating Pencil 5

    Fig. 4.4 Levitating train 5

    Fig. 5.1 Dimensions of AMB 6

    Fig. 5.2 Passive magnetic bearing 6

    Fig. 6 Five axis shaft control 7

    Fig. 7 Bearing & Sensor Location 8

    Fig. 9.1 Rotor flux path 10

    Fig. 9.2 Cut section of AMB 10

    Fig. 10.1 Overview of Control System 13

    Fig. 10.2 Types of Controllers 14

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    List of Tables:

    Sr. No. Name Page No.

    i List of applications. 22

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    Abstract:

    Electromagnetic components are replacing mechanical components to reduce

    moving parts and hence reduce friction and wear. Magnetic bearing drives open new

    application domains that are either impossible or severely limited using drives with

    conventional bearings. Magnetic bearings are increasingly being used for a large variety

    of applications. Their unique features make them attractive for solving classical rotor-

    bearing problems in a new way and allow novel design approaches for rotating

    machinery.

    In recent years it has been possible to reduce substantially the manufacturing costs

    of systems in significant areas and thus to achieve a higher degree of acceptance in the

    market. Considering the constantly declining price/performance ratio of electronic

    components, it can be assumed that in the future the application of magnetic bearing

    technology will increase in special industrial applications.

    Keywords: Magnetic Bearings, AMB, non contact bearings.

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    1. Introduction:

    A magnetic bearing is a bearing which supports a load using magnetic levitationMagnetic bearings support moving machinery without physical contact, for example, they

    can levitate a rotating shaft and permit relative motion without friction or wear. They are

    in service in such industrial applications as electric power generation, petroleum refining,

    machine tool operation and natural gas pipelines. Magnetic bearings are used in turbo

    molecular pumps where oil-lubricated bearings are a source of contamination. Magnetic

    bearings support the highest speeds of any kind of bearing; they have no known

    maximum relative speed.

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    2. History:

    The evolution of active magnetic bearings may be traced through the patents

    issued in this field. The table below lists several early patents for active magnetic

    bearings. Early active magnetic bearing patents were assigned to Jesse Beams at the

    University of Virginia during World War II and are concerned with ultracentrifuges for

    purification of the isotopes of various elements for the manufacture of the first nuclear

    bombs, but the technology did not mature until the advances of solid-state electronics and

    modern computer-based control technology with the work of Habermann and Schweitzer.

    Extensive modern work in magnetic bearings has continued at the University of Virginia

    in the Rotating Machinery and Controls Industrial Research Program. The first

    international symposium for active magnetic bearing technology was held in 1988 withthe founding of the International Society of Magnetic Bearings by Prof. Schweitzer

    (ETHZ), Prof. Allaire (University of Virginia), and Prof. Okada (Ibaraki University).

    In 1987 further improved AMB designs were created in Australia by E.Croot but

    these designs were not manufactured due to expensive costs of production. However,

    some of those designs have since been used by Japanese electronics companies, they

    remain a specialty item: where extremely high RPM is required.

    Since then there have been eleven succeeding symposia. Kasarda reviews the

    history of AMB in depth. She notes that the first commercial application of AMBs was

    with turbo machinery. The AMB allowed the elimination of oil reservoirs on compressors

    for the NOVA Gas Transmission Ltd. (NGTL) gas pipelines in Alberta, Canada. This

    reduced the fire hazard allowing a substantial reduction in insurance costs. The success of

    these magnetic bearing installations led NGTL to pioneer the research and development

    of a digital magnetic bearing control system as a replacement for the analog control

    systems supplied by the American company Magnetic Bearings Inc. (MBI). In 1992,

    NGTL's magnetic bearing research group formed the company Revolve Technologies

    Inc. to commercialize the digital magnetic bearing technology. This firm was later

    purchased by SKF of Sweden.

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    The French company S2M, founded in 1976, was the first to commercially

    market AMBs. Extensive research on magnetic bearings continues at the University of

    Virginia in the Rotating Machinery and Controls Industrial Research Program.

    Starting from 1996 the Dutch oil and gas company NAM installed over a period

    of 10 years 20 large E-motor driven (with variable speed drive) gas compressors of 23

    MW fully equipped with AMB's on both the E-motor and the compressor.

    These compressors are used in the Groningen gas field to deplete the remaining

    gas from this large gas field and to increase the field capacity.

    The motor - compressor design is done by Siemens and the AMB are delivered by

    Waukesha (owned by Dover). (Originally these bearings were designed by Glacier, this

    company is later on taken over by Federal Mogul and now part of Waukesha) By using

    AMB's and a direct drive between motor and compressor (so no gearbox in between) and

    applying dry gas seals a full so called dry-dry system (=fully oil free) has been installed.

    A few of the main advantages by applying AMB's in the driver as well as in the

    compressor (compared to the traditional configuration with a gearbox, plain bearings and

    a gas turbine-driver) is a relative simple system with a very wide operating envelope,

    high efficiencies (particularly at partial load) and also, as done in the Groningen field, to

    install the full installation outdoors (no large compressor building needed.

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    3 Failures/Limitations in conventional contact bearings:

    Fig. 3.1 Skewed rollers & cage Fig.3.2 Scoring of roller ends

    Fig. 3.3 Flaking of rollers & race Fig. 3.4 Bending of cage

    Fig. 3.5 Pitting of ball Fig. 3.6 Indentation in race

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    4. Principle of Magnetic Levitation:

    Fig. 4.1 Levitating plate Fig. 4.2 Levitating ball

    Fig. 4.3 Levitating Pencil Fig. 4.4 Levitating train

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    5. Types of Magnetic Bearings:

    Fig. 5.1 Dimensions of AMB Fig. 5.2 Passive magnetic bearing

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    6. Basic operation

    Basic Operation for a Single Axis

    An active magnetic bearing (AMB) consists of an electromagnet assembly, a set of power

    amplifiers which supply current to the electromagnets, a controller, and gap sensors with

    associated electronics to provide the feedback required to control the position of the rotor

    within the gap. These elements are shown in the diagram. The power amplifiers supply

    equal bias current to two pairs of electromagnets on opposite sides of a rotor. This

    constant tug-of-war is mediated by the controller which offsets the bias current by equal

    but opposite perturbations of current as the rotor deviates by a small amount from its

    center position.

    The gap sensors are usually inductive in nature and sense in a differential mode. The

    power amplifiers in a modern commercial application are solid state devices which

    operate in a pulse width modulation (PWM) configuration. The controller is usually a

    microprocessor or DSP

    Fig. 6 Five axis shaft control

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    7. Bearing and Sensors:

    Fig. 7 Bearing & Sensor Locations

    To provide support in more than one direction, magnetic poles are oriented about

    the periphery of a radial bearing. This is shown in the drawing on your right. Radial

    bearing construction is very similar to that of an electric motor, involving the use of

    stacked laminations of steel, around which power coils are wound. Stacked laminations

    are also used in the rotor to minimize eddy current losses, which are a very small source

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    of drag in a magnetic bearing and cause localized heating on the rotor. The sensors are

    also oriented about the periphery of the stator, usually inside a ring or individual tubes

    mounted adjacent to the actuator poles. Inductive sensors are used, that measure the

    inductance of the gap between the sensor and the rotor laminations. Two measurements

    are taken for each radial axis and the rotor center position calculated by means of a bridge

    circuit.

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    A typical rotating machine will experience forces in both the radial and axial

    directions. Typically, a 5-axis orientation of bearings is used, incorporating 2 radial

    bearings of 2 axes each, and 1 thrust bearing.

    Thrust bearings provide a magnetic flux path in the axial direction, between 2

    stators oriented on either side of a thrust rotor, or disc, mounted on the rotating shaft as

    shown below. An axial sensor measures the position of the shaft.

    8. Precision:

    Precision in rotating machinery means most often how precise can the position of the

    rotor axis be guaranteed. This has consequences for machining tools, and for the surface

    quality of parts that are being machined by grinding, milling or turning. In addition, thequestion of how precise can magnetic bearings become in principle, is of interest for

    applications such as optical devices, optical scanner, wafer stepper, or lithography. These

    machines and processes are key elements for semiconductor industry. Active magnetic

    bearings levitate an object, rotating or not, with feedback control of measured

    displacement sensor signal. The performance of AMB systems is therefore directly

    affected by the quality of a sensor signal. Precision control is facilitated by the absence of

    hysteresis and of deformation-prone heat sources, which touches upon material and

    design aspects. The probe type displacement sensors most widely used in AMB system

    are very sensitive to the surface quality of a rotor, so they require additional algorithms to

    detect and compensate the unnecessary signal contents induced by the geometric errors of

    a rotor. Accordingly, on-line control with the probe type sensors becomes more

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    bothersome and more complicated as soon as high precision is aimed at. Orbits with

    rotating errors of 10 to 20 m have been obtained.

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    9.Operation of AMB:

    Fig. 9.1 Rotor flux path

    Fig. 9.2 Cut section of AMB

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    Magnetic bearings use electromagnetic coils to suspend or levitate a rotating shaft in

    whatever the surrounding medium might be usually air, but the bearings will function

    in a vacuum or other medium. Sensors monitor the shafts position and supply those data

    to a digital controller. In turn, the controller can change the current in the coils and

    thereby change the electromagnetic forces on the shaft. In terms of control loop speed,

    these changes happen very quickly, allowing the shafts position to be precisely

    maintained at very high rotational speeds.

    With the rotating shaft suspended in space, there is no metal-to-metal contact.

    Consequently, magnetic bearings require no lubrication. That means there are no regular

    bearing lubrication schedules for compressors with magnetic bearings, and it also means

    that no elaborate lubrication systems are required for them.

    Generators with magnetic bearings enable the manufacture of smaller, faster units. The

    ability to run faster means these generators have greater power density. Consider, for

    example, a one-megawatt wind turbine. The generators rotor weighs several tons. In a

    typical design, the wind drives the turbine blades, which turn a low-speed shaft at 30 to

    60 revolutions per minute (rpm). A gearbox converts this rotational speed to about 1200

    to 1500 rpm. Contrast the wind turbine with a high-speed generator that operates at

    20,000 rpm. A one-megawatt power generator running that fast would have a rotor

    weight of less than 100 kilogram. Thats the advantage that speed provides. Low-speed

    generators are very large; high-speed generators are small and compact.

    Magnetic bearings provide attractive electromagnetic suspension by application of

    electric current to ferromagnetic materials used in both the stationary and rotating parts

    (the stator and rotor, respectively) of the magnetic bearing. This creates a flux path that

    includes both parts, and the air gap separating them, through which non-contact operationis made possible.

    As the air gap between these two parts decreases, the attractive forces increase, therefore,

    electromagnets are inherently unstable. A control system is needed to regulate the current

    and provide stability of the forces, and therefore, position of the rotor.

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    The control process begins by measurement of the rotor position with a position sensor.

    The signal from this device is received by the control electronics, which compares it to

    the desired position, input during machine start-up. Any difference between these two

    signals results in calculation of the force necessary to pull the rotor back to the desired

    position. This is translated into a command to the power amplifier connected to the

    magnetic bearing stator. The current is increased, causing an increase in magnetic flux, an

    increase in the forces between the rotating and stationary components, and finally,

    movement of the rotor toward the stator along the axis of control.

    The entire process is repeated thousands of times per second, enabling precise control of

    machinery rotating at speeds in excess of 100,000 rpm.

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    10. Control System:

    Fig. 10.1 Overview of Control System

    The control system consists of:

    Digital signal processor (DSP electronics)

    Power amplifiers

    Power supply

    Additional circuitry is present for conditioning of the signals from the position sensors,

    and conversion of the digital outputs from the signal processor to the amplifiers. Finally,

    a user interface allows input of the desired rotor position information, and logic to be

    coordinated with other machine systems (start-up, warm-up, shutdown, etc.).

    Control systems for magnetic bearing systems can be of the analog

    or digital type. Analog control systems have been used in magnetic

    bearing control for over 30 years, but are rapidly being displaced bydigital control systems.

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    Fig. 10.2 Types of Controllers

    Digital control systems take advantage of the tremendous developments in digital signal

    processing over the past decade, and permit more types of control algorithms to be used,

    enabling more results to be achieved.

    Sub-systems in magnetic bearing digital controllers include position signal processing,

    digital signal processing, D/A conversion, power amplifiers and power supply.

    Small control systems, suitable for control of a turbomolecular pump, are about the size

    of a shoebox, providing as little as 25W of power for the bearing system. Larger control

    systems, providing up to 10 kW of power for bearings used in large frameturbomachinery such as centrifugal compressors, pumps and turbines, are designed to

    meet industrial electronic rack standards

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    http://www.skf.com/portal/skf_rev/home/technology?contentId=081012&lang=enhttp://www.skf.com/portal/skf_rev/home/technology?contentId=081012&lang=enhttp://www.skf.com/portal/skf_rev/home/technology?contentId=081012&lang=en
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    11. Cost:

    The initial cost of a small backup generator using magnetic bearings could be an order of

    magnitude greater than the initial cost of system using conventional bearings. Most of the

    additional cost is due to the relatively sophisticated system required to control the

    bearings. The hardware associated with a magnetic-bearing system is rather inexpensive.

    For example, the cost of winding a magnetic-bearing coil is comparable to the cost of

    winding a motor stator. By contrast, a magnetic bearings control system includes such

    items as an advanced digital controller, sensors to monitor shaft position, cables to

    convey the shaft-position data to the controller, and other cables to carry the power from

    amplifiers in the controller to the bearings electromagnetic coils.

    So, these new compact machines presently cost more per installed kilowatt-hour thanconventional low-speed generators. Compared to conventional generators, generators

    with magnetic bearings are less costly to operate and produce more electrical power per

    horsepower expended to run them. There are significantly fewer mechanical losses. If a

    driver puts energy into a generator and the bearings consume (via friction) a large

    fraction of that energy, less energy is available for generating electricity. The power

    consumption of a standard bearing can be ten times that of a magnetic bearing. Reduced

    energy consumption has a positive environmental impact, too. As noted, magnetic-

    bearing units also have fewer associated maintenance costs than conventional units. That

    fact does not mean, however, that magnetic-bearing systems are maintenance free.

    Today, there are several kinds of distributed power applications that favor the use of

    magnetic-bearing technology in compressors. These applications include 1) operations

    with power demands that cannot be controlled or scheduled, 2) operations with excessive

    and presently unused potential energy sources, 3) activities in remote, off-the-grid

    locations and 4) recovery, rescue, and reconstruction operations at disaster sites.

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    12. Losses:

    With contact-free rotors there is no friction in the magnetic bearings. The operation of

    active magnetic bearings causes much less losses than operating conventional ball or

    journal bearings, but, nevertheless, the losses have to be taken into account, and

    sometimes they lead to limitations. Losses can be grouped into losses arising in the

    stationary parts, in the rotor itself, and losses related to the design of the control.

    Losses in the stationary parts of the bearingcome mainly from copper losses in thewindings of the stator and from losses in the amplifiers. The copper losses are a heat

    source, and, if no sufficient cooling is provided, can limit the control current and hence

    the maximal achievable carrying force. Losses in the rotor partare more complex andlead to more severe limitations. These losses comprise iron losses caused by hysteresisand eddy currents, and air drag losses. The losses heat up the rotor, cause a breaking

    torque on the rotor, and have to be compensated by the drive power of the motor. In

    general, the eddy current losses are the largest ones.

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    13. Magnetic-Bearing System Maintenance and Reliability:

    While magnetic-bearing systems require none of the traditional mechanical

    maintenance associated with traditional bearing systems, there are, nonetheless, some

    diagnostic assessments that should be performed regularly. These evaluations are easily

    done, since the control system provides constant feedback about the state of the system.

    Among the important diagnostic reviews is a check of internal clearances--the gaps

    between the shaft and the mechanical backup bearings that limit the shafts axial and

    radial movement.

    Technicians can keep records over time to verify that a bearing is performing as it

    was built to perform. If there has been a change, the techs can document the change and

    analyze the data to find the cause.

    Another regular maintenance task required for a magnetic-bearing system relates

    to the fact that most controllers have cooling systems that circulate air to cool the power

    electronics. The filters on these cooling systems require periodic cleaning or replacement.

    Frequency of this maintenance is a function of the operating environments cleanliness.

    Most maintenance tasks for magnetic-bearing systems are common-sense items. What

    maintenance personnel do not have to do is lubricate the bearings periodically and

    replace them every few years. In other words, magnetic bearings require none of the

    upkeep traditionally associated with bearings.

    Controller power electronics have finite lives. The mean time between failures for

    controllers is roughly eight to 12 years depending on how hard the electronics have been

    stressed and if adequate cooling has been provided. End users can expect to make

    changes in the power and control systems for magnetic bearing after eight to 15 years of

    service. Like an electric motor, a magnetic bearing will last 20 to 30 years, depending

    upon the environment in which it operates and how fast the insulation breaks down in

    that environment.

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    14. Advantages:

    1. High Reliability

    With magnetic bearings there is no contact between the rotating and stationary parts,meaning there is no wear. In most cases failure modes are limited to control electronics,

    power electronics, and electrical windings. These components have designs lives far

    greater than that of conventional bearings. Magnetic bearings are the only type of bearing

    which is fitted with protective back-up bearings. In addition, magnetic bearings have a

    built-in overload protection. Magnetic bearings can signal process control equipment to

    stop the machine instantaneously in the case of excessive load.

    Magnetic bearings are providing high reliability and long service intervals in time critical

    applications in semiconductor manufacturing; vacuum pumps; and natural gas pipeline

    compression equipment.

    2. Clean Environments

    In a magnetic bearing system, particle generation due to wear and the need for lubrication

    are eliminated. There is therefore no chance of contaminating a clean process with oil,

    grease or solid particles.

    Magnetic bearings offer a dry, clean and economic solution for semiconductor fabrication

    equipment, vacuum pumps, gas and air compressors, and various other turbo machines

    that require submersion in a process fluid, even under pressure.

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    3. High Speed Applications

    The fact that a rotor spins in space without contact with the stator means drag on the rotoris minimal. That opens up the opportunity for the bearing to run at exceptionally high

    speeds, where the only limitation becomes the yield strength of the rotor material.

    Magnetic bearings have been designed with surface speeds up to 250 m/s or 4.5 millionDN, where DN is the diameter of the rotor (mm) times the rotational spend (rpm). In

    order to achieve one quarter of this kind of speed with conventional bearings, a complex

    lubrication system is required.

    No other type of bearing, can match magnetic bearings for shear speed. Magnetic

    bearings open new possibilities for extreme high-speed applications such as machine tool

    spindles and turbo compressors.

    4. Position and Vibration Control

    Magnetic bearings use advanced control algorithms to influence the motion of the shaft

    and therefore have the inherent capability to precisely control the position of the shaft

    within microns and to virtually eliminate vibrations.

    Magnetic Bearings offer a straightforward solution to the following problems /

    requirements:

    Vibration of the rotating part due to unbalance - controlling unbalance vibration is

    important in most applications, particularly turbo machinery; machine tool spindles, and

    vacuum pumps;

    Transmission of vibrations from the moving part to the stationary parts where it is

    transmitted to other equipment - important in vibration sensitive applications such as

    semiconductor fabrication equipment and analytical instruments;

    Precisely controlling the location of the rotor regardless of outside disturbances - high

    speed machine tool spindles

    Locating the rotor based on some external variable - process equipment and high speedmachine tool spindles

    Controlling structural resonance frequencies coming from the rotor or from elastic

    supports - high speed turbo machinery and drives

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    5. Extreme Conditions:

    Temperature:

    The magnetic bearing system is capable of operating through an extremely wide

    temperature range. Revolve has applications as low as -256C and as high as 220C, thus

    allowing operation where traditional bearings will not function.

    Corrosive Fluids:

    Magnetic bearings can operate in corrosive environments by means of canning both the

    stationary and rotating parts.

    Pressure:

    Magnetic bearings are virtually insensitive to pressure. They can be submerged in process

    fluid under pressure without the need for seals, as is the case with conventional bearings.

    Magnetic bearings can also operate in vacuum where their operation is even more

    efficient due to lack of windage.

    6. Equipment Design, Development and Testing:

    A magnetic bearing system can be used as an exciter, where the bearing force is

    modulated for deliberately exciting vibrations. The excitation force is applied to the rotor

    without contact and can be measured exactly. This makes magnetic bearings a valuable

    tool in equipment design, development and testing as well as in rotor dynamic research.

    7. Machine Diagnostics / Smart Machines:

    In order to function, a magnetic bearing must determine rotor position, rotor vibration

    and bearing load. This information which is processed in the electronic control cabinet,can be given as an output to the OEM or end user such that there is a constant knowledge

    of the operating state of the machine. This allows the user to detect incipient faults, plan

    maintenance and optimize performance.

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    15. Disadvantages/Limitations:

    1. Larger Bearings:

    Magnetic bearings have a specific load capacity (maximum load per unit of area of

    application)lower than most other bearings systems. This results in bearings which may

    be physically larger than other similarly specified bearings.

    2. Higher Complexity:

    The higher complexity of magnetic bearings often means the initial purchase price is

    higher than competing technologies. However, magnetic bearings' life cycle cost can

    often be less than traditional bearings. This is particularly true where the alternatives are

    exotic bearings.

    3. Requires Electrical Power:

    Magnetic bearing require power to drive the control systems, sensors and electromagnets.

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    16. Applications:

    Table 16.1 List of applications:

    Machine Tools Aircraft Specialty Equipment Medical

    Turning Auxiliary power units Vacuum pumps X-rays

    Milling Blowers Robotics Dental drills

    Grinding Actuators Textile equipments CAT scanners

    Machining centers Gyros Food processing Medical centrifuges

    Ball screw support Air handling Maglev trains Heart pumps

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    22

    Conclusions:

    Limitations in Active Magnetic Bearings arise from two reasons: the state of the actual

    technology in design and material, and from basic physical relations.

    The various issues are summarized subsequently:

    - the maximal load depends on design

    - the specific load depends on the available ferromagnetic material and its saturation

    properties, and is therefore limited to 32 to 60 N/cm2

    - the frequency and the amplitude of disturbances acting on the rotor, such as unbalance

    forces, that can be adequately controlled, depend on the design of the power amplifier

    (power and bandwidth)

    - the maximally achieved rotation speed is about 300 kHz in physical experiments. For

    industrial applications values of about 6 kHz have been realized

    - circumferential speeds, causing centrifugal loads, are limited by the strength of material.

    Values of about 250 to 300 m/s have been realized with actual design

    - supercritical speed means that one or more critical speeds can be passed by the elastic

    rotor. It appears to be difficult to pass more than two or three

    - the size of the bearing depends on design and manufacturability. There are largebearings with dimensions and loads in meters and tons. The smallest bearings actually

    built have dimensions in the range of mm, with a thickness being as small as 150 m

    - high temperature bearings have been realized, running in experiments at an operating

    temperature of 600oC (1100oF). For ferromagnetic material the Curie temperature would

    be a physical limit

    - the losses of magnetic bearings at operating speed are much smaller than that of

    classical bearings. Eddy current losses will limit the rotation frequency of massive rotors

    (heating up, driving power), the air drag will be crucial at high circumferential speeds

    (driving power)

    - a high precision of the position of the rotor axis (in the range of mm) requires high

    resolution sensors and adequate signal processing to separate disturbance signals from the

    desired ones

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    References:

    [1].[DL2000], Tracking the Polar Principal Axis for Magnetic Bearing Control

    and flywheel Balancing, Dzu K. Le and Andrew J. Provenza, NASA Glenn

    Research Center at Lewis Field.Society of Automotive Engineers, Inc.,2000

    [2].[JW1999], Auxiliary Bearings in Support of Magnetic Bearings for Turbine

    Engines,James F. Walton ll, Mohawk Innovative Technology Inc.Society of

    Automotive Engineers, Inc.1999

    [3].[PHG2000], Magnetic Bearing Controls for a High Speed, High Power

    Switched Reluctance Machine (SRM) Starter/Generator, Charl

    Potgieter,Winston Hope, Earl GregorySociety of Automotive Engineers,

    Inc.2000

    [4]. [NM2002], Improvements of the integration of active magnetic bearings,

    Norbert Skricka, Richard Markert Department of Applied Mechanics,

    Darmstadt University of Technology, Hochschulstrasse 1, D-64289

    Darmstadt, Germany. Elsevier Science Ltd.2002

    [5].[CK2006], Active magnetic bearings for machining applications, Carl R.

    Knospe Department of Mechanical & Aerospace Engineering, University of

    Virginia, Charlottesville, VA, USA. Elsevier Science Ltd.2006

    [6]. [HC2002], Nonlinear control of a 3-pole active magnetic bearing system,

    Chan-Tang Hsua, Shyh-Leh Chenb;Information & Communication ResearchDivision, Chung-Shan Institute of Science and Technology, Kaohsiung,

    Taiwan, ROC Department of Mechanical Engineering, National Chung-

    Cheng University, Chia-Yi 621, Taiwan, ROC. Elsevier Science Ltd.2002

    [7]. Active magnetic bearings - chances and limitations. Schweitzer G

    International Centre for Magnetic Bearings, ETH Zurich, CH-8092 Zurich.

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