Friday, October 23, 2009

Frequency


Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

Definitions and units

For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles, or periods, per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by a Greek letter ν (nu).
In SI units, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. For example, 1 Hz means that an event repeats once per second.
The period is usually denoted as T, and is the reciprocal of the frequency f:
T = \frac{1}{f}.
The SI unit for period is the second.

Measurement

By timing

To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.
In experimental work (for example, calculating the frequency of an oscillating pendulum) it is generally more accurate to measure the time taken for a fixed number of occurrences, rather than the number of occurrences within a fixed time. The latter method introduces — if N is the number of counted occurrences — a random error between zero and one count, so on average half a count, causing a biased underestimation of f by ½ f / (N + ½)[citation needed] in its expected value. In the first method, which does not suffer this particular error, frequency is still calculated by dividing the number of occurrences by the time interval; however it is the number of occurrences that is fixed, not the time interval.

By stroboscope effect, or frequency beats

In case when the frequency is so high that counting is difficult or impossible with the available means, another method is used, based on a source (such as a laser, a tuning fork, or a waveform generator) of a known reference frequency f0, that must be tunable or very close to the measured frequency f. Both the observed frequency and the reference frequency are simultaneously produced, and frequency beats are observed at a much lower frequency Δf, which can be measured by counting. This is sometimes referred to as a stroboscope effect. The unknown frequency is then found from f=f_0\pm \Delta f.

Frequency of waves

Frequency has an inverse relationship to the concept of wavelength, simply, frequency is inversely proportional to wavelength λ (lambda). The frequency f is equal to the phase speed v of the wave divided by the wavelength λ of the wave:
f = \frac{v}{\lambda}.
In the special case of electromagnetic waves moving through a vacuum, then v = c , where c is the speed of light in a vacuum, and this expression becomes:
f = \frac{c}{\lambda}.
When waves from a monochromatic source travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change.

Examples

Physics of light

Radiant energy is energy which is propagated in the form of electromagnetic waves. Most people think of natural sunlight or electrical light, when considering this form of energy. The type of light which we perceive through our optical sensors (eyes) is classified as white light, and is composed of a range of colors (red, orange, yellow, green, blue, indigo, violet) over a range of wavelengths, or frequencies.
Visible (white) light is only a small fraction of the entire spectrum of electromagnetic radiation. At the short end of that wavelength scale is ultraviolet (UV) light from the sun, which cannot be seen. At the longer end of that spectrum is infrared (IR) light, which is used for night vision and other heat-seeking devices. At even shorter wavelengths than UV are X-rays and Gamma-rays. At longer wavelengths than IR are microwaves, radio waves, electromagnetic waves in megahertz and kHz range, as well as natural waves with frequencies in the millihertz and microhertz range. A 2 millihertz wave has a wavelength approximately equal to the distance from the earth to the sun. A microhertz wave would extend 0.0317 light years. A nanohertz wave would extend 31.6881 light years.
Complete spectrum of electromagnetic radiation with the visible portion highlighted
Electromagnetic radiation is classified according to the frequency (or wavelength) of the light wave. This includes (in order of increasing frequency): natural electromagnetic waves, radio waves, microwaves, terahertz radiation, infrared (IR) radiation, visible light, ultraviolet (UV) radiation, X-rays and gamma rays. Of these, natural electromagnetic waves have the longest wavelengths and gamma rays have the shortest. A small window of frequencies, called the visible spectrum or light, is sensed by the eye of various organisms, with variations of the limits of this narrow spectrum.

Physics of sound

Sound is vibration transmitted through a solid, liquid, or gas; particularly, sound means those vibrations composed of frequencies capable of being detected by ears. For humans, hearing is limited to frequencies between about 20 Hz and 20,000 Hz (20 kHz), with the upper limit generally decreasing with age. Other species have a different range of hearing. For example, some dog breeds can perceive vibrations up to 60,000 Hz.[1] As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication.
The mechanical vibrations that can be interpreted as sound are able to travel through all forms of matter: gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium. Sound cannot travel through vacuum.

Longitudinal and transverse waves

Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves. Through solids, however, it can be transmitted as both longitudinal and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves in solids, are waves of alternating shear stress.
Matter in the medium is periodically displaced by a sound wave, and thus oscillates. The energy carried by the sound wave converts back and forth between the potential energy of the extra compression (in case of longitudinal waves) or lateral displacement strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium.

Sound wave properties

Sound waves are characterized by the generic properties of waves, which are frequency, wavelength, period, amplitude, intensity, speed, and direction (sometimes speed and direction are combined as a velocity vector, or wavelength and direction are combined as a wave vector).
Transverse waves, also known as shear waves, have an additional property of polarization.
Sound characteristics can depend on the type of sound waves (longitudinal versus transverse) as well as on the physical properties of the transmission medium.
Whenever the pitch of the soundwave is affected by some kind of change, the distance between the sound wave maxima also changes, resulting in a change of frequency. When the loudness of a soundwave changes, so does the amount of compression in airwave that is travelling through it, which in turn can be defined as amplitude.
In music and acoustics, the frequency of the standard pitch A above middle C on a piano is usually defined as 440 Hz, that is, 440 cycles per second (Media-440Hz.ogg Listen (help·info)) and known as concert pitch, to which an orchestra tunes.

Other examples

In Europe, Africa, Australia, Southern South America, most of Asia, and Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), whereas in North America and Northern South America, the frequency of the alternating current is 60 Hz (between the tones B♭ and B — that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency.

Period versus frequency

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. These commonly used conversions are listed below:
Frequency 1 mHz (10-3) 1 Hz (100) 1 kHz (103) 1 MHz (106) 1 GHz (109) 1 THz (1012)
Period (time) 1 ks (103) 1 s (100) 1 ms (10-3) 1 µs (10-6) 1 ns (10-9) 1 ps (10-12)

Other types of frequency

  • Angular frequency ω is defined as the rate of change in the orientation angle (during rotation), or in the phase of a sinusoidal waveform (e.g. in oscillations and waves):
\omega=2\pi f\,.
Angular frequency is measured in radians per second (rad/s).
  • Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
  • Wavenumber is the spatial analogue of angular frequency. In case of more than one spacial dimension, wavenumber is a vector quantity
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Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonance frequencies, with greater amplitude than at others. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones.
A cavity resonator, usually used in reference to electromagnetic resonators, is one in which waves exist in a hollow space inside the device. Acoustic cavity resonators, in which sound is produced by air vibrating in a cavity with one opening, are known as Helmholtz resonators.

Explanation

A physical system can have as many resonance frequencies as it has degrees of freedom; each degree of freedom can vibrate as a harmonic oscillator. Systems with one degree of freedom, such as a mass on a spring, pendulums, balance wheels, and LC tuned circuits have one resonance frequency. Systems with two degrees of freedom, such as coupled pendulums and resonant transformers can have two resonance frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next.
Resonators can be viewed as being made of millions of coupled moving parts (such as atoms). Therefore they can have millions of resonance frequencies, although only a few may be used in practical resonators. The vibrations inside them travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. The oppositely moving waves interfere with each other to create a pattern of standing waves in the resonator. If the distance between the sides is d\,, the length of a round trip is 2d\,. In order to cause resonance, the phase of a sinusoidal wave after a round trip has to be equal to the initial phase, so the waves will reinforce. So the condition for resonance in a resonator is that the round trip distance, 2d\,, be equal to an integral number of wavelengths \lambda\, of the wave:
2d = N\lambda,\qquad\qquad N \in \{1,2,3...\}
If the velocity of a wave is c\,, the frequency is f = c / \lambda\, so the resonance frequencies are:
f = \frac{Nc}{2d}\qquad\qquad N \in \{1,2,3...\}
So the resonance frequencies of resonators, called normal modes, are equally spaced multiples (harmonics), of a lowest frequency called the fundamental frequency. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, and that the shape of the resonator is rectilinear. If the resonator is inhomogeneous or has a nonrectilinear shape, like a circular drumhead or a cylindrical microwave cavity, the resonance frequencies may not occur at equally spaced multiples of the fundamental frequency. They are then called overtones instead of harmonics. There may be several such series of resonance frequencies in a single resonator, corresponding to different modes of vibration.

Electromagnetic


A distributed parameter resonator of the distributed network type has capacitance, inductance, and resistance which cannot be isolated into separate lumped capacitors, inductors, or resistors. The time factor of propagation of wave energy in the network is appreciable. Resonators can be of the dielectric type or magnetic type. A hollow conductor that uses resonance to amplify an electromagnetic wave is called a cavity resonator. A single layer coil (or solenoid) that is used as a secondary or tertiary winding in a Tesla Coil or Magnifying Transmitter is also called a resonator.

Cavity resonators

The cavity has interior surfaces which reflect a wave of a specific frequency. When a wave that is resonant with the cavity enters, it bounces back and forth within the cavity, with low loss (see standing wave). As more wave energy enters the cavity, it combines with and reinforces the standing wave, increasing its intensity.

Examples

RF cavities in the linac of the Australian Synchrotron are used to accelerate and bunch beams of electrons; the linac is the tube passing through the middle of the cavity
An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator
The cavity magnetron is a vacuum tube with a filament in the center of an evacuated, lobed, circular cavity resonator. A perpendicular magnetic field is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this anode. Spaced about the rim of the chamber are cylindrical cavities. The cavities are open along their length and so connect the common cavity space. As electrons sweep past these openings they induce a resonant high frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular cross section). The waveguide directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high gain antenna in the case of radar.
The klystron, tube waveguide, is a beam tube including at least two apertured cavity resonators. The beam of charged particles passes through the apertures of the resonators, often tunable wave reflection grids, in succession. A collector electrode is provided to intercept the beam after passing through the resonators. The first resonator causes bunching of the particles passing through it. The bunched particles travel in a field-free region where further bunching occurs, then the bunched particles enter the second resonator giving up their energy to excite it into oscillations. It is a particle accelerator that works in conjunction with a specifically tuned cavity by the configuration of the structures. On the beamline of an accelerator system, there are specific sections that are cavity resonators for RF.
The reflex klystron is a klystron utilizing only a single apertured cavity resonator through which the beam of charged particles passes, first in one direction. A repeller electrode is provided to repel (or redirect) the beam after passage through the resonator back through the resonator in the other direction and in proper phase to reinforce the oscillations set up in the resonator.
In a laser, light is amplified in a cavity resonator which is usually composed of two or more mirrors. Thus an optical cavity, also known as a resonator, is a cavity with walls which reflect electromagnetic waves (light). This will allow standing wave modes to exist with little loss outside the cavity.

Mechanical

Mechanical resonators are used in electronic circuits to generate signals of a precise frequency. These are called piezoelectric resonators, the most common of which is the quartz crystal. They are made of a thin plate of quartz with metal plates attached to each side, or in low frequency clock applications a tuning fork shape. The quartz material performs two functions. Its high dimensional stability and low temperature coefficient makes it a good resonator, keeping the resonant frequency constant. Second, the quartz's piezoelectric property converts the mechanical vibrations into an oscillating voltage, which is picked up by the plates on its surface, which are electrically attached to the circuit. These crystal oscillators are used in quartz clocks and watches, to create the clock signal that runs computers, and to stabilize the output signal from radio transmitters. Mechanical resonators can also be used to induce a standing wave in other medium. For example a multiple degree of freedom system can be created by imposing a base excitation on a cantilever beam. In this case the standing wave is imposed on the beam [1]. This type of system can be used as a sensor to track changes in frequency or phase of the resonance of the fiber. One application is as a measurement device for dimensional metrology[2].

Acoustic

The most familiar examples of acoustic resonators are in musical instruments. Every musical instrument has resonators. Some generate the sound directly, such as the wooden bars in a xylophone, the head of a drum, the strings in stringed instruments, and the pipes in an organ. Some modify the sound by enhancing particular frequencies, such as the sound box of a guitar or violin. Organ pipes, the bodies of woodwinds, and the sound boxes of stringed instruments are examples of acoustic cavity resonators.

Automobiles

The exhaust pipes in automobile exhaust systems are designed as acoustic resonators that work with the muffler to reduce noise, by making sound waves "cancel each other out"[1]. The "exhaust note" is an important feature for many vehicle owners, so both the original manufacturers and the after-market suppliers use the resonator to enhance the sound. In 'tuned exhaust' systems designed for performance the resonance of the exhaust pipes is also used to 'pull' the combustion products out of the combustion chamber quicker.

Percussion instruments

In many keyboard percussion instruments, below the centre of each note is a tube, which is an acoustic cavity resonator, referred to simply as the resonator. The length of the tube varies according to the pitch of the note, with higher notes having shorter resonators. The tube is open at the top end and closed at the bottom end, creating a column of air which resonates when the note is struck. This adds depth and volume to the note. In string instruments, the body of the instrument is a resonator.
The tremolo effect of a vibraphone is obtained by a mechanism which opens and shuts the resonators.

Stringed instruments

String instruments such as the bluegrass banjo may also have resonators. Many five-string banjos have removable resonators, to allow the instrument to be used with resonator in bluegrass style, or without in folk music style. The term resonator, used by itself, may also refer to the resonator guitar.
The modern ten-string guitar, invented by Narciso Yepes, adds four string resonators to the traditional classical guitar. By tuning these resonators in a very specific way (C, Bb, Ab, Gb) and making use of their strongest partials (corresponding to the octaves and fifths of the strings' fundamental tones), the bass strings of the guitar now resonate equally with any of the 12 tones of the chromatic octave.
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Wednesday, October 21, 2009

Energy storage

Energy storage is the storing of some form of energy that can be drawn upon at a later time to perform some useful operation.
Energy storage media are matter that store some form of energy that can be drawn upon at a later time to perform some useful operation. A device that stores energy is sometimes called an accumulator. All forms of energy are either potential energy (eg. chemical, gravitational or electrical energy) or kinetic energy (eg. thermal energy). A wind up clock stores potential energy (in this case mechanical, in the spring tension), a battery stores readily convertible chemical energy to keep a clock chip in a computer running (electrically) even when the computer is turned off, and a hydroelectric dam stores power in a reservoir as gravitational potential energy. Ice storage tanks store ice (thermal energy)at night to meet peak demand for cooling. Fossil fuels such as coal and gasoline store ancient energy from sunlight. Even food (which is made by the same process as was fossil fuel) is a form of energy stored in chemical form.

Types of energy storage

History of energy storage

 

Energy storage as a natural process is as old as the universe itself - the energy present at the initial creation of the Universe has been stored in stars such as the Sun, and is now being used by humans directly (e.g. through solar heating), or indirectly (e.g. by growing crops or conversion into electricity in solar cells). Storing energy allows humans to balance the supply and demand of energy. Energy storage systems in commercial use today can be broadly categorized as mechanical, electrical, chemical, biological, thermal and nuclear. As a purposeful activity, energy storage has existed since pre-history, though it was often not explicitly recognized as such. An example of deliberate mechanical energy storage is the use of logs or boulders as defensive measures in ancient forts - the logs or boulders were collected at the top of a hill or wall, and the energy thus stored used to attack invaders who came within range. A more recent application is the control of waterways to drive water mills for processing grain or powering machinery. Complex systems of reservoirs and dams were constructed to store and release water (and the potential energy it contained) when required. Energy storage became a dominant factor in economic development with the widespread introduction of electricity and refined chemical fuels, such as gasoline, kerosene and natural gas in the late 1800s. Unlike other common energy storage used in prior use, such as wood or coal, electricity has been used as it has been generated. It has not been stored on a major scale but that may soon change. In the U.S, the 2009 Stimulus plan is researching energy storage and how it may be used with the new plans for a Smart Grid. [1]. Electricity is transmitted in a closed circuit, and for essentially any practical purpose cannot be stored as electrical energy. This means that changes in demand could not be accommodated without either cutting supplies (as by brownouts or blackouts) or by storing the electric energy in another medium. Even renewable energy must be stored in order to make it reliable. Wind blows intermittently and so some form of storage is required to compensate for calm periods, and solar energy is not effective on cloudy days so stored energy must be available to compensate for the loss of sun energy. An early solution to the problem of storing energy for electrical purposes was the development of the battery, an electrochemical storage device. It has been of limited use in electric power systems due to small capacity and high cost. A similar possible solution with the same type of problems is the capacitor. In the 1980s, a small number of manufacturers carefully researched thermal energy storage (TES) to meet the growing demand for air-conditioning during peak hours. Today a few companies continue to manufacture TES. [2] The most popular form of thermal energy storage for cooling is ice storage, since it can store more energy in less space than water storage and it is also cheaper than fuel cells & flywheels. Thermal storage has shifted jiggawatts of power away from daytime peaks, cost-effectively, and is used in over 3,300 buildings in over 35 countries. It works by storing ice at night when electricity is cheap, and then using the ice to cool the air in the building the next day. Chemical fuels have become the dominant form of energy storage, both in electrical generation and energy transportation. Chemical fuels in common use are processed coal, gasoline, diesel fuel, natural gas, liquefied petroleum gas (LPG), propane, butane, ethanol, biodiesel and hydrogen. All of these materials are readily converted to mechanical energy and then to electrical energy using heat engines (turbines or other internal combustion engines, or boilers or other external combustion engines) used for electrical power generation. Heat-engine-powered generators are nearly universal, ranging from small engines producing only a few kilowatts to utility-scale generators with ratings up to 800 megawatts. Electrochemical devices called fuel cells were invented about the same time as the battery. However, for many reasons, fuel cells were not well-developed until the advent of manned spaceflight (the Gemini Program) when lightweight, non-thermal (and therefore efficient) sources of electricity were required in spacecraft. Fuel cell development has increased in recent years due to an attempt to increase conversion efficiency of chemical energy stored in hydrocarbon or hydrogen fuels into electricity. At this time, liquid hydrocarbon fuels are the dominant forms of energy storage for use in transportation. However, these produce greenhouse gases when used to power cars, trucks, trains, ships and aircraft. Carbon-free energy carriers, such as hydrogen, or carbon-neutral energy carriers, such as some forms of ethanol or biodiesel, are being sought in response to concerns about the possible consequences of greenhouse gas emissions. Some areas of the world (Washington and Oregon in the USA, and Wales in the United Kingdom are examples) have used geographic features to store large quantities of water in elevated reservoirs, using excess electricity at times of low demand to pump water up to the reservoirs, then letting the water fall through turbine generators to retrieve the energy when demand peaks. Several other technologies have also been investigated, such as flywheels or compressed air storage in underground caverns, but to date no widely available solution to the challenge of mass energy storage has been deployed commercially.

General energy storage concepts

1. Using a high density magnetic field. Energy E in terms of magnetic field strength B is
E = \frac{1}{2}B^2 = \frac{1}{2}Li^2
where L is the inductance of the electromagnet and i is the current.
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Tuesday, October 20, 2009

sensor

A sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument. For example, a mercury-in-glass thermometer converts the measured temperature into expansion and contraction of a liquid which can be read on a calibrated glass tube. A thermocouple converts temperature to an output voltage which can be read by a voltmeter. For accuracy, all sensors need to be calibrated against known standards.

Use

Sensors are used in everyday objects such as touch-sensitive elevator buttons and lamps which dim or brighten by touching the base. There are also innumerable applications for sensors of which most people are never aware. Applications include cars, machines, aerospace, medicine, manufacturing and robotics.
A sensor's sensitivity indicates how much the sensor's output changes when the measured quantity changes. For instance, if the mercury in a thermometer moves 1 cm when the temperature changes by 1 °C, the sensitivity is 1 cm/°C. Sensors that measure very small changes must have very high sensitivities. Sensors also have an impact on what they measure; for instance, a room temperature thermometer inserted into a hot cup of liquid cools the liquid while the liquid heats the thermometer. Sensors need to be designed to have a small effect on what is measured, making the sensor smaller often improves this and may introduce other advantages. Technological progress allows more and more sensors to be manufactured on a microscopic scale as microsensors using MEMS technology. In most cases, a microsensor reaches a significantly higher speed and sensitivity compared with macroscopic approaches.

Classification of measurement errors

A good sensor obeys the following rules:
  • Is sensitive to the measured property
  • Is insensitive to any other property
  • Does not influence the measured property
Ideal sensors are designed to be linear. The output signal of such a sensor is linearly proportional to the value of the measured property. The sensitivity is then defined as the ratio between output signal and measured property. For example, if a sensor measures temperature and has a voltage output, the sensitivity is a constant with the unit [V/K]; this sensor is linear because the ratio is constant at all points of measurement.
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Transducer

A transducer is a device, electrical, electronic, electro-mechanical, electromagnetic, photonic, or photovoltaic, that converts one type of energy or physical attribute to another for various purposes including measurement or information transfer (for example: pressure sensors).
There are two kinds of transducers. A sensor is used to detect a parameter in one form and report it in another form of energy (usually an electrical or digital signal), such as a tachometer. An actuator is used for the transformation of energy or in other words, actuator is the one which gets actuated or stands responsible for the output action, in that it converts electrical signal into generally nonelectrical energy. An example of an actuator is a loudspeaker which converts an electrical signal into a variable magnetic field and, subsequently, into acoustic waves. The third kind of transducer has both functions -- for example, a typical ultrasonic transducer switches back and forth many times a second between acting as an actuator to produce ultrasonic waves, and acting as a sensor to detect ultrasonic waves.

 Types of transducers

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Monday, October 19, 2009

eddy current brake

An eddy current brake, like a conventional friction brake, is responsible for slowing an object, such as a train or a roller coaster. Unlike friction brakes, which apply pressure on two separate objects, eddy current brakes slow an object by creating eddy currents through electromagnetic induction which create resistance, and in turn either heat or electricity.

Construction and operation

Circular eddy current brake

Circular eddy current brake on 700 Series Shinkansen
Electromagnetic brakes are similar to electrical motors; non-ferromagnetic metal discs (rotors) are connected to a rotating coil, and a magnetic field between the rotor and the coil creates a resistance used to generate electricity or heat. When electromagnets are used, control of the braking action is made possible by varying the strength of the magnetic field. A braking force is possible when electric current is passed through the electromagnets. The movement of the metal through the magnetic field of the electromagnets creates eddy currents in the discs. These eddy currents generate an opposing magnetic field, which then resists the rotation of the discs, providing braking force. The net result is to convert the motion of the rotors into heat in the rotors.
Japanese Shinkansen trains had employed circular eddy current brake system on trailer cars since 100 Series Shinkansen. However, N700 Series Shinkansen abolished eddy current brake system because it can utilize regenerative brake easily due to 14 electric motor cars out of 16 cars trainset.

Linear eddy current brake

The principle of the linear eddy current brake has been described by the French physicist Foucault, hence in French the eddy current brake is called the "frein à courants de Foucault".
The linear eddy current brake consists of a magnetic yoke with electrical coils positioned along the rail, which are being magnetized alternating as south and north magnetic poles. This magnet does not touch the rail, as with the magnetic brake, but is held at a constant small distance from the rail (approximately 7 millimeters). It does not move along the rail, exerting only a vertical pull on the rail.
When the magnet is moved along the rail, it generates a non-stationary magnetic field in the head of the rail, which then generates electrical tension (Faraday's induction law), and causes eddy currents. These disturb the magnetic field in such a way that the magnetic force is diverted to the opposite of the direction of the movement, thus creating a horizontal force component, which works against the movement of the magnet.
The braking energy of the vehicle is converted in eddy current losses which lead to a warming of the rail. (The regular magnetic brake, in wide use in railways, exerts its braking force by friction with the rail, which also creates heat.)
The eddy current brake does not have any mechanical contact with the rail, and thus no wear, and creates no noise or odor. The eddy current brake is unusable at low speeds, but can be used at high speeds both for emergency braking and for regular braking.[1]
The TSI (Technical Specifications for Interoperability) of the EU for trans-European high speed rail recommends that all newly built high speed lines should make the eddy current brake possible.
Eddy current brakes at the Intamin roller coaster Goliath in Walibi World (Netherlands)
The first train in commercial circulation to use such a braking is the ICE 3.
Modern roller coasters use this type of braking, but utilize permanent magnets instead of electromagnets, and require no electricity. However, their braking strength cannot be adjusted.
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eddy current

An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist François Arago in 1824. It is caused when a conductor is exposed to a changing magnetic field due to relative motion of the field source and conductor; or due to variations of the field with time. This can cause a circulating flow of electrons, or a current, within the body of the conductor. These circulating eddies of current create induced magnetic fields that oppose the change of the original magnetic field due to Lenz's law, causing repulsive or drag forces between the conductor and the magnet. The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field that the conductor is exposed to changes, then the greater the currents that are developed and the greater the opposing field.
The term eddy current comes from analogous currents seen in water when dragging an oar breadthwise: localised areas of turbulence known as eddies give rise to persistent vortices.
Eddy currents, like all electric currents, generate heat as well as electromagnetic forces. The heat can be harnessed for induction heating. The electromagnetic forces can be used for levitation, creating movement, or to give a strong braking effect. Eddy currents can often be minimised with thin plates, by lamination of conductors or other details of conductor shape

Explanation

As the circular plate moves down through a small region of constant magnetic field directed into the page, eddy currents are induced in the plate. The direction of those currents is given by Lenz's law.
When a conductor moves relative to the field generated by a source, electromotive forces (EMFs) can be generated around loops within the conductor. These EMFs acting on the resistivity of the material generate a current around the loop, in accordance with Faraday's law of induction. These currents dissipate energy, and create a magnetic field that tends to oppose the changes in the field.
Eddy currents are created when a moving conductor experiences changes in the magnetic field generated by a stationary object, as well as when a stationary conductor encounters a varying magnetic field. Both effects are present when a conductor moves through a varying magnetic field, as is the case at the top and bottom edges of the magnetized region shown in the diagram. Eddy currents will be generated wherever a conducting object experiences a change in the intensity or direction of the magnetic field at any point within it, and not just at the boundaries.
The swirling current set up in the conductor is due to electrons experiencing a Lorentz force that is perpendicular to their motion. Hence, they veer to their right, or left, depending on the direction of the applied field and whether the strength of the field is increasing or declining. The resistivity of the conductor acts to damp the amplitude of the eddy currents, as well as straighten their paths. Lenz's law encapsulates the fact that the current swirls in such a way as to create an induced magnetic field that opposes the phenomenon that created it. In the case of a varying applied field, the induced field will always be in the opposite direction to that applied. The same will be true when a varying external field is increasing in strength. However, when a varying field is falling in strength, the induced field will be in the same direction as that originally applied, in order to oppose the decline.
An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where the currents cannot circulate due to the geometry of the conductor. In these situations charges collect on or within the object and these charges then produce static electric potentials that oppose any further current. Currents may be initially associated with the creation of static potentials, but these may be transitory and small.
Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. In many devices, this Joule heating reduces efficiency of iron-core transformers and electric motors and other devices that use changing magnetic fields. Eddy currents are minimized in these devices by selecting magnetic core materials that have low electrical conductivity (e.g., ferrites) or by using thin sheets of magnetic material, known as laminations. Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs. Charges gather at the lamination boundaries, in a process analogous to the Hall effect, producing electric fields that oppose any further accumulation of charge and hence suppressing the eddy currents. The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to the applied field), the greater the suppression of eddy currents.
The conversion of input energy to heat is not always undesirable, however, as there are some practical applications. One is in the brakes of some trains known as eddy current brakes. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. The eddy currents meet resistance as charges flow through the metal, thus dissipating energy as heat, and this acts to slow the wheels down. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion.

Strength of eddy currents

Some things usually increase the size and effects of eddy currents:
  • stronger magnetic fields
  • faster changing fields (due to faster relative speeds or otherwise)
  • thicker materials
  • lower resistivity materials (aluminium, copper, silver etc.)
Some things reduce the effects
  • weaker magnets
  • slower changing fields (slower relative speeds)
  • thinner materials
  • slotted materials so that currents cannot circulate
  • laminated materials so that currents cannot circulate
  • higher resistance materials (silicon rich iron etc.)
  • very fast changing fields (skin effect)

Applications

Repulsive effects and levitation

In a fast varying magnetic field the induced currents, in good conductors, particularly copper and aluminium, exhibit diamagnetic-like repulsion effects on the magnetic field, and hence on the magnet and can create repulsive effects and even stable levitation, albeit with reasonably high power dissipation due to the high currents this entails.
They can thus be used to induce a magnetic field in aluminum cans, which allows them to be separated easily from other recyclables. With a very strong handheld magnet, such as those made from neodymium, one can easily observe a very similar effect by rapidly sweeping the magnet over a coin with only a small separation. Depending on the strength of the magnet, identity of the coin, and separation between the magnet and coin, one may induce the coin to be pushed slightly ahead of the magnet - even if the coin contains no magnetic elements, such as the US penny.
Superconductors allow perfect, lossless conduction, which creates perpetually circulating eddy currents that are equal and opposite to the external magnetic field, thus allowing magnetic levitation. For the same reason, the magnetic field inside a superconducting medium will be exactly zero, regardless of the external applied field.

Identification of metals

In coin operated vending machines, eddy currents are used to detect counterfeit coins, or slugs. The coin rolls past a stationary magnet, and eddy currents slow its speed. The strength of the eddy currents, and thus the amount of slowing, depends on the conductivity of the coin's metal. Slugs are slowed to a different degree than genuine coins, and this is used to send them into the rejection slot.

Vibration | Position Sensing

Eddy currents are used in certain types of proximity sensors to observe the vibration and position of rotating shafts within their bearings. This technology was originally pioneered in the 1930s by researchers at General Electric using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by Donald E. Bently at Bently Nevada Corporation. These sensors are extremely sensitive to very small displacements making them well suited to observe the minute vibrations (on the order of several thousandths of an inch) in modern turbomachinery. A typical proximity sensor used for vibration monitoring has a scale factor of 200 mV/mil. Widespread use of such sensors in turbomachinery has led to development of industry standards that prescribe their use and application. Examples of such standards are American Petroleum Institute (API) Standard 670 and ISO 7919.

Electromagnetic braking


Eddy currents are used for braking at the end of some roller coasters. This mechanism has no mechanical wear and produces a very precise braking force. Typically, heavy copper plates extending from the car are moved between pairs of very strong permanent magnets. Electrical resistance within the plates causes a dragging effect analogous to friction, which dissipates the kinetic energy of the car. The same technique is used in electromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws.

Structural testing

Eddy current techniques are commonly used for the nondestructive examination (NDE) and condition monitoring of a large variety of metallic structures, including heat exchanger tubes, aircraft fuselage, and aircraft structural components.

Side effects

Eddy currents are the root cause of the skin effect in conductors carrying AC current.
Similarly, in magnetic materials of finite conductivity eddy currents cause the confinement of magnetic fields to only a couple skin depths of the surface of the material. This effect limits the flux linkage in inductors and transformers having magnetic cores.

Other applications

Diffusion Equation

The derivation of a useful equation for modeling the effect of eddy currents in a material starts with the differential, magnetostatic form of Ampère's Law[4], providing an expression for the magnetic field H surrounding a current density J,
\nabla \times \mathbf{H} = \mathbf{J}.
The curl is taken on both sides of the equation,
\nabla \times \left(\nabla \times \mathbf{H} \right) = \nabla \times \mathbf{J},
and using a common vector calculus identity for the curl of the curl results in
\nabla \left( \nabla \cdot \mathbf{H} \right) - \nabla^2\mathbf{H} = \nabla \times \mathbf{J}.
From Gauss's law for magnetism, \nabla \cdot \mathbf{H} = 0, which drops a term from the expression and gives
-\nabla^2\mathbf{H}=\nabla\times\mathbf{J}.
Using Ohm's law, \mathbf{J}=\sigma \boldsymbol{\Epsilon}, which relates current density J to electric field Ε in terms of a material's conductivity σ, and assuming isotropic conductivity, the equation can be written as
-\nabla^2\mathbf{H}=\sigma\nabla\times\boldsymbol{\Epsilon}.
The differential form of Faraday's law, \nabla \times \boldsymbol{\Epsilon} = -\frac{\partial \mathbf{B}}{\partial t}, provides an equivalence for the change in magnetic flux B in place of the curl of the electric field, so that the equation can be simplified to
\nabla^2\mathbf{H} = \sigma \frac{\partial \mathbf{B}}{\partial t}.
By definition, \mathbf{B}=\mu_0\left(\mathbf{H}+\mathbf{M}\right), where M is the magnetization of a material, and the diffusion equation finally appears as
\nabla^2\mathbf{H} = \mu_0 \sigma \left( \frac{\partial \mathbf{M} }{\partial t}+\frac{\partial \mathbf{H}}{\partial t} \right).
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