DC Motors Quiz

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Questions and Answers

A permanent magnet DC motor with a back EMF constant (K) of $10^{-3}$ V/rpm and an armature resistance ($R_a$) of 3.5 ohms is supplied with 12V. At no load, the armature current ($I_a$) is 0.2A. What is the induced voltage (EMF)?

  • 12.7 V
  • 11.3 V
  • 3.5 V
  • 0.7 V (correct)

Using the information from the previous question (K = $10^{-3}$ V/rpm, $R_a$ = 3.5 ohms, Voltage = 12V, $I_a$ = 0.2A at no load), what is the rotor speed at no load?

  • 11300 rpm
  • 3429 rpm
  • 1200 rpm
  • 700 rpm (correct)

A permanent magnet DC motor is operating at full load with an armature current ($I_a$) of 0.83 A. Given an armature resistance ($R_a$) of 3.5 ohms, what are the copper losses?

  • 10.0 W
  • 3.5 W
  • 2.49 W (correct)
  • 2.91 W

A permanent magnet DC motor's electromagnetic torque is directly proportional to the armature current ($I_a$). If the torque/current ratio is 9.55 x $10^{-3}$ Nm/A, what is the electromagnetic torque when the armature current is 0.5 A?

<p>0.0047 Nm (B)</p> Signup and view all the answers

A permanent magnet DC motor with an armature resistance of 3.5 ohms is directly connected to a 12V source. What is the starting current?

<p>4.2 A (B)</p> Signup and view all the answers

What is the primary function of the field winding in a DC machine?

<p>To provide the excitation flux (B) for torque production. (B)</p> Signup and view all the answers

Why are DC machines considered straightforward for understanding machine operations and mathematical modeling?

<p>Because they offer relatively simple operational and modeling characteristics. (C)</p> Signup and view all the answers

In a DC machine, what component ensures the current in the conductors changes direction as the rotor rotates from one pole to another?

<p>Commutator (C)</p> Signup and view all the answers

What is the primary consequence of maintaining a constant field current in a DC machine?

<p>The torque becomes directly proportional to the armature current. (D)</p> Signup and view all the answers

What is the purpose of the commutator in a DC machine?

<p>To facilitate the transfer of current from the armature winding to an external circuit, while ensuring current direction is optimal for torque production. (D)</p> Signup and view all the answers

Which of the following is a characteristic of the armature winding in a DC machine?

<p>High volt-amp product and responsible for energy conversion (A)</p> Signup and view all the answers

What is the significance of achieving independent control of field and armature currents in an electrical machine?

<p>It allows for precise control over both the machine's torque and speed. (B)</p> Signup and view all the answers

What is the main purpose of 'commutation' in the context of DC machines?

<p>Changing the direction of current in the conductors as they move between poles. (B)</p> Signup and view all the answers

What parameters determine the electrical loading (A) in an electrical machine?

<p>The total number of slots (S), the number of conductors per slot (z), the RMS current (I), and the airgap radius (R). (D)</p> Signup and view all the answers

How does the airgap length affect the magnetic flux density (B) and the required magnetomotive force (NI) in a system with a movable slotted element carrying a conductor?

<p>A smaller airgap length (lg2) increases B and reduces the required NI. (A)</p> Signup and view all the answers

Which method relies on heavily saturating the field poles to minimize the impact of armature MMF?

<p>Utilizing a very large field MMF. (A)</p> Signup and view all the answers

What is a drawback of using a series machine to counteract armature reaction?

<p>Unstable and widely varying speeds with changing loads. (C)</p> Signup and view all the answers

In an ideal DC motor, if the magnetic loading (B) is doubled and the electrical loading (A) is halved, what is the resulting change in torque (Te), assuming the volume (V) remains constant?

<p>The torque (Te) remains the same. (D)</p> Signup and view all the answers

For a DC motor with a salient field winding tooth spanning 70% of the pole pitch, how does this affect the torque equation compared to an ideal DC motor?

<p>The torque equation is multiplied by 0.7 (70%). (D)</p> Signup and view all the answers

In a compound machine, what role does the shunt field play in mitigating armature reaction challenges?

<p>It ensures stable, constant speed by preventing sharp reductions in field flux when the load changes. (B)</p> Signup and view all the answers

How does using a separately excited machine with power electronic speed control help in managing armature reaction?

<p>It causes the armature voltage to drop as the load is applied, effectively reducing field flux and preventing instability. (D)</p> Signup and view all the answers

Based on the Lorentz force equation, $dF = B L dI$, how does increasing the magnetic flux density (B) and the length of the conductor (L) affect the force (dF) on the conductor?

<p>The force (dF) increases proportionally to the increase in B and L. (A)</p> Signup and view all the answers

What assumptions are made about magnetic flux distribution when force is acting on a conductor in a slot?

<p>All flux passes through the magnetic teeth on either side of the conductor; negligible flux passes through the slot. (D)</p> Signup and view all the answers

What is the primary operational principle behind using compensating windings to mitigate armature reaction?

<p>Mirroring the rotor winding to cancel out the armature reaction. (D)</p> Signup and view all the answers

Based on the commutation example provided, what would be the impact of increasing the machine speed to 6000 rpm, assuming all other parameters remain constant?

<p>The commutation time (tc) would halve, and di/dt would double. (B)</p> Signup and view all the answers

Given the torque equation $T_e = L \int_0^{2\pi} B(\theta) \cdot A(\theta) \cdot R^2 \cdot d\theta$, what does the integral represent?

<p>The total torque developed around the air gap circumference considering the spatial distribution of magnetic and electrical loadings. (C)</p> Signup and view all the answers

If the airgap radius (R) of an electrical machine is increased by 20%, and all other parameters (B, A, L) remain constant in the torque equation $T_e = 2 \cdot B \cdot L \cdot A \cdot R^2 \cdot \pi$, by what percentage does the torque increase?

<p>44% (B)</p> Signup and view all the answers

What is the most immediate, observable indicator of poor commutation in a DC machine?

<p>Sparking at the brushes, particularly at the trailing edge. (C)</p> Signup and view all the answers

What are the two primary factors that hinder the current reversal in the coil during commutation?

<p>Coil inductance and speed EMF induced in the coil because of armature flux. (A)</p> Signup and view all the answers

Why is the speed EMF generated in the shorted coil significant during the commutation process in a DC machine?

<p>It counteracts the Ldi/dt voltage, facilitating smoother current reversal. (B)</p> Signup and view all the answers

How do interpoles compensate for the effect of increased armature reaction flux in a DC machine when the load increases?

<p>By producing an opposing MMF (magnetomotive force) to counteract the armature reaction flux. (C)</p> Signup and view all the answers

In a DC machine with interpoles, what happens to the balance between the induced speed EMF from the interpole flux and the Ldi/dt voltage as the machine's rotational speed increases?

<p>Both the speed EMF and Ldi/dt voltage increase proportionally, maintaining a balance that supports effective commutation. (D)</p> Signup and view all the answers

What is the primary reason for connecting interpole windings in series with the armature winding in a DC machine?

<p>To ensure the interpole flux varies proportionally with the armature current, maintaining effective commutation under varying loads. (B)</p> Signup and view all the answers

What limits the size and design of DC machines regarding commutation, and what practical voltage values are typically allowed per commutator segment pair in compensated machines?

<p>Commutation requirements; up to 20V per segment pair. (C)</p> Signup and view all the answers

If the number of parallel paths in an armature winding ($c$) increases in a DC motor, how does this affect the armature current ($I_w$) for a given total armature current ($I_a$)?

<p>The armature current ($I_w$) decreases proportionally with $c$. (A)</p> Signup and view all the answers

How does the field flux ($\Phi_p$) relate to the air gap flux density ($B$) and the pole area in a DC machine?

<p>$\Phi_p$ is directly proportional to $B$ and the pole area. (D)</p> Signup and view all the answers

In a DC motor, if the ratio $\frac{\lambda_f}{\lambda_p}$ increases, how is the electromagnetic torque ($T_e$) affected, assuming all other parameters remain constant?

<p>$T_e$ increases linearly with the increase in $\frac{\lambda_f}{\lambda_p}$. (C)</p> Signup and view all the answers

What does the term $2V_{brush}i_a$ represent in the power equation of a DC machine armature circuit?

<p>Power lost due to contact voltage drop at the brushes. (A)</p> Signup and view all the answers

How is the induced EMF ($E_a$) related to the number of conductors ($Z$), flux per pole ($\Phi_p$), mechanical speed ($N_m$), and number of parallel paths ($a$) in a DC machine?

<p>$E_a = \frac{Z \cdot \Phi_p \cdot N_m \cdot p}{60a}$ (C)</p> Signup and view all the answers

In a DC motor, if the armature current ($i_a$) increases while the armature resistance ($R_a$) remains constant, what happens to the power lost in the armature resistance?

<p>The power lost increases quadratically. (B)</p> Signup and view all the answers

What is the relationship between the electromagnetic torque ($T_e$) and the armature current ($I_a$) in a DC motor, assuming the flux per pole ($\Phi_p$) remains constant?

<p>$T_e$ is directly proportional to $I_a$. (A)</p> Signup and view all the answers

If the mechanical speed of rotation ($N_m$) of a DC motor doubles, how does this affect the induced EMF ($E_a$), assuming all other factors remain constant?

<p>$E_a$ doubles. (B)</p> Signup and view all the answers

In the power segregation of a DC machine, what is the initial power input to the armature circuit represented by?

<p>Terminal power ($V_a i_a$). (D)</p> Signup and view all the answers

How does the total number of conductors ($Z$) in a DC machine relate to the torque ($T_e$), assuming all other factors including armature current ($I_a$) and flux per pole ($\Phi_p$) are constant?

<p>Torque ($T_e$) is directly proportional to $Z$. (C)</p> Signup and view all the answers

Flashcards

Speed EMF

Electromotive force induced by the armature rotation, opposing current change.

Interpoles

Windings added to motors to aid in commutation by generating opposing flux.

Commutation

The process of reversing the direction of current in the armature of a DC motor.

Di/dt

Rate of change of current with respect to time, crucial for motor operation.

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Armature reaction flux

The effect of armature current on the distribution of magnetic field in a machine.

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Electromagnetic Torque

The torque produced by the electromagnetic interaction in electrical machines.

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Voltage Induced in Armature

The voltage generated in the armature winding based on rotor speed and back EMF.

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Input Power

The total power supplied to the motor from the DC source.

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Copper Losses

Power loss in the armature due to its resistance and current.

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Motor Efficiency

The ratio of output power to input power, indicating performance efficiency.

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Electrical Loading

Total effective (RMS) current per unit length in machine's air gap.

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RMS Current

Root mean square current value, represents effective current.

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Torque in Electrical Machines

Torque produced by the magnetic field on current-carrying conductors.

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Lorentz Equation

Describes the force on a current-carrying conductor in a magnetic field.

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Torque Development in DC Motors

Torque equation combines electrical and magnetic loading with volume.

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Magnetic Loading

Amount of magnetic flux per unit area in a motor's air gap.

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Conductors in Slots

Conductors create a force in the magnetic circuit of a motor.

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Torque Equation Components

Formula linking torque to electrical and magnetic factors and volume.

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DC Machine

An electrical machine that operates using direct current, with field and armature windings.

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Field Winding

The winding on the stator providing excitation flux for torque production.

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Armature Winding

The winding on the rotor that generates torque via current; linked to machine's terminals through a commutator.

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Operating Characteristics

The performance specifications and behaviors of a DC machine under various conditions.

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Constant Field Current

Maintaining a steady field current allows direct proportionality of torque to armature current in DC machines.

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Armature Reaction

The effect of the armature current on the distribution of the magnetic field in a machine.

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Field MMF

Magnetomotive force produced by the field winding in an electrical machine.

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Separately Excited Machine

A type of machine where the field winding is energized independently of the armature.

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Under-commutation

A faulty commutation where current jumps from commutator to brush, causing sparking.

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Coil Inductance

The property of a coil that causes it to resist changes in current.

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Armature Current (𝑖𝑎)

The current flowing through the armature windings of a DC motor.

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Field Current (𝑖𝑓)

The current used to produce a magnetic field in a DC motor.

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Total Conductors (Z)

The total number of conductors in the armature of the machine.

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Number of Slots (S)

Total number of slots available on the armature of the motor.

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Torque (Te)

The rotational force produced by the motor, calculated based on various parameters.

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Back EMF (Ea)

Electromotive force generated by the motor opposing the applied voltage.

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Flux per Pole (𝜙𝑝)

The magnetic flux linked with the armature winding per magnetic pole.

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Parallel Paths (c)

Number of parallel paths in the armature winding of a DC motor.

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Power Conversion Equation

Equation relating armature voltage, current, and torque for energy balance.

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Mechanical Speed (Nm)

The speed at which the motor's rotor turns, measured in revolutions per minute (rev/min).

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Study Notes

EE 261 - Asynchronous and DC Machines

  • This course covers asynchronous and DC machines.
  • The lecturer is Ing. Francis Boafo Effah, PhD.
  • The course is part of the provision of quality education (SDG 4).
  • The course is offered at KNUST, ranking No. 1 globally

Unit 2 - DC Machines

  • This unit focuses on DC machine characteristics.
  • Topics included are:
    • Principles of operation
    • The commutator
    • Equivalent circuit
    • Winding connections
    • Operating characteristics
    • Torque and size

DC Machine Basics (1)

  • The DC machine has two windings.
  • Field winding is generally on the stator providing excitation flux (“B”).
  • Armature winding is generally on the rotor providing the current (“I”).
  • The commutator ensures orthogonal field and torque-producing currents.

DC Machine Basics (2)

  • DC machines are straightforward regarding electrical machine operations and modelling.
  • The field current can be maintained constant for control, giving a constant field.
  • Torque is directly proportional to armature current.
  • In an ideal machine, the field and armature currents would be independently controlled.

The Commutator (1)

  • The commutator is essential for DC machines, ensuring correct current direction for net positive torque.
  • As the rotor rotates, conductors move between poles changing the sign of "B".
  • The current direction in conductors must change to maintain the direction of force and torque.
  • This process is known as commutation.

The Commutator (2)

  • Diagrams showing the commutator and brushes.
  • The provided link is a YouTube video about the commutator.

The Commutator (3)

  • Currents in the conductor change direction frequently, causing high di/dt.
  • This high di/dt is related to inductance and creates large associated voltages.
  • Brush contact drops are typically 1V and often neglected in calculations.

Equivalent Circuit

  • Presents the equivalent circuit equations for DC machines.
  • Included are diagrams of the equivalent circuit.

Winding Connections (1,2)

  • Describes different winding connections (separately excited, series, shunt, compound).
  • Diagrams show the different circuits.

Operating Characteristics (1)

  • Covers mechanical and electrical power conversion in DC machines.
  • Explains the torque equation and generated EMF with equations.

Operating Characteristics (2)

  • Discusses constant torque or constant field operation.
  • Explains how armature voltage increases with speed at constant field.
  • Discusses the methods for limiting current flow during operation from fixed DC voltage source.

Operating Characteristics (3)

  • Provides an example of a 35 kW, 440 V DC machine.
  • Shows typical armature current and zero speed current values.
  • Discusses different operational techniques for DC machines.

Operating Characteristics (4)

  • Explains constant power region of operation.
  • Discusses how increasing speed in this region is achieved by reducing the field current.
  • Torque reduction is inversely proportional to the increase in speed.

Torque in a DC Motor

  • Discusses definitions of torque produced by an electrical machine.
  • Covers torque production physics.
  • Provides discussions on practical issues, such as the relationship between copper and iron in machines.

Definitions

  • Defines magnetic loading as the average airgap flux density per pole.
  • Defines electrical loading as effective (root mean square) current per unit length of airgap periphery.

Torque in an Electrical Machine

  • Explains the concept of force in an orthogonal field based on Lorentz Equation.
  • Presents the equation for torque produced at a radius and explains figures.
  • Provides an equation for the torque produced by a machine.

Torque in an Ideal DC Motor

  • Contains an equation for the torque developed in an ideal DC motor.
  • Defines current and magnetic loading.

Conductors in Slots

  • Discusses how magnetic circuits provide forces on conductors.
  • Explaining flux directions and forces on conductors in slots.

Conflict between copper and iron

  • Discusses the conflict between conductor area and the maximum air gap flux density (limited by iron saturation).
  • Explains how maximizing force involves optimal design of conductors and teeth spacing.

Summary

  • Summarizes the key points regarding the relationship between torque, volume, electrical, and magnetic loading.
  • Emphasizes the importance of high flux density, conductor placement, and efficient steel utilization.

DC Machines

  • Outlines winding arrangements, torque and EMF, and EMF as a function of field current.

DC Machine Windings

  • Explains the differences between lap and wave windings regarding parallel paths and brushes.

Torque and Back EMF (1, 2, 3)

  • Defines important parameters (armature current, field current, total number of slots, conductor per slot, air gap, poles, etc.) relevant to DC motor torque and Back EMF calculations.
  • Presents equations for torque and flux calculation.

Torque and Back EMF (4)

  • Presents power segregation equations for DC machines.

Torque and Back EMF (5)

  • Provides equations relating electromagnetic force to mechanical speed, number of poles and winding parameters.

Example

  • Presents an example problem and its solution for calculating torque, speed, and terminal voltage.

Simple Test to determine E and Ka (1, 2, 3)

  • Outlines a simple test for determining generated EMF (E) and the constant Ka related to a DC machine.
  • Explains diagrams corresponding to the simple test.

Non-linearities in DC Machines

  • Lists specific non-linearity characteristics of DC machines like armature reaction.

Armature Reaction (1, 2, 3, 4, 5, 6)

  • Presents diagrams/figures related to armature reaction (MMF and flux) discussions
  • Explains how armature reaction opposes or aids in the field flux in different half- sections of the pole.
  • Discusses why practical consideration of armature reaction is required.
  • Indicates problems with armature reaction in shunt motors concerning speed, current, and force.
  • Presents solutions to armature reaction problems in different motor configurations.

Commutation (1, 2, 3, 4)

  • Explains how commutation, including the concept of coil current, occurs.
  • Includes explanations of possible problems related to commutation and solutions.

Adding Interpoles (1, 2, 3 ,4)

  • Presents conceptual diagrams explaining how interpole winding functions.
  • Describes how interpoles help with commutation.
  • Explains how interpoles contribute to reducing commutation problems.

Power and Commutation (1, 2, 3)

  • Describes why there are limitations to the size of DC machines.
  • Provides equations for maximum induced voltage between commutator segments and average voltage per turn in DC machines.

Starting of DC Motor

  • Explains how starting current is limited for large DC motors.
  • Indicates factors contributing to current limit for various DC motors during start.

Grading Starting Resistance (for Shunt and Separately Excited Motors)

  • Describes the need for graded resistance for smooth motor starting.
  • Outlines the sequence of cutting out resistances per step for n sections of resistance in series.

Manual Starters (Faceplate, Drum Controller)

  • Describes manual starters (faceplate and drum type).
  • Explains their working mechanism.

Automatic Starters (Direct-on-line)

  • Discusses how automatic starters operate using push-buttons and contactors.

DC Machines Exercises

  • Provides example exercise problems with multiple sections and their expected solutions.

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