Electric Machines.pdf

Chapter 3 – Electrical Engineering Process Engineering Guidebook July 2005

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ELECTRIC MACHINES

Original draft by Phil Riche - 1985

Edited by MSU Engineering - 2002


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ELECTRIC MACHINES

1.0 INTRODUCTION

2.0 ELECTRIC AND MAGNETIC FUNDAMENTALS2.1 MAGNETIC FIELDS2.1.1 MAGNETIC FIELD OF A PERMANENT MAGNET2.1.2 MAGNET FIELD OF A CURRENT CARRYING CONDUCTOR2.2 MAGNETIC MATERIALS AND MAGNETIC CIRCUITS2.3 INDUCED VOLTAGE AND GENERATOR ACTION2.4 MOTOR ACTION

3.0 GENERATORS3.1 ELEMENTARY SYNCHRONOUS GENERATOR3.2 WOUND FIELD, SALIENT POLE SYNCHRONOUS

GENERATOR3.3 PERMANENT MAGNET GENERATOR3.4 BRUSHLESS AIRCRAFT GENERATOR3.5 HOMOPOLAR GENERATOR3.6 LUNDELL GENERATOR3.7 BRUSHLESS LUNDELL GENERATOR3.8 HYBRID GENERATOR3.9 SWITCHED RELUCTANCE GENERATOR3.10 AXIAL GAP, SEMA GENERATOR

4.0 MOTORS4.1 DC MOTOR4.2 INDUCTION MOTOR4.3 SYNCHRONOUS MOTOR4.4 BRUSHLESS DC MOTOR4.5 SWITCHED RELUCTANCE MOTOR4.6 AXIAL GAP, SEMA MOTOR

5.0 INVERTERS AND CONVERTERS

6.0 ELECTRONIC CONTROLLERS

Appendix 1 SPEED’s Brushless DC Motors by TJE Miller - underlying theory forthe design of electric motors and there associated drives andcontrols


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1.0 INTRODUCTION

An electric motor is a device for converting electrical energy tomechanical energy. An electric generator converts mechanical energyto electrical energy. In general, generators may act as motors, andconversely, motors may act as generators.

The history of electric motors and generators began with Hans ChristianOersted in 1820 when he discovered that an electric current produces amagnetic field, as shown by the deflection of a compass needle. Thisimmediately raised the question of whether or not a current could beproduced by a magnetic field. In searching for the converse of Oersted'’discovery, Michael Faraday built a device that demonstrated theprinciple of the electric motor. But it was not until 1831 that Faradaydiscovered electromagnetic induction, in which an electrical voltage isinduced in a circuit subjected to a changing magnetic field. During thatsame time period, it was discovered that a current carrying conductor ina magnetic field has a force acting on it.

Within a year of Faraday’s discovery a small hand generator wasdemonstrated. The first generators were little more than an assembly ofcoils and permanent magnets that could be kept in relative motion anddid not bear any resemblance to modern generators. The slottedarmature didn’t appear until 1880. The first generators were direct-current (dc) and were used for lighting only. Alternating current (ac)generators were developed around 1885 when the advantages of acover dc transmission became apparent. The first practical electric motorwas demonstrated in 1873 by Zenobe Theophile Gramme, a Belgian-born electrical engineer. He was the inventor of the ring armature whichgreatly improved the efficiency of motors and generators. As in the caseof generators, the first motors were dc. The first alternating-currentmotor was invented in 1888 by Nikola Tesla. He invented the inductionmotor which was the forerunner of most of today’s motors.

Electric motors and generators have been considerably improved overthe past 100 years. They are smaller, lighter, more efficient andcheaper. Some of these improvements have been due to a betterunderstanding of how motors and generators work and the developmentof better design procedures. Other improvements have resulted fromimproved manufacturing methods and better materials.

Insulating materials and varnishes available today are rated in excess often years continuous operation at 220 degrees C and can operate forshort periods at temperatures as high as 400 degrees C. Not too manyyears ago maximum operating temperatures were limited to 100 degrees


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C. Magnetic materials have also improved over the years and havelower losses and require less current to produce the same magnetic flux.These improvements in materials have resulted in motors andgenerators that are smaller and more efficient. In many cases cost hasbeen reduced also.

Rare earth permanent magnets are now commercially available and incommon usage for dc and brushless dc motors. Their use hasdrastically reduced motor size and improved performance. A newpermanent magnet material made from iron, boron, and neodymium hasan even higher energy product and is considerably cheaper. However, itis more susceptible to temperature (the flux decreases with increasingtemperature) and it has a considerably lower maximum operatingtemperature.

Brushless dc motors which were rare not too many years ago are nowfairly common and have many advantages over other types of motors.Electronically controlled motors, such as variable speed inductionmotors, have undergone considerable development and are now quitesophisticated.

The analytical methods used to analyze and design electric machineswere developed over a considerable period of time and until fairlyrecently were very similar to those used 30 to 40 years ago. Althoughcomputer programs have been used to design electric machines forquite some time, the design procedure has been the same as for handcalculations. The computer reduces the time to calculate theperformance of a generator or motor from days or weeks to seconds,and since the effect of varying a parameter can be determined fairlyquickly, more optimum machine designs have resulted. A fairly recentdevelopment in electric machine design has been the use of electro-magnetic finite element analysis programs to calculate machineperformance. Finite element analysis calculates the flux density in allparts of the machine including leakage paths, thus enabling optimizationof the dimensions. In addition, knowledge of the flux density distributionallows more accurate calculation of the machine parameters.

2.0 ELECTRIC AND MAGNETIC FUNDAMENTALS

A basic understanding of electricity and magnetism is necessary tounderstand how motors and generators work.

Magnetism is generally though of in terms of permanent magnets suchas the needle of a compass that indicates the direction of the earth’spoles and the small permanent magnets used in household fixtures andchildren’s toys. However, a magnetic field can be produced by either a


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permanent magnet or an electric current. Most of the importantproperties of magnetism are connected with the relations betweenmagnetism and electric currents. There are three basic relationships:

1. An electric current flowing through a conductor generates amagnetic field in the space around the wire.

2. A current carrying conductor in a magnetic field has a mechanicalforce acting on it. The magnetic field may be produced by apermanent magnet or by a second coil. Magnetic forces producedin this manner are the fundamental basis of electric motors.

3. When a coil of wire is situated in a magnetic field that is increasingor decreasing, an electrical voltage proportional to the rate ofchange of the field is generated in the coil. This is the phenomenonknown as electromagnetic induction that forms the basis of theelectric generator.

These three principles form the basis of the theory of electric motors andgenerators. Electric and magnetic phenomena are interrelated with eachother and motors and generators rely on a combination of electric andmagnetic effects.

2.1 MAGNETIC FIELDS

Magnetic fields can be produced either by permanent magnetsor electric currents.

2.1.1 MAGNETIC FIELD OF A PERMANENT MAGNET

Permanent magnets occur naturally as magnetite which is amagnetic oxide of iron (Fe304). Another name for magnetite islodestone and it was first mentioned in Greek writings as earlyas 8Q0 BC and was originally used in the compass. The namelodestone means leading stone, referring to its first use.

If a permanent magnet is suspended so that it can rotate freelyabout a vertical axis, one end seeks the earth’s magnetic northpole and the other the magnetic South Pole. This is theprinciple of the magnetic compass.

If iron filings are sprinkled over a magnet, they cling to it in adefinite pattern. Each filing becomes magnetized by themagnet and is then attracted by the magnet. The filings clingmost densely near the ends of the magnet where the poles arelocated. Poles always appear in pairs of opposite kind, north


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and south, and it is not possible to isolate them. If a magnet isbroken, new poles appear near the break in such a way thateach piece has two opposite poles.

If two magnets are placed close together, they will either attractor repel one another. The force of attraction or repulsion issmall when the magnets are far apart, but it increases rapidlyas the magnets are moved closer. Attractive forces occurbetween opposite poles and repulsive forces occur betweenidentical poles. In other words, like poles repel and oppositepoles attract.

The fact that magnets not in contact with one another exertforces on each other is difficult to explain. This phenomenon isexplained by the theory that every magnet is surrounded by amagnetic field and that a magnet placed in a magnetic field issubject to a magnetic force produced by that field. Thisconcept of a field of force can be visualized by scattering ironfilings over a smooth surface lying on top of a magnet. Eachfiling acts as a miniature compass needle, indicating thedirection of the magnetic field at the point where it lies. Thefilings are also attracted into positions where the field is thestrongest, so that regions where the density of the filings is thegreatest are those of largest field strength; that is, close to thepoles of the magnet.

If a tiny compass needle is suspended near a magnet, thedirection it assumes can be marked on a sheet of paper. If it ismoved a little in the direction it points, it takes up a slightlydifferent orientation. If this process is repeated continuously,the lines that are traced begin at one pole of the magnet andend at the other pole as shown in Figure 2.1.1-1. These linesare known as lines of magnetic force and show the orientationof the magnetic field of the magnet. These lines are identicalwith those indicated by the iron filings but may be mappedmore accurately with a compass.

The magnetic force lines are also known as flux lines. They are closedloops and flow from a north to a South Pole. Collectively the flux lines of amagnet are known as the magnetic flux produced by the magnet. Thestrength of the magnetic field is represented by the number of flux lines;the stronger the magnetic field, the more flux lines there are in a givenarea. The magnetic flux density (B) is defined as the number of flux linesper unit area and is a vector whose direction is tangent to the flux lines atany point. The unit for flux (Ø) is lines in the English system and webersin the SI system. One weber equals 108 lines. The unit for flux density is


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tesla or webers/meter2 in the SI system and lines per square inch in theEnglish system.

2.1.2 MAGNETIC FIELD OF A CURRENT CARRYINGCONDUCTOR

If an electric current is passed through a conductor, a magneticfield is established around it as shown in Figure 2.1.2-1. As inthe case of a permanent magnet, a compass can be used toverify the existence of this magnetic field. The compass pointsin the direction of the magnetic field and as the compass ismoved further from the wire, the force tending to align theneedle decreases. If the current reverses, the magnetic fieldreverses and the needlepoints in the opposite direction. This isthe discovery that ultimately led to the development of electricmotors and generators. The flux lines are circular and extendout indefinitely. The flux density is inversely proportional to thesquare of the distance from the conductor. The right hand ruleas shown in Figure 2.1.2-2 can be used to determine thedirection of the flux lines. If the thumb of the right hand pointsin the direction of the current, then the fingers curl in thedirection of the flux.

If a current carrying conductor is formed in the shape of a loopall of the magnetic flux lines leave the loop at one face andenter at the other face. Because of this the loop exhibitsmagnetic polarities and acts as a disc magnet. This is shownin Figure 2.1.2-3. If a number of loops are wound to form a


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solenoid as shown in Figure 2.1.2-4, the magnetic field will bemuch stronger since this is equivalent to stacking up a numberof disc magnets. The flux lines form continuous loops, leavingthe solenoid at one end and returning at the other end. Themagnetic field extends out indefinitely although it decreasesrapidly with distance. Again, the directions of the current andflux are related by the right hand rule. If the fingers curl in thedirection of the current, the thumb points in the direction of theflux.

2.2 MAGNETIC MATERIALS AND MAGNETIC CIRCUITS

An electron revolving in its orbit around the nucleus of anAtom forms a tiny current loop. Since a current loop has amagnetic field and all atoms have revolving electrons, then allmaterials should exhibit magnetic effects. This is true, but mostmaterials are very weak magnetically. There is a group ofmaterials iron, nickel, and cobalt in which the magnetic effectsare very strong. These materials are called ferromagneticmaterials.

A ferromagnetic material may be thought of as consisting of alarge number of tiny magnets as shown in Figure 2.2-1 which inthe absence of a magnetic field are randomly oriented andsince they cancel each other out there is no external magneticfield created by the ferromagnetic material. If a ferromagneticmaterial is placed in a magnetic field and the magnetic field isstrong enough the atomic magnets align themselves with themagnetic field as shown in Figure 2.2-2. Some materials retainthis alignment after the magnetic field is removed while otherslose their alignment. Retentivity is the property of a material toretain its magnetic alignment and may be regarded as thefriction between atoms that makes them hard to align. By thesame token, once they are aligned, they lose their alignmentonly with great difficulty. Residual magnetism is the amount ofmagnetism left after the external field is removed and it is ameasure of the number of atoms that remain in alignment. Amaterial with good retentivity will have a strong residualmagnetism and will make good permanent magnets. Othermaterials although they magnetize easily, lose most of theirmagnetism when the magnetic field is removed. Thesematerials are known as soft magnetic materials whereas thematerials that retain their magnetism are known as hardmagnetic materials.


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When a ferromagnetic material is exposed to an external magnetic and themagnetic field of the atoms aligns with the external field, the result is that themagnetic field in the material is stronger than it would be in air. The amount bywhich it is stronger is known as the relative permeability (ur) of the material.


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If a ferromagnetic material is formed in a continuous path suchas a torroid as shown in Figure 2.2-3 and if a coil is woundaround the torroid, the magnetic field set up by the currentthrough the winding will be mostly concentrated in the material.


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The magnetic flux in the material is due to the magnetizingforce which is given by

H = NIL

Where N is the number of turns of the coil, I is the currentthrough the coil, and L is the length of the magnetic path whichin this case would be the average circumference of the torroid.The unit for magnetizing force is ampere-turns/inch in theEnglish system and ampere-turns/meter in the SI system. Theflux density (B) in the torroid is given by

B = uH

where U is the permeability of the material and is given by

u = uruo

where ur is the relative permeability of the material and uo is thepermeability of air. The flux (Ø) is given by

Ø = BA

where A is the area.

As the magnetizing force is increased, the flux densityincreases. However, it doesn’t increase linearly but rather isextremely non-linear as is shown in Figure 2.2-4. This isbecause the permeability of the material is not constant butvaries with the flux density. Eventually, as the magnetizingforce is increased, the flux density levels out. The flux densitylevel at which this occurs is known as the saturation fluxdensity. Different ferromagnetic materials saturate at differentlevels. Silicon steel which we use in most of our motorssaturates at 130,000 lines/in2 whereas vanadium permendur orHiperco which we use in most of our generators saturates at148,000 lines/in2. Use of vanadium permendur generallyresults in a lighter and smaller motor or generator, because not


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as much magnetic material is required to carry the flux.

Figure 2.2-5 shows what is known as the hysteresis loop. Forthe wound torroid, if the iron is initially demagnetized and thecurrent is increased from zero until the iron is saturated, theflux density follows the dc magnetization curve. The maximumflux density is called the saturation flux density, Bs. Now, if thecurrent is reduced to zero, the flux density doesn’t return tozero but ends up at a positive value that is called the residualflux density Br. If the current is reversed and then increased, avalue of current will be found that results in zero flux density.This value of current results in a magnetizing force that iscalled the coercive force, Hc. If the current is increased in thenegative direction, the flux density will increase until thesaturation flux density in the negative direction is reached. Ifthe current is now reduced to zero, the flux density will fall tothe negative residual flux density. Reversing the current andincreasing it will again reduce the flux density to zero andincreasing it some more will eventually saturate the iron.

The phenomenon which causes the flux density to lag behindthe magnetizing force so that the magnetization curve for


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increasing and decreasing fields is not the same, is calledhysteresis and the loop traced out is called the hysteresis loop.If an alternating current is applied to the winding, thehysteresis loop is traversed once for each cycle. There is aloss for each cycle that is the hysteresis loss which isproportional to the area of the hysteresis loop.

When an alternating magnetic field is present, in addition to thehysteresis loss there is another loss that is called the eddycurrent loss. The alternating flux induces small alternatingvoltages in the magnetic material, which in turn produce eddycurrents in the material which result in the eddy current loss.This loss can be reduced by laminating the magnetic material.Typically laminations are .007 to .014” thick, the thinner onesbeing used at high frequencies. The combination of the eddycurrent loss and the hysteresis loss is called the core loss. Thecore loss results in heating which must be taken into account inthe design of motors, generators, and other magnetic devices.At this point it will be useful to introduce a new term calledreluctance. Referring to Figure 2.2-3 the flux is given by

Ø = BA

and the flux density is given by

B = uH

and sinceHL – NI

H = NIL

Substituting the value for H into the equation for B and thensubstituting the result into the equation for the flux yields

Ø = NIL/uA

The quantity L/uA is defined as the reluctance of the magneticcircuit and is the magnetic equivalent of electrical resistance.

R = LUA

If a magnetic circuit has an air gap as shown in Figure 2.2-6,there are two reluctance’s in series: the reluctance of the air


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gap and the reluctance of the path in the iron. Sincereluctance’s in

serie s add, theflux is given by

Ø = NIRiRg

where Ri is the reluctance of the path in the iron and Rg is thereluctance of the air gap. RI and Rg are given by

RI LI , Rg = Lg

UA uoA

Where LI and Lg are the length of the magnetic flux path in theiron and the air gap respectively. The area, neglecting fringing,is the same for both the iron and the air gap. Ideally, the fluxlines are confined to the magnetic material and travel straightacross the air gap. In practice this doesn’t happen. Some ofthe flux lines are outside the air gap as shown and this is calledfringing. Fringing is minimized by keeping the air gap as smallas possible. In addition to fringing, there is flux leakage asshown where some of the flux lines do not travel across the airgap, but rather leak across the iron. In electric machineleakages is kept as low as possible because leakage flux is notuseful flux but does require power to produce and hencereduces efficiency.

Permanent magnet materials have a large magnetic hysteresiswhen saturated. The chief distinguishing characteristics of apermanent magnet material are its high coercive force and highresidual flux density. A permanent magnet will support amagnetic field external to itself after removal of the magnetizingfield. Its operating point will be somewhere along the


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hysteresis curve in the second quadrant. That portion of theloop is called the demagnetization curve and is shown in Figure2.2-7. The point (Hd, Bd) on the demagnetization curve atwhich a permanent magnet will operate depends on thereluctance of the external magnetic circuit. Consider themagnetic circuit shown in Figure 2.2-8. Since the permeabilityof the iron is very high compared to air, the reluctance of theiron path is low and the total reluctance of the magnetic circuitexternal to the permanent magnet is very nearly equal to thereluctance of the air gap. Th permanent magnet establishesthe flux in the circuit and the ampere-turns in the permanentmagnet are equal to the ampere turns in the air gap.

(NI)pm = (NI)gap

since Ø = NI/R and Øpm = Øgap = Ø


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ØRpm = ØRgap

Rpm = Rgap

Lpm = Lgap

upmApm uoAgap

upm = uoAgapLpm = Bd

ApmLgap Hd

This is the operating point on the demagnetization curve andcan be found by drawing a straight line with a slope of Bd/Hd asshown in Figure 2.2-7 and finding the intersection of this linewith the demagnetization curve. This line is known as the loadline and its’ slope is called the permeance coefficient.

An important property of a permanent magnet is the product ofB and H at any point (Bd, Hd) along the demagnetization curve.This is called the energy product and it is proportional to theenergy in the magnetic field which the magnet will supportexternal to itself when operating at the point (Bd, Hd). Themaximum energy product is a criterion for comparing differentpermanent magnet materials.


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Demagnetization curves of several permanent magnetmaterials are shown in Figure 2.2-9. Until recently, the rareearth cobalt permanent magnets, specifically samarium-cobalt,had the highest available energy product. However,neodymium-iron-boron permanent magnets are available withenergy products up to 35 x 106 gauss-oersteds. They are alsocheaper than samarium-cobalt permanent magnets. However,samarium-cobalt permanent magnets have lower temperaturecoefficients and can operate at higher temperatures.Samarium-cobalt permanent magnets can operate up to 350°Cwhereas Neodymium magnets are limited to 150°C.

Permanent magnets can be demagnetized either by removingthem from the magnetic circuit or by applying an externaldemagnetizing field. Figure 2.2-10 shows a demagnetizationcurve for a permanent magnet material.

Suppose that this material is used for the permanent magnet inthe magnetic circuit shown in Figure 2.2.-8. If the magnet ismagnetized while it is in the magnetic circuit it ends upoperating at point A. If it is removed from the magnetic circuit,the reluctance of the flux path external to the magnet increasesand the magnet operates at a new point B, further down thedemagnetization curve where Bd is lower and therefore the fluxis lower. If the magnet is placed back in the circuit, it does notreturn to the original operating point but to a new operatingpoint C. Rather than moving along the demagnetization curvewhen the magnet is placed back in the circuit, the operatingpoint moves along a minor hysteresis loop to point C. Afterseveral cycles of removing and replacing the magnet this minorloop will stabilize into a straight line. The slope of this line iscalled the recoil permeability and is an intrinsic property of thepermanent magnet material. In general the recoil permeabilityslope is the slope of the demagnetization curve at Br.Subjecting a permanent magnet to an external demagnetizingmmf Ni will have a similar effect. Some materials such asferrite, samariumcobalt, and neodymium-iron-boron havestraight line demagnetization curves and the recoil loop is verynearly the same as the demagnetization curve. Thesematerials can be removed from their magnetic circuits and willreturn to very nearly the same operating point and thereforecan be magnetized by themselves and then assembled. Theyare also less susceptible to demagnetization by an externalfield.


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Motors, generators,and other magnetic devices have air gaps out of necessity.The result of an air gap is that more ampere- turns are requiredto produce the same magnetic flux. This is true because thetotal ampere-turns is the sum of the ampere-turns for the airgap and the iron and additional ampere turns are required topush the flux across the air gap. It is desirable to keep thecurrent as low as possible since the copper losses reduceefficiency and result in heating. Therefore, air gaps arenormally kept as small as possible and are dictated bymechanical considerations such as tolerances, run-out, andthermal expansion.

2.3 INDUCED VOLTAGE AND GENERATOR ACTION

If a conductor is moved up or down in a magnetic field asshown in Figure 2.3-1, a voltage is induced in the conductorand if the conductor is connected to a closed circuit, current willflow. This is the basic principle of electric generators.

In general if a conductor cuts across flux lines of a magneticfield at a right angle, a voltage is induced in the conductor. Ifthe conductor is parallel to the flux lines, no voltage is induced.

If the motion of the conductor is perpendicular to the flux lines,the induced voltage is given by

e = Blv,

where B is the flux density, 1 is the length of the conductor, andv is the velocity of the conductor.

A more general law for induced voltage is Faraday’s law:


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e = - ddt

According to this law, the voltage induced in a closed circuit isequal to the time rate of decrease of the magnetic flux linkingthe circuit. The negative sign indicates that the voltage andcurrent direction is positive when the flux is decreasing withtime. The right hand rule shown in Figure 2.3-2 is used todetermine the relationship between the voltage and fluxdirections.

2.4 MOTOR ACTION

If a current carrying wire is placed in a magnetic field as shownin Figure 2.4-1, a force is exerted on the wire that isproportional to the current, the magnitude of the flux density,and the sine of the angle between the flux direction and thecurrent direction. In other words, if the current and flux are atright angles to each other, the force is a maximum. The forcedirection is mutually perpendicular to the current and the flux.This is the theoretical basis for how motors produce torque. Allconventional motors produce torque by this means. Thedirection of the force can be determined by several methods.Probably the easiest method is to use the right hand rule asshown in Figure 2.4-2. The magnetic field is circular andtherefore increases the flux density on one side of theconductor and decreases it on the other. The conductor tendsto move away from the denser field. Fleming'’ left hand rule formotors can also be used. Using the left hand, if the indexfinger points in the direction of the flux and the middle finger inthe direction of the current, then the thumb points in thedirection of the force. Another method is to use the right handscrew method where if the current vector is considered to beattached to a right hand screw and is rotated towards the fluxdensity vector, then the force is in the direction that the screwadvances.


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3.0 GENERATORS

Generators can be classified into two types: ac and dc. In reality, thereis only one type and that is ac, since a dc generator generates an acvoltage which is converted to dc by means of a commutator andbrushes. Since dc generators have little application for aerospaceapplications, they won’t be discussed here.

A generator consists of a winding or group of windings in which a voltageinduced and an assembly for establishing a magnetic field. Thewindings in which the voltage is induced is called the armature winding.A voltage is generated in the armature winding by rotating the windingthrough a magnetic field or by rotating the magnetic field past thearmature winding. Therefore, the armature can be either stationary inwhich case it is the stator or it can be the rotating member or the rotor.Regardless of whether it is stationary or rotating it is still called thearmature. The member that establishes the magnetic field is called the


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field assembly and if a winding is used to establish the field it is calledthe field winding.

3.1 ELEMENTARY SYCHRONOUS GENERATOR

An elementary ac generator is shown in Figure 3.1-1. It consists ofa stationary field assembly and a rotating armature winding. Notshown are the slip rings and brushes which are necessary in orderto have an electrical connection to the armature. The fieldassembly establishes a magnetic field through the armature. Thearmature consists of a winding on an iron core. The purpose ofwinding the armature on a high permeability iron core is to minimizethe field current since it takes less current to establish flux throughhigh permeability iron than through air. For this reason, the air gapis kept as small as possible. The armature winding is a single coilof N turns and is indicated in cross section by the two coil sides aand –a placed in diametrically opposite narrow slots on the rotor.The conductors forming these coil sides are parallel to the shaft ofthe machine and are connected in series by end connections whichare not shown in the figure.

As the armature rotates, the flux that links the coil variessinusoidally and according to Faraday’s law a voltage is induced inthe coil that is given by

e = - d = -N d (Ømcoswt) = NØmwsinwt

Where e is the induced voltage in volts, N the number of turns, Øm

the maximum flux linkage in webers, and w is the angular velocityin radians per second. The machine shown is a two-pole machineand there is one cycle of the output voltage for each revolution.Therefore, the frequency in cycles per second or hertz is the sameas the speed of rotation in revolutions per second. The electricalfrequency is synchronized with the mechanical speed, hence thename synchronous machine. If there are more than two poles


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there is a complete cycle for every pair of pole and the frequency isgiven by

f = P x n = pn2 60 120

where n is the mechanical speed in rpm and n/60 is the speed inrevolutions per second.

3.2 WOUND FIELD, SALIENT POLE SYNCHRONOUS GENERATOR

The elementary generator described in 3.1 has a stationary fieldwinding and a rotating armature winding. DC generators are builtlike this because they need a rotating commutator to convert the acto dc. Although an ac generator could be built this way, mostpractical synchronous generators have a stationary armaturewinding (stator) and a rotating field winding. Practicalconsiderations of design dictate this orientation of the two windings.The field current is usually much smaller than the armature currentand it is desirable to have the low power winding on the rotor sinceit is more difficult to remove heat from the rotor. The field windingrequires two slip rings whereas a three-phase armature wouldrequire three or four slip rings. With a stationary armature the coilsand insulation are not subject to centrifugal stresses and are lessexposed to mechanical vibration.

A cross section of a single phase, would field, salient polesynchronous generator is shown in Figure 3.2-1. Not shown arethe slip rings and brushes necessary for conducting current to therotating field assembly. This is a two-pole machine and the rotorhas two field coils. The armature winding consists of a single coil ofN turns represented by the two coil sides a and –a.


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A three-phase generator is similar to a single-phase generator,except that it has three windings that are displaced 120 degreesfrom each other as shown in Figure 3.2-2. Therefore, there arethree output voltages that are displaced 120 degrees from eachother. The three windings can be connected in either a wye ordelta configuration as shown in Figure 3.2-3. The majority of threephase generators have wye connections. The advantages of thewye connection are:


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1. Two voltages are obtainable from a wye connection if a fourthwire is connected to the neutral. For example, if the line toneutral voltage is 115 volts then the line to line voltage is 115 x3 = 200 volts.

2. If a three-phase induction motor is operated from a four-wirewye generator, if a phase opens up the motor will continue torun on two phases with somewhat reduced performance.

3. With a delta connection, if third harmonics or their multiples arepresent, circulating currents in the winding result which causeunnecessary losses and dangerous heating.

Most generators have more than two poles. A four pole, singlephase, synchronous generator is shown in Figure 3.2-4. The fieldcoils are connected so that the field poles are of alternate north andsouth polarity. The rotor poles are 90 mechanical degrees apartrather than 180 degrees for the two-pole generator. The armaturewinding consists of two coils a1, -a1, and a2, -a2 connected in series.The generated voltage goes through 2 complete cycles for onerevolution of the rotor and the frequency in cycles per second istwice the rotor speed in revolutions per second. When a machinehas more than two poles it is more convenient to express theangles in electrical degrees than in mechanical degrees. Sincethere is one complete electrical cycle for each pair of poles theelectrical angle is related to the mechanical angle by

Øe = P Øm

2

where Øe is the electrical angle, Øm is the mechanical angle and Pis the number of poles.


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The generators shownso far have had one coil per phase per pair of poles. Practicalgenerators usually have more coils because this makes moreeffective use of the machine and increases the output power. Theyalso are wound in such a fashion that there are two coil sides perslot. A winding with 2 coil sides per slot is termed a two layerwinding and allows the use of chorded coils to reduce or eliminateharmonics. A chorded coil is one that has a pitch less than 180electrical degrees. A four pole, three phase, wound field,synchronous generator with 24 stator coils is shown in Figure 3.2-5.The coils have a 150-degree pitch which greatly reduces the fifthand seventh harmonics.

It is desirable for a synchronous generator to have a lowimpedance which means low reactance because the windingresistance is kept as low as possible to maximize the efficiency.The lower the reactance the less the voltage drop or rise when aload is suddenly applied or removed. Also, a low reactance meansa smaller time constant which improves the transient response.Finally, synchronous machines operating in parallel tend to


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maintain synchronism inherently and the lower the reactance thehigher the synchronizing torque.

The wound field, salient pole synchronous generator is thestandard generator of the electrical industry because it has thehighest electrical output per pound of any practical generator. Inaddition it has the lowest reactances which means that it has thebest regulation and transient performance. It is used on bothaircraft and utility systems almost exclusively. Its maindisadvantage is that it is speed limited due to centrifugal loading ofthe pole pieces by the field coils. Until just recently all aircraftgenerators had four poles and ran at 12,000 rpm to produce 400hertz. Sundstrand is now building a two pole; 24,000 rpmgenerator that is smaller and lighter than a four pole; 12,00 rpmgenerator. This design is based on a Lucas patent.

3.3 PERMANENT MAGNET GENERATOR

A permanent magnet generator utilizes rotating permanentmagnets to establish the rotating field. A cross-section of a four-pole permanent magnet generator is shown in Figure 3.3-1. Thepermanent magnets are radially oriented and establish the fluxpaths as shown. A nonmagnetic shrink ring is used over themagnets to retain them. The center section of the rotor is amagnetic material since it is in the magnetic circuit. A permanentmagnet generator with tangentially oriented permanent magnets isshown in Figure 3.3-2. The center section of this rotor isnonmagnetic since it would short out the magnets if it weremagnetic. The choice of which configuration to use depends onspecific requirements to be met.

The advent of rare earth cobalt magnets has greatly influenced thedesign of permanent magnet generators. Their high energyproduct has greatly reduced the size as has their resistance todemagnetization since smaller magnets can be used. Samarium-cobalt permanent magnet generators are generally smaller andlighter than wound field generators.

Permanent magnet generators are inherently brushless since thereis no field winding and they are more efficient since there are nofield winding losses.

Permanent magnet generators have one main disadvantage. Sincethe field is not variable the output voltage varies with the load andtherefore they are not suitable for use in applications that require a


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constant ac voltage independent of load. Figure 3.3-3 shows howthe output voltage of a permanent magnet generator varies with theload. Consequently they are used when the desired output is dcsince the output can be rectified and maintained at a constant dcvoltage electronically.

3.4 BRUSHLESS AIRCRAFT GENERATOR

Generators originally used for aircraft generators were air cooled,wound field, synchronous generators with slip rings and brushes.The brushless aircraft generator shown in Figure 3.4-1 wasdeveloped to solve the life and reliability problems associated withbrushes and slip rings. It consists of three generators mounted onthe same shaft: the main generator which is a wound field, salient-pole generator; the exciter generator; and a permanent magnetgenerator (PMG). The PMG has a rotating permanent magnet fieldand a stationary armature. The exciter generator is an inside-outgenerator with a stationary field assembly and a rotating armature.Figure 3.4-2 shows how the generators are connected. The outputof the PMG is rectified to obtain dc and used to excite the exciterfield. The output of the exciter is connected to a rotating full-warebridge rectifier whose output is fed to the main generator fieldwinding. The field excitation is then varied by controlling the exciterfield current.

Sundstrand generators use Hiperco laminations for the maingenerator to minimize weight and spray oil cooling allows highcurrent densities which also minimizes weight.

The rotating-rectifier, wound-field, salient-pole, synchronousgenerator is excellent as long as its limitations are not exceeded.Maximum speed is 24,000 rpm because of centrifugal loading ofthe pole pieces by the field windings and the rotating rectifiers aresubject to temperature and mechanical limitations.


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3.5 HOMOPOLAR GENERATOR

The homopolar generator has been around for over 85 years and isan extremely rugged brushless machine. It has a solid iron rotorand is capable of extreme high temperature and high-speedoperation. It is used for ORC engine applications for speeds ashigh as 36,000 rpm where high rotor temperatures areencountered.

In a conventional generator, the rotor has alternate north and southpoles as shown in Figure 3.2-4. For the four pole generator shown,there are four flux paths as shown, where the flux travels from anorth pole across the air gap to the stator, through the stator, andthen back across the air gap to a south pole.

As shown in Figure 3.5-1, a homopolar generator consists of twoidentical stators wound with a common winding, a double rotor withall the north poles on one end and all the south poles on the otherend, and a stationary field coil. The flux established by the field coilflows axially down the rotor, crosses the air gap at the rotor poles,flows through the stator teeth to the stator yoke, through the outershell to the other stator, through the stator teeth of the other stator,and across the air gap to the rotor. The magnetic flux from therotor poles passing through each stator section, is unidirectional.The magnetic flux never changes direction in a stator section andthe poles of a rotor section are of one polarity, hence the namehomopolar generator.

As mentioned previously, the homopolar generator is capable ofoperation at extremely high speeds. It is simple in design andinherently reliable. However, it is very heavy due to the two statorsand the double rotor. The long rotor is subject to critical speedproblems and high windage losses. The homopolar generator is


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less efficient due to the double stator which increases the statorresistance. It also has larger harmonics than the wound field,salient pole generator and higher reactances which effects transientresponse.

3.6 LUNDELL GENERATOR

A Lundell Generator is shown in Figure 3.6-1. It consists of aconventional stator and a rotor assembly with a rotating field coil.The rotor has two end pieces with projecting fingers that are thepoles and the flux path as shown in along the shaft, out throughone of the rotor cups, across the air gap into the stator, and backacross the air gap into the other cup and back through the shaft.

The Lundell generator is the basic ac generator that has been usedfor years on cars. However, in its basic form it does requirebrushes and slip rings. It is not used for aerospace applicationsand is discussed here because the brushless Lundell generatorsevolved from it.


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3.7 BRUSHLESS LUNDELL GENERATOR

There are a number of variations of the basic Lundell generator thathave stationary field coils thereby eliminating the brushes and sliprings. One such version is the Rice generator shown in Figure 3.7-1. This generator was patented by Lewis C. Rice in 1897. Therotor is similar to the Lundell rotor except that it doesn’t have a fieldcoil. The generator has two field coils, one at each end, andutilizes an auxiliary air gap to transfer the flux from the rotor to thegenerator housing. The Rice generator can also be built with asingle field coil as shown in Figure 3.7-2.

The Rice generator is smaller than a homopolar generator but isnot capable of as high a speed. It is more efficient than ahomopolar generator because it has one stator. However, the rotorconstruction is more complex. There are two overlapping polestructures that need to be assembled together using a nonmagneticsupporting structure.

3.8 HYBRID GENERATOR

The main disadvantage of the permanent magnet generator is theinability to adjust the field strength to maintain the output voltageconstant independent of the load.

A PMG and a homopolar generator can be combined as shown inFigure 3.8-1 to achieve adjustable output voltage. This hybridgenerator consists of a PMG and a homopolar generator section ateach end. The stator assembly is common to all three sections.Each homopolar section has one half the number of poles that thepermanent magnet has and one section has all north poles and theother section has all south poles. The PMG section provides themain output of the generator and the two homopolar sectionsprovide a means of adjusting the output voltage by establishing aflux that either aids or opposes the PMG flux. The PMG rotor


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section is the same as a standard PMG rotor. The homopolarsections are similar to a homopolar generator in that each sectionhas all north or all south poles. There is an auxiliary air gap asshown to provide a return flux path from the stator to the rotor. Ahybrid generator can be built with only one homopolar section asshown in Figure 3.8-2. This is the generator that is beingconsidered for the Space Station solar dynamic system. There isone concern with this generator. It has two poles to yield 400 Hz at24,000 rpm which means the homopolar has only one pole whichcreates a rotating magnetic force that has to be taken intoconsideration.


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4.0 MOTORS

4.1 DC MOTOR

The first practical electric motors were brush type dc motors. Anelementary dc motor as shown in Figure 4.1-1 consists of a coilmounted on a shaft so it is free to rotate in the magnetic field, acommutator, a field assembly to produce the magnetic field, and aset of brushes. If a current is caused to flow, forces will be exertedon each coil side. When the coil is horizontal a downward force willbe exerted on the left side of the coil and an upward force will beexerted on the right side, and the coil will tend to rotate in acounter-clock-wise direction. The torque varies with the cosine ofthe angle of rotation so that the torque is a maximum when the coilis horizontal and zero at plus and minus 90 degrees. The currentmust be reversed at the 90-degree position in order to obtain apositive torque from 90 to 270 degrees. This is accomplished withthe commutator, which consists of an insulating member carryingtwo copper segments connected to the coil ends, that rotates withthe coil. Two brushes that are fixed to the motor frame ride on thecommutator and carry the current to the coil.

An actual motor is constructed somewhat differently as shown inFigure 4.1-2. This is a simplified cross section of a wound field dcmotor. The number of coils is increased to smooth out the torqueand eliminate the zero torque points. The number of coils may varyfrom as few as three (in very small, low-voltage motors such asthose used in toys) to several hundred in extremely large motors.The number of commutator segments also increases since ingeneral there must be one for every coil.

When the current in a coil is suddenly reversed, the coil ismomentarily shorted and the resultant induced voltage in thewinding may cause sparking at the brushes. The sparking canresult in brush and commutator wear and produces electromagneticinterference (EMI). Brush and commutator wear is minimized byproper design and brush material selection. DC motors usuallyrequire EMI filters.

The operating characteristics of dc motors are determined by themethod of field excitation. Wound field motors are classified by thetype of field connection: shunt, series, and compound. Permanentmagnet dc motors use a permanent magnet field structure toprovide the magnetic flux.


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As shown in Figure 4.1-3, a shunt motor has the field and armatureconnected in parallel across the power supply. This results in aconstant magnetic field and a linear speed-torque curve as shown.In practice the speed torque curve deviates from a straight line dueto armature reaction which is demagnetization of the main field duethe magnetic field resulting from the armature currents.

A series motor is shown in Figure 4.1-4. It has the field windingconnected in series with the armature. This results in a high noload speed and a very high starting torque.

A compound motor is shown in Figure 4.1-5. It has both shunt andseries field windings which yields a composite characteristic. Theseries winding usually has little effect at no load and if it isconnected so as to aid the shunt winding a high starting torqueresults.


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A series motor is shown in Figure 4.1-4. It has the field windingconnected in series with the armature. This results in a high noload speed and a very high starting torque.

A compound motor is shown in Figure 4.1-5. It has both shunt andseries field windings which yields a composite characteristic. Theseries winding usually has little effect at no load and if it isconnected so as to aid the shunt winding a high starting torqueresults.

A cross-section of a permanent magnet dc motor is shown in Figure4.1-6. Permanent magnet motors are smaller than wound fieldmotors and are more efficient because of the elimination of the fieldwinding copper losses.

The advantages of dc motors are as follows:

1. The speed of a dc motor can be controlled in a variety of waysdepending on the type of field. Shunt motors can be separatelyexcited and the field excitation varied to control the speed. Inaddition, smooth speed control down to zero speed is possible.

2. Very high starting torque can be obtained with dc motors whichenables the use of a smaller motor for loads that have highinertia, but low running torque requirements. The high startingtorque is also an advantage for actuators and other types ofintermittent duty applications.

3. Permanent magnet and separately excited dc motors can bedynamically braked by placing a resistor across the motorterminals or shorting out the terminals after removing theexcitation.


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The disadvantages of dc motors are as follows:

1. The life of dc motors is limited because of brush andcommutator wear. Brushes must be replaced and thecommutator re-machined periodically.

2. Because the armature is somewhat isolated thermally, dcmotors have a higher temperature rise than motors withstationary armatures and are harder to cool. Bearing life isreduced because heat is conducted along the shaft and intothe bearings.

3. DC motors generate electrical noise and consequently requireEMI filters.

4. Satisfactory brush life is dependent on establishing alubricating film on the commutator. A film is established due tothe presence of moisture and oxygen. If this film is absent,extremely rapid brush wear results. Therefore, high altitudebrushes and special treatments are required for aircraft andspace applications.


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4.2 INDUCTION MOTOR

A cross section of a three phase, squirrel cage induction motor isshown in Figure 4.2-1. The stator winding is identical to that of asynchronous generator. The rotor has what is called a squirrelcage winding. The rotor consists of iron laminations with slots verymuch like the stator laminations, copper or aluminum bars that gothrough the slots, and end rings that are either welded or brazed tothe bars or cast in place with the bars. Figure 4.2-2 shows the rotorbars and end rings with the rotor laminations removed. It is easy tosee how this motor got its’ name.

The stator winding is usually wye connected for the same reasonsthat generators are. When a three-phase voltage is applied to thestator winding, a rotating magnetic field is established in the air gapand the rotor. This magnetic field rotates at a speed given by

N = 120fP

Which is the same equation that relates the synchronous speedand frequency for a generator. If the rotor is standing still, a voltagewill be induced in the rotor bars which will cause a current to flow inthe rotor bars. The interaction of the rotating magnetic field and theRotor bar current results in a torque acting on the rotor. As long asthe rotor speed is less than the speed of the rotating magnetic fieldthere will be an induced current in the rotor bars and a resultanttorque. However, if the rotor is rotating at the synchronous speed,


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there is no relative motion between the rotor bars and the magneticfield set up by the stator, and therefore there is no induced voltage.Because of this, an induction motor cannot operate at synchronousspeed even at no load because a small amount of torque isrequired to overcome the bearing friction and windage. Therefore,the no-load speed is slightly less than the synchronous speed. Atypical speed torque curve of an induction motor is shown in Figure4.2-3. The maximum torque, which occurs at a speed somewhatless than the normal operating speed, is known as the pullouttorque. Typically, this torque is 150 to 250 percent of the normalrunning torque. The starting torque is usually a little more than therated torque. The shape of the speed torque curve can be changedby increasing or decreasing the rotor resistance as shown in Figure4.2-4. Lowering the rotor resistance causes the pullout torque tooccur at a lower speed and increases the stall torque. If theresistance is lowered enough the pullout torque occurs at zerospeed and the speed-torque curve approaches a straight line.

The operating speed of an induction motor is often expressed interms of slip rather than rpm. Slip is defined as the differencebetween the synchronous speed and the rotor speed divided by thesynchronous speed and is given by

Ns - NS = Ns x 100


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The significance of this term is that in order for the induction motor to producetorque, the rotor speed has to be less than the speed of the rotating field and thisdifference in speed can be expressed as slip. The maximum slip of course is100 percent at stall. The normal operating speed for an induction motor isbetween four and five percent slip.

Induction motors tend to run at a constant speed because of the shape of thespeed torque curve. Because of this they are not normally suited for applicationsrequiring variable speed. However, the advent of adjustable frequency driveshas changed this. If the frequency is varied while maintaining a constant voltageto frequency ratio, the speed-torque curves shown in Figure 4.2-5 result. Anelectronic variable-speed drive system to achieve this is shown in Figure 4.2-6.The voltage to frequency ratio can be varied to obtain a wide variety of speedtorque curves. Pulse width modulation (PWM) is used to vary the applied voltageto the motor. The voltage waveform is shown in Figure 4.2-7.

Induction motors are the simplest and most rugged of all electric motors. Theycan be made very efficient (90 to 95 percent) in the larger sizes. They are mostsuitable for loads that have low starting torques such as pumps or fans and if thestarting torque has to be increased the efficiency is less.

4.3 SYNCHRONOUS MOTOR

A synchronous motor is almost identical to a synchronousgenerator. If a three-phase voltage is applied to the stator of a

wound field synchronous generator, a rotating field results. If therotor is then accelerated to the synchronous speed and the fieldwinding excited, there will be a torque acting on the rotor and therotor will run at synchronous speed. However, some means is

required to accelerate the rotor to synchronous speed.Synchronous generators usually have damper windings on the rotoras shown in Figure 4.3-1 for a two-pole machine. The purpose of

this winding is to minimize the effects of unbalanced loads andprevent hunting when operating generators in parallel. The damper

winding can also be used to provide a starting torque since it isessentially the same as the rotor winding for a squirrel cage

induction motor.


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The speed torque curve for a synchronous motor is shown in Figure4.3-2. The maximum torque is called the pull out torque. This isthe maximum torque that the motor can maintain at synchronous

speed.

Synchronous motors are primarily used where absolute constantspeed is required. They are more complicated than inductionmotors and except for permanent magnet synchronous motorsrequire slip rings and brushes and special controls for starting.Permanent magnet synchronous motors can be built with rotordamper windings for starting but they have a pulsating torqueduring startup because of the permanent magnet field.


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A better way of starting a synchronous motor is to start out byexciting the motor with a low frequency and slowly increase thefrequency to the desired frequency. However, this does requirespecial electronics.

4.4 BRUSHLESS DC MOTORS

Brushless dc motors operate on the same principle as brush typedc motors except that transistors are used to reverse the coilcurrents instead of a commutator. Also, the armature is stationaryand the field rotates which is exactly opposite to a conventional dcmotor. In addition to this being a necessary arrangement toeliminate slip rings and brushes, this has the additional advantagesof lower rotor inertia and better heat dissipation.

A typical brushless dc motor is shown in Figure 4.4-1. It consists ofa permanent magnet rotor assembly, a three phase wye-connectedstator, and a position transducer. The stator is identical to asynchronous generator stator or an induction motor stator and therotor is the same as a permanent magnet generator rotor. Theelectrical diagram for the motor is shown in Figure 4.4-2. Thetransistors are turned on and off at specific rotor angles asindicated by the position transducer.

The transistor firing sequence and the resultant phase voltages areshown in Figure 4.4-3. The three voltages are 120 degrees apart inphase and produce a rotating magnetic field in the air gap thatstays at a fixed angle to the magnetic field produced by thepermanent magnets on the rotor. The interaction of the two fieldsresults in a torque acting on the rotor. The transistor switching isdone in such a manner that the two magnetic fields are 90 electricaldegrees displaced from teach other. The torque is proportional tothe product of the two magnetic field strengths times the sine of theangle between them. The torque is a maximum for 90 degreesdisplacement and zero when the two fields are aligned. This isdifferent from a synchronous motor. A synchronous motor alwaysoperates at synchronous speed and the angle between the statorand the rotor field varies depending on the load. At light loads theangle is low and as the load is increased the angle between the twofields increases until the maximum torque is reached at 90 degrees.This maximum torque is the pullout torque. In contrast a brushlessdc motor has a straight-line speed-torque curve as shown in Figure4.4-4.

Different speed torque curves can be obtained by varying the dcinput voltage as shown in Figure 4.4-4. Pulse width modulation


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(PWM) can also be employed to achieve the same result byeffectively varying the input voltage to the motor windings. WithPWM, the transistors are turned off during their normal on cycle asshown in Figure 4.4-5. There are various PWM schemes, some ofwhich can be used to minimize the harmonics.

Brushless dc motors have high stall torques and low inertias whichmakes them ideal for actuators that have high responserequirements that require large torque to inertia ratios. They arehighly efficient and easily controllable which makes them useful forjust about any application. Their main disadvantages are that theyare expensive and complex. They require a position transducerand complex electronics. ________________________________________________________________ more space than themotor.


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SPEED’s Electric Motors

By TJE MillerProfessor of Electrical Engineering

University of GlasgowSPEED Laboratory

8 August 2001


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1. SIZING, GEARING, COOLING, MATERIALS and DESIGN

1.1 MOTION CONTROL SYSTEMS

Technology is so saturated with developments in microelectronics that it is easy to forget the vitalinterface between electrical and mechanical engineering. This interface is found wherevermechanical motion is controlled by electronics, and pervades a vast range of products. A littleconsideration reveals a large and important area of technology, in which motor drives arefundamental. In Japan the term ‘mechatronics’ is applied to this technology, usually with theconnotation of small drives. In the west the term ‘motion control system’ is often used for smallcontrolled drives such as position or velocity servos. In the larger industrial range the term ‘drive’usually suffices.

Many engineers have the impression that the technology of motors and rives is mature, evenstatic. But there is more development activity in drives today than at any time in the past, and it isnot confined to the control electronics. Two important reasons for the development activity andthe increasing technical variety are:

(1) Increasing use of computers and electronics for motion control. Automation demandsdrives with a wide variety of physical and control characteristics.

(2) New technology in power semiconductors, sensors, integrated circuits, andmicrocontrollers, facilitating the development of nonclassical motors such as brushlessDC motors, steppers and switched reluctance motors in a wide variety of designs.

1.2 WHY ADJUSTBLE SPEED?

Three common reasons for preferring an adjustable-speed rive over a fixed-speed motor are:

(a) energy saving;

(b) velocity or position control; and

(c) amelioration of transients


(a) Energy saving. In developed economies about one-third of all primary energy is convertedinto electricity, and about two-thirds of that is re-converted in electric motors and drives, mostlyintegral-kW induction motors running essentially at fixed speed. If a constant-speed motor isused to drive a flow process (such as a fan or pump), the only ways to control the flow rate are bythrottling or by recirculation, Fig. 1. Since the motor runs at full speed regardless of the flowrequirement, there can be excessive energy losses in the recirculation valve. Similarconsiderations apply to the control of airflow by adjustable baffles in air-moving plant.

Fig. 1.1 Flow Proc

In such applications itusing adjustable-speedThe additional losses iand recirculation losseThe adjustable-speedenergy savings and the

Recirculation in a flow-adjustable series resisimplement, it is increaspollution, even at low p

Recirculation

Fixed-speed motor

Pump or

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ess Controlled by Recirculation can Produce Energy Losses in the FlowControl Valve

is often possible to reduce average energy costs by 50 per cent or more bydrives, which eliminate the throttling or recirculation loss; see Fig. 1.2.

n the adjustable-speed drive are generally much less than the throttlings, since the drive efficiency is usually of the order of 90 per cent or more.drive may be more expensive, but its capital cost can be offset against

reduction of maintenance requirements on mechanical components.

control process is analogous to the control of a DC motor by means of antance. The technique is inherently wasteful, and although it is cheap toingly hard to justify in the face of concerns about energy efficiency andower levels.

Flow control valve

blower


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Fig. 1.2 Flow Control Efficiency is Improved by Adjustabl

(b) Velocity or position control. Obvious examples of speed controlportable hand tools, and domestic washing-machine drives. In buildininteresting examples in which not only position and velocity are controand its derivative (jerk). Countless processes in manufacturing industvelocity control of varying degrees of precision. Particularly with the trthe technical and commercial growth in drives below about 20 kW is vsystem-level products incorporate an adjustable-speed drive as a comexample, may contain between 3 and 6 independent drives, one for eaOther familiar examples are found in office machinery: positioning mecprintheads, magnetic tape, and read/write heads in disk drives.

(c) Amerlioration of transients. The electrical and mechanical stresmotor starts can be eliminated by adjustable-speed drives with controladjustable-speed drive is used in this situation only with very large mocycles are so frequent that the motor is effectively operating as a variastarting applications are less onerous than this, and usually it is sufficiemploy series SCR’s (or triacs with smaller motors) which ‘throttle’ thecontrolled value, and are bypassed by a mechanical switch when the mThe soft-starter is less expensive than a full adjustable-speed drive, weconomical for short-time duty during starting._______________________

1 Series control of induction motors is inefficient; produces excessive line harmThese factors can usually be tolerated for a few seconds during starting, but they rendecontinuous speed control.

1.3 LARGE VERSUS SMALL DRIVES

There are marked design differences between large and small drives.always chosen from one of the classical types: DC commutator (with wand synchronous. The main reasons are the need for high efficiency amaterials; and the need for smooth, ripple-free torque. In small drivesbecause of the need for a wider range of control characteristics. Effici

ConFixed Speed motor

Adjustablespeed drive

Pump or

e-Speed Drive

are the electric train,gs, elevators or lifts arelled, but also accelerationry require position andend towards automation,ery vigorous. Manyponent. A robot, forch axis of movement.hanisms for paper,

ses caused by direct-on-lineled acceleration. A fulltors or where the start-stopble speed drive. Most soft-ent (with AC motors) tostarting current to aotor reaches full speed.

1

hich helps to make it

onics; and is not very stable.r the soft-starter unsuitable for

Large motors are almostound field); AC induction;nd efficient utilization ofthere is greater varietyency and materials

blower

trolled flow


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utilization are still important, but so are control characteristics such as torque/inertia ratio,dynamic braking, speed range, acoustic noise and torque ripple.

There are also several breakpoints in the technology of power semiconductors. At the highestpower levels (up to 20MW) SCRs (thyristors) and GTOs (gate turn-off thyristors) are the onlydevices with sufficient voltage and current capability, but IGBTs (insulated-gate bipolartransistors) also now have voltage ratings measured in kV and current ratings of hundreds ofamps. Naturally-commutated or load-commutated converters are preferred, because of thesaving in commutation components and for reliability and efficiency reasons. In the mediumpower range (up to a few hundred kW) forced commutation and PWM are normal, and IGBT’s arevery widely used. At low powers (below a few kW) the power MOSFET is attractive because if iseasy to switch at high chopping frequencies.

1.4 STRUCTURE OF DRIVE SYSTEMS

The general structure of a drive system is shown in Fig. 3. It comprises the load, the motor, theelectronic drive, and the control.

Fig. 1.3 Drive System Structure


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The range of modern motion-control applications is virtually unlimited. Any random list illustratesthe variety – aerospace actuators; washing machines; computer disk and tape drives; printerplattens and printheads; inertial guidance systems; adjustable-speed pumps, blowers, fans andcompressors; locomotive and subway traction; automatic machine tools and machining centers;servo drives and spindle drives; robots; automotive auxiliaries; refrigeration and air-conditioningdrives; and many others.

Loads have widely differing requirements. The commonest requirement is for speed control, withvarying degrees of precision and accuracy. Position control is of increasing importance,particularly in automated plants and processes, and in office machinery and computerperipherals. In some cases it is the steady-state operation that is most important, for example inair-conditioning and pump drives.

1. Compliance with national, EC, USA and industry standards2. Maximum continuous power or torque requirements3. Forward/reverse operation4. Motoring/braking operation5. Dynamic or regenerative braking6. Overload rating and duration7. Supply voltage (AC or DC) and frequency8. Type of control: speed, position, etc.9. Precision required in controlled speed or position10. Programmability: speed and/or position profiles, start/stop ramps etc.11. Interface with plant control and communications12. Dynamic requirements: torque/inertia ratio, acceleration/deceleration13. Gearbox or direct drive; gear ratio14. Reliability and redundancy of components15. Protection arrangements, both mechanical and electrical16. Maximum level of acoustic noise; noise spectrum17. Compliance with EMC regulations18. Limitation of harmonics in the supply system19. Maintenance; spare parts; provision for expansion or reconfiguration

20. Environment: indoor/outdoor installation; enclosure; temperature;humidity; pollution; wind and seismic factors; type of coolant.

Table 1.1Drive System Requirements Checklist


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In other cases, such as in robots, tape drives, and actuators, dynamic performance is importantbecause of the need to minimize the time taken to perform operations or effect control changes.In these cases the torque/inertia ratio of the motor is an important parameter. In automotiveapplications the prime requirements are low cost and low noise. Efficiency is important in motorsthat run continuously, e.g. heater blowers, but not in intermittent-duty motors such as window-winders. Torque ripple is increasingly important in servo motors and applications such asautomotive power steering, where less than 1% ripple is typically required.

1.5 DRIVE SYSTEM REQUIREMENTS

Table 1.1 provides a checklist of application requirements. The speed/torque capability diagramis especially important, Fig. 4. Typically at low speed the drive operates under current limit, andsince torque is generally proportional to current (or nearly so), the torque is controlled in thismode of operation, such that any value can be obtained up to the value corresponding tomaximum current. At high speed, the back-EMF increases to a level at which the drive cannotmaintain maximum current; or even if it can maintain maximum current, it may not have sufficientvoltage to maintain the correct phase angle or waveform of the current. Base speed is themaximum speed at which rated torque can be developed. Above this speed, drives are oftenevaluated according to the speed range over which they can maintain constant power, the torquedecreasing as the speed increases. Some drives (such as triac-controlled AC universal motors)have almost no constant-torque region and their characteristics are said to be “highly inverse”.On the other hand, brushless PM motors tend to have a predominantly constant-torquecharacteristic with limited speed range above base speed.

1.6 NEW TECHNOLOGY

Several new technologies are contributing to the development of motion control systems.

Digital electronics. It would be hard to overstate the importance of microelectronics in motioncontrol. At the ‘heavy’ end of the spectrum are the multiple drives found in steel rolling mills,paper mills, and other heavy process plants, where it is normal to coordinate the motion of all theshafts by means of a computer or a network of computers, some of which may be quite large. Atthe light end of the power range are the drives found in office machinery, small computers, andportable goods such as cameras and compact-disk players, where custom integrated circuits andgate arrays are common. Between these extremes there are many microprocessor-controlledsystems of all levels of complexity.


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Fig. 1.4 Speed/Torque Characteristic

The first functions implemented with microprocessors were low-speed functions such asmonitoring and diagnostics, but digital control has penetrated from outer position loops throughthe intermediate velocity loop and is now routinely used even in high-bandwidth currentregulators. The development of field-oriented control for AC induction and synchronous motordrives would not have been practical without the microprocessor. Field-oriented control is basedon reference-frame transformation which may require rapid computation of trigonometricfunctions of rotor position. It permits the outer control loops of AC and DC drives to be the same,both in hardware and software, and improves the dynamic performance of the AC drive. Itsdevelopment since the mid 1970’s was a key factor enabling the AC induction motor to competein precision speed control with the DC motor, which had been preferred for speed control for atleast 50 years before then.

Such is the sophistication and speed of modern microelectronics that the PWM schemesemployed to regulate the voltage and current can be optimized with respect to many attributes,such as efficiency, acoustic noise, dynamic response, and harmonic content. There is increasinguse of field-programmable gate arrays for the high-speed functions, often combined withmicrocontrollers. Digital signal processors (DSP) are also used in advanced drives, and many ofthese operate with “sensorless” control, i.e., without shaft position sensing.

In motion control systems the ultimate objective is true instantaneous control of the torque,preferably with a minimum or reliance on shaft position sensors and detailed knowledge of motorparameters. In pursuit of this objective the processing power of modern microcomputers andDSPs has been exploited together with new forms of control based on neutral networks or fuzzylogic. At the other end of the drive, communication with computers and other controllers isanother area of continuous development.

Power semiconductor devices. The IGBT is the most popular device in integral-kW drives, andthe power MOSFET in low-power drives, especially at low voltage. GTO thyristors are still usedin large drives especially above 1 MW.

New magnetic materials. The permanent-magnet industry has continued to improve thecharacteristics of the main families of magnet used in electric machines: neodymium-iron boron,which was pioneered by Sumitomo and General Motors; rare-earth/cobalt; and ferrite. At roomtemperature NdFeB has the highest energy product of all the common magnet materials. In itsearly days the performance was rather sensitive to temperature, but it is now widely used even inautomotive and industrial servo applications where high operating temperatures up to andexceeding 100ºC are common, even in the presence of strong demagnetizing fields.

CAD and numerical analysis in design. Motor design has been computerized since the earlydays of computers, initially with the coding of well established design procedures. The last 20years has seen a steady development of commercially available finite-element software capableof analyzing fields in machines in two and three dimensions. The most advanced programs candetermine eddy-currents and transients, but the coupling of finite-element solvers to circuit-analysis and simulation algorithms is still in the research laboratory. In spite of the technicaladvances it remains the case that finite-element analysis requires the application of highly skilledpersonnel, and although machine designers use it fairly widely, they either follow well-establishedprocedures or rely on specialists to practice computations in support of more conventional designcalculations.

The finite-element method is still far from being a complete design tool and is too slow for manyof the routine processes. It is fundamentally an analysis tool rather than a design tool: and it


59

suffers from certain limitations when applied to motor design. It requires detailed input data andthe results need skilled interpretation. It is accurate only in idealized situations where parasiticeffects have been removed. It is too slow to be cost-effective as part of a synthesizing CADpackage, and is likely to remain so for some time. It is most useful in helping to understand atheoretical problem that is too difficult for conventional analysis, and in this role it has undoubtedlyhelped to refine many existing motor designs and improve some new ones.

At the same time the development of special design software for electric machines has produceda number of products which are much faster and are specifically intended for motor and generatordesign. Such programs are widely used in the industry for initial design, for “what-if” analysis,and (with suitable calibration against test data) for recording the characteristics of entire lines of

motor products. One example is the SPEED software from the University of Glasgow, which isused in places to illustrate this book.

2

The primary problems in motor and generator design are not simply electromagnetic, but requirean integrated approach to materials utilization and design-for-manufacture. The philosophyneeds to be a synthesizing one rather than an analytical one. This multidisciplinary problemincludes heat transfer and mechanical design as well as electromagnetics. The situation is morecomplicated in adjustable-speed drives where the supply waveforms are ‘switchmode’ choppedwaveforms rather than pure sinewaves or DC. In these cases time-stepping simulation may benecessary to determine the expected performance of a given design over a wide range ofoperating conditions.

Because of the fact that finite-element analysis usually requires foreknowledge of the currentwaveform, it could be argued that preoccupation with this class of software tool could hinder thedevelopment of drive systems which escape from the classical DC and sinusoidal waveforms inorder to explore the possibilities of a wider class of drive current waveforms, coupled with newconcepts in motor geometry. The key lies in using the finite-element tool in the correct way todetermine parameters that can be used in time-stepping simulations that will be executed byother software.

It is perhaps surprising that design software for electric machines is rarely capable of synthesis inthe true sense. It is much more common to find “optimization” techniques which rely on theautomatic generation of large numbers of “feasible” designs, and then rank them according to amore or less complex criterion which includes constraints on particular dimensions and otherparameters. The imaginative element in the design process remains in the human mind, and thecomputer appears to be far from taking it over.

For simulation of complete systems, such as an automotive power steering system or an aircraftflight control surface actuation system, there are several software packages, such as Simulink

TM,

SaberTM

, SimplorerTM

, Easy5TM

and many others. Suitably modified and extended, some of thesepackages permit the simulation of detailed motor models and their drives and controls. They maybe used for the development of control algorithms that are subsequently programmed in amicroprocessor or gate array.

Other contributing technologies. Plastics and composite materials find many applications inmotors. Fans, slot liners and wedges, end-bells and covers, an winding supports are thecommonest, but molded slot insulation and

2Others include design programs from Trimerics in Stuttgart, Germany and Yeadon Engineering Services,Wisconsin.


60

encapsulation of rotors are also widely used. In brushless motors designed for high peripheralspeeds, the magnets are often restrained against centrifugal force by banding or tubes made ofKevlar

TM, glass-reinforced plastics, or carbon fiber.

Motor drives generally require transducers for control and protection, and there has beenprogress in current-sensor and shaft position sensor technology.

In particular the linearity and temperature-independence of Hall-effect current sensors hasimproved greatly, and it is common to mount these devices in the same package, or on the sameprinted-circuit card, as the driver stage of the power electronics in small drives. For larger drivesflux-nulling current sensors can be used with bandwidths of up to several kHz and isolation atleast as good as that of a C.T.

In brushless drives the commutation signals are often derived from Hall sensors, activated eitherby the rotor magnet or by a separate magnet ring. Alternatively, optical interrupters may be usedwith a shaft-mounted slotted disk. At high speeds the commutation sensor can be used togenerate a speed signal via a frequency-to-voltage conversion. For motion control systems andservo-quality drives separate velocity and position transducers usually have to be used. For suchsystems the resolver is attractive because of its ruggedness, resolution, and its ability to provideaccurate absolute position and velocity signals from one sensor.

1.7 WHICH MOTOR?

The proliferation of new ideas, materials and components obviously generates manyopportunities but also complicates the question, what is the best drive for a particular job? Wecan perhaps address this by attempting to trace the evolution of the different motor types in sucha way as to bring out their most important advantages and disadvantages. It is the motor thatdetermines the basic characteristics of the drive system, and it also determines the requirementson the power semiconductors, the converter circuit, and the control.

Evolution of motors. The evolution of brushless motors is shown in Fig. 5. Row 1 contains thethree ‘classical’ motors: DC commutator (with wound field); AC synchronous; and AC induction.The term ‘classical’ emphasizes the fact that these motors satisfy three important criteria:

(1) they all produce essentially constant instantaneous torque (i.e., very little torque ripple);

(2) they operate from pure DC, or AC sinewave supplies, from which

(3) they can start and run without electronic controllers.

The classical motor of row 1 are readily coupled to electronic controllers to provide adjustablespeed; indeed it is with them that most of the technical and commercial development of powerelectronic control has taken place. Together with the PM DC commutator motor in row 2 and theseries-wound AC commutator motor or ‘universal’ motor, the row 1 motors account for the lion’sshare of all motor markets, both fixed-speed and adjustable-speed, even though they representonly a minority of the many different principles of electromechanical energy conversion on whichmotor designs may be based. By contrast, the non-classical motors are essentially confined tospecialist markets and until recently, few of them except the brushless DC motor have beenmanufactured in large numbers. Table 1.2 is a classification of some common types of motoraccording to these criteria.

The motors in row 2 are derived from those in row 1 by replacing field windings and permanentmagnets. The synchronous motor immediately becomes brushless, but the DC motor must go


61

through an additional transformation, from row 2 to row 3 with the inversion of the stator androtor, before the brushless version is achieved. The induction motor in row 1 is, of course,already brushless in its ‘cage’ version, but not in its wound-rotor or slip-ring version. Thebrushless motors are all those with three terminals, together with the switched reluctance motor,which cannot be derived from any of the other motors. Its awkward placement in Fig. 5 reflectsthe fact that it has various properties in common with all the brushless motors. Obviously theemphasis in this book is on the brushless motors, with only a relatively superficial treatment of theDC motor and the induction motor. Stepper motors are also excluded.

The DC commutator motor. The traditional DC commutator motor with electronically adjustablevoltage has always been prominent in motion control. It is easy to control, stable, and requiresrelatively few semiconductor devices in the drive. For many years the wound-field DC motor heldits own against the challenge of AC drives – arguably for at least fifty years from the mid-1930’suntil the mid-1980’s – but AC field oriented control, manufacturing cost structures, thedevelopment of the IGBT, and huge R&D investments finally forced it into a declining role.


62


63

Fig. 1.5 Evolution of Brushless Motors from Classical AC and DC Motors

The main objections to the commutator motor are brush and commutator wear, and the fact thatthe losses arise mostly on the rotor, making cooling more difficult than in AC motors where thelosses arise mostly on the stator. It is not that brush gear is unreliable – on the contrary, it isreliable, well-proven, and ‘forgiving’, as is proven by the widespread use of DC motors in railwaysystem throughout the world, and in automotive auxiliaries where the life of the brushes is not aserious limitation.

The PM DC commutator motor. In small DC commutator motors, replacing the field windingand pole structure with permanent magnets usually permits a considerable reduction in statordiameter, because of the efficient use of radial space by the magnet and the elimination of fieldlosses. Armature reaction is reduced and commutation is improved, owing to the lowpermeability of the magnet. The loss of field control is not as important as it would be in a largerdrive, because it can be overcome by the controller. In small drives the need for field weakeningis less common anyway. The PM DC motor is usually fed from an adjustable voltage supply,either linear or pulse-width modulated.

In automotive applications the PM DC motor is well entrenched because of its low cost andbecause of the low-voltage DC supply. Here it is usually operated at fixed speed or with series-resistance control. For safety-critical and demanding applications such as electric power steeringand braking, brushless motor drives are more suitable. The development of higher-voltageautomotive power supply systems (above 40V) will help to make brushless motors moreacceptable by reducing the current levels and therefore the size and cost of MOSFETs requiredin the drive.

AC induction motor drives. AC induction or synchronous motors are often preferred becauseof the limitations of commutation and rotor speed in DC motors. Slip is essential for torqueproduction in the induction motor, and it is impossible, even in theory, to achieve zero rotorlosses. This is one of the limitations of the induction motor, since rotor losses are more difficult toremove than stator losses, and it is one main reason to use permanent-magnet and/orreluctance-type synchronous motors.

Fig. 1.6 Integrated Motor/Inverter and Hand-Held Controller(courtesy of Grundfos A/S, Denmark)

The efficiency and power factor of induction motors falls off in small sizes because of the naturallaws of scaling, particularly at part load. As a motor of given geometry is scaled down, if alldimensions are scaled at the same rate the MMF required to product a given flux-densitydecreases in proportion to the linear dimension. But the cross-section available for conductorsdecreases with the square of the linear dimension, as does the area available for heat transfer.This continues down to the size at which the mechanical airgap reaches a lower limit determinedby manufacturing tolerances. Further scaling-down results in a more-or-less constant MMFrequirement while the areas continue to decrease with the square of the linear dimension. Thereis thus an “excitation penalty” or “magnetization” penalty” which becomes rapidly more severe asthe scale is reduced. It is for this reason that permanent magnets are so necessary in smallmotors. By providing flux without copper losses, they directly alleviate the excitation penalty.


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The induction motor is “brushless” and can operate with simple controls without a shaft positiontransducer. The simplest type of inverter is the six-step inverter. With no shaft position feedback,the motor remains stable only as long as the load torque does not exceed the breakdown torque,and this must be maintained at an adequate level by adjusting the voltage in proportion to thefrequency as the speed changes. At low speeds, oscillatory instabilities may appear. Toovercome these limitations there have been several improvements including slip control and,ultimately, full field-oriented or “vector” control in which the phase of the stator currents isregulated to control the angle between stator MMF and rotor flux. Field orientation usuallyrequires a shaft position encoder and may include an in-built control model whose parameters arespecific to the motor, and which must be compensated for changes caused by changing load andtemperature. Such controls are complex and generally cannot be justified in very small drives,but excellent results have been achieved in larger sizes (above a few kW).

In the fractional and low integral-horsepower range the complexity of the AC drive is a drawback,especially when dynamic performance, high efficiency, and a wide speed range are among thedesign requirements. These requirements cannot be met adequately with series-or triac-controlled induction motors, which are therefore restricted to applications where low cost is theonly criterion. Together these factors favour the use of brushless PM motor drives in the lowpower range.

The brushless DC PM motor. The smaller the motor, the more sense it makes to usepermanent magnets for excitation. There is no single ‘breakpoint’ below which PM brushlessmotors outperform induction motors, but it is usually in the 1-10kW range. Above this size theinduction motor improves rapidly, while the cost of magnets works against the PM motor. Belowit, the PM motor has better efficiency, torque per ampere, and effective power factor. Moreover,the power winding is on the stator where its heat can be removed more easily, while the rotorlosses are extremely small. These factors combine to keep the torque/inertia ratio high in smallmotors. The brushless DC motor is also easier to control, especially in its ‘squarewave’configuration (Chapter 4). Although the inverter is similar to that required for induction motors,usually with six transistors for a 3-phase system, the control algorithms are simpler and readilyimplemented in ‘smartpower’ or special-purpose ICs.

Fig. 1.7 The Minas brushless PM motor produced by Matsushita with itsstator fabricated from segments. Courtesy of Matsushita Ltd., Japan

The brushless PM AC synchronous motor. In Row 2 of Fig. 5 the brushless synchronousmachine has permanent magnets instead of a field winding. Field control is again sacrificed forthe elimination of brushes, sliprings, and field copper losses. This motor is a classical salient-pole synchronous AC motor with approximately sine-distributed windings, and it can therefore runfrom a sinewave supply without electronic commutation. If a cage winding is included, it can self-start ‘across-the-line’.


65

The magnets can be mounted on the rotor surface (Chapter 5) or they can be internal to the rotor.The interior construction simplifies the assembly and relieves the problem of retaining themagnets against centrifugal force. It also permits the use of rectangular instead of arc-shapedmagnets, and usually there is an appreciable reluctance torque which leads to a wide speedrange at constant power.

The PM synchronous motor operates as a synchronous reluctance motor if the magnets are leftout or demagnetized. This provides a measure of fault-tolerance in the event of partial or totaldemagnetization through abnormal operating conditions. It may indeed be built as a magnet-freereluctance motor, with or without a cage winding for starting ‘across-the-line’. Although the powerfactor and efficiency are not as good as in the PM motor, synchronous reluctance motors can bedesigned with wide speed range and substantial short-term overload capacity.

In larger sizes the brushless synchronous machine is sometimes built with a brushless exciter onthe same shaft, feeding a rotating rectifier which passes DC to a field winding on the main rotor.This motor has full field control. It is capable of a high specific torque and high speeds. As agenerator, this configuration is popular in high-speed aircraft generators (at 24,000 and 12,000rpm, 400 Hz) and in a wide variety of small industrial applications.

All the motors on the diagonal of Fig. 5 operate with inverters that share the same power circuittopology (three ‘totem-pole’ phase legs with the motor windings connected in star or delta to themidpoints). This gives rise to the concept of a family of motor drives providing a choice of motorsand motor characteristics, but with a high degree of commonality in the control and powerelectronics and all the associated transducers. The trend towards integrated phase legs, orindeed complete three-phase bridges, with in-built control and protection circuitry makes thisconcept more attractive. This family of drives covers a wide range of requirements, the maintypes being the conventional brushless DC (efficient in small sizes with good dynamics); theinterior-magnet synchronous motor (wide speed range); the synchronous reluctance motor (freefrom magnets and capable of high speeds or high-temperature operation); and the inductionmotor. It should be noted that all these drives are essentially “smooth-torque” systems with lowtorque ripple.

Stepper motors represent a major class of motors not included in Fig. 5. Steppers are alwaysbrushless and usually operate without shaft position sensing. Although they have manyproperties in common with synchronous and brushless DC motors, they cannot naturally beevolved from the motors in Fig. 5. By definition they are pulsed-torque machines incapable ofachieving ripple-free torque by normal means. Variable-reluctance (VR) and hybrid steppers canachieve an internal torque multiplication through the use of multiple teeth per stator pole andthrough the ‘vernier’ effect of having different numbers of rotor and stator poles. Both theseeffects work by increasing the number of torque impulses per revolution, and the price paid is anincrease in commutation frequency and iron losses. Steppers therefore have high torque-to-weight and high torque-to-inertia ratios, but are limited in top speed and power-to-weight ratio.The fine tooth structure requires a small airgap, which adds to the manufacturing cost. Beyond acertain number of teeth per pole the torque gain is “washed out” by scale effects that diminish theinductance variation on which the torque depends. Because of the high magnetic frequency andthe effect of MMF drop in the iron, such motors require expensive lamination steels to get thebest out of them.

Switched reluctance motors are derived from the single-stack VR stepper, in which the currentpulses are phased relative to the rotor position to optimize operation in the ‘slewing’ (continuousrotation) mode. This usually requires a shaft position transducer similar to that which is requiredfor the brushless DC motor, and indeed the resulting drive is like a brushless DC drive withoutmagnets. With this form of control the switched reluctance motor is not a stepper motor becauseit can produce continuous torque at any rotor position and any speed. There is still an inherenttorque ripple, however, which can be compensated only by current waveform profiling and


66

accurate phase control of the current waveform relative to the shaft position. The switchedreluctance motor suffers the same ‘excitation penalty’ as the induction motor and cannot equalthe efficiency or power density of the PM motor in small sizes.

When the classical motors are interfaced to switch mode converters (such as rectifiers, choppers,and inverters) they continue to respond to the average voltage (in the case of DC motors) or thefundamental voltage (in the case of AC motors). The harmonics associated with the switchingoperation of the converter cause parasitic losses, torque ripple, and other undesirable effects inthe motors, so that de-rating may be necessary. The non-classical motors are completelydependent on the switch mode operation of power electronic converters. In steppers it isacceptable for the torque to be pulsed, but most brushless drives are designed for smooth torqueeven though the power is switched.


67

Table 1.2 A Selection of Motors with Typical Applications


68

1.8 SIZING

When a new electric machine is to be designed from scratch, the requirements usually includes aset of performance specifications and a set of constraints or limitations such as the maximumphysical size, the maximum temperature rise, and the supply voltage. This section explains howthe basic size of a machine can be determined, starting from the performance specifications andworking within the limits of material properties and temperature rise.

In many cases, new machine designs are evolved from existing ones, by modifying existinglaminations and components to minimize the cost of changes in tooling and components. Evenso, the same principles determine how much power and performance can be achieved from amachine of given size and temperature rise.

The output equation. The classical output equation applies to (and unifies) all electricalmachines from the tiniest micromotors (a few µW) up to the largest AC motors used in processplants or ship propulsion (up to 20MW). Intuitively it comes from the fundamental law ofelectromagnetic force which is often loosely stated as “force = flux x current”, according to theleft-hand rule. For engineering purposes we need to derive a more precise statement of this law.Except in linear motors, we are more interested in torque than force. It is convenient to work withflux-density and current-density, because these parameters have values which do not changegreatly from one machine to another. Further, the flux and current densities are closely related tothe power loss density which determines the cooling requirements and temperature distributionthroughout the machine.

Specifically, the output equation relates the torque per rotor volume (TRV) to the electric loadingA and the magnetic loading B. We will define A and B first before deriving a precise form of theoutput equation. The definitions are written in a form suitable for AC synchronous and inductionmachines. For other types of machine the definitions are similar, but with slight variationsmultiplying constants and interpretation.

The electric loading A is defined as the linear current density around the airgap circumference,that is, the number of ampere-conductors per metre around the stator surface that faces theairgap.

(1.1)

where I is the RMS phase current, m is the number of phases, Nph is the number of turns in seriesper phase, and D is the diameter of the airgap. The airgap is assumed to be small compared tothe rotor diameter and the stator diameter. The RMS current is used because it determines theI2R heating, which is what limits the electric loading.

The magnetic loading B is defined as the average flux-density over the rotor surface. In ACmotors the flux-density is distributed sinusoidally so that the fundamental flux/pole is

(1.2)

mAD

ImN

umferenceAirgapCirc

conductorseTotalAmperA

ph/

2

Wbp

DLB stk

I2

*


69

where p is the number of pole-pairs and Lstk is the stack length, i.e., the axial length of the activepart of the machine. In slotted stators and rotors, the peak flux density in the teeth Bt(pk) must belimited to about 1.6t, otherwise the magnetizing current and/ or the iron loses may becomeexcessive. The peak flux-density Bg(pk) in the airgap is therefore Bg(pk) Bg(pk), where is the ratioof tooth width to slot pitch, measured at a diameter where the tooth flux-density is maximum; seefig 1.8. Typically is of the order of 0.5. Thus B=2 Bg(pk) /=2 Bt(pk) /, so B is normally limited toaround 2 x .05 x 1.6/= 0.5T.

Fig 1.8 Definition of tooth pitch and

The generated EMF per phase is given by the standard equation3

(1.3)

where f is the fundamental frequency, kw1 is the fundamental harmonic winding factor, and theproduct kw1Nph is the effective number of turns in series per phase. The maximum availableelectromagnetic power at the airgap is mEI. We consider this as being converted into mechanicalpower Tw/p, where w/p = 2πf is the speed in rad/sec. (Note also that w = 2π/60 x rpm). We can obtain the TRV as T/(πD

2Lstk/4), and substituting from equations 1.1, 1.2 and 1.3 we get

(1.4)

This equation reflects the “flux-current product” in the form of AB. The multiplying factor is simplya constant multiplied by the winding factor kw1, which incidentally casts kw1 in the role of autilization factor- the higher the winding factor, the greater is the utilization of flux and current inproducing torque. Since kw1 is usually about 0.85-0.95, TRV=2AB.

The TRV is also related to the airgap shear stress , which is the tangential (torque-producing)force per unit of swept rotor surface area; see Figs. 1.9 and 1.10. For every unit of rotor surfacearea, the electromagnetic torque is r =D/2 so the total torque is T= D x D/2=D

2/2 from

which it follows that

.22

22

1 Vp

fBDLNkfNkE

stkphwt

Iphw

ABkV

TTRV w

r

12

./ 3mNm


70

(1.5)

Fig 1.19 Airgap shear stress Fig1.10 Airgap sheer stress

The airgap sheer stress is measured in kN/m2. Typical values are given in Table 1.3.

4The

winding factor Kw1 is generally between 0.8 and 0.95, so that the

3 See chapter 2.

4 In Imperial units, if D Lstk are in inches, then T is in lbf-in. if = 1lbf/in2, TRV=13.8kNm/m3.

TRV= 2BA and = BA. For example, if the electric loading A=20 A/mm and themagnetic loading B=0.5T, = .05 x 20 x 10

3= 10kN/m

2. For totally-enclosed motors the lower

values of and TRV apply with natural convection, while the higher values would apply withforced-air cooling supplied by an external or shaft mounted fan.

5

Table 1.3TYPICAL VALUES FOR TRV AND (CONTINUOUS OPERATIONS)

The coefficient πkw1/√2 in eqn. (1.11) is peculiar to AC machines where the ampere-conductor distribution and the flux-density are sinusoidally distributed in space around the airgap; this canbe written

(1.6)

.2rV

TTRV

and .sin)( )( pkBB


71

The product A(Θ)B(Θ) is the force per unit of rotor surface in N/m2, and therefore the torque can

be obtained by integrating rA(Θ)B(Θ)dΘ = rA(pk)sin2Θ over the entire rotor surface, where r=D/2,

and dividing by the rotor volume πD2Lstk/4. This gives TRV=A(pk)B(pk). But the RMS value of A is

A(pk)/√2, while the average value of B is πB(pk)/2, giving TRV= πAB/√2. The winding factor appears because only the fundamental space-harmonic component of the current distributionproduces torque, in conjunction with the fundamental component of flux-density, and theeffectiveness of the winding in producing the fundamental component is represented by kw1.

In DC machines the integral rA(Θ)B(Θ)dΘ has no sin2 Θ term, and the result is TRV=2AB, where

B is the average value of flux-density over the whole rotor

5 In some references the output coefficient K is defined as T/(d2L), so K=TRV x /4.

periphery. The RMS value of A is equal to the peak value, since the current is uniformlydistributed around the rotor, and

A = ZIa/a

ΠD (1.7)

where Z is the number of rotor conductors, a is the number of parallel paths, Ia is the armaturecurrent, and D is the armature (rotor) diameter.

The electric loading A is limited by the slot fill factor, the depth of slot, and the cooling. It is alsorelated to the current density J in the conductors. Suppose the area of one slot is Aslot. Letd=slot-depth, t=tooth width, w=slot width, and λ=slot width, and λ=slot pitch=πD/Ns, where Ns isthe number of slots. Also let =t/. Then t + w = and Aslot=wd = (1-t) d. Now if the slot-fillfactor Fslot is defined as the ratio of actual copper cross-section area to the total area of each slot,we can write

J = A___ = A____FslotAslot Fslotd(1 - ) (1.8)

For example, if the slot depth is d = 15mm, the slot-fill factor is Fslot = 0.4, the tooth-width/slot-pitch ratio is = 0.5, and the electric loading is A = 20 A/mm, the current density is

J = 20 __ = 6.7 A/mm2

(1.9)0.4 x 15 x (1 – 0.5)

Typical values of current density for use in AC or brushless machines for different applicationsare given in Table 1.4. Note that in machines operated from electronic drives there are usuallytime-harmonics in the current which increase the current-density without increasing the torque-producing value of A, and it may be necessary to allow for this by multiplying J by a form factor kf.In AC machines this will be the ratio of the true RMS current to the RMS value of its fundamentalcomponent. In DC machines it will be the ratio of the RMS current to the average current.

Condition A/mm2

A/in2

Totally enclosed 1.5-5 1000-3000Air-over, fan-cooled 5-10 3000-6000

sin)( )( pkAA


72

Liquid cooled 10-30 6000-20000

Table 1.4

Typical Current Densities (Continuous Operation)

These current-density values assume that the windings are varnished for good heat transfer. Inair-cooled machines, the fan is mounted on the rear of the motor outside the frame with a shroudwhich focuses the air over the outside of the motor. Liquid cooled motors may have apassageway around the outside of the stator with a cooling fluid circulating to remove the heat.The highest values are obtained with hollow conductors with coolant flowing through them (“directconductor cooling”).

It might seem strange to evaluate the magnetic loading as the average flux-density in the airgaprather than the peak or RMS value, but the idea behind this is to indicate how well the entirecylinder of steel is being utilized.

6Its value is limited by the available MMF of the excitation

source, and by core losses which increase rapidly at high flux-density.

It is interesting to see why it is the rotor volume and not its surface area that primarily determinesthe torque capability or ‘specific output’. As the diameter is increased, both the current and theflux increase if the electric and magnetic loadings are kept the same. Hence the diameter (orradius) appears squared in any expression for specific output. On the other hand, if the length isincreased, only the flux increases, not the current. Therefore the length appears linearly in thespecific output. Thus the specific output is proportional to D

2Lstk, or rotor volume. In practice as

the diameter is increased, the electric loading can be increased also, because more intense fan-cooling or liquid cooling can be used without reducing the efficiency. Consequently the specificoutput (TRV) increases faster than the rotor volume.

Although it is theoretically possible to write one general equation from which the torque of anyelectric motor can be calculated, in practice a different torque equation is used for every differenttype of motor. Only in certain cases is it possible to discern in this equation an explicit product offlux and current, or even of quantities directly related to them. For example, in the DCcommutator motor the electromagnetic torque is given by

T = kIa (1.10)

Where is the flux and k is a constant. Here the flux-current product is obvious. In rotating-fieldAC machines the classical torque equations do not contain this product explicity. However, therecent development of ‘field-oriented’ or ‘vector’ controls has necessitated the transformation ofthe classical equations into forms in which the flux and current may appear explicity in a scalar orvector product. In eqn. (1.6) it is tacitly assumed that the flux and current are oriented at such________________

6Switched reluctance machines have very high local flux-densities but a comparatively low magnetic loading,because the high flux-density is limited to a small fraction of the stator periphery.

angles as to maximize the torque, but this is not automatically the case except in field-orienteddrives. By contrast, in DC machines the commutator automatically maintains the optimumrelative angle of orientation between the flux and the ampere-conductor distribution. In the caseof doubly-salient motors such as the switched reluctance motor and stepper motors, the torquecannot be expressed as the explicit product of a flux and a current. However, the TRV can still beused for initial sizing provided that A and B can be meaningfully defined (Miller, [1993]).

So far we have restricted attention to the torque per unit rotor volume, a natural consequence ofthe fact that the torque appears at the rotor surface. For a very rough estimation of overall sizeincluding the stator, we can use a typical value of ‘split ratio’ S (i.e., rotor/stator diameter ratio):thus


73

Rotor volumeStator volume = S

2(1.11)

A typical value of split ratio for an AC motor is in the range 0.55-0.65. For switched reluctancemotors rather smaller values are found. For DC commutator motors the value is usuallysomewhat higher.

The best way to acquire typical practical values of or TRV is by experience. An engineer who isfamiliar with a particular design of motor will have built and tested several, and the test dataprovides values of TRV correlated with temperature rise, electric and magnetic loadings etc. Thevalues quoted in Table 1.3 relate to the continuous rating. Peak ratings may exceed these valuesby 2-3 times, depending on the duration and other factors.

The TRV determines the volume of the rotor but not its shape. To estimate the rotor diameterand length separately, a length/diameter ratio should be specified. A value around 1 is common;however, it is also common to design motors of different ratings using the same laminations butwith different stack lengths. The length/diameter ratio may then vary over a range of 3:1 or more.Very large length/diameter ratios are undesirable because of inadequate lateral stiffness, but maybe used where a high torque/inertia ratio is desired, or in special cases where the motor has to fitinto a narrow space.

The foregoing discussion concerns the electromagnetic torque, that is, the raw torque producedby the electromechanical energy conversion process at the airgap. The actual torque available atthe shaft coupling is less than this in motors, or greater in generators, by the amount of themechanical losses which include friction, windage, and certain electromagnetic losses appearingon the rotor. Allowance should be made for these losses, which typically amount to less that 5%of the electromagnetic torque, and in larger machines or high-efficiency machines, less than 1%.

1.9 GEARING

Compared to the torque density in mechanical and hydraulic devices, the torque density (TRV) inelectric motors is miserably low in comparison with what engineers would really like to achieve

7.

It always has been low, and it always will be low until someone discovers or invents a materialthat can carry ten times as much flux as steel for the same magnetizing force; or a material thathas a fraction of the resistivity of copper. Such inventions would not by themselves be enough toincrease the flea-power of the electric motor by an order of magnitude, unless they weremanufacturable in reasonable quantity at reasonable cost-a test which has been repeatedly failedby laboratory prototypes and “wonder motors” for many decades.

For this reason motors are often used with gearboxes to drive the load. A gearbox is the obviousway to step up the torque. If the gear ratio is n, and Tm is the motor torque, the torque applied tothe load is nTm. The motor speed m is increased over the load speed L by the same ratio.Thus

TL = nTm and m = nL. (1.12)

In most cases the increased motor speed falls in a standard speed range for ‘high-speed’ motors,which may be typically anywhere from a few hundred rev/min to 30,000 rev/min or more.

If the gearbox efficiency is 100%, the output power of the motor is equal to the power applied tothe load. The choice of gear ratio depends on how the drive operates. If the speed is constant it


74

is usually a simple matter of matching the load torque TL to the rated continuous motor torqueTmc:

TL

n = Tmc (1.13)

If, however, the load has a ‘dynamic’ requirement which specifies a profile of speed or position asa function of time, the choice of the gear ratio and the motor parameters is more complicated.

___________

7This assertion is valid only in the normal range of sizes. In large intensively-cooled machines such as power-station generators, the electric machine clearly outperforms the steam turbine-it is typical for the generator to be dwarfedby the turbines.

Simple acceleration of pure inertia load. Referring to Fig. 1.11, if the motor torque is its peakrated torque Tmp, the acceleration of the load is given by

Tmp

A = n (Jm + JL) (1.14)N

2

Fig. 1.11 Gear Ratio

Where the term in brackets is the inertia of the motor combined with the load inertia, referred tothe motor shaft. If n is large the gearing makes the load inertia insignificant, but it reduces theload speed and acceleration relative to those of the motor. If n is small the referred load inertia islarge, and this limits the acceleration. Between the extremes of large and small n, there is avalue that gives maximum acceleration for fixed values of Tmp and the separate inertias. This‘optimum’ value can be determined by equating the differential coefficient da/dn to zero, giving

(1.15)

M

L

J

Jn


75

which is a well-known result. This value of n makes the referred load inertia equal to the motorinertia. The maximum acceleration of the load is therefore

(1.16)

The corresponding acceleration of the motor is n times this value. In this analysis, the inertias ofthe pinions (gearwheels) have been ignored. For a very precise evaluation, in the case of asingle-stage gearbox, the pinion inertias can be combined with (added to) the respective motorand load inertias.

Acceleration of inertia with fixed load torque. A slightly more complicated example is wherethe load has a fixed torque TL in addition to its inertia.

Again there is one value of gear ratio n that produces maximum acceleration, and by the samedifferentiation process it is found to be

If the inertias are unchanged from the previous case, the gear ratio is increased. The expressionfor the optimum ratio can be substituted back in the formula for acceleration to find the maximumload acceleration. The result is the same as eqn. (1.16); the difference is that with a larger ratio nthe load acceleration will be smaller. It is interesting to note that the maximum acceleration of themotor is unchanged, and is equal to one-half the torque/inertia ratio of the motor.

Peak/continuous torque ratio of motor. In the constant-speed case, the choice of n maximizesthe utilization of the continuous torque rating of the motor, Tmc. In the acceleration case, thechoice of n maximizes the utilization of the motor’s peak acceleration capability as expressed byits peak torque/inertia ratio Tmp/Jm. Consider a load that requires both short periods ofacceleration and long periods at constant speed. Then there is a question, can the two values ofn be the same? If so, the utilization of both aspects of motor capability will be maximized at thesame time.

This problem can be solved analytically in a few special cases, and one solution is given here asan example of the kind of analysis that is needed to get a highly optimized system design.Assume that the load torque is constant at all times, but that short bursts of acceleration (ordeceleration) are required from time to time. The peak rated torque of the motor will be used for

nJ

T

M

mp 1

2

1

./

/2nJJn

nTT

mm

Lmp

..112

2

L

mp

m

l

np

L

T

T

J

J

T

Tn


76

acceleration, and the continuous rated torque for constant speed. If we equate the two separatevalues of n from the appropriate formulas given above, and if we write

Tmp = kTmc (1.19)

Where k is the ratio of peak motor torque to continuous motor torque, then the followingrelationship can be derived:

(1.20)

The left-hand expression is the ratio of the referred motor inertia to the load inertia, and we canrefer to it as the ‘referred inertia ratio’ or just ‘inertia ratio’. For a range of values of the inertiaratio, the equation can be solved to find the values of k that simultaneously optimize n for both theconstant-speed and acceleration periods. The most interesting result of this is that a large rangeof inertia ratio is encompassed by only a small range of values of k: as the inertia ratio changesfrom infinity downt o 2, k changes only from 2 to 4. But values of k in this range are extremelycommon: so common, in fact, as to appear to be a natural characteristic of electric motors. Thisimplies that for most inertia ratios where the referred motor inertia is more than twice the loadinertia, the gear ratio can be chosen to make good utilization of both the continuous torque andthe peak acceleration of the motor, provided k ≥2.Ifk<2, the gear ratio must be chosen for constant speed or for acceleration, and cannot be optimal for both. The property of electricmotors to provide short bursts of peak torque for acceleration is one of the most importantaspects of their use in motion control systems.

General speed and position profiles. The cases considered are all idealized by ratherrestrictive assumptions that may be too simple in a complex motion-control system. For detailedwork it is desirable to simulate the performance of the whole system using system-simulationsoftware.

1.10 COOLING

The need for cooling

1. heat removal; and2. temperature distribution within the motor.

The main reasons for limiting the temperature rise of the windings and frame of a motor are:

1. to preserve the life of the insulation and bearings;2. to prevent excessive heating of the surroundings; and3. to prevent injury caused by touching hot surfaces.

Insulation life. The “life” of electrical insulation is inversely related to the temperature. A

sustained 10C increase in temperature reduces the insulation life by approximately 50%. Theextent to which excessive temperatures can be tolerated depends on the duration and the actualtemperatures reached.

.

112

22

k

k

J

Jn

l

m


77

An interesting example of a motor designed for exceptionally high temperatures is the FUMEXmotor manufactured by Invensys Brook Hansen, used to extract fumes via the ventilation systemsof public buildings in the event of fire; these motors can operate in an ambient temperature of300C for a limited period of 30 minutes. Similar considerations apply to bearings. Grease-lubricated bearings may be filled with high-temperature grease for hot-running applications, butan aerospace machines the bearings are usually lubricated by separately-cooled oil or oil mist.

Heating of the surrounds is obviously undesirable especially if the motor is heating theequipment it is driving. For this reason it is important to minimize rotor losses conducted alongthe shaft. PM motors have cooler rotors than DC or induction motors. In some applications suchas hermetic compressors used in air-conditioning, refrigeration, etc., the motor losses areremoved by the working fluid, reducing the thermodynamic efficiency of the system.

To prevent injury or harm from touching, exposed surfaces must be kept below 50C. Incertain applications (e.g., under car bonnets), this requirement is impossible to meet because the“ambient” temperature under the bonnet may reach 100C. In industrial applications the ambienttemperature is generally less than 50C, and NEMA ratings for electrical insulation assume anambient temperature of 40C. In aerospace applications motors and generators may be directlycooled by oil or fuel and coolant temperatures can be as high as 100C.

The increase in winding temperature increases the resistivity of the windings: a 50C rise by 20%,and a 135C rise by 53%, increasing the I

2R losses by the same amount if the current remains

the same. The resistance increase is used in test procedures to determine the actualtemperature rise of the winding, but this is obviously an average temperature; hot-spottemperatures can be 10-20 higher. At any temperature TC the resistivity of copper can becalculated as

= 20 [1 = (T – 20)] ohm-m (1.21)

where =0.00393/C, is the temperature coefficient of resistivity and 20 is the resistivity at 20C,that is, 1.728 x 10

-8ohm-m.

Heat Removal

In most industrial and commercial motors, heat is removed by a combination of

1. conduction to the frame mountings;2. air convection, which may be natural or forced; and3. radiation.

In highly-rated machines direct cooling methods are used:

1. oil mist, especially in aerospace machines;2. immersion in refrigerant, in “hermetic” motors used in refrigerator compressors;3. direct conductor cooling, with hydrogen, oil, or water forced through hollow conductors,

especially in turbine-generators.

Conduction. The conduction equation for a block of thickness t and area A is

Q = k A dT = k A T W (1.22)dx t

where T is the temperature difference through the thickness t. The coefficient k is the thermalconductivity, with units (W/m

2) per (C/m), i.e. W/C-m. The thermal conductivity is a material


78

property, and usually it is a function of temperature. Most metals have high thermalconductivities, especially those which are also good electrical conductors. On the other hand,electrical insulating materials and most fluids have low thermal conductivities.

As an example, consider the flow of heat along a conductor whose cross-section area is A = 64mm

2and length 50 mm, when the RMS current-density is 7 A/mm

2. The electrical resistivity of

copper is 1.7x10-8

ohm-m, so heat is produced at the rate of J2=(7x10

6)2x1.7x10

-8=833,000

W/m3. In one conductor the I

2R loss is therefore 833,000 x 64 x 10

-6x 50 x 10

-3= 2.7W. To take

the most pessimistic estimate, assume that all of this heat is generated at the mid-point of thecoil-side, half-way along the motor. The thermal conductivity of copper is 387 (W/m

2) per (C/m).

So the temperature gradient along the coil-side is given by eqn. (1.22) as

dT = Q = 2.7 = 108C/m (1.23)dx kA 387 x 64 x 10

-6

Since the heat can flow in both directions, the temperature-gradient is only half this value, and thetemperature rise between the ends of the stack and the center is therefore 110/2 x 50 x 10

-

3/2=1.4 C, which is negligible. A more thorough analysis would have to consider the full diffusion

equation along the length of the coil-side, but this quick calculation reveals that suchsophistication is not needed in the example considered.

Thermal resistance and contact resistance. Eqn. (1.24) can be used to define thermalresistance as the ratio of temperature difference T to heat flow rate Q: the symbol used forthermal resistance is R, with units C/W. Thus

T = t C/W (1.24)R = Q kA

The thermal resistance is a “lumped parameter” that can be used to model the conductionthrough a region or interface where the individual values of k, A, and t may be difficult todetermine. The contact resistance between two surfaces is usually treated in this way, as, forexample, between the frame and the stator core. The temperature drop across a thermalresistance is given by eqn. (1.24) as T = QR. For example, if the contact resistance betweenthe motor flange and the mounting plate is 1C/W, then with 40W flowing through the temperaturedifference across the interface would be 40C.

Radiation. Radiation is described by the Stefan-Boltzmann equation

QA = е (T1

4– T2

4) W/m

2(1.25)

Where is the Stefan-Boltzmann constant, 5.67 x 10-8

W/m2/K

4for a black body, T1 is the

absolute surface temperature of the radiating body in degrees Kelvin, and T2 is the absolutetemperature of the surroundings

8. A black body is a

perfect radiator, that is, one which reflects no radiated heat but absorbs all the heat radiatedtowards it. Real surfaces are imperfect radiators, and their radiative effectiveness relative to thatof a black body is called the emissivity e. A black lacquered surface can achieve an emissivity ashigh as 0.98, but a more practical rule of thumb is to take 0.9 for black-painted or lacqueredsurfaces. For example, a surface with an emissivity of 0.9 that is 50C above the surroundings at50C, has a net heat transfer rate of

0.9 x 5.67 x 10-8

x ((50+50+273)4) (1.26)

which is 432 W/m2

or 0.28 W/in2. A surface 30C above the surroundings at ____________________


79

8The absolute temperature in degrees Kelvin (K) is the temperature in C

20C has a rate of 186 W/m2

– quite a useful component of the heat-removal capability of theframe.

Convection. Heat removal by convection is governed by Newton’s Law:

Q = h T W/m2

(1.27)A

Where T is the temperature difference between the cooling medium and the surface beingcooled, and h is the heat-transfer coefficient. The units of h are W/m

2/C. The value of h

depends on the viscosity, thermal conductivity, specific heat, and other properties of the coolant,and also on its velocity. In natural convection the flow of coolant is not assisted by fans, blowers,pumps etc. In forced convection the flow is assisted by one of these external means.

The heat transfer coefficient for natural convection around a horizontally-mounted unfinnedcylindrical motor can be roughly estimated as

h = 7.5 (T¼) W/m

2/C (1.28)

( D )

where D is in mm. For example, for an unfinned cylinder of diameter D = 100 mm and a

temperature rise of 50C, the natural-convection heat-transfer coefficient is calculated as 6.3W/m

2/C. For a T of 50C, the heat transfer rate is then given by eqn. (1.28) as 6.3 x 50=315

W/m2. As a first approximation this value can be applied to the whole surface including the ends,

but if the motor is flange-mounted then only one end is available for convective cooling.

Forced convection (with a shaft-mounted fan or an external blower) increases the heat-transfercoefficient by as much s 5-6 times, depending on the air velocity. The increase in heat-transfercoefficient is approximately proportional to the square-root of the air velocity. An approximateformula for the forced-convection heat-transfer coefficient is

h = 125 √V W/m2/C (1.29)

L

Where V is the actual air velocity [m/s] and L is the frame length [mm] (assumed parallel to thedirection of airflow). For a motor of length 100 mm, if the air velocity is 4 m/s, this formulapredicts h =25 W/m

2/C. This is 4 times higher than for natural convection.

Some rules of thumb for “calibration”. In a water-immersed wire 1 m long, 1 mm diameter, apower loss of 22 W (0.022 W per mm length) is sufficient to boil the water at the wire surface.

The wire surface temperature is 114C and the heat transfer coefficient (see below) is 5000W/m

2/C. The heat flow at the wire surface is 0.07 W/mm

2and the current-density in the wire is

approximately 35 A/mm2. In normal motors, the rate at which heat can be abstracted is far less

than this, and current-densities over 30 A/mm2

is sufficient to fuse a copper wire in free air.

The maximum rate of heat removal by natural convection and radiation (with 40C rise) is onlyabout 800 W/m

2. With forced air convection the rate increases to about 3000 W/m

2, and with

direct liquid cooling about 5000 W/m2. A motor that generates more heat than can be removed at

these rates must absorb the heat in its thermal mass, which permits the output power to be


80

increased for a short time. These rates limit the heat generated per unit volume to about 0.012W/cm

3for natural convection, 0.3 W/cm

3for direct liquid cooling.

The permissible current-density cannot be directly related to the temperature rise of the windingby a simple general equation, because the heat transfer rate depends on the shape of theconductors. As an example, 1 cm

3of copper can be made into a stubby cylinder of 1 cm

diameter and 1.27 cm length, or a long wire of 1 mm diameter and 1.27 m length. The shortcylinder has a cylindrical surface area of 4 cm

2while the long wire has a surface area of 40 cm

2.

The loss density in the conductor is J2 where J is the current density and is the resistivity.

With ten times the surface area the long wire can dissipate ten times the heat, assuming thesame heat transfer coefficient in both cases. This suggests that the permissible current-density inthe long wire can be 10 times that in the short stubby cylinder.

If rated torque is required at very low speed, a shaft-mounted fan may not provide enough coolantflow to keep the motor cool. DC motors often have separate AC-driven fans, because they haveto work for prolonged periods at low speed with high torque. Since most of the heat in a DCmotor is generated on the rotor, good internal airflow is essential. In DC motors, the external fanis usually mounted to one side of the motor, where it is easily accessible, and does not increasethe overall length. With vector-controlled induction motors a common practice is to mount the fanin line with the motor at the non-drive end, and arrange it to blow air over the outside of the finnedframe. The fan may increase the overall length by up to 60%. Brushless motors have lesssevere problems because most of the heat at low speed is generated in the stator windings, andvery little on the rotor.

Internal temperature distribution

The steady-state temperature distribution within the motor is essentially a diffusion problem. Themost important aspect of the problem is finding the hottest temperature in the motor, given acertain distribution of losses and a known rate of heat removal. It is difficult to solve precisely,because of three-dimensional effects and because some thermal resistances (such as theresistance between slot conductors and slot liner) are hard to calculate.

The differential equation for three-dimensional conduction of heat is the so-called diffusionequation:

2T = 1 q = 1 T (1.30)

k t t

where

2T = 2T + 2T + 2T (1.31)

2

y2

z2

and

= k m2/s (1.32)

c

is the diffusivity in SI units. In SI units, k is the thermal conductivity in W/mC; c is the specificheat in kJ/kgC, and is the density in kg/m

3. In a structure as complex as an electric motor the

heat conduction equation is a complex boundary-value problem that is best solved by computer-based numerical methods such as the finite-element method.

In electric motors internal convection and radiation may be as important as conduction, and whenthe differential equation is extended to include them, matters become very complicated, even for


81

steady-state calculations. During transients the temperature distribution can be very differentfrom the steady-state distribution, and different methods of analysis may be needed for the twocases.

Thermal equivalent circuit. For most purposes it is sufficient to use a thermal equivalent circuitof the interior of the motor, Fig. 1.12. This is analogous to an electric circuit, in that heat isgenerated by “current sources” and temperature is analogous to voltage. The rate of generationof heat in a source is measured in Watts. The heat flow rate, which is also measured in Watts, isanalogous to current. Resistance is measured in C/W. The copper losses, core losses, andwindage & friction losses are represented by individual current sources, and the thermalresistances of the laminations, insulation, frame, etc. are represented as resistances. In thesimplest possible model, all the losses are represented

together as one total source, i.e. the individual sources are taken as being in parallel. Thethermal equivalent circuit is really a lumped-parameter model of all the heat-flow processes withinthe motor as well as the heat removal processes discussed earlier.

The thermal equivalent circuit should ideally take into account the anisotropy effects: for example,the effective thermal conductivity through a lamination stack is lower in the axial than the radialdirection. A more complex thermal equivalent circuit may include provision for direct cooling ofthe winding conductors, or for direct cooling of the rotor shaft. If it also includes the thermalmasses or capacities of the winding, the rotor and stator laminations, the frame, the shaft andother massive components, then it can be solved for transient as well as steady-state heattransfer. The heat removal routes by conduction, radiation, and convection are represented bythermal resistances. For convection the appropriate resistance Rv is given by

Rv = 1 C/W (1.33)HA

Where A is the appropriate surface area for convective heat-transfer and the subscript “v” standsfor convection. If h is a function of the temperature-difference, the equivalent circuit becomesnon-linear and requires an iterative solution. For radiation the equivalent thermal resistance Rv isthe ratio of the temperature difference T1 – T2 to the radiation heat exchange rate Q in eqn.(1.25). Clearly this is non-linear. However, the non-linearity is often neglected and a fixed valueof Rv is calculated assuming that the case temperature is known.


82

Fig. 1.12 Thermal equivalent circuit. S = stator (tooth center), T = tooth (at airgap), Y= stator yoke, E = end-winding, C = conductors (at central plane), G =airgap, H = shaft, A = ambient. BloCool = heat abstracted by throughairflow (W), R = radiation, U = conduction, V = convection. Double lettersrefer to thermal resistances, e.g., CT = thermal resistance from theconductors to the stator teeth.

Some useful data is provided in the following tables.

Motor Type Class B Class F Class H1.15 Service Factor 90 115 1401.00 Service Factor 85 110 135TEFC 80 105 125TENV 85 110 135

TABLE 1.5TEMPERATURE RISE BY RESISTANCE AND INSULATION

(NEMA Standard MG-1), C. Assumes 40C Ambient Temperature.

Material EmissivityPolished aluminum 0.4Polished copper 0.025


83

Mild steel 0.2-0.3Grey iron 0.3Stainless steel 0.5-0.6Black lacquer 0.9-0.95Aluminum paint 0.5

TABLE 1.6SELECTED EMISSIVITIES

1. Sizing, gearing, cooling, materials and design

Material (20C)ohm-mx10

-8k(W/mK)

Sp.HeatkJ/kg/C

Densitykg/m

3

Copper 1.72 360 0.38 8950Aluminum 2.8 220 0.90 27000.1% Carbon steel 14 52 0.45 7850Silicon steel 30-50 20-30 0.49 7700Cast iron 66 45 0.5 7900Cobalt-iron 40 30 0.42 8000Ceramic magnet 10

44.5 0.8 4900

Re-Co magnet 50 10 0.37 8300NdFeB magnet 160 9 0.42 7400

Kapton 303 V/m* 0.12 1.1 1420

Teflon 260V/m* 0.20 1.2 2150

Pressboard/Nomex 10kV/0.22mm* 0.13 ---- 1000Epoxy resin 30kV/mm* 0.5 1.7 1400

Water (20C) 0.0153 4.18 997.4

Freon 0.0019 0.966 1330Ethylene Glycol 0.0063 2.38 1117Engine oil 0.0037 1.88 888

TABLE 1.7 SELECTED MATERIAL PROPERTIES*Dielectric strength

1.11 INTERMITTENT OPERATION


84

Fig. 1.13 Intermittent Operation

Intermittent operation is normal for brushless PM motors, because most of the applications thatuse them are motion-control applications with programmed moves, accelerations, decelerations,stops, starts, and so on. Consequently the temperatures of the windings and magnets areconstantly varying. A simple example is shown in Fig. 1.13, where the motor executes a simpleon-off sequence: on for tON and off for tOFF, after which the on/off cycle repeats indefinitely. Thecycle time tcy is

tcy = tON = tOFF (1.34)

The duty-cycle d is defined as

d = tON = tON (1.35)tcy tON tOFF

The most efficient use of the thermal capability of the motor will be made if the maximum windingtemperature TMAX just reaches the rated value Tr at the end of each on-time. Because the powerdissipation is interrupted with cool-down intervals tOFF , the power Pd that can be dissipated duringthe on-times may exceed the steady-state continuous dissipation rating of the motor Pr, andtherefore the motor may be permitted to exceed its steady-state output power rating during theon-times. The simplified thermal equivalent circuit model in Fig. 1.14 makes it possible tocalculate the permissible overload factor as a function of the on-time tON and duty-cycle d for agiven motor.

Fig. 1.14 Simple Thermal Equivalent Circuit for Transient Calculations

The thermal equivalent circuit is a parallel combination of thermal resistance R and thermalcapacitance C. R represents the steady-state thermal resistance between the winding and thesurrounds in C/W. C represents the thermal capacity of the entire motor in J/C. The thermaltime-constant is given [in seconds] by eqn. (1.36):

= RC (1.36)


85

The analysis proceeds by equating the temperature rise during the on-time with the temperaturefall during the off-time. To do this we need the equations for the temperature rise and thetemperature fall.

Temperature rise during ON-time. During the on-time tON, the power dissipation in the motor isPd and the temperature rises according to the equation

T - To = RPd (1 – e-t/) + (Tc - To) e

t/ (1.37)

The temperature rise is expressed relative to the ambient temperature (Tc - To) at t = 0.At t = ton,

TMAX - To = RPd (1 – e-t

ON/) + (Tc - To) e

-tON

/ (1.38)

By definition, the steady-state rated temperature-rise (T - To) is given by

Tr – To = RPr, (1.39)

Where Pr is the rated steady-state power dissipation in the motor, i.e., the continuous powerdissipation that produces rated temperature rise. We can use this to “calibrate” Pd in eqns. (1.37)and (1.38), by defining the dissipation overload factor k

2, where

K2

= Pd (1.40)Pr

The reason for using k2

instead of k is that in most types of brushless servomotor the losses aredominated by I

2R losses while the load torque is proportional to the current I. If the load is

increased by a factor k, it means that the current and torque are increased by the factor k whilethe losses increase by k

2. Thus k is the overload factor for torque and current.

Substituting equations 1.39 and 1.40 in eqn. (1.38) and rearranging, and assuming that

Tmax = Tr, (1.41)

we obtain the following equation relating the temperature rise to the overload factor and the on-time:

(Tr - T0) [1 – k2

(1 – e-t

ON/)] = (Tc – Tc – T0) e

-tON

/ (1.42)

Temperature fall during OFF-time. When the motor is switched off, the power dissipation fallsto zero and the winding temperature falls according to the equation

T – T0 = (Tr - T0)e-t/ (1.43)

Where t is measured from the end of the on-time, i.e. the beginning of the off-time. At tOFF,

Tc - T0 = (Tr – T0) e-t

OFF/. (1.44)

Steady-state: equating the temperature rise and fall. First, multiply eqn. (1.44) by e-t

ON/:


86

(Tc - T0)e-t

ON/ = (Tr – T0)e

-(tON

+tOFF

)/. (1.45)

The left-hand side of eqn. (1.45) is identical to the right-hand side of eqn. (1.42), to the right-handside of eqn. (1.45) can be equated to the left-hand side of eqn. (1.42). With suitablerearrangement, the result can be expressed in different ways, all of which are useful for differentpurposes.

Maximum overload factor. First, we get a solution for the dissipation overload factor k2

in termsof the on-time and the duty-cycle: writing tON/d instead oftON + tOFF, i.e., instead of tcy, the expression is

k2

= 1 – e-t

ON/d

1 – e-t

ON/ (1.46)

For example, if the duty-cycle is 25% (d = 0.25) and tON=0.2 x , the dissipation overload factor is

K2

= 1 – e-0.2/0.25

= 3.04, (1.47)

1 – e-0.2

which means that the dissipation can be increased to 304% of its rated steady-stage value for aperiod of tON=0.2 in every cycle of length tON/d = (0.2/0.25)=0.8. If =40 min, the dissipationcan be raised to 304% for 8 minutes followed by a cool-down period of 24 minutes. Increasingthe dissipation to 304% corresponds to an increase in current and torque to k=3.04=1.74 timestheir rated values.

If tcy<<, then eqn. (1.46) simplifies so thatK

2= 1 (1.48)

d

This means that when the on/off cycles are very short compared with the thermal time-constant ofthe motor, the mean dissipation will be equal to Pr when the peak dissipation Pd=k

2Pr is equal to

Pr /d. This simple result is intuitive.

Maximum overload for a single pulse. Eqn. (1.46) can also be used to calculate the maximumdissipation overload factor for a single pulse, for whichd = 0. In this case

k2

= 1 (1.49)1 – e

-tON

/

For example, if tON=8 min and =40 min, then the maximum dissipation overload factor k2

is 5.5 or550%, and the maximum overload factor k is 2.35 or 235%.


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Required cool-down period for a given overload factor and on-time. The second result thatarises from equating the temperature rise and temperature fall is an expression for the necessarycool-down time tOFF as a function of the dissipation factor k

2and the on-time tON. The expression

is

tOFF = - 1n [k2

– (k2

– 1)etON

/]. (1.50)

Together with eqn. (1.35), this can be used to determine the maximum duty-cycle d that can beused with a given dissipation overload factor k

2and a given on-time tON, for a motor of thermal

time-constant . For example, if the dissipation is 200% of rated, and if tON=8 min, =40 min,

tOFF = - 40 x 1n [2 – (2 – 1) x e8/40

] = 10.0 min. (1.51)

The minimum cycle time is therefore 18 min and the maximum duty-cycle (with 8 minutes’ on-time) is 8/18=0.44 or 44%.

Maximum on-time for a given overload factor and cool-down time. A third result obtained byequating the temperature rise and fall is an expression for the maximum on-time tON as a functionof the dissipation overload factor k

2and the off-time tOFF. The expression is

tON = In [k2

– e-t

OFF/] (1.52)

[ K2

- 1 ]

Maximum duration of single pulse. This expression can be used to calculate the maximumduration of a single pulse having a given dissipation overload factor k

2. For a single pulse, tOFF is

infinite and

tON = In [ k2

]. (1.53)[K

2- 1]

For example, if k2

= 5.5 and = 40 min, then tON = 8 min.

Graphical transient heating curves. Fig. 1.15 shows the relationship expressed by eqn. (1.53)graphically in terms of the duty-cycle d, the on- time tON as a fraction of the time-constant , andthe overload factor k.

This graph can be used in a number of ways. For example, to determine the maximumpermissible duration of a single pulse with a given overload factor k, the duty-cycle d should beset to zero. Thus with k = 1.5 the maximum pulse duration is 0.58. With a time-constant of 40min this is 23.2 min.

The graph shows the maximum duty-cycle that can be used with a given overload factor. Forexample, at 200% load the maximum duty-cycle is 0.25 or 25%, but in this limiting case the on-time must be vanishingly small. With an on-time of 0.1 at 200% load, the maximum duty-cycle isapproximately 0.2, which means that the cool-down period in each cycle must be (1-d) = 0.9. If is 40 min, this means a maximum operating time at 200% load of 4 min, followed by a cool-down period of 36 min before the cycle can be repeated. Operations that need a short on-timewith a high duty-cycle must use a lower overload factor.


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Fig. 1.15 Intermittent Heating Curves

1.12 PERMANENT MAGNET MATERIALS AND CIRCUITS

The permanent-magnet industry has continually improved the properties of PM materials in thepast 20-30 years, mainly by painstaking development of the metallurgy of existing materials.Samples of the main families of PM materials used in electric machines are shown in Table 1.8.

Property Units Alnico 5-7 Ceramic Sm2Co17 NdFeBRemanence Br T 1.35 0.41 1.06 1.2Coercivity Hc KA/m 60 325 850 1000Energy product (BH)max KJ/m

360 30 210 250

Relative recoil permeabilityrec 1.9 1.1 1.03 1.1

Specific gravity 7.3 4.8 8.2 7.4Resistivity -cm 47 >10

486 150

Thermal expansion coefficient10

-6/C 11.3 13 9 3.4

Temperature coefficient of Br

%/C -0.02 -0.2 -0.025 -0.1

Saturation H KA/m 280 1120 >3200 >2400TABLE 1.8

TYPICAL MAGNET PROPERTIES

The ‘strength’ of a magnet is sometimes measured by its ‘energy product’ (see below). At roomtemperature NdFeB has the highest energy product of all commercially available magnets. The


89

high remanence and coercivity permit marked reductions in motor size, compared with motorsusing Ferrite (ceramic) magnets. However, ceramic magnets are considerably cheaper thanRare Earth or NdFeB.

Fig. 1.16 B-H Loop of a Hard PM Material with Electrical Steel Shown for Comparison

Both ceramic and NdFeB magnets are sensitive to temperature and special care must be taken ifthe working temperature is above 100C. For very high temperature applications Alnico or RareEarth/Cobalt magnets must be used, for example Sm2Co17 which is useable up to 200C or even250C.

NdFeB is produced either by a mill-and-sinter process (Neomax) or by a melt-spin castingprocess similar to that used for amorphous alloys (Magnequench). NdFeB magnets are oftenmade in rings which may be sintered r polymer bonded, but they can be formed in a wide varietyof other shapes. They are not 100% dense and coatings or electroplating may be necessary toprevent corrosion.

B-H loop and demagnetization characteristics. The starting-point for understanding magnetcharacteristics is the B-H loop or ‘hysteresis loop’, Fig. 1.16. The x-axis is the magnetizing forceor ‘magnetic field intensity’ Hm in the material. The y-axis is the magnetic flux-density Bm in thematerial. An unmagnetized sample has Bm=0 and Hm=0 and therefore starts out at the origin. If itis subjected to a magnetic field, as for example in a magnetizing fixture, Bm and Hm in the magnetwill follow the initial magnetization curve as the external ampere-turns are increased. If theexternal ampere-turns are switched off, the magnet relaxes along the curve shown by the arrow.Its operating point (Hm,Bm) will depend on the shape of the magnet and the permeance of thesurrounding ‘magnetic circuit’. If the magnet is surrounded by a highly permeable magneticcircuit, that is, if it is ‘keepered’, then it poles are effectively shorted together so that Hm=0 and theflux-density is then equal to the remanence Br. This is the maximum flex-density that can beretained by the magnet at a specified temperature after being magnetized to saturation.


90

External ampere-turns applied in the opposite direction (i.e., Hm<0) cause the magnet’s operatingpoint to follow the curve through the second and third quadrants until the magnet is saturated inthe opposite direction. Again, if the current is switched off the operating point returns towards thepoint (0,-Br), but because of the demagnetizing effect of the external magnet circuit, Bm falls to a(negative) value smaller than Br. It is now magnetized in the opposite direction and the maximumflux-density it can retain when ‘keepered’ is -Br.

To bring the flux-density to zero from the original positive remanence point (0,Br), the externalampere-turns must provide within the magnet a negative magnetizing force –Hc, called thecoercivity. Likewise, to return the flux-density to zero from the negative remanence point (0, -Br), the field +Hc must be applied. The entire loop is usually symmetrical and can be measuredusing instruments designed specially for magnet testing.

If negative external ampere-turns are applied, starting from the positive remanence point (0,Br),and switched off at R, the operating point of the magnet ‘recoils’ and will operate along the lowercurve of a ‘minor loop’. For practical purposes the minor loop of high-coercivity magnets is verynarrow and can be taken as a straight line, the recoil line, whose slope is equal to the recoilpermeability, rec. This is usually quoted as a relative permeability, so that the actual slope isrec0 H/m. Operation along the recoil line is stable provided that the operating point does not gooutside the original hysteresis loop.

A ‘hard’ PM material is one whose recoil lines are straight throughout all or most of the secondquadrant, which is where the magnet normally operates in service. In very hard magnets that arefully magnetized, the recoil line is coincident with the second-quadrant section of the hysteresisloop. This is characteristic of ceramic, Rare Earth/Cobalt, and NdFeB magnets, which usuallyhave rec between 1.0 and 1.1. ‘Soft’ PM materials have a ‘knee’ in the second quadrant, such asAlnico. While Alnico magnets have very high remanence and excellent mechanical and thermalproperties, they have low coercivity and are therefore limited in the demagnetizing field they canwithstand.

Compared with ‘electrical steel’ used in laminations, even the ‘soft’ PM materials are very ‘hard’:in other words, the hysteresis loop of a typical nonoriented electrical steel is very narrow and hasa low coercivity and a high permeability; see Fig. 1.16. The high permeability is desirable in orderto minimize the magnetizing MMF (which is supplied by the magnets in PM motors, or by themagnetizing current in induction motors). The narrow loop is desirable because the loop arearepresents an energy loss or “hysteresis” loss which is dissipated every time the loop istraversed, and in AC motors (including brushless PM motors) the loop is traversed at thefundamental frequency.

The most important part of the B-H loop is the second quadrant, Fig. 1.17. This is called thedemagnetization curve. In the absence of externally applied ampere-turns, the magnet operatesat the intersection of the demagnetization curve and the ‘load line’, whose slope is the product of0 and the ‘permeancecoefficient’ (PC) of the external circuit: i.e., at (HmBm), with Hm <0.

Since Bm and Hm in the magnet both vary according to the external circuit permeance, it is naturalto ask what it is about the magnet that is ‘permanent’. The relationship Between Bm and Hm canbe written.


91

Fig. 1.17 2nd

-Quadrant Demagnetization Characteristic Showing Intrinsic Curve

Bm = 0Hm + J. (1.54)The first term is the flux-density that would exist if the magnet were removed and the magnetizingforce remained at the value Hm. Therefore the second term can be regarded as the contributionof the magnet to the flux-density within its own volume; accordingly, J is called the magnetizationand it is measured in tesla.

9

If the demagnetization curve is straight, and if its relative slope rec = 1, then J is constant. This isshown in Fig. 1.17 for negative values of Hm up to the coercivity –Hc. In most hard magnets rec isslightly greater than 1 and there is a slight decrease of J as the negative magnetizing forceincreases, but this is reversible down to the ‘knee’ of the B-H loop (which may be in either thesecond or the third quadrant, depending on the material and its grade). Evidently the magnet canrecover or recoil back to its original flux-density as long as the magnetization is constant. Thecoercive force required to demagnetize the magnet permanently is called the intrinsic coercivityand this is shown as Hci.

For engineering purposes we normally represent the recoil line by the equation

Bm = 0rec Hm + Br (1.55)

which can be related to eqn. (1.54) by expanding it as follows:

Bm = 0Hm + 0 (1 - rec) Hm + Br (1.56)

which indicates that

J = 0(1-rec) Hm + Br = 0Hm + Br (1.57)

_____________________________


92

9Sometimes eqn.(1.54) is written Bm=0(Hm+M) and then the

where is the susceptibility, 1 - rec.

Another parameter often calculated is the magnet energy product, BmHm. This is not the actualstored magnet energy but simply indicates how hard the magnet is working against thedemagnetizing influence of the external circuit. Contours of constant energy product arerectangular hyperbolas BmHm = constant, often drawn on data sheets. The maximum energyproduct (BH)max occurs where the demagnetization characteristic is tangent to the hyperbola of its(BH)max value. If the relative recoil permability is unit, this occurs for a permeance coefficient ofunity, with Bm=Br/2, provided that there are no externally applied ampere-turns from windings orother magnets.

Fig 1.18 Closed and gapped magnetic circuits

Calculation of Magnet operating Point. Fig 1.18 shows a simple magnetic circuit in which the

magnet is “keepered” by a material or core of relative permeability r. The core and the magnettogether form a closed magnetic circuit. Applying Ampere’s law, and assuming uniformmagnetizing force in both the magnet and the core,

Hmlm + HFelFe = 0. (1.58)

Where Hm is the magnetic field in the magnet, HFe is the magnetic field in the iron core(assumedto be uniform around the core length lFe, and lm is the length of the magnet in the direction of themagnetization. This is effectively the line integral of H around the magnetic circuit, and it is zerobecause there are no externally applied ampere-turns. Hence

Fe

m

Fem H

l

lH

(1.59)


93

which establishes that the magnet works in the second quadrant of the B-H loop. Now considerthe gapped magnetic circuit in fig. 1.18, in which there is an airgap in series with the magnet andthe two sections of the iron core. Now

.0 ggFeFemm lHlHlH (1.60)

where the Hg is the magnetic field in the airgap and lg is the airgap length. The permeability of the

electrical steel used in motors is usually several thousand times higher than 0 , so that the term

HFe lFe can be neglected as a first approximation, even though, lFe may be much bigger than lg.Then

g

m

g

m Hl

lH

(1.61)

Now by Gauss’ Law, the flux-densities in the magnet and the airgap are related by

ggmm ABAB (1.62)

so that if we take the ratio of Bm/ 0Hm, recognizing that in the airgap Bg/ 0Hg, we get

PClA

IA

H

B

mm

mg

m

m *00 (1.63)

where the PC is the permeance coefficient. The ratio of the magnet pole area to the airgap areais sometimes called the flux-concentration factor or flux-focussing factor:

.g

m

A

AC (1.64)

In order to minimize the risk of demagnetization we need to operate the magnet fairly close to theBr, i.e., with a high permeance coefficient. On the other hand, the airgap flux density Bg isincreased if we use a high value of the flux concentration factor Am/Ag. But this reduces thepermeance coeffiecient and eqn (1.63) shows that this reduces the ratio Bm/Hm, which increasesthe risk of demagnetization because it moves the operating point further down the recoil line awayfrom the Br towards the knee of the B-H curve.

To achieve a high permeance coefficient with a high flux-concentration factor we must increasethe ratio lm/lg to compensate for the demagnetizing effect of the airgap: in other words, use amagnet that is long in the direction of magnetization and also long relative to the airgap length. Itdoes not mean long in relation to the lateral dimensions of the magnet, and indeed most modernmagnets except Alnico have such high coercivity that the length in direction of the magnetizationis the smallest dimension and is intuitively referred to as the ‘thickness’!

m

g

mm

gggg

mmV

W

lA

lAHBHB

2 (1.65)

where Wg is the magnetic energy stored in the airgap volume and Vm is the volume of themagnet. This shows that the minimum magnet volume required to magnetize a given workingvolume of airspace is inversely proportional to the working energy product BmHm. Therefore, inthese cases it pays to design the magnet length and pole area in such proportions relative to the


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length and area of the airspace, as to cause the magnet to work at (BH)max, which is a property ofthe particular material at a given temperature. In motors this principle cannot be applied sosimply, because the armature current produces demagnetizing ampere-turns that may be verygreat under fault conditions. To eliminate the risk of demagnetization, motors are designed sothat on open-circuit or no-load, the magnet operates at a high permeance coefficient with anadequate margin of coercive force to resist the maximum demagnetizing ampere-turns expectedunder load or fault conditions.

The lower diagrams Fig 1.18 illustrate the relative intensities of the Bm and the Hm under differentworking conditions, in all cases with no externally applied ampere-turns. Note that B is continuousthroughout the magnetic circuit (because it obeys Gauss’ law), but His not. The discontinuities ofH are associated with the appearance of the magnetic poles at the interfaces between differentsections of the magnetic circuit, notably at the ‘poles’ of the magnet and the working airspace.The polarization of the surfaces gives rise to a magnetic potential difference across the airspacewhich is useful for calculating flux distribution in motors. In Fig 1.18 this potential difference is

tAlHu gg (1.66)

If the magnetic potential drop in the steel is neglected, the corresponding magnetic potentialdifference across the magnet is

tAlHu gg (1.66)

C.g.s. units are still widely used in the magnetic industry, whereas motors are usually designed inmetric (SI) units in Europe and Japan, and in metric or Imperial units in the U.S.A. Someconversion factors are as follow:

1 inch 25.4mm1 T 10kG1 kA/m 4 Oe

1 kJ/m3 /25 MGOe

Table 1.9Conversion Factors

Temperature effects; reversible and irreversible losses

High-temperature effects. Exposure to high temperature for long periods can producemetallurgical changes which may impair the ability of the material to be magnetized and mayeven render it nonmagnetic. There is also a temperature, called the Curie temperature, at whichall magnetization is reduced to zero. After a magnet has been raised above the Curietemperature it can be re-magnetized to its prior condition provided that no metallurgical changeshave taken place. The temperature at which significant metallurgical changes begin is lower thanthe Curie temperature in the case of the Rare Earth/ Cobalt magnets, NdFeB, and Alnico; but inceramic ferrite magnets it is the other way round. Therefore ceramic magnets can be safelydemagnetized by heating them just above the Curie point for a short time. This is useful if it isrequired to demagnetize them for handling or finishing purposes. Table 1.10 shows thesetemperatures for some of the important magnets used in motors.

Metallurgical (change C) Curie Temperature (C)Alnico 5 550 890Ceramic 1080 450Sm2Co17 350 800


95

NdFeB 200 310Table 1.10

METALLURGICAL CHANGE AND CURIE TEMPERATURE

Material Temp. coefft. Of Br %/ C

Alnico 5 -0.02

Ceramic -0.19

Sm2Co17 -0.02

NdFeB -0.11

Table 1.11REVERSIBLE TEMPERATURE COEFFICIENT OF Br

Reversible losses. The B-H loop changes shape with the temperature. Over a limited range thechanges are reversible and approximately linear, so that temperature-coefficients for theremanence and coercivity can be used. Table 1.11 gives some typical data. Ceramic magnetshave a positive coefficient of Hc, whereas the high energy magnets lose coercivity astemperature increases. In ceramic magnets the knee in the demagnetization curve moves downtowards the third quadrant, and the permeance coefficient at the knee decreases. Thus ceramicmagnets become better able to resist demagnetization as the temperature increases up to about120 C. The greatest risk of demagnetization is at low temperatures when the remanent fluxdensity is high and the coercivity is low in a motor, this results in the highest short-circuit currentwhen the magnet is least able to resist the demagnetizing ampere-turns. In high energy magnetsthe knee moves the other way, often starting in the third quadrant at room temperature andmaking its way well into the second quadrant at 150 C. Grades with a high resistance totemperature are more expensive, yet these are often the ones that should be used in motors,particularly if high temperatures are possible( as they usually are under fault conditions).

All the magnets lose remanence as temperature increases. For a working temperature of 50 Cabove an ambient of 20 C for instance, a ceramic magnet will have lost about 10%. This isspontaneously recovered as the temperature falls back to ambient.

Irreversible losses recoverable by remagnetization. (a) Domain relaxation. Immediately aftermagnetization there is a very slow relaxation, starting with the least stable domains returning to astate of lower potential energy. The relaxation rate depends on the operating point and is worsebelow (BH)max, i.e. at low permeance coefficients. In modern high-coercivity magnets at normaltemperatures this process is usually negligible, particularly if the magnets have been stabilized(by temperature cycling and/ or Ac flux reduction) immediately after magnetization. Elevatedtemperatures during subsequent operation may however, cause an increased relaxation rate.This can be prevented by temperature-cycling in the final assembly over a temperature rangeslightly wider than the worst –case operating range. Subsequent relaxation is reduced tonegligible levels by this means. Table 1.12 shows the stability of different magnet materials at 24C.

Material % loss after 10 years (typ.)Ceramic <0.01Rare earth/Cobalt 0.2Alnico 0.5

TABLE 1.12LONG-TERM STABILITY OF MAGNET MATERIALS

(b)Operating point effect. Temperature alters the B-H loop. If this causes the operating pointto ‘fall off’ the lower end of the recoil line, there will be an irreversible flux loss. This isillustrated in Fig 1.19. Initial operation is at point a on the load line Oa, which is assumed to


96

remain fixed. The remanence corresponding to point a is at point A. When the temperature israised from T1 to T2 the operating point moves from a to b, and the correspondingremanences moves from A to B. Note that because the knee of the curve has risen abovepoint b, the effective remanence at B’ is less than that at B, which is what it would have beenif the magnet had been working at a high permeance coefficient.

Fig 1.19 Reversible and irreversible loss caused by operating at a high temperature with alow permeance coefficient

If the temperature is now reduced to T1 the operating point can recover only to a`, which lieson the recoil line through A`. The recovery from b to a` is reversible, but there has beenirreversible loss of flux-density bm in the magnet, relative to point a, the remanence at T1 hasfallen from A to A`. The loss can be recovered only by re-magnetization at the lowertemperature.

Manufacturers’ data for irreversible loss should be interpreted carefully to distinguish betweenthe long-term stability and the effects just described. Irreversible loss over is quoted at a fixedpermeance coefficient. If the magnet is used at a lower permeance coefficient, theirreversible loss over the same temperature range will be higher.

Mechanical properties, handling, and magnetization

Magnets are often brittle and prone to chipping, but proper handling procedures arestraightforward enough as long as the rules are followed. Modern high-energy magnets areusually shipped in the magnetized condition, and care must be taken in handling to avoidinjury that may be caused by trapping fingers. A further hazard is that when two or moremagnets are brought close together they may flip and jump, with consequent risk to eyes.Table 1.13 summarizes some of the important safety precautions.

The best way to ‘tame’ magnetized magnets is to keeper them. Fixtures for inserting magnetscan be designed so that the magnets slide along between steel guides which aremagnetically short-circuited together. There still remains the problem of entering the magnets


97

between the guides but usually there is enough space to provide for this to be done gently.Obviously it is important to keep the magnets clear of watches and electronic equipment thatis sensitive to magnetic fields. Floppy disks, magnetic tapes, credit cards and key cards areparticularly vulnerable, and high-energy magnets can distort the image on computer terminalsand monitors.

Magnets are usually held in place by bonding or compression clips. In motors with magnetson the rotor, adhesive bonding is adequate for low peripheral and moderate temperatures,but for high speeds a kevlar banding or stainless steel retaining shell can be used. In motorsit is not advisable to make the magnet an integral part of the structure. Mechanically, themagnet should be regarded as a ‘passenger’ for which space and fixturing must be provided.The important requirements are that the magnet should not move and that is should beprotected from excessive temperatures.

Permanent Magnets require strict adherence to safety procedures at all stages of handling andassemblyAlways wear safety glasses when handling magnets. This is particularly important whenassembling magnets into a motor. When a large pole magnet is being assembled from smallermagnets, the magnets have a tendency to flip and jump unexpectedly and may fly a considerabledistanceWork behind a plexiglass screen when experimenting or assembling magnet assemblies.Watch out for trapped fingers especially with large magnets or high-energy magnets..Avoid chipping by impact with hard materials, tools or other magnets.Never dry-grind rare-earth magnets- the powder is combustible. In case of fire, use LP argon ornitrogen dry chemical extinguishers- never use water of halogens.Use suitable warning labels, especially on large machines. PM motors generate voltage when theshaft is rotated, even when disconnected from all power supplies. This may be obvious to anengineer, but is a potential safety hazard for electricians and maintenance personnel.Never leave magnetized members open or unprotected. When assembling a rotor to a stator, witheither one magnetized, the rotor must be firmly guided and the stator firmly located.

TABLE 1.13MAGNETIC SAFETY

A wide range of shapes is available, but in motors the most common are arcs and rectangles.Close tolerances of +/-.01 mm can be held in the magnetized direction even for standardmagnets. But if the design permits a relaxation of the required tolerance, particularly in thedimensions perpendicular to the magnetic axis, this should be exploited because it reduces thecost of the finished magnets.

Thermal expansion of magnets is usually different in the directions parallel and perpendicular tothe magnetic axis. The coefficients in Table 1.8 are along the direction of magnetization. Mostmagnets have a high compression strength but should never be used in tension of bending.

Magnetization of high-energy magnets requires such a high magnetizing force that specialfixtures and power supplies are essential, and this is one reason why high-energy magnets areusually magnetized before shipping. The magnetizing force Hm must be raised at least to thesaturation level shown in Table 1.8, and this normally requires ampere-turns beyond the steady-state thermal capability of copper coils. Therefore pulse techniques are used, or in some casessuperconducting coils. Ceramic and Alnico magnets can sometimes be magnetized in situ in thefinal assembly, but this is impractical with high-energy magnets.

Application of permanent magnets in motors


98

Permanent magnets provide a motor with life-long excitation. The only cost is the initial cost,which is buried in the cost of the motor. It ranges from a few pennies for small ferrite motors, toseveral pounds for rare-earth motors. Even so, the cost of magnets is typically only a smallfraction of the total cost of the motor. Broadly speaking, the primary determinants of magnet costare the torque per unit volume of the motor; the operating temperature range; and the severity ofthe operational duty.

Power density. We have seen that for maximum power density the product of the electric andmagnetic loadings must be as high as possible. The electric loading is limited not only by thermalfactors, but also by the demagnetizing effect on the magnet. A high electric loading necessitatesa long magnet length in the direction of magnetization, to prevent demagnetization. It alsorequires a high coercivity, and this may lead to the more expensive grades of material (such asSM2Co17, for example), especially if high temperatures will be encountered. The magneticloading, or airgap flux, is directly proportional to the remanence, and is nearly proportional to thepole face area of the magnet. A high power density therefore requires the largest possiblemagnet volume (length times pole area).

With ceramic magnets the limit on the magnet volume is often the geometrical limit on the volumeof the rotor itself, and the highest power densities cannot be obtained with these magnets. Withrare-earth or other high energy magnets, the cost of the magnet may be the limiting factor.

The airgap flux-density of AC motors is limited by saturation of the stator teeth. Excessivesaturation absorbs too much excitation MMF (requiring a disproportionate increase in magnetvolume); or causes excessive heating due to core losses. For this reason there is an upper limitto the useable energy of a permanent magnet. With a straight demagnetization characteristicthroughout the second quadrant and a recoil permeability of unity, the maximum energy-product(BH)max is given by

3

0

2

max /4

mJB

BH r

(1.68)

Assuming that the stator teeth saturate at 1.6T and that the tooth width is half the tooth pitch, themaximum airgap flux-density cannot be much above 0.8T and is usually lower than this.Therefore there will be little to gain from a magnet with a remanent flux-density above about 1 or1.2T, implying that the highest useable energy product is about 300 kJ/m

3. At 100 C, such

characteristics are just within range of available high-energy magnets. Evidently it is just asimportant to develop magnet materials with ‘moderate’ properties and low cost, rather than todevelop ‘super magnets’.

Operating temperature range. Because of the degradation in the remanence and coercivity withtemperature, the choice of material and the magnet volume must usually be determined withreference to the highest operating temperature. Fortunately brushless PM motors have very lowrotor losses. The stator is easily cooled because of the fine slot structure and proximity of theoutside air. Consequently the magnet can run fairly cool (often below 100 C) and it is furtherprotected by its own thermal mass and that of the rest of the motor. The short-time thermaloverload capability of the electronic controller would normally be less than that of the motor,providing a further margin of protection against magnet overtemperature.

Severity of operational duty. Magnets can be demagnetized by fault currents such as short-circuit currents produced by inverter faults. In brushless motors with electronic control theproblem is generally limited by the protective measures taken in the inverter and the control. Withan over-running load, or where two motors are coupled to a single load, shorted turns or windingscan be troublesome because of drag torque and potential overheating of the stator. But by thesame token, the dynamic braking is usually excellent with a shirt-circuit applied to the motorterminals, and motors may well be designed to take advantage of this. As is often the care,


99

characteristics that are desirable for one application are undesirable for another. The design mustaccommodate all the factors that stress the magnet: electromagnetic, thermal, and mechanical.

1.13 PROPERTIES OF ELECTRICAL STEELS

Fig. 1.20 shows that DC B-H curves in the first quadrant for two steels. The lower curve is atypical electrical motor steel having 1.5% Silicon to increase the resistivity to limit eddy-currentlosses. The saturation flux density of such steels (i.e. the flux-density at which the incrementalpermeability becomes equal to is typically about 2.1T. The upper curve is for a cobalt-ironalloy with a saturation flux-density of about 2.3T. This material is much more expensive thannormal electrical steel, and is only used in special applications such as highly rated aircraftgenerators, where light weight and high power density are at a premium.

The maximum permeability of electrical steels is of the order of 5000 , and usually occursbetween 1 and 1.5T. In Fig 1.20, the total permeability of the electrical steel at 2.0T is about2.0/3,000 which is approximately 530 .

Fig 1.20 DC B-H curve for electrical steels

Losses. Under AC conditions, a power loss arises in electrical steel as shown in Fig 1.21, whichindicates increasing loss as the frequency and flux-density increase. The loss is attributed to

(a) hysteresis;(2) eddy-currents; and(3) “anomalous loss”.

The hystersis component is associated with the changing magnitude and direction of themagnetization of the domains, while the eddy- current loss is generated by induced currents.Eddy-currents can be inhibited by laminating the steel, so that the eddy-currents becomesresistance limited and the loss is then inversely proportional to the resistivity. If the eddy-currentsare resistance-limited the loss is also proportional to 1/t

2, where t is the lamination thickness. At

higher frequencies the resistance limited condition is lost, and the losses increase rapidly with


100

frequency. For this reason, very thin laminations as thin as 0.1 mm may be used at very highfrequencies (such as 400 Hz in aircraft generators or 3000 Hz in certain specialty machines). The“anomalous loss” is associated with domain wall movement and is not often accounted for inempirical expressions of the iron loss.

Figure 1.21 typical for of variation of losses in electrical steel, versus frequency and flux density

Characterization of core loss. Core-loss data from steel suppliers is almost always obtained frommeasurements in which a sinusoidal flux waveform is applied to a sample of laminations in theform of a stack of rings or an “Epstein square” made up from strips interleaved at the corners.The loss may be characterized by the so-called Steinmetz equation with separate terms forhysteresis and eddy-current loss:

.22pke

npkh BfCfBCP (1.69)

The units of P are usually W/kg or W/lb. Bpk is the peak flux-density in T, and f is the frequency inHz.Ch is the hysteresis loss coefficient and Ce is the eddy-current loss coefficient. The exponentn is often assumed to be 1.6-1.8 but it varies to a certain extent with Bpk. To a first approximationwe can write n= a +bBpk. With this modification,

.22pke

bBa

pkh BfCfBCP pk

(1.70)

The flux-density in motor laminations may be far from sinusoidal, and one approximate way todeal with this is to modify the Steinmetz equation in the following way, recognizing that the eddy-current loss component is expected to vary as the square of the EMF driving the eddy-currents,and that this EMF varies in proportion to dB/dt. Thus

.2

1

dt

dBCfBCP e

bBa

pkhpk (1.71)

The hysteresis loss component is unchanged, but the eddy-current component is taken to beproportional to the mean squared value of dB/dt over one cycle of the fundamental frequency.Eqn. (1.71) can be applied in the respective sections of the magnetic circuit, after calculating therelevant flux-density waveforms. The eddy-current loss coefficient Ce1 in the modified form can bederived from the sinewave coefficient Ce if we assume that eqn. (1.71) holds with B=Bpksin(2ft).Then dB/dt=2fbpkcos(2ft) and density, equations 1.70 and 1.71 give the same result if


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.2 21

ee

CC (1.72)

Extracting the core loss coefficients from test data. Two procedures are used for extractingthe coefficients Ch, Ce1, a and b from sinewave loss data. The more elaborate of these requires acomplete set of curves of core loss vs, frequency at different flux-densities. When this data is notavailable, a simpler procedure is used based on five parameters.

Simple procedure- It is often the case that only a single value of P is available, for example,8W/kgat 50 Hz, measured with Bpk=1.5T. There is not enough data to determine the four losscoefficients uniquely, so we use an estimate for n in the eqn. (1.69); for example n =1.7. It isfurther necessary to estimate the split between hysteresis and eddy-current loss. If h is thefraction to the total loss attributed to hysteresis, then it can be shown that

22

1

pk

eBf

hPC

and .

fB

hPC

npk

h (1.73)

Then a=n; b=0, and Ce1 = Ce/22.

Procedure used with complete set of core-loss data- The core loss data is usually in the form ofgraphs of P vs. f at different flux-densities, or P vs. Bpk at different frequencies. The procedures isto try to separate the hysteresis and eddy-current components of P. First we divide eqn. (1.70) byf:

2pke

bBa

pkh fBCBCf

Ppk

(1.74)

We then plot graphs of P/f vs. f for three values of Bpk, e.g. 1, 1.5 and 2T with f from 50 to thehighest frequency. The graphs should be straight lines and can be represented by

.EfDf

P (1.75)

The intercept D on the vertical (P/f) axis must be equal to

.pk

pk

bBa

h BCD

(1.76)

The intercepts D1, D2 and D3 for the three values of Bpk are substituted into the logarithm of eqn.(176), giving three simultaneous linear algebraic equations for Ch, a and b of the form

.log)(loglog 111 pkpkh BbBaCD (1.77)

These are solved for log Cb, a and b; Ch is then obtained from log Cb. Next, three values of Ce areobtained from the gradients of the three graphs of P/f vs. f, eqn. (1,74). The average or thehighest value can be taken for Ce. Finally Ce1=Ce/2

2. The loss curves may be re-plotted from the

formula as a check. Any extrapolation to higher Bpk or f should be checked carefully.

Note that Ce is approximately inversely proportional to t2, where t is the lamination thickness. This

can be used to modify Ce (or Ce1) for different thickness if test data is not available.


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1.14 MACHINE AND DRIVE DESIGN

The equation TRV=2AB reflects the fact that torque is produced by the interaction between fluxand current. This simple equation is the cornerstone of electrical machine design. It leads to themore advanced work of

Machine design which is concerned with producing thetorque with a minimum of material and power loss; and

Drive design which is concerned with the control of torque and speed, subject to constraintson the electric and magnetic loadings

In relation to the machine design, it is always important to minimize power lossesand temperature rise caused by I2R heating of the conductors, core lossescaused by hysteresis and eddy-currents in the magnetic steel, and other losses.But there are many other aspects, such as the need to minimize torquepulsations and acoustic noise, and to use materials economically. There is ahuge variety of different types of electrical machine, arising partly fromconstraints imposed by the available power supply. For example, in automobilesthe DC commutator motor is universally used because of the low voltage DCpower supply. But in industry, AC induction motors are used primarily because ofthe availability of polyphase AC power (which has a natural rotation between thephases), and because the induction motor has no brushes and therefore requiresvery little maintenance. In traction applications (railways, transit vehicles, etc.),traditionally DC motor was used because although AC supplies were available,the control equipment was expensive for DC drives. Since the 1980’s, modernpower electronics has become so cost- effective that AC drives have steadilytaken over from DC drives even in the most demanding traction applications.

At the same tome the variety in types of design of electrical machines has greatlyincreased in many other fields of application because of the advances made inpower electronics and microelectronic control. This is clearly evident in suchproducts as tape drives, computers, office machinery, and so on; but there aremany others less will known- for example, the use of very high-speed brushlesspermanent-magnet motors in machine tools. These motors can run at severaltens of kW and several tens of thousands of revolutions per minutes.

In relation to the drive design, one of the fundamental aspects of electricalmachines is the orientation of the flux and the ampere-conductor distribution inrelation to one another. The flux and MMF10 must be orthogonal in space, i.e. theaxes of their spatial distribution must be displaced by /2p radians, if theelectromagnetic torque is to be maximized for a given flux and current. If thedisplacement angle is zero, there is no torque and the power factor is zero. In DCcommutator machine the orientation between the flux and the armature MMF ismaintained at /2p radians by the action of the commutator, and therefore if themachine is controlled by a chipper or a phase-controlled rectifier the controller is


103

not concerned with orientation and need do no more than regulate current. Bycontrast, in AC induction motors and synchronous machines, the orientation isnot guaranteed to be /2p radians, even thought the machines might bedesigned to achieve this approximately under normal operation. For this reason,modern AC drives employ filed-oriented control, (also called vector control), toorient the MMF and the flux orthogonally.

10The ampere conductor distribution is often loosely termed the MMF(magneto motive force), or MMF distribution.

This is quite complex and typically requires the use of microcontrollers or DSP’s(digit signal processors). The most modern embodiments of field oriented controlare sophisticated enough to include estimators for important parameters such asthe flux, the direction of the flux, the rotor temperature, and the electromagnetictorque itself.

Computer-aided design

When new designs are evolved from old ones, computer-aided design is valuablefor

1. calculating and evaluating a large number of options, often characterizedby small changes in a large number of parameters; and

2. performing detailed electromagnetic and mechanical analysis to permitthe design to be “stretched” to its limit. With accurate computer software,we can reduce the need for prototypes, which are expensive and time-consuming.

Modern computer methods are rapidly reaching the stage where a new prototypecan be designed with such confidence that it will be “right first time”, without theneed for reiteration of design and test that would otherwise be necessary.Computer-aided design goes hand-in –hand with the modern design engineeringenvironment. Custom designs are often required within a very short space oftime, while cost pressures force the designer ever closer to the limits of materialsand design capabilities.

Moreover customers are becoming more and more sophisticated in theirrequirements, and may specify (or ask to see) particular parameters that thattraditionally were part of the “black art” of the motor builder. Often theseparameters are required for system simulation purposes long before the motor isactually manufactured. Regulatory pressures on matters such as energyefficiency, acoustic noise, and EMC also tighten the constraints on the motordesign.


104

No matter how effective the computer software available it is always important tocheck the overall parameters of a motor design using common sense andfundamental engineering principles. For this reason it will always be necessary tobe able to perform a single set of design calculations on the computer and checkthe results against manual calculations. The next stage is to repeat designcalculations, modifying the dimensions and parameters until the performanceobjectives are attained. These processes are illustrated graphically in Fig. 1.22.The SPEED software is designed to be used in this way.

The synthesis of a design by an optimization process is a much more complexundertaking beyond the scope of this book. However, the development ofscripting languages which can run programs such as SPEED motor designprograms automatically opens up new opportunities for user-defined designautomation procedures.

Fig 1.22 design loop

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