DC Motor

By: Dr. Sweta Shah

DC Motor

Working Principle of DC Motor

• A DC motor is an electrical machine which converts electrical energy into mechanical energy.

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• The basic working principle of the DC motor is that whenever a current carrying conductor places in the magnetic field, it experiences a mechanical force.

Back EMF and Its Significance in DC Motors

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Since the armature of a DC motor rotates in a magnetic field, an emf is induced in the conductors of the armature due to electromagnetic induction (as in a generator). This induced emf acts in the opposite direction to the applied voltage (according to Lenz’s law) and hence is known as back emf or counter emf. It is denoted by Eb.

When dc voltage V is applied across the motor terminals, the field magnets are excited and armature conductors are supplied with current.

Therefore, driving torque acts on the armature which begins to rotate.

Back EMF and Its Significance in DC Motors

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As the armature rotates, back emf Eb is induced which opposes the applied voltage V.

The applied voltage V has to force current through the armature against the back emf Eb.

The electric work done in overcoming and causing the current to flow against Eb is converted into mechanical energy developed in the armature.

It follows, therefore, that energy conversion in a dc motor is only possible due to the production of back emf Eb.

Back EMF and Its Significance in DC Motors

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Net voltage across armature circuit = V – Eb

If Ra is the armature circuit resistance, then, Ia = (V – Eb)/Ra

Since V and Ra are usually fixed, the value of Eb will determine the current drawn by the motor. 

If the speed of the motor is high, then back e.m.f. 

Eb (= PφZN/60 A) is large and hence the motor will draw less armature current and vice-versa.

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Back EMF and Its Significance in DC Motors

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Difference between DC Motor and DC Generator

• The most significant difference between DC motor and DC generator lies in the conversion mechanism.
• DC motor converts electrical energy into mechanical energy whereas DC generator converts mechanical energy into an electrical energy.
• Furthermore, in DC motors, EMF in the armature is less than its terminal voltage (E_b < V) whereas in DC generators, generated EMF is more than its terminal voltage (E_g > V).

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Voltage Equation of a DC Motor

• Input Voltage provided to the motor armature performs the following two tasks:

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• Controls the induced Back E.M.F “Eb” of the Motor.
• Provides supply to the Ohmic IaRa drop.
• i.e.

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• V = Eb + IaRa ….. (1)

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• Where

Eb = Back E.M.F

IaRa = Armature Current X Armature Resistance

• The above relation is known as “Voltage Equation of the DC Motor”.

Power Equation of DC Motor

• The power developed by motor can be determined by multiplying the voltage applied (V) to armature current(I_a).
• By Multiplying both sides of equation(1) by I_a, we get power equation of DC Motor.

A d.c. motor  operates froma 240 V supply . The armature resistance is 0.2Ω .- Determine the back e.m.f. when thearmature current is 50 A.

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Solution: V = E + IaRa

Ans: 230 V 

The armature of a d.c. machine has a resistance of 0.25Ω  and is connected to a 300 V supply .- Calculate the e.m.f. generated  when it is running:

(a) as a generator giving 100 A.

(b) as a motor taking 80 A

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Ans: (a) 325 V (b) 280 V

Condition for Maximum Power

Condition for Maximum Power

• Thus the motor will deliver maximum power when the back EMF is equal to half of the applied armature voltage.

Torque Equation of a DC Motor

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Let

Tg = armature or gross torque (N-m) = Force × radius.

r = radius of the armature in m.

N = speed of the armature in rpm = N/60 rps.

Work done/revolution = force × distance moved per revolution

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Torque Equation of a DC Motor

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The expression for voltage in dc motor is given by,

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Torque Equation of a DC Motor

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Electrical input =

electrical power equivalent to mechanical power developed + armature copper loss

Mechanical power developed,

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Torque Equation of a DC Motor

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Since equation (1) = equation (2),

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Torque Equation of a DC Motor

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Hence torque of a dc motor is directly proportional to the flux/pole and armature current.

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Torque Equation of a DC Motor

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An 8-pole d.c. motor  has a wave-wound armature with 900 conductors. The useful flux per pole is 25 mWb. Determine the torque exerted when a current of 30A flows in each armature conductor. Consider A = 2.

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Ans: 429.3 Nm

Determine the torque developed by a 350V d.c . motor having an armature resistance of 0.5Ω  and running at 15 rev/s. The armature current is 60 A.

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Solution:

Step 1: Calculate Back emf

Step 2: Calculate Torque T = E I_a / (2 π n)

Ans: 203.8 Nm

Speed of a DC Motor

• The expression for the speed of a DC motor can derived as follows −

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• The back EMF of a DC motor is given by,

E_b=V−I_aR_a…(1)

• Also,

E_b=NPφZ/60A…(2)

Speed of a DC Motor

• From eq. (1) & (2), we get,

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NPφZ/60A=V−I_aR_a

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N=(V−I_aR_a/φ)×(60A/PZ)

• For a given DC motor, the (60A/PZ) = K (say) is a constant.

N=K(V−IaRa/φ)

Speed of a DC Motor

• But,

(V−IaRa)=Eb

Therefore,

N=K(Eb/φ)…(3)

N∝Eb/φ ......(4)

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Hence, the speed of a DC motor is directly proportional to back emf and is inversely proportional to flux per pole.

Characteristics Of DC Series Motors

Torque Vs. Armature Current (T_a-I_a)

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This characteristic is also known as electrical characteristic.

We know that torque is directly proportional to the product of armature current and field flux,

T_a ∝ ɸ.I_a.

In DC series motors, field winding is connected in series with the armature, i.e. I_a = I_f.

Torque Vs. Armature Current (T_a-I_a)

• Therefore, before magnetic saturation of the field, flux ɸ is directly proportional to Ia. Hence, before magnetic saturation T_a α I_a². Therefore, the T_a-I_a curve is parabola for smaller values of I_a.
• After magnetic saturation of the field poles, flux ɸ is independent of armature current I_a. Therefore, the torque varies proportionally to I_a only, T ∝ I_a.Therefore, after magnetic saturation, T_a-I_a curve becomes a straight line.

• In DC series motors, (prior to magnetic saturation) torque increases as the square of armature current, these motors are used where high starting torque is required.
• Hence DC Series motor is used for traction applications.

Torque Vs. Armature Current (T_a-I_a)

Speed Vs. Armature Current (N-I_a)

• We know the relation, N ∝ Eb/ɸ
• For small load current (and hence for small armature current) change in back emf Eb is small and it may be neglected. Hence, for small currents speed is inversely proportional to ɸ. As we know, flux is directly proportional to Ia, speed is inversely proportional to Ia. Therefore, when armature current is very small the speed becomes dangerously high. That is why a series motor should never be started without some mechanical load.
• But, at heavy loads, armature current Ia is large. And hence, speed is low which results in decreased back emf Eb. Due to decreased Eb, more armature current is allowed.

Speed Vs. Torque (N-Ta)

• This characteristic is also called as mechanical characteristic. From the above two characteristics of DC series motor, it can be found that when speed is high, torque is low and vice versa.

Characteristics Of DC Shunt Motors

• Torque Vs. Armature Current (T_a-I_a)

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• In case of DC shunt motors, we can assume the field flux ɸ to be constant.
• Though at heavy loads, ɸ decreases in a small amount due to increased armature reaction.
• As we are neglecting the change in the flux ɸ, we can say that torque is proportional to armature current.

Torque Vs. Armature Current (T_a-I_a)

• Hence, the T_a-I_a characteristic for a dc shunt motor will be a straight line through the origin.
• Since heavy starting load needs heavy starting current, shunt motor should never be started on a heavy load.

Speed Vs. Armature Current (N-I_a)

• As flux ɸ is assumed to be constant, we can say N ∝ Eb.
• But, as back emf is also almost constant, the speed should remain constant.
• But practically, ɸ as well as Eb decreases with increase in load.
• Back emf Eb decreases slightly more than ɸ, therefore, the speed decreases slightly.

Speed Vs. Armature Current (N-I_a)

• Generally, the speed decreases only by 5 to 15% of full load speed.
• Therefore, a shunt motor can be assumed as a constant speed motor.
• In speed vs. armature current characteristic in the following figure, the straight horizontal line represents the ideal characteristic and the actual characteristic is shown by the dotted line.

Characteristics Of DC Compound Motor

• DC compound motors have both series as well as shunt winding.
• In a compound motor, if series and shunt windings are connected such that series flux is in direction as that of the shunt flux then the motor is said to be cumulatively compounded.
• And if the series flux is opposite to the direction of the shunt flux, then the motor is said to be differentially compounded.

Cumulative compound motor

• Cumulative compound motors are used where series characteristics are required but the load is likely to be removed completely.
• Series winding takes care of the heavy load, whereas the shunt winding prevents the motor from running at dangerously high speed when the load is suddenly removed.
• These motors have generally employed a flywheel, where sudden and temporary loads are applied like in rolling mills.

Differential Compound Motor

• Since in differential field motors, series flux opposes shunt flux, the total flux decreases with increase in load.
• Due to this, the speed remains almost constant or even it may increase slightly with increase in load (N ∝ Eb/ɸ).
• Differential compound motors are not commonly used, but they find limited applications in experimental and research work.

Necessity of Starter

• The starter is nothing but a variable resistance. Which is connected in a series with armatures winding in dc motor. Its main function is to reduce the starting current of the motor to its safe value.
• When the motor is in off condition, the armature is stationary and the back EMF which is proportional to speed is also zero.

Necessity of Starter

• In Motor armature resistance is very low. If the rated voltage is applied to the armature, it will draw heavy current many times that of full load current. And there is more possibility of damaging the armature due to heavy starting current.

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• So, we need to limit the starting current to its safe value. This is possible by inserting a resistance in series with the armature at the time of starting for a short period.

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• As the motor gains rated speed, back EMF is built up in it, and then the starting resistance could be gradually cut off in step by step.

3- Point Starter

3- Point Starter

• The Three Terminals are L, A & F
• L is known as Line terminal, which is connected to the positive supply.
• A is known as the armature terminal and is connected to the armature windings.
• F is known as the field terminal and is connected to the field terminal windings.

Working

• To start with the handle is in the OFF position when the supply to the DC motor is switched on.
• Then handle is slowly moved against the spring force to make contact with stud No. 1. At this point, field winding of the shunt or the compound motor gets supply through the parallel path provided to starting the resistance, through No Voltage Coil.
• While entire starting resistance comes in series with the armature.
• The high starting armature current thus gets limited as the current equation at this stage becomes

Working

• As the handle is moved further, it goes on making contact with studs 2, 3, 4, etc., thus gradually cutting off the series resistance from the armature circuit as the motor gathers speed.
• Finally, when the starter handle is in 'RUN' position, the entire starting resistance is eliminated, and the motor runs with normal speed.
• This is because back emf is developed consequently with speed to counter the supply voltage and reduce the armature current.

Function of No Voltage Coil (NVC)

• The field winding is supplied through NVC and field current makes it an electromagnet.

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• When the handle is at the RUN position, the soft iron piece on handle gets attracted by the magnetic force produced by NVC.

Function of No Voltage Coil (NVC)

• Whenever there is supply failure or field supply is broken then NVC loses its magnetism and unable to hold the handle.
• The spring action brings back the handle to OFF position.
• NVC perform the similar action during low voltage condition and Save the device.

Functions of Overload release (OLR)

• The motor current is supplied through OLR coil, which makes it an electromagnet.
• Below the OLR coil, there is an arm which is fixed or lying horizontally.
• At the end of the arm, a small triangular iron piece is fitted which is in the proximity of two ends of the shorting cable of NVC.

Functions of Overload release (OLR)

• It is so designed that, till the full load current OLR coil magnetism and gravitational force are balanced and OLR is unable to lift the lever.
• Whenever motor draws high current the magnetism of the OLR coil pull the arm and triangular piece of the arm shorts both point of NVC coil.
• NVC coil loses its magnetism and leaves the handle. the handle than retracts back to OFF position because of spring action. The motor will stop.

Drawbacks of Three-Point Starter

• The three-point starter suffers from a serious drawback for motors with large variation of speed by the adjustment of the field rheostat. As in the 3-point starter, the NVC is connected in series with the shunt field circuit, thus it carries the shunt field current.

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• While exercising the speed control through the field rheostat, the shunt field current may reduce to such an extent that the NVC may not be able to hold the handle in the ON position during the normal operation of the motor. This may disconnect the motor from the line, which is not desirable.

4-Point Starter

• The circuit diagram of the four-point starter is shown in the figure. It consists of a graded starting resistance to limit the starting current and is connected in series with the armature of the motor.
• The tapping points of the starting resistance are taken out to a number of studs.
• It is called 4-point starter because it has 4 terminals viz. L, N, F and A.

4 - Point Starter

4 - Point Starter

• The one end of the armature coil is connected to the terminal A and of the shunt field winding to the terminal F.

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• The other ends of the armature and the shunt field windings are directly connected to the negative terminal of the supply.

4 - Point Starter

• The no-volt trip coil (NVC) is connected directly across the line with a current limiting resistor R in series.
• The NVC is also known as under-voltage protection of the motor.
• One end of the handle is connected to the terminal L through the overload trip coil (OLC) and the other end of the handle moves against the force of control spring and makes contact with each stud during the starting period of operation.
• The starting resistance is cutting out gradually as the handle passes over each stud in clockwise direction.

4 - Point Starter

• Therefore, with this arrangement, a change in the field current for the variation of the speed of the motor does not affect the current through the NVC, as the two circuits are independent of each other.