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– A single-phase electromechanical device with the statorwinding as shown can develop an average torque in eitherdirection of rotation.– Note that this device is a two-pole device, even thoughthere are two two-pole sets, as only one set interacts withthe rotor to produce a torque with a nonzero average.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig27

Two-Phase Devices– Consider the two-pole, two-phase sinusoidally distributedstator windings shown.– For balanced (i.e., variables are equal-amplitude sinusoidalquantities and 90 out of phase) steady-state conditions, thestator currents may be expressed as:I as 2I s cos ω e t θ esi ( 0 ) I bs 2Is sin ω e t θ esi ( 0 ) – The reason for selecting this set of stator currents willbecome apparent.– The total air gap mmf due to both stator windings (assumedto be sinusoidally distributed) may be expressed by addingmmfas and mmfbs to give mmfs.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig28

– The total air gap mmf due to the stator windings is:Nsmmf as i as cos φ s2Nsmmf bs i bs sin φ s2Nsmmf s ( i as cos φ s i bs sin φ s )2– Substitution:I as 2I s cos ω e t θ esi ( 0 ) I bs 2Is sin ω e t θ esi ( 0 ) – Result:Nsmmf s ( i as cos φ s i bs sin φ s )2Nsmmf s 2Is cos ω e t θ esi ( 0 ) φ s 2Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig29

Elementary Two-Pole, Two-PhaseSinusoidally-Distributed Stator WindingActuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig30

– It is interesting to note that we have only one rotating airgap mmf or rotating magnetic field.– Set the argument equal to a constant, take the derivativewith respect to time, and we find that the argument isconstant ifdφ s ωedt– If we travel around the air gap in the CCW direction at ω e,we will always see a constant mmfs for the balanced set ofcurrentsI 2I cos ω t θ ( 0 ) asI bs s eesi 2Is sin ω e t θ esi ( 0 ) – Hence a single rotating air gap mmf is produced. Theactual value that we would see as we travel around the airgap at ω e would depend upon the selection of time zero andour position on the stator at time zero.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig31

– With the assigned positive direction of current in the givenarrangement of the as and bs windings shown, the balancedset of stator currents produces a mmfs that rotates CCW,which is desired for conventional purposes.– In the case of the single-phase stator winding with asinusoidal current, the air gap mmf can be thought of astwo oppositely-rotating, constant-amplitude mmf’s.However, the instantaneous air gap mmf is pulsating evenwhen we are traveling with one of the rotating air gapmmf’s. Unfortunately, this pulsating air gap mmf or set ofpoles gives rise to steady-state pulsating components ofelectromagnetic torque.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig32

– In the case of the two-phase stator with balanced currents,only one rotating air gap mmf exists. Hence, the steadystate electromagnetic torque will not contain a pulsating ortime-varying component; it will be a constant with thevalue determined by the operating conditions.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig33

Three-Phase Devices– The stator windings of a two-pole, three-phase device areshown in the figure.– The windings are identical, sinusoidally distributed with Nsequivalent turns and with their magnetic axes displaced120 ; the stator is symmetrical.– The positive direction of the magnetic axes is selected so asto achieve counterclockwise (CCW) rotation of the rotatingair gap mmf with balanced stator currents of the abcsequence.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig34

– The air gap mmf’s established by the stator windings maybe expressed by inspection as:Nsmmf as i as cos φ s2Ns2 mmf bs i bs cos φ s π 23 Ns2 mmf cs i cs cos φ s π 23 – As before, Ns is the number of turns of the equivalentsinusoidally distributed stator windings and φ s is theangular displacement about the stator.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig35

ted StatorWindingsActuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig36

– For balanced steady-state conditions, the stator currents foran abc sequence may be expressed as:I as 2I s cos ω e t θ esi ( 0 ) I bs 2I s cos ω e t 2 π θ esi ( 0 ) 3 I cs 2I s cos ω e t 2 π θ esi ( 0 ) 3 – Substitution:I bs 2I s cos ω e t 2 π θ esi ( 0 ) 3 Nsmmf as i as cos φ s2Ns2 mmf bs i bs cos φ s π 23 I cs 2I s cos ω e t 2 π θ esi ( 0 ) 3 Ns2 mmf cs i as cos φ s π 23 I as 2I s cos ω e t θ esi ( 0 ) Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig37

– Add the resulting expressions to yield an expression for therotating air gap mmf established by balanced steady-statecurrents flowing in the stator windings:Ns3mmf s 2I s cos ω e t θ esi ( 0 ) φ s 22– Compare this with the mmfs for a two-phase device:Ns3mmf s 2I s cos ω e t θ esi ( 0 ) φ s 22Nsmmf s 2Is cos ω e t θ esi ( 0 ) φ s 23-Phase2-Phase– They are identical except that the amplitude of the mmf forthe 3-phase device is 3/2 times that of a 2-phase device.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig38

– It can be shown that this amplitude for multiphase deviceschanges from that of a two-phase device in proportion tothe number of phases divided by 2.– It is important to note that with the selected positivedirections of the magnetic axes a counterclockwise rotatingair gap mmf is obtained with a three-phase set of balancedstator currents of the abc sequence.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig39

Introduction to Several ElectromechanicalMotion Devices Rotational electromechanical devices fall into threegeneral classes:– Direct-current– Synchronous– Induction We have already covered dc machines. Synchronous Machines– They are so called because they develop an average torqueonly when the rotor is rotating in synchronism(synchronous speed) with the rotating air gap mmfestablished by currents flowing in the stator windings.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig40

– Examples are: reluctance machines, stepper motors,permanent-magnet machines, brushless dc machines, andthe machine which has become known as simply thesynchronous machine. Induction Machines– Induction is the principle means of converting energy fromelectrical to mechanical.– The induction machine cannot develop torque atsynchronous speed in its normal mode of application.– The windings on the rotor are short-circuited and, in orderto cause current to flow in these windings which producetorque by interacting with the air gap mmf established bythe stator windings, the rotor must rotate at a speed otherthan synchronous speed.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig41

Here we will show the winding arrangement forelementary versions of these electromechanicaldevices and describe briefly the principle of operationof each.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig42

Reluctance Drives– Elementary single-, and two-phase two-pole reluctancemachines are shown in the figure.– Stator windings are assumed to be sinusoidally distributed.– The principal of operation is quite straightforward. In an electromagnetic system a force (torque) is produced in anattempt to minimize the reluctance of the magnetic system. We have established that, with an alternating current flowing in thewinding of the single-phase stator, two oppositely-rotating mmf’sare produced. Therefore, once the rotor is rotating in synchronism with either ofthe two oppositely-rotating air gap mmf’s, there is a force (torque)created by the magnetic system in an attempt to align theminimum-reluctance path of the rotor with the rotating air gapmmf.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig43

When there is no load torque on the rotor, the minimum-reluctancepath of the rotor is in alignment with the rotating air gap mmf. When a load torque is applied, the rotor slows ever so slightly,thereby creating a misalignment of the minimum-reluctance pathand the rotating air gap mmf. When the electromagnetic torque produced in an attempt tomaintain alignment is equal and opposite to the load torque on therotor, the rotor resumes synchronous speed. If the load torque is larger than the torque which can be producedto align, the rotor will fall out of synchronism and, since themachine cannot develop an average torque at a speed other thansynchronous, it will slow to stall. The operation of a two-phase device differs from that of the singlephase device in that only one constant-amplitude rotating air gapmmf is produced during balanced steady-state conditions. Hence, a constant torque will be developed at synchronous speedrather than a torque which pulsates about an average value as is thecase with the single-phase machine.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig44

Although the reluctance motor can be started from a source whichcan be switched at a frequency corresponding to the rotor speed asin the case of stepper or brushless dc motors, the devices cannotdevelop an average starting torque when plugged into a householdpower outlet. Many stepper motors are of the reluctance type. Some steppermotors are called variable-reluctance motors. Operation is easilyexplained. Assume that a constant current is flowing the bswinding of the figure with the as winding open-circuited. Theminimum reluctance path of the rotor will be aligned with the bsaxis, i.e., assume θr is zero. Now let’s reduce the bs windingcurrent to zero while increasing the current in the as winding to aconstant value. There will be forces to align the minimumreluctance path of the rotor with the as axis; however, this can besatisfied with θr ½ π. There is a 50-50 chance as to which wayit will rotate. We see that we need a device different from a singleor two-phase reluctance machine to accomplish controlledstepping. Two common techniques are single-stack and multistackvariable-reluctance steppers.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig45

Elementary Two-Pole Reluctance Machines:Single-Phase and Two-PhaseActuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig46

Induction Machines– Elementary single- and two-phase induction machines areshown in the figure.– The rotors of both devices are identical in configuration;each has the equivalent of two orthogonal windings whichare assumed to be sinusoidally distributed. The ar and brwindings are equivalent to a symmetrical two-phase set ofwindings and, in the vast majority of applications, theserotor windings are short-circuited.– Let’s look at the operation of the two-phase device first. For balanced steady-state operation, the currents flowing in thestator windings produce an air gap mmf which rotates about the airgap at an angular velocity of ωe.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig47

With the rotor windings short-circuited, which is the only mode ofoperation we will consider, a voltage is induced in each of the rotorwindings only if the rotor speed ωr is different from ωe. The currents flowing in the rotor circuits due to induction will be abalanced set with a frequency equal to ωe- ωr, which will producean air gap mmf that rotates at ωe- ωr relative to the rotor or ωerelative to a stationary observer. Hence, the rotating air gap mmf caused by the currents flowing inthe stator windings induces currents in the short-circuited rotorwindings which, in turn, establish an air gap mmf that rotates inunison with the stator rotating air gap mmf (mmf s). Interaction of these magnetic systems (poles) rotating in unisonprovides the means of producing torque on the rotor. An induction machine can operate as a motor or a generator.However, it is normally operated as a motor.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig48

As a motor it can develop torque from 0 ωr ωe. At ωr ωe, therotor currents are not present since the rotor is rotating at the speedof the stator rotating air gap mmf and, therefore, the rotor windingsdo not experience a change of flux linkages, which is, of course,necessary to induce a voltage in the rotor windings. The single-phase induction motor is perhaps the most widely usedelectromechanical device. The figure shown is not quite the wholepicture of a single-phase induction motor. Recall that the singlephase stator winding produces oppositely rotating air gap mmf’s ofequal amplitude. If the single-phase induction motor is stalled, ωr 0, and if asinusoidal current is applied to the stator winding, the rotor will notmove. This device does not develop a starting torque. Why? The rotor cannot follow either of the rotating mmf’s since itdevelops as much torque to go with one as it does to go with theother. If, however, you manually turn the rotor in either direction, itwill accelerate in that direction and operate normally.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig49

Although single-phase induction motors normally operate with onlyone stator winding, it is necessary to use a second stator winding tostart the device. Actually single-phase induction motors we use aretwo-phase induction motors with provisions to switch out one ofthe windings once the rotor accelerates to between 60 and 80percent of synchronous speed. How do we get two-phase voltages from a single-phase householdsupply? Well, we do not actually develop a two-phase supply, butwe approximate one, as far as the two-phase motor is concerned, byplacing a capacitor (start capacitor) in series with one of the statorwindings. This shifts the phase of one current relative to the other,thereby producing a larger rotating air gap mmf in one directionthan the other. Provisions to switch the capacitor out of the circuitis generally inside the housing of the motor.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig50

Elementary Two-Pole Induction Machines:Single-Phase and Two-PhaseActuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig51

Synchronous Machines– Shown are elementary single- and two-phase two-polesynchronous machines. However, they are but one ofseveral devices which fall into the synchronous machinecategory. We honor convention here and refer to thesedevices as synchronous machines.– The single-phase synchronous machine has limitedapplication. The same can be said about the two-phasesynchronous machine. It is the three-phase synchronousmachine which is used to generate electric power in powersystems such as in some automobiles, aircraft, utilitysystems, and ships. Nevertheless, the theory of operationof synchronous machines is adequately introduced byconsidering the two-phase version.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig52

The elementary devices shown have only one rotor winding – thefield winding (f winding). In practical synchronous machines, therotor is equipped with short-circuited windings in addition to the fwinding which help to damp oscillations about synchronous speedand, in some cases, these windings are used to start the unloadedmachine from stall as an induction motor. The principle of operation is apparent once we realize that thecurrent flowing in the field winding is direct current. Although itmay be changed in value by varying the applied field voltage, it isconstant for steady-state operation of a balanced two-phasesynchronous machine. If the stator windings are connected to a balanced system, the statorcurrents produce a constant-amplitude rotating air gap mmf. Arotor air gap mmf is produced by the direct current flowing in thefield winding. To produce a torque or transmit power, the air gap mmf producedby the stator and that produced by the rotor must rotate in unisonabout the air gap of the machine. Hence, ωr ωe.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig53

Elementary Two-Pole Synchronous Machines:Single-Phase and Two-PhaseActuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig54

Permanent-Magnet Devices– If we replace the rotor of the synchronous machines justconsidered with a permanent-magnet rotor, we have the socalled permanent-magnet devices shown in the figure.– The operation of these devices is identical to that of thesynchronous machine.– Since the strength of the rotor field due to the permanentmagnet cannot be controlled as in the case of thesynchronous machine which has a field winding, it is notwidely used as a means of generating power.– It is, however, used widely as a drive motor.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig55

– In particular, permanent-magnet motors are used as steppermotors and, extensively, as brushless dc motors, whereinthe voltages applied to the stator windings are switchedelectronically at a frequency corresponding to the speed ofthe rotor.Actuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig56

Elementary Two-Pole Permanent-Magnet Devices:Single-Phase and Two-PhaseActuators & Sensors in Mechatronics:Brushless DC MotorsK. Craig57

Brushless DC Motors Introduction– Permanent magnet DC motors all have brushes to transmitpower to the armature windings. Brush arcing causeselectronic noise and maintenance problems from excessivewear.– A Brushless DC Motor has been developed to overcomethese problems. It substitutes electronic commutation forthe conventional mechanical brush commutation.– Because the electronic commutation exactly duplicates thebrush commutation in c

machines, stepper motors, and brushless dc motors (permanent-magnet synchronous machines), all develop torque in this manner. – There are features of these devices which are common to all, in particular: Winding arrangement of the stator Method of p