DC Motors:.

DC Motors:

DC MOTORS INTRODUCTION
Five major types of dc motor: 1- separately excited dc motor 2-shunt dc motor 3-permnent-magnet dc motor 4- series dc motor 5-compounded dc motor

DC MOTOR EQUIVALENT CIRCUIT
Figure below shows a dc motor equivalent cct. Armature cct. represented by an ideal voltage source EA & a resistor RA This is thevenin equivalent of entire rotor, including coils, interpoles & compensating windings Brush voltage drop represented by a small battery Vbrush opposing direction of current flow

A simplified equivalent circuit eliminating the brush voltage drop and combining Radj with the field resistance shown in (b) Some of the few variations and simplifications: 1- brush drop voltage is often only a very tiny fraction of generated voltage in the machine. where it is not too critical, brush drop voltage may be left out or included in the RA. 2- internal resistance of field coils is sometimes lumped together with variable resistor and total is called RF 3- Some generators have more than one field coil, all of which appear on the equivalent circuit

The internal generated voltage is given by: EA = K φω and the torque induced is ind = K φ IA The Magnetization Curve of a DC Machine - EA is directly proportional to flux and the speed of rotation of the machine EA is therefore related to the field current field current in a dc machine produces a field mmf given by mmf=NFIF

mmf produces a flux in the machine in accordance with its magnetization curve

DC MOTOR:EQUIVALENT CCT
Since If is proportional to mmf & since EA is proportional to flux, magnetization curve can represented as a plot of EA vs field current for a given speed ω0

SEPARATELY EXCITED AND SHUNT DC MOTORS
Equivalent cct. of separately excited dc motor shown below

SEPARATELY EXCITED AND SHUNT DC MOTORS
separately excited dc motor is a motor whose field cct. is supplied by another constant-voltage supply shunt dc motor is a motor whose field circuit gets its power directly from armature terminals of motor When supply voltage to a motor assumed constant, there is no practical difference in behavior between these two machines Kirchhoff’s voltage law KVL equation for armature cct. of these motors is: VT=EA+IARA

TERMINAL CHARACTERISTIC of a SHUNT DC MOTOR
Terminal characteristic of a motor is a plot of output torque versus speed If load on shaft of a shunt motor is increased, then load torque Tload exceed induced torque Tind & motor will start to slow down & Its internal generated voltage EA=Kφω decrease Then IA= (VT-EA)/ RA increases consequently Tind=KφIA increases & finally Tind will equal Tload at a lower mechanical speed

O/P characteristic of shunt dc motor can be derived using Tind, EA equations & KVl Combing these three equations: VT=EA+IARA  VT=Kφω+IARA & IA = Tind /(Kφ)  VT=Kφω+ Tind /(Kφ) RA  ω = VT / (Kφ) - Tind/(Kφ)^2 RA This equation is a straight line with a negative slope

Torque – speed characteristic of a shunt or separately excited dc motor

Armature reaction affect the torque speed characteristic As shown in last slide, as load increase, flux weakening effect reduce the flux in shunt motor And according to speed equation, reduction in flux will increase speed If a motor has compensating winding, then there would be no flux weakening & flux remain constant

TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
If a shunt dc motor has compensating windings so that flux is constant regardless of load, & motor’s speed & armature current known at any one value of load , then speed at any other load can be determined if IA is known at that load

TERMINAL CHARCATERISTIC of a SHUNT DC MOTOR
Torque – speed characteristic of motor

NONLINEAR ANALYSIS of a SHUNT DC MOTOR
flux φ & EA of a dc machine is a nonlinear function of mmf  anything that changes mmf cause a nonlinear effect on EA mmf should be used to determine EA & mmf determined based on field current and A.R. magnetization curve is a direct plot of EA versus IF for a given speed ω0  effect of variation in field current can be determined directly from its magnetization curve

If a machine has armature reaction, its flux will be reduced with each increase in load. The total mmf in a shunt dc motor is the field circuit mmf less the mmf due to armature reaction (AR): Fnet = NFIF – FAR magnetization curves are expressed as plots of EA vs field current, normally an equivalent field current is defined that would produce the same output voltage as the combination of all the mmf in the machine The equivalent field current :

one other effect must be considered when non linear analysis is used to determine EA of a dc motor The magnetization curves for a machine are drawn for a particular speed, usually the rated speed of the machine How can the effects of a given field current be determined if the motor is turning at other than rated speed? The equation for the induced voltage in a dc machine when speed is expressed as rev/min: EA = K’φn , For a given effective field current, the flux in the machine is fixed, so the EA is related to speed by

Torque-speed characteristic of motor with armature reaction

SPEED CONTROL of SHUNT DC MOTOR
Two common methods: 1- Adjusting the field resistance RF (and thus the field flux) 2- Adjusting the terminal voltage applied to the armature Less common method: 3- Inserting a resistor in series with the armature circuit

Changing the Field Resistance If the field resistance increases, field current decreases (IF↓ = VT/RF↑), and as the field current decreases, flux decreases as well. A decrease in flux causes an instantaneous decrease in the internal generated voltage EA↓ (=Kφ↓ω), which causes a large increase in the machine’s armature current since

Induced torque in a motor is given by ind =KφIA since flux in machine decreases while current IA increases, which way does the induced torque change? Look at this example:  armature current flow is IA=(250V-245V)/ 0.25Ω= 20A

back to original discussion, the increase in current predominates over the decrease in flux so, ind>load , the motor speeds up However, as the motor speeds up, EA rises, causing IA to fall. Thus, induced torque ind drops too, and finally ind equals load at a higher steady-sate speed than originally Summarizing behaviour: 1- increasing RF causes IF (=VT/RF) to decrease 2- decreasing IF decrease φ

3 – Decreasing φ lowers EA(=Kφω) 4 - Decreasing EA increases IA (=VT-EA)/RA 5- increasing IA increases Tind (=KφIA), with change in IA dominant over change in flux 6-increasing Tind makes Tind>Tload & speed ω increases 7-increase in ω, increases EA= Kφω again 8-increasing EA decreases IA 9-Decreasing IA decreases Tind until Tind=Tload at a higher ω Effect of increasing RF on O/P characteristic of a shunt motor shown in next figure

Effect of RF speed control on a shunt motor’s torque-speed (over motor’s normal operating range)

Effect of RF speed control on a shunt motor’s torque-speed (over entire range from no-load to stall conditions)

According to equation of speed presented before: (a) no-load speed is proportional to reciprocal of flux in motor (b) while slope of the curve is proportional to reciprocal of flux squared Therefore a decrease in flux causes slope of torque-speed to become steeper over this range, an increase in field resistance increases motor’s speed For motors operating between no-load & full-load conditions, an increase in RF may reliably be expected to increase operating speed

In previous figure (b) terminal characteristic of motor over full range from no-load to stall shown In figure can see at very slow speeds, an increase in field resistance will actually decrease speed of motor This effect occurs because at very low speeds, the increase in armature current caused by decrease in EA not enough to compensate for decrease in flux in induced torque field resistance Some small dc motors used for control purposes operate at speeds close to stall conditions For these motors, an increase in RF might have no effect or it might even decrease speed of motor Since the results are not predictable, field resistance speed control should not be used in these types of dc motors. Instead, the armature voltage method should be employed

CHANGING ARMATURE VOLTAGE This method involves changing the voltage applied to the armature of the motor without changing the voltage applied to the field If the voltage VA is increased, then the IA must rise [ IA = (VA ↑ -EA)/RA]. As IA increases, the induced torque ind =KφIA↑ increases, making ind > load , and the speed of the motor increases But, as the speed increases, the EA (=Kφω↑) increases, causing the armature current to decrease This decrease in IA decreases the induced torque, causing ind = load at a higher rotational speed

Effect of armature voltage speed control

Inserting a Resistor in Series with the Armature Circuit If a resistor is inserted in series with the armature circuit, the effect is to drastically increase the slope of the motor’s torque-speed characteristic, making it operate more slowly if loaded. This fact can be seen from the speed equation: The insertion of a resistor is a very wasteful method of speed control, since the losses in the inserted resistor are very large. For this reason, it is rarely used

Effect of Armature motor’s resistance speed control on a shunt motor’s torque-speed Only used in applications in which: - motor spends almost all its time operating at full speed or - inexpensive to justify a better form of speed control

In field resistance control, lower IF  higher its speed, & higher IF causes a decrease in speed there is always a minimum achievable speed by IF control Minimum speed occurs when IF has maximum permissible value if motor operate at its rated terminal voltage, power, & IF then it will be running at rated speed this is known also as : “base speed” to achieve a reduction in this speed by IF control, require excessive IF that may burn up field windings

In armature voltage control, lower armature voltage on separately excited motor, reduce its speed & higher armature voltage increase its speed There is a maximum achievable speed, in maximum permissible armature voltage level Armature voltage control would require excessive armature voltage, which may damage armature circuit Armature voltage control works well for speeds below base speed & field current control works well for speeds above base speed By combining two speed-control techniques in same motor, it is possible to get a range of speed variations of up to 40 to 1 or more Shunt & S.E. motors have excellent speed control characteristics

There is significant difference in torque & power limits on machine under two types of speed control Limiting factor in either case is heating of armature conductors, which places an upper limit on magnitude of IA For armature voltage control, flux in motor is constant, so maximum torque in motor is: Tmax=KφIA,max maximum torque is constant, regardless of speed

power o/p, P=T.ω maximum power of motor at any speed under armature voltage control is: Pmax=Tmax ω Thus maximum power out of motor is directly proportional to its operating speed under armature voltage control on the other hand, while RF control used flux changes & speed increase by decrease in flux In order that IA do not exceed its limit, Tind must decrease as speed of motor increases

since P=T.ω, & torque limit decreases as speed of motor increases: - max. power out of dc motor under field current control is constant, while max. torque varies as reciprocal of motor’s speed These shunt dc motor power & torque limitations for safe operation as a function of speed shown next

Power & Torque limits as a function of speed for a shunt motor under VA & RF control

SPEED CONTROL of SHUNT DC Effect of an Open Field Circuit
Two other causes of field weakening: (a) in shunt motors operating with light fields if A.R. effects severe enough, in case of an increase in load can weaken its flux and cause rise of speed until motor over-speed known as runaway (b) motors operating with severe load changes & duty cycles, this flux weakening problem solved by installing compensating windings Unfortunately compensating windings too expensive for use on ordinary run-of-the-mill motors Solution: to use a turn or 2 turns of cumulative compounding to motor’s poles As load increases mmf from series turns increases, which counteracts demagnetizing mmf of A.R. A shunt motor equipped with just few series turns like this is called: stabilized shunt motor

Example 3: figure, shows a 100 hp, 250 V, 1200 r/min shunt dc motor with an armature resistance of 0.03 Ω & a field resistance of Ω Motor has compensating windings, so armature reaction can be ignored Mechanical & core losses may be ignored assumed to be driving a load with a line current of 126 A & an initial speed of 1103 r/min, to simplify the problem assume armature current drawn by motor remains constant

SPEED CONTROL of SHUNT DC MOTOR-Example 3
(a) machine magnetization curve shown in next slide, what is motor’s speed if RF raised to 50 Ω (b) calculate & plot speed of motor as a function of RF assuming a constant-current load SOLUTION Initial IA1= IL1-IF1= /41.67=120 A  EA1=VT-IA1RA= x 0.03=246.4 V RF increased to 50 Ω,  IF2=VT/RF=250/50=5 A

Magnetization curve

EA2/EA1=[K’φ2n2]/[K’φ1n1], and since IA assumed constant  EA1 = EA2  1=[φ2n2]/[φ1n1] or n2= [φ1 / φ2] n1 Last Plot is EA versus IF , for a given speed EA directly proportional to flux  on this curve: EA2/EA1 =φ2/φ1 At IF=5 A, EA0=250 V, while at IF=6 A, EA0=268 V  φ2/φ1= 268/250 =1.076 New speed of motor: n2= φ1/φ2 n1=(1.076)(1103)=1187 r/min

Note: assumption of constant IA not a good assumption for real loads IA vary with speed in a fashion dependent on torque required by type of load attached to motor these differences cause a motor’s speed –versus-RF curve slightly different than shown in last figure.

Motor in Example-3 now connected separately excited, as shown below:

Motor is initially running with VA=250 V, IA=120 A, and n=1103 r/min, while supplying a constant torque load. What will the speed of this motor be if VA is reduced to 200 V? SOLUTION:EA=VT-IARA= x0.03=246.4 V Since flux is constant: EA2/EA1=[K’φ2n2]/[K’φ1n1]=n2/n1  n2= EA2/EA1 n1 Since torque is constant & flux is constant  IA is constant: EA2= x0.03=196.4 V n2= EA2/EA1 x n1=196.4/246.4 x 1103=879 r/min

SPEED CONTROL of SHUNT DC Effect of an Open Field Circuit
As shown speed increase as RF increased, what would happen if field circuit open while motor is running? The flux in machine would drop drastically, and reach φres & EA=Kφω would drop with it cause an enormous increase in IA & resulting Tind would be quite a bit higher than load torque on motor. Therefore motor’s speed starts to rise & just keeps going up

PERMANENT-MAGNET DC MOTOR
A permanent magnet dc motor (PMDC) is a dc motor whose poles are made of permanent magnets. PMDC motor offer a number of benefits compared with shunt dc motors in some applications Advantage: Since these motors do not require an external field circuit, they do not have the field circuit copper losses. Because no field windings are required, they can be smaller than corresponding shunt dc motors

Disadvantages: (a) Permanent magnets cannot produce as high flux density as an externally supplied shunt field so a PMDC motor will have a lower induced torque per ampere of armature current than a shunt motor of the same size. (b) PMDC motors run risk of demagnetization due to A.R. effect which reduces overall net flux, also if IA become very large there is a risk that its mmf demagnetize poles, permanently reducing & reorienting residual flux (c) A PMDC motor is basically the same machine as a shunt dc motor, except that flux of a PMDC motor is fixed. Therefore, it is not possible to control the speed of the PMDC motor by varying the field current or flux. The only methods of speed control available for a PMDC motor are armature voltage control and armature resistance control.

The magnetization curve of typical ferromagnetic material Note: after a large magnetizing intensity H applied to core & removed, a residual flux Bres remains behind in core Flux can be brought to zero if a coercive magnetizing intensity Hc is applied to core with opposite polarity in this case, a relatively small value of it will demagnetize the core

(a)Typical ferromagnetic material & its Bres (b) suitable for P.M. (c) second quadrant rare earth magnets combine High residual flux and high coercive magnetizing intensity

SERIES DC MOTOR A series DC motor is a dc motor whose field windings consist of relatively few turns connected in series with the armature circuit KVL for this motor is VT = EA + IA (RA + RS)

SERIES DC MOTOR The Tind=KφIA while flux in this machine directly proportional to IA (at least until metal saturates) Flux in machine can be given by: φ=c IA Where c is constant of proportionality.  Tind=KφIA = K c IA^ (1) Torque in motor proportional to square of IA As a result of this relationship, series motor gives more torque per ampere than any other dc motor Therefore it is used in applications requiring very high torques Examples: starter motors in cars, elevator motors, and tractor motors locomotives

TERMINAL CHARCATERISTIC SERIES DC MOTOR
As seen before an increase in flux cause a decrease in speed. in series motor a sharply drooping torque-speed characteristic exist (since IA pass field winding) Analysis is based on assumption of linear magnetization curve, & then effects of saturation considered in a graphical analysis therefore: φ=c IA (2) VT = EA + IA (RA + RS) (3) From (1) IA=√Tind /Kc & EA=Kφω  VT = Kφω + √Tind /Kc (RA + RS) (4)

To eliminate flux from equation (4): IA=φ/c and Tind=K/c φ^2  φ=√c/K √Tind (5) Substituting equation (5) in (4) and solving for speed: VT=K √c/K √Tind ω + √Tind /Kc (RA + RS) √c/K √Tind ω= VT - (RA + RS) / [Kc] x √Tind ω= VT / [Kc] x 1/√Tind - (RA + RS) / [Kc] (6) Note: for unsaturated series motor; speed of motor varies as reciprocal of square root of Tind & its torque-speed characteristic shown next

Torque-speed characteristic of a series motor One disadvantage can be seen from Eq.(6) - when Tind goes to zero speed goes to infinity - in practice torque can never go zero due to mechanical, core & stray losses that must be overcome, however if no other load exist, can turn fast enough to seriously damage itself

Therefore; Never completely unload a series motor & never connect one to a load by a belt or other mechanism that could break nonlinear analysis of a series dc motor with magnetic saturation effects, ignoring A.R. illustrated in EXAMPLE-5 Example 5: consider the equivalent cct. of a series dc motor with a 250 V series dc motor having compensating windings, and atotal series resistance RA+RS of 0.08 Ω. The series field consists of 25 turns per pole, with magnetization curve shown next

SERIES DC MOTOR EXAMPLE-5
Magnetization Curve

SERIES DC MOTOR find speed & induced torque of this motor for
when its armature current is 50 A (b) calculate & plot torque-speed characteristic for this motor SOLUTION : Pick points along operating curve & find torque & speed for each point for IA=50 A EA=VT-IA(RA+RS) =250 – 50 x 0.08 =246 V since IA=IF=50 A, mmf=25 x 50=1250 A.turns

SERIES DC MOTOR From magnetization curve at mmf =1250 A.turns  EA0=80 V Speed can be found: n= EA/EA0 x n0=246/80 x 1200= 3690 r/min Pconv=EAIA=Tind ω  Tind=EAIA/ω=[246 x50]/[3690x1/60x2π]=31.8 N.m. (b) to calculate complete torque-speed characteristic, the same steps of (a) should be repeated for may values of IA, this can be done using a M-file of MATLAB

SERIES DC MOTOR SPEED CONTROL
Unlike shunt dc motor, there is only one efficient way to change speed of a series dc motor Method is to change terminal voltage of motor If terminal voltage is increased, first term in Eq. (6) increased, result in a higher speed for any given torque speed of series dc motors can be controlled by insertion of a series resistor however is very wasteful of power & only used for very short time during start-up Now with introduction of solid-state control, techniques available for variable terminal voltages

COMPOUND DC MOTOR A compound dc motor is a motor with both a shunt & a series field Such a motor shown below: (a) long-shunt connection

COMPOUND DC MOTOR (b) Compound dc motor with short-shunt connection

COMPOUND DC MOTOR Current flowing into dot produces a positive mmf (same as in transformer) If current flows into dots on both field coils, resulting mmfs add to produce a larger total mmf This situation is known as cumulative compounding If current flows into dot on one field coil & out of dot on other field coil resulting mmfs subtract In previous (a)&(b) figures round dots correspond to cumulative compounding & squares corresponds to differential compounding

COMPOUND DC MOTOR KVl for the compound motor: VT=EA+IA(RA+RS)
Currents in compound motor are related by: IA=IL-IF IF=VT/RF - Net mmf & effective shunt field currnt in compound motor: Fnet =FF(+,-) FSE-FAR IF*=IF(+,-) NSE/NF IA – FAR/NF (+) in equations associated with cumulatively compounded (-) associated with differentially compound motor

COMPOUND DC MOTOR Torque-Speed Characteristic
In cumulatively compound dc motor, a component of flux is constant & another one which is ~ to IA (& thus to its load)  cumulatively compound motor has a higher starting torque than a shunt motor (whose φ constant) but lower than a series motor (whose entire φ ~ to IA ) Cumulatively compound motor combines best features of both shunt & series motors: Like a series motor has extra torque for starting; Like a shunt motor it does not overspeed at no load

At light load, series field has very small effect, so motor behaves approximately as a shunt dc motor As load gets very large series flux becomes quite important & torque-speed curve begins to look like a series motor’s characteristic A comparison of torque-speed characteristics of each of these types of machines shown next

(a) T-ω curve of cumulatively compound, compared to series & shunt motors with same full-load rating (b) T-ω curve of cumulatively compound, compared to shunt motor with same no-load speed

Torque-Speed of Differentially Compound dc motor In a differentially compounded dc motor, the shunt mmf and series mmf subtract from each other. This means that as the load on the motor increases, IA increases and the flux in the motor decreases. But as the flux decreases, the speed of the motor increases. This speed increase causes another increase in load, which further increases IA, further decreasing the flux, and increasing the speed again

The result is that a differentially compounded motor is unstable and tends to runaway This instability is much worse than that of a shunt motor with armature reaction. It is so bad that a differentially compounded motor is unsuitable for any application.

Differentially compounded motor is also impossible to start At starting conditions, the armature current and the series field current are very high Since the series flux subtracts from the shunt flux, the series field can actually reverse the magnetic polarity of the machine’s poles The motor will typically remain still or turn slowly in the wrong direction while burning up, because of the excessive armature current

When this type of motor is to be started, its series field must be short-circuited, so that it behaves as an ordinary shunt motor during the starting period Nonlinear Analysis of Compound dc Motors Example 6: a 100 hp, 250 V compounded dc motor with compensating windings has an internal resistance, including series winding, of 0.04 Ω. There are 1000 turns per pole on shunt field & 3 turns per pole on series windings The machine shown in next figure, & its magnetization curve shown also. At no load field resistor has been adjusted to make motor run at 1200 r/min. core, mechanical & stray losses negligible

(a) what is the shunt current in this machine at no load? (b) if motor is cumulatively compounded, find its speed when IA=200 A (c) if motor is differentially compounded, find its speed when IA=200 A SOLUTION: (a) At no load, IA=0, so internal generated voltage equal VT =250 V. & from Mag. Curve a IF=5 A  EA=250 V at 1200 r/min (& IF=5 A )

Compound dc motor of example 6:

(b) when IA=200 A flows in motor, machine’s internal voltage: EA=VT-IA(RA+RS)= x0.04=242 V effective field current of cumulatively compounded motor is: IF*=IF+NSE/NF IA- FAR/NF =5 +3/1000 x 200=5.6A From mag. Curve, EA0=262 V at n0=1200 r/min therefore motor’s speed will be: n =EA/EA0xn0=242/262 x 1200 = 1108 r/min (c) If machine is differentially compounded, IF*=IF-NSE/NF IA- FAR/NF=5 – 3/1000 x 200=4.4 A

from mag. Curve EA0=236 V at n0=1200 r/min  n=EA/EA0 x n0=242/236 x 1200 = 1230 r/min Note: speed of cumulatively compounded motor decreases with load, while speed of differentially compounded motor increases with load

Speed Control in Cumulatively Compounded DC Motor Techniques available for control of speed in a cumulatively compounded dc motor are the same as those available for a shunt motor 1- change in field resistance 2- change armature voltage 3- change armature resistance Differentially compounded dc motor could be controlled in a similar manner. Since differentially compounded motor almost never used, that fact hardly matters

DC MOTOR STARTERS Equipments used for protection of dc motors, for the following reasons: 1- protect motor against damage due to short circuits in equipment 2- protect motor against damage from long-term overloads 3-protect motor against damage from excessive starting currents 4- provide a convenient manner in which to control the operating speed of motor

DC MOTOR PROBLEMS on STARTING
In order for a dc motor to function properly, it must be protected from physical damage during starting period At starting conditions, motor is not turning & so EA=0 V since internal resistance of a normal dc motor is very low compared to its size (3 to 6 percent per unit for Medium size motors) a very high current flows Consider for example, 50 hp, 250 V motor of EXAMPLE 1, RA is 0.06 Ω, & full-load current less than 200 A, but current on starting is: IA=[VT-EA]/RA=[250-0]/0.06=4167 A This current is over 20 times motor’s rated full-load current It is possible a motor severely damaged by such current

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