1 DC Motors The construction of a DC motor is essentially the same as the construction of a DC generator. In general the same machine can be used as either a motor or as a generator. If power is supplied to the armature terminals causing the machine to turn then its a motor. If mechanical power is supplied to the machine by turning it and it supplies electrical power to an electrical load then its a generator. Like DC generators there are several variants of the basic DC motor. These are shunt motors series motors and compound motors. 2 DC Motors Consider a DC machine with its armature connected to a DC source. Well ignore (for now) the field connections and assume that excitation current is somehow supplied to the field windings. When the connection to the DC source is made (by closing a switch) current flows in the armature windings. This current is equal to the source voltage Es divided by the armature resistance R. R is simply the resistance of the armature windings which is usually very small this means the armature current is quite large. The armature coils are immersed in a magnetic field so the Lorentz force appears as soon as armature current begins to flow. The large current thus causes a large torque and the armature begins to rotate. R
S N f Es - 3 DC Motors What happens when an armature rotates in a field An armature voltage is induced across the brushes. This occurs in a generator and the only difference between that and our motor is the generators armature is made to turn by an external mechanical torque. The fact that the motors armature is made to turn by an internal electromagnetic torque makes no difference. A voltage Eo porportional to the speed of rotation is induced across the brushes R The polarity of the induced voltage is always opposite the voltage supplied to the armature Eo. Because of this its called the counter-electromotive force (cemf) or back emf.
S N Eo f Es - - - 4 DC Motors Now because of the counter emf the voltage across the armature resistance R is the difference between the source voltage Es and the back emf Eo. This means that when the armature starts to turn and the cemf increases the armature current starts to decrease As the motors speed increases the counter emf increases and the armature current decreases. This continues until the counter emf nearly equals the source voltage. At this speed the armature current is quite low just enough that the armature power is sufficient to maintain the motors speed. R
S N Eo f Es - - - 5 DC Motors The only purpose of a motor is to supply power and torque to a load. From our study of DC generators we know that the counter emf developed by a lap-wound armature is R
S N Eo f Es - - - 6 DC Motors Weve already seen that the armature current is And its obvious that the power supplied to the armature is But with a little manipulation we see that R
R is the armature resistance so the second term is the power dissipated as heat by the armature. The first term represents the power delivered to the mechanical load. S N Eo f Es - - - 7 DC Motors The electrical power converted to mechanical power is But we have an expression which relates torque and mechanical power Where n is the motor speed in rpm and T is the torque. Combining the last two expressions R
S N Eo f And with a little more manipulation Es - - - 8 Speed Control When a motor is driven at less than full load the armature voltage drop is always much smaller than the source voltage Es. This means that the second term in Is negligible so We know that the counter emf is given by so R
The speed of the motor can be controlled by varying the voltage supplied to the armature or by varying the field flux. S N Eo f Es - - - 9 Ward-Leonard Speed Control Controlling the motor speed via the armature voltage is an attractive idea. Nowadays this can be done by means of a variable-output DC supply but it was formerly done by an interesting electromechanical arrangement called a Ward-Leonard system. In this system we have a fixed-speed motor (probably a 3-phase synchronous AC motor) driving a separately-excited DC generator with variable field current. The output voltage of the DC generator can be controlled by varying the excitation current providing a means to vary the Ix R armature voltage and control the speed of the DC motor.
Ix Es Eo DC motor 3-f motor DC Generator - 10 Ward-Leonard Speed Control In the Ward-Leonard system as long as the DC motor is supplying mechanical power to a mechanical load it absorbs electrical power from the generator. Suppose we decide to reduce the motor speed by reducing Es. For some period of time Eo is greater than Es so current flows from the motor to the generator. For this period of time the motor actually operates as a generator and vice-versa. This briefly causes the AC motor to act as a generator and deliver power back to its supply. The kinetic energy given up by the slowing mechanical Ix R Load is converted to electrical power which drives the DC generator (operating as a motor) and finally is delivered to
Ix Es Eo DC motor 3-f motor DC Generator - the 3-phase power supply temporarily reducing or reversing the systems energy consumption. 11 Armature Speed Control Of course its also possible to control the motor speed by means of a rheostat in series with the armature. This is simple but inefficient due to the power dissipated by the rheostat. Furthermore it results in poor speed regulation. If the mechanical load increases the armature current increases. This increases the voltage drop across the rheostat which effectively reduces the armature voltage further reducing the motor speed. R
Ix Es Eo DC motor - 12 Flux Speed Control Another way to control the motor speed is by varying the field flux. The relationship between speed armature voltage and flux is This says that increasing the flux reduces the speed and vice versa. If the motor is running at its rated speed and the excitation current is reduced the counter emf is also reduced. This causes an increase in armature current which causes the speed to increase until the counter emf is again nearly equal to the supply voltage. Rf R
Ix Es Eo DC motor - 13 Series Motor Heres a series DC motor where the field winding is connected in series with the armature. This means that the excitation current and the armature current are the same. If an increasing load causes the armature current to increase the increasing excitation current increases the field flux which reduces the motor speed but increases the torque R
Es At low speeds under heavy loads the series motor can produce a very large torque. This is good for applications such as railroad locomotives. Under light load when the field current is low it may tend to run at a dangerously high speed. This is called runaway. Eo DC motor Series Field Winding - 14 Compound Motor A compound motor has both a shunt field winding and a series field winding. If the two field windings are connected so their mmfs have the same direction then the two mmfs add to produce the total field. This is called a cumulative compound motor. When the motor is lightly loaded the armature current is very small so the series field winding produces a very small mmf. A series motor would run at an excessive speed and possibly run away. In the cumulative compound motor excitation Current still flows in the shunt field winding producing an mmf which does not vary with load. This protects the motor from running away. As the load increases the series field mmf increases which increases the total mmf and reduces the speed of the motor. Thus the speed of a cumulative compound motor drops by 10 - 30 as the motors load is increases from no-load to full-load. Series Field
Armature Es Eo Shunt Field - 15 Differential Compound Motor It is also possible to connect the series and shunt field windings so their mmfs have opposite directions. In this case the series field mmf subtracts from the shunt field mmf. This is called a differential compound motor. When the motor is lightly loaded the armature current is very small so the series field winding produces a very small mmf. When the load increases the series field current increases but this causes a reduction in total mmf and a resulting increase in speed. As the load increases the motors speed increases which can cause instability. For this reason there are few applications for the differential compound motor. Series Field
Armature Es Eo Shunt Field - 16 Reversing a motor To reverse the direction of rotation (e.g. a reversible drill) we must reverse the direction of the Lorentz force on the armature coils. How to do this There are two ways. Either reverse the direction of the current flowing in the armature coils by reversing the polarity of the voltage supplied to the armature or reverse the direction of the field mmf by reversing the polarity of the field connections.If the motor is A compound motor both the shunt and series field connections must be reversed. R
S N Eo f Es - - - 17 Starting a motor Weve previously observed that for a separately excited motor (or a shunt motor) the armature current is given by If Es is suddenly connected to a motor whose armature is at rest the counter emf Eo is zero so the armature current is only limited by R the resistance of the armature windings. R is usually very small so the armature current is very high. This would produce a very high starting torque which may be desirable but it also causes excessive heating (and possibly burnout) of the armature heavy sparking of the commutator and brushes tripped circuit breakers in the power supply and mechanical shock. R
S N Eo f Es - - - 18 Starting a motor Obviously some means of controlling the armature current during startup is desirable. Wed usually like to limit the armature current during startup to no more than 1.5 2 times the full load current. This can be done by connecting a variable resistance (a rheostat) in series with the armature to control the armature current. As the speed of the motor increases causing the counter emf to increase the resistance of the rheostat is reduced until the motor is running at full speed. A faceplate starter described in detail by Wildi is a similar arrangement. The rheostat is replaced by a set of current limiting resistor which are switched in or out of the armature circuit by a movable contact arm. This provides acceleration of the motor in steps with limited current and torque. R
S N Eo f Es - - - 19 Dynamic Braking One way of stopping the motor electrically is called dynamic braking. Consider the shunt motor below. When the switch is in the position shown power is applied to the armature and the motor runs normally driving whatever mechanical load it is coupled to. The counter emf is Eo. When the switch is thrown the armature is disconnected from the power supply and connected to a load resistor R. Initially the armature is still turning at full speed so the counter emf is still Eo. Now the motor acts as a generator causing current to flow through the load resistor. This current flows through the armature but The armature current is reversed in direction when the switch is thrown. This reverses the resulting torque on the armature and the torque now acts in the direction opposing the rotation of the armature. This torque will bring he motor promptly to a stop.
Armature Es Eo R Shunt Field - 20 Dynamic Braking The resistor R is usually chosen so the braking current is initially (when the switch is thrown) about 2 times the rated motor current. This makes the braking torque twice the normal motor torque. Of course as the motor slows down the counter emf is reduced. This reduces the braking current and therefore the braking torque. The motors speed decays exponentially like the voltage across a discharging capacitor. While the initial deceleration is quite rapid it tapers off. If wed like to stop the motor even faster we can use a technique called plugging.
Armature Es Eo R Shunt Field - 21 Plugging Plugging means abruptly reversing the armature current. Shown below is a simplified arrangement for doing this Throwing the switch reverses the polarity of the armature connection reversing the direction of the armature current. Before throwing the switch the counter emf across the armature is Eo and the armature current is Where Ro is the series resistance of the armature. The polarity of the counter emf is opposite that of the armature supply so the two subtract. After throwing the switch the polarity of the armature supply is reversed so the two emfs add
Armature Es Eo Shunt Field - 22 Plugging Throwing the switch causes a VERY large reverse current to flow in the armature which would cause a correspondingly huge braking torque if the armature or brushes and commutators were not destroyed in the process. Or if the shaft or motor mounts didnt shatter. These undesirable consequences can be avoided by adding a series resistor R as shown below. R should be chosen to limit the initial braking current to about twice the normal full-load motor current. With this arrangement when the motor comes to a stop the reverse torque will still be the torque developed by an armature current of
Armature Es Eo R Shunt Field In dynamic braking the braking torque approaches zero as the speed approaches zero. In plugging the braking torque never approaches zero. - 23 Plugging Plugging will obviously stop the motor faster than dynamic braking but when the armature stops the reverse torque is still applied. If the armature supply is not disconnected the motor will immediately start to rotate in the opposite direction. In a practical plugging system a means must be provided to disconnect the armature the moment it stops turning. Plugging has the advantage of speed but dynamic braking is simpler and more common.
Armature Es Eo R Shunt Field - 24 Mechanical Time Constant As weve observed with dynamic braking the motors speed decays exponentially like the voltage across a discharging capacitor. As a discharging RC circuit has a time constant we can define a mechanical time constant T for a motor under dynamic braking. T would be the amount of time required for the motor to slow to 36.8 of its initial speed. Well define another constant To as the ammount of time required for the motor to slow to 50 of its initial speed. The two constants are related by
Armature Es Eo R Shunt Field - 25 Mechanical Time Constant The mechanical time constant is related to the initial speed moment of inertia and the power delivered to the braking resistor R by Where J is the moment of inertia for all rotating parts (armature shaft load etc.) in kg-m2 n1 is the initial speed of the motor (when braking is first applied) in rpm and P1 is the power initially dissipated by the braking resistor. As a practical matter the motor will be brought to a stop by a combination of dynamic braking and mechanical friction (imperfect bearings) in approximately 5T0. If plugging is used the motor will stop in 2T0.
Armature Es Eo R Shunt Field - 26 Armature Reaction As we saw with DC generators a current flowing in the armature makes the armature a source of MMF. This MMF interacts with the pole flux in a way which weakens and distorts the shape of the pole flux. This is called armature reaction. This does not happen when the motor runs under no-load conditions but does occur when a load causes the armature to draw current. The consequences are the same as for the DC Generator Poor commutation sparking and loss of power and efficiency. A small series field winding may be added to compensate for some of the loss in field flux this is called a stabilized-shunt winding. R Commutating poles may also be used as in DC Generators to compensate for the neutral zone shift.
R S N Eo f - - - 27 Armature Reaction Some large motors which must be started stopped and reversed rapidly incorporate compensating windings. These are stationary windings distributed in slots cut into the faces of the pole pieces connected in series with the armature but so their mmf is equal and opposite to the armature mmf. Because theyre distributed across the poles they almost completely cancel the field distortion due to armature reaction. This results in several advantages A shorter air gap can be used because the armature no longer causes demagnetization. This means the shunt field strength can be reduced. Second the inductance of the armature coils is reduced by a factor of up to 5. This obviously improves commutation it also improves the response of the motor to control input. Finally such a motor can briefly develop up to 4 times its rated torque. R
S N Eo f - - - 28 Variable Speed Control One of the most attractive features of the DC motor is that it offers the ability to control speed. This is an advantage in many industrial applications and also in vehicular applications such as electric cars locomotives and submarines. We should take a closer look at controlling the speed of a DC motor. Well consider a separately-excited motor with per-unit values for the armature current Ia armature voltage Ea torque T and field flux ff. This means the rated values of Ea has a value of 1 p.u. the rated armature current has a value of 1 p.u. etc. This makes it easy to apply the results of this discussion to any motor of the same type. The torque and the armature voltage are given by R
S N Eo f - - - 29 Variable Speed Control Notice that speed is proportional to Ea but torque is only related to flux and armature current. This means that we can vary the speed from zero to rated speed (n 1 p.u.) by increasing Ea from zero to rated voltage (Ea 1 p.u.). At the same time if we keep Ia and ff at their rated values the torque remains constant at 1 p.u. However we cannot increase the speed above the rated speed this way because that would require exceeding the rated armature voltage. If we need to increase the speed further we must do so by reducing the flux. This causes a reduction in torque. The plot here illustrates the relationship between flux and speed. 30 Variable Speed Control Because torque is proportional to flux the speed-torque curve looks identical to the previous plot. It shows that torque is constant from zero to rated speed so when the motor is operated on this portion of the curve it is operating in constant-torque mode. If we increase the speed above rated speed by reducing the flux we can keep the armature current constant at 1 p.u. and also keep the armature voltage at 1 p.u. (rated value) 31 Variable Speed Control When operating above rated speed we keep Ea and Ia constant at 1 p.u. Since the product of Ea and Ia is the power supplied to the motor the power remains constant. Weve assumed that the motor is ideal so the mechanical power delivered to the load is also constant. Thus when operated above Rated speed the motor is said to be operating in constant-horsepower mode. If we operate a motor below rated speed its ventilation is reduced and it may overheat. This requires reducing the armature current which reduces torque. Thus as a practical matter the torque may not really be constant below rated speed. 32 Permanent Magnet Motors Weve talked about motors that have field windings to produce the flux that results in the Lorentz force on the armature. These field windings may be connected in shunt in series or both. Of course its also possible to use permanent magnets as field poles. This eliminates the heat due to the field current and reduces the space required for the poles resulting in a smaller and more efficient motor. A larger air gap may also be used reducing armature reaction and reducing the inductance of the armature. Permanent magnets are often used as field poles in motors smaller than 5 hp. R
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