DC Motor Principle MCQ Quiz - Objective Question with Answer for DC Motor Principle - Download Free PDF

Explanation:

Characteristic Equation of Armature Controlled DC Motor

Definition: The characteristic equation of a system represents the mathematical relationship between input and output variables, governing the system's dynamic behavior. For an armature-controlled DC motor, the characteristic equation is derived based on the electrical and mechanical dynamics of the motor.

Working Principle: In an armature-controlled DC motor, the armature voltage is varied to control the motor's speed, while the field current is kept constant. The motor's behavior can be described by equations that relate the electrical and mechanical components, including the armature circuit, back EMF, torque, and rotational dynamics.

The system's characteristic equation is typically obtained from the transfer function, which is derived using Kirchhoff's Voltage Law (KVL) for the armature circuit and Newton's Second Law for rotational dynamics.

Mathematical Derivation:

For an armature-controlled DC motor:

• Armature Circuit: Applying KVL:
  \( V_a = I_aR_a + L_a\frac{dI_a}{dt} + E_b \)
  Where:
  • \( V_a \): Armature voltage
  • \( I_a \): Armature current
  • \( R_a \): Armature resistance
  • \( L_a \): Armature inductance
  • \( E_b \): Back EMF (\( E_b = K_e\omega \))
  • \( \omega \): Angular velocity
  • \( K_e \): Motor constant
• Mechanical Equation: Using Newton's Second Law:
  \( J\frac{d\omega}{dt} + B\omega = T \)
  Where:
  • \( J \): Moment of inertia
  • \( B \): Damping coefficient
  • \( \omega \): Angular velocity
  • \( T \): Developed torque (\( T = K_tI_a \))
  • \( K_t \): Torque constant

Combining these equations and eliminating intermediate variables results in a first-order differential equation relating the system's input (\( V_a \)) to its output (\( \omega \)). This equation represents the characteristic equation of the armature-controlled DC motor.

Correct Option Analysis:

The correct option is:

Option 1: First order equation

This option correctly represents the characteristic equation of an armature-controlled DC motor. The system dynamics involve the electrical and mechanical components, which combine to form a first-order differential equation. The inductance of the armature and the moment of inertia contribute to this first-order behavior.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: Second order equation

This option is incorrect because the characteristic equation of the armature-controlled DC motor is not second-order. A second-order system requires two energy storage elements (e.g., inductance and capacitance in an electrical system or inertia and elasticity in a mechanical system). In this case, the motor's dynamics involve only one energy storage element, resulting in a first-order system.

Option 3: Zero order equation

A zero-order equation implies that the output is directly proportional to the input without any dynamic behavior. This is not applicable to an armature-controlled DC motor, as the motor exhibits dynamic behavior governed by differential equations involving time-dependent terms.

Option 4: Third order equation

A third-order equation would arise in systems with three energy storage elements or complex dynamics involving higher-order derivatives. The armature-controlled DC motor does not exhibit such complexity, as its dynamics are adequately described by a first-order equation.

Conclusion:

The armature-controlled DC motor's characteristic equation is first-order, as derived from the combination of electrical and mechanical equations governing the motor's dynamics. Understanding these dynamics is crucial for designing control systems and analyzing motor performance. Other options are incorrect as they do not accurately represent the system's behavior.

The correct answer is option "3"

Concept:

• Fleming's Left-Hand Rule is a mnemonic used to predict the direction of force experienced by a current-carrying conductor placed in a magnetic field.
• This rule is particularly useful in contexts such as electric motors. The rule is named after John Ambrose Fleming, a British engineer and physicist.
• To use Fleming's Left-Hand Rule, extend the thumb, forefinger, and middle finger of your left hand so that they are mutually perpendicular (at right angles) to each other.
• Each finger then represents a different component of the motion:
  • Thumb represents the direction of the Force (or thrust) acting on the conductor. In the case of a motor, this would be the direction of motion of the conductor.
  • Forefinger represents the direction of the external Magnetic Field (B field). This is the direction from the north pole to the south pole of the magnetic field in which the conductor is placed.
  • Middle Finger represents the direction of the Current (I) flowing through the conductor. This is the direction from the positive to the negative potential (conventional current direction).
• Thus, when a conductor carries a current through a magnetic field, it experiences a force perpendicular to both the direction of the magnetic field and the current. This is encapsulated in the physical principle known as the Lorentz force.
• Fleming's Left-Hand Rule is especially instrumental in understanding and designing electric motors, where an electric current and magnetic field interact to produce motion.
• It's also a mirror principle to Fleming's Right-Hand Rule, which is used for generators to determine the direction of induced current when a conductor moves within a magnetic field.

The direction of rotation of the DC motor conductor can be determined by Fleming's left-hand rule.

Fleming's left-hand rule:

• This method is used to find the direction of the force on the conductor put in a magnetic field when the direction of the magnetic field and current is known.
• According to this rule, if we arrange our thumb, forefinger, and middle finger of the left-hand perpendicular to each other then the thumb points towards the direction of the magnetic force, the forefinger points toward the direction of the magnetic field, and the middle finger points towards the direction of the current.

Additional Information

•  Fleming's right-hand rule is used in DC generators to determine the direction of induced current in the conductors.
• Lenz's law determines the direction of induced emf in the transformers.
• Faraday's law is used to determine the magnitude of induced emf in the transformers.

Conversion of energy by electrical machine:

1.) Motor:

• It converts electrical energy into mechanical energy.
• It works on Fleming's Left-hand rule.

2.) Generator:

• It converts electric energy from mechanical rotary motion into electric energy 
• It works on Fleming's Right-hand rule.

3.) Transformer:

• It is used to transfer power from one circuit to another without a change in frequency.
• It works on Faraday's Law of electromagnetic induction

Commutator in DC machine:

• The commutator on the DC generator converts the AC into pulsating DC.
• In the case of a DC generator, the induced EMF is AC in nature. To convert the AC-induced EMF into the required DC, a commutator is required.
• In the case of a DC motor, the input to the motor must be DC in nature, but the available supply is AC in nature. So, to convert the AC supply into DC for the motor operation, commutators are used.
• The other function of the commutator in the DC machine is to collect the current from the armature conductor as well as supply the current to the load using brushes.
• DC generator produces electrical power from mechanical input whereas DC motor produces mechanical power from an electrical input.
• As per requirements, the same DC machine can be operated as a DC generator or DC motor.

CONCEPT:

• Fleming's left-hand rule: When we arrange three fingers (point, middle, and thumb) as such all three are perpendicular to each other. Then,
  • The pointer finger points in the direction of the magnetic field.
  • The middle finger points in the direction of the current.
  • The thumb points in the direction of the magnetic thrust of force.

EXPLANATION:

• Fleming’s left hand is used to find the direction of force or motion acting on the moving coil in the DC motor.
• Electric motors have magnets, a coil, and use electricity to move.

So option 2 is correct.

Important Point

• Loudspeakers, Dynamos, and Microphones are also based on Fleming's left-hand rule.

Mistake Point

• DC Generators use Fleming's right-hand rule to find the direction, not use Fleming’s left-hand rule.

The direction of rotation of the DC motor conductor can be determined by Fleming's left-hand rule.

Fleming's left-hand rule:

• This method is used to find the direction of the force on the conductor put in a magnetic field when the direction of the magnetic field and current is known.
• According to this rule, if we arrange our thumb, forefinger, and middle finger of the left-hand perpendicular to each other then the thumb points towards the direction of the magnetic force, the forefinger points toward the direction of the magnetic field, and the middle finger points towards the direction of the current.

Additional Information

•  Fleming's right-hand rule is used in DC generators to determine the direction of induced current in the conductors.
• Lenz's law determines the direction of induced emf in the transformers.
• Faraday's law is used to determine the magnitude of induced emf in the transformers.

Commutator in DC machine:

• The commutator on the DC generator converts the AC into pulsating DC.
• In the case of a DC generator, the induced EMF is AC in nature. To convert the AC-induced EMF into the required DC, a commutator is required.
• In the case of a DC motor, the input to the motor must be DC in nature, but the available supply is AC in nature. So, to convert the AC supply into DC for the motor operation, commutators are used.
• The other function of the commutator in the DC machine is to collect the current from the armature conductor as well as supply the current to the load using brushes.
• DC generator produces electrical power from mechanical input whereas DC motor produces mechanical power from an electrical input.
• As per requirements, the same DC machine can be operated as a DC generator or DC motor.

Concept:

Commutator:

• In the case of the DC generator, the commutator is used to convert generated AC in armature into DC.
• In the case of the DC motor, the commutator is used to convert DC to A.C.
• Due to the limitation of commutator dc generators are not usually designed beyond 650 V

• The physical connection to the armature winding is made through a commutator-brush arrangement.
• The function of a commutator in a dc generator is to collect the current generated in armature conductors.
• While in the case of a dc motor, the commutator helps in providing current to the armature conductors.
• A commutator consists of a set of copper segments which are insulated from each other.
• The number of segments is equal to the number of armature coils. Each segment is connected to an armature coil and the commutator is keyed to the shaft.

DC Machine:

The above figure shows the constructional details of a simple 4-pole DC machine.

A DC machine consists of two basic parts: stator and rotor.

Basic constructional parts of a DC machine:

Yoke:

• The outer frame of a dc machine is called as the yoke.
• It is made up of cast iron or steel.
• It not only provides mechanical strength to the whole assembly but also carries the magnetic flux produced by the field winding.

Poles and pole shoes:

• Poles are joined to the yoke with the help of bolts or welding.
• They carry field winding and pole shoes are fastened to them.
• Pole shoes serve two purposes: (i) they support field coils and (ii) spread out the flux in the air gap uniformly.

Field winding:

• They are usually made of copper.
• Field coils are a former wound and placed on each pole and are connected in series.
• They are wound in such a way that, when energized, they form alternate North and South poles.

Armature core:

• The armature core is the rotor of a dc machine. It is cylindrical in shape with slots to carry armature winding.
• The armature is built up of thin laminated circular steel disks for reducing eddy current losses.
• The armature core is made of silicon steel laminations that are insulated from each other by insulating varnish coating. These laminations are used to reduce eddy current losses.
• It may be provided with air ducts for the axial airflow for cooling purposes.
• The armature is keyed to the shaft.

Armature winding:

• It is usually a former wound copper coil which rests in armature slots.
• The armature conductors are insulated from each other and also from the armature core.
• Armature winding can be wound by one of the two methods; lap winding or wave winding.
• Double layer lap or wave windings are generally used. A double layer winding means that each armature slot will carry two different coils.

Brushes:​

• Brushes are usually made from carbon or graphite.
• They rest on commutator segments and slide on the segments when the commutator rotates keeping the physical contact to collect or supply the current.

Concept:

For lap wound, the number of parallel path (A) is equal to the number of poles (P)

Explanation:

Armature current in the each parallel path = I/A \({I_A} = \frac{I}{A}\) 

Where,

A= No. of parallel paths

In this case A=4 for lap connected winding

So, current in armature conductor = 10 A​
\({N_S} = \frac{{120f}}{P} = 600 rpm\)

 f = 20 H. 

so, T = 50 msec with straight line commutation.

When dc current passes through simulator and goes inside armature, its shape will be that of shown is option (C)

Torque of D.C. Motor:

Torque is meant the turning or twisting moment of a force about an axis.

Torque is the turning moment of a force about an axis and is measured by the product of force (F) and radius (r) at a right angle to which the force acts i.e.
D.C. Motors

In a DC Motor, each conductor is acted upon by a circumferential force F at a distance r, the radius of the armature as shown below.

T = F × r.

Let in a DC Motor
r = average radius of armature in m
\(l\) = effective length of each conductor in m
Z = total number of armature conductors
A = number of parallel paths
i = current in each conductor = Ia/A
B = average flux density in Wb/m2
ϕ = flux per pole in Wb
P = number of poles

Force on each conductor, (F) = \(\large{B\ i\ l}\) newtons

Torque due to one conductor = F × r newton- meter

Total armature torque, (T_a) = Z F r newton- meter

∴ \(\large{T_a=ZBilr}\) newton- meter ... (1)

Now,

i = I_a/A, (current in each conductor)

B = ϕ/a; where a is the x-sectional area of flux path per pole a radius r.

And, \(\large{a=\frac{2\pi rl}{P}}\)

Substitute these values in equation (1),

\(\large{T_a=Z\times \frac{ϕ}{a}\times \frac{I_a}{A}\times l\times r}\)

\(\large{T_a=Z\times \frac{ϕ}{2\pi rl/P}\times \frac{I_a}{A}\times l\times r}\)

\(\large{T_a=0.159Zϕ I_a\times(\frac{P}{A})}\)

Since, number of Poles (P) and number of the parallel paths (A) is constant,

∴ T_a ∝ ϕ Ia

(i) For a shunt motor, flux ϕ is practically constant

∴ T_a ∝ ϕ I_a

(ii) For a series motor, flux ϕ is directly proportional to armature current Ia provided magnetic saturation does not take place.

∴ T_a ∝ (I_a)²

Concept:

Commutator:

• In the case of the DC generator, the commutator is used to convert generated AC in armature into DC.
• In the case of the DC motor, the commutator is used to convert DC to A.C.
• Due to the limitation of commutator dc generators are not usually designed beyond 650 V

• The physical connection to the armature winding is made through a commutator-brush arrangement.
• The function of a commutator in a dc generator is to collect the current generated in armature conductors.
• While in the case of a dc motor, the commutator helps in providing current to the armature conductors.
• A commutator consists of a set of copper segments which are insulated from each other.
• The number of segments is equal to the number of armature coils. Each segment is connected to an armature coil and the commutator is keyed to the shaft.

DC Machine:

The above figure shows the constructional details of a simple 4-pole DC machine.

A DC machine consists of two basic parts: stator and rotor.

Basic constructional parts of a DC machine:

Yoke:

• The outer frame of a dc machine is called as the yoke.
• It is made up of cast iron or steel.
• It not only provides mechanical strength to the whole assembly but also carries the magnetic flux produced by the field winding.

Poles and pole shoes:

• Poles are joined to the yoke with the help of bolts or welding.
• They carry field winding and pole shoes are fastened to them.
• Pole shoes serve two purposes: (i) they support field coils and (ii) spread out the flux in the air gap uniformly.

Field winding:

• They are usually made of copper.
• Field coils are a former wound and placed on each pole and are connected in series.
• They are wound in such a way that, when energized, they form alternate North and South poles.

Armature core:

• The armature core is the rotor of a dc machine. It is cylindrical in shape with slots to carry armature winding.
• The armature is built up of thin laminated circular steel disks for reducing eddy current losses.
• The armature core is made of silicon steel laminations that are insulated from each other by insulating varnish coating. These laminations are used to reduce eddy current losses.
• It may be provided with air ducts for the axial airflow for cooling purposes.
• The armature is keyed to the shaft.

Armature winding:

• It is usually a former wound copper coil which rests in armature slots.
• The armature conductors are insulated from each other and also from the armature core.
• Armature winding can be wound by one of the two methods; lap winding or wave winding.
• Double layer lap or wave windings are generally used. A double layer winding means that each armature slot will carry two different coils.

Brushes:​

• Brushes are usually made from carbon or graphite.
• They rest on commutator segments and slide on the segments when the commutator rotates keeping the physical contact to collect or supply the current.

Field’s test:

• This test is applicable to two similar DC series motors of large capacity
• Series motors which are mainly used for traction work are easily available in pairs
• The two machines are coupled mechanically
• One machine runs normally as a motor and drives generator whose output is wasted in a variable load R
• Iron and friction losses of two machines are made equal by joining the series field winding of the generator in the motor armature circuit so that both machines are equally exciting and by running them at equal speed
• Load resistance R is varied till the motor current reaches its full-load value indicated by ammeter A1
• After this adjustment for full-load current, different ammeter and voltmeter readings are noted

Conversion of energy by electrical machine:

1.) Motor:

• It converts electrical energy into mechanical energy.
• It works on Fleming's Left-hand rule.

2.) Generator:

• It converts electric energy from mechanical rotary motion into electric energy 
• It works on Fleming's Right-hand rule.

3.) Transformer:

• It is used to transfer power from one circuit to another without a change in frequency.
• It works on Faraday's Law of electromagnetic induction

• An electric motor is an electrical machine that converts electrical energy into mechanical energy.
• Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate force in the form of rotation of a shaft.
• An electric generator is mechanically identical to an electric motor, but operates in the reverse direction, converting mechanical energy into electrical energy.
• Transformer is a device, which is used to transform power at the same frequency.