DC Machines

Introduction and Context

Direct-current (DC) machines are electromechanical energy converters that transform mechanical energy into electrical energy as generators, or electrical energy into mechanical energy as motors. Although many large modern systems use AC machines and power electronic converters, DC machines remain important in laboratories, traction training systems, hoists, rolling mills, battery-powered equipment, actuators, and applications requiring a wide and easily controlled speed range.

The essential feature of a conventional DC machine is the interaction between a stationary magnetic field and current-carrying conductors on a rotating armature. A commutator and brushes provide mechanical rectification: they convert the internally alternating armature emf into unidirectional terminal voltage in generator operation, and ensure approximately unidirectional torque in motor operation.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Identify the constructional parts and operating principles of DC machines.
2. Distinguish shunt, series, compound, separately excited, and permanent-magnet excitation.
3. Derive and apply the emf and torque equations.
4. Explain armature reaction, commutation, and methods of improvement.
5. Interpret generator and motor characteristics.
6. Explain starting, speed control, braking, losses, efficiency, and testing.
7. Select appropriate DC-machine arrangements for industrial applications.

1. Construction of a DC Machine

A DC machine may operate as either a motor or generator because the same electromechanical energy-conversion principle applies in both directions. Its principal parts are as follows.

Yoke

The yoke is the outer frame. It provides mechanical support, protects internal components, and carries part of the magnetic flux. In small machines it is commonly made of cast iron or fabricated steel; larger machines generally use rolled or welded steel.

Poles and field system

Each pole consists of a pole core and pole shoe. The pole shoe spreads flux over the armature surface and reduces magnetic reluctance. Field windings placed around the poles produce the main magnetic field. A separately excited field winding receives power from an external source; a self-excited winding receives power from the machine itself.

Armature core

The armature core is a laminated cylindrical rotor mounted on a shaft. Laminations, usually made of silicon steel, reduce eddy-current loss. Slots on the core carry the armature conductors. The core provides a low-reluctance path for magnetic flux and supports the conductors mechanically.

Armature winding

The winding is placed in the armature slots. In a lap winding, the number of parallel paths is approximately equal to the number of poles, making it suitable for low-voltage, high-current machines. In a wave winding, the number of parallel paths is normally two, making it suitable for higher-voltage, lower-current machines.

Commutator and brushes

The commutator consists of insulated copper segments connected to armature coils. Carbon or graphite brushes press against the segments and conduct current between the rotating armature and the stationary external circuit. The commutator switches coil connections at appropriate positions so that torque remains unidirectional in motor operation.

Bearings, shaft, and ventilation

Bearings support the shaft, while a fan or ventilation passages remove heat. Mechanical alignment, brush pressure, commutator surface condition, and insulation integrity strongly affect reliability.

2. Operating Principles and Fundamental Equations

Generator action

When an armature conductor moves through magnetic flux, an emf is induced according to Faraday’s law. The generated emf is proportional to flux per pole, rotational speed, and the number of effective conductors.

Here, E_g is generated emf in volts, P is the number of poles, Φ is flux per pole in webers, Z is the total number of armature conductors, N is speed in revolutions per minute, and A is the number of parallel paths. This equation assumes a uniform average flux and applies to a conventional machine under steady operation.

For a lap winding, A=P; for a simplex wave winding, A=2. Thus, in general,

where ω is angular speed in radians per second and k_e is a machine constant. The two forms are equivalent when the winding and unit conventions are used consistently.

Motor action

When armature current flows in a magnetic field, each conductor experiences a force. The combined effect produces electromagnetic torque. The motor develops a back emf opposing the applied voltage:

where V is terminal voltage, E_b is back emf, I_a is armature current, R_a is armature-circuit resistance, and V_br represents brush voltage drop. If brush drop is neglected, V = E_b + I_a R_a.

The electromagnetic torque is

where T_e is electromagnetic torque in newton-metres and k_t is the torque constant when SI units are used. In a consistent SI model, the numerical values of the torque and emf constants are equal: k_t = k_e. Mechanical output torque is lower than electromagnetic torque because of friction, windage, and other rotational losses.

The approximate speed relation is

This relation is valid when the machine constant and winding are fixed. It explains why speed rises when field flux is weakened and falls when armature voltage is reduced.

Power conversion

The converted electromagnetic power is

The generator expression uses generated emf and armature current; the motor expression uses back emf and armature current. In both cases, the equality with torque–speed power assumes SI units and neglects sign-convention differences.

3. Excitation Systems

Separately excited machine

The field winding is supplied by an independent DC source. Flux can be controlled without depending directly on terminal voltage, giving excellent control flexibility. This arrangement is common in laboratory drives and controlled industrial systems.

Shunt machine

The shunt field winding is connected in parallel with the armature terminals. It has many turns of fine wire and high resistance. A shunt motor has nearly constant speed because its flux remains approximately constant over its normal operating range.

Series machine

The series field is connected in series with the armature and carries the full armature current. It has relatively few turns of thick wire. A series motor produces high starting torque, but it must never be operated without mechanical load: under no-load conditions its flux may become weak and speed can rise to a dangerous value.

Compound machine

A compound machine has both shunt and series field windings. In cumulative compounding, the series field reinforces the shunt field, improving torque and voltage regulation. In differential compounding, it opposes the shunt field; this may cause unstable characteristics and is rarely selected for ordinary drives.

Permanent-magnet DC machine

Permanent magnets supply the field flux, eliminating field copper loss and simplifying construction. These machines are widely used in low- and medium-power servo systems, automotive actuators, toys, and battery equipment. Their flux cannot be adjusted over a wide range, and magnets may suffer thermal demagnetization.

4. Armature Reaction

Armature current produces its own magnetomotive force. This armature field distorts and may weaken the main field. The effects include:

• flux distortion and unequal flux density under pole faces;
• shift of the magnetic neutral axis;
• reduction of generated emf or torque-producing flux;
• increased tendency toward sparking at the brushes.

In a generator, the magnetic neutral axis is the location where coil emf is ideally zero during commutation. Armature reaction shifts this axis. If brushes remain in their original position, commutation becomes imperfect.

Compensating measures include interpoles, compensating windings, brush adjustment, and suitable magnetic-circuit design. Interpoles are small poles between the main poles and are connected in series with the armature, so their corrective flux increases with load current. Compensating windings embedded in the pole shoes counteract armature mmf directly under the pole arc and are used in machines subject to severe load changes.

5. Commutation

Commutation is the reversal of current in an armature coil while that coil passes under a brush. Ideally, current reverses without sparking. In practice, the coil possesses inductance, so its current cannot change instantaneously. The resulting reactance emf can cause sparking, brush wear, radio interference, and commutator damage.

Good commutation depends on correct brush position, adequate brush material and pressure, smooth commutator surfaces, appropriate interpole strength, and sound insulation. Excessive brush pressure increases friction; insufficient pressure causes intermittent contact. Carbon brushes are commonly used because their relatively high resistance helps equalize current and improves commutation.

6. DC Generator Characteristics

A separately excited generator has a terminal voltage that generally decreases with load because of armature resistance drop, brush drop, and armature reaction. A shunt generator can build up voltage only if residual magnetism exists, the field connection aids the residual flux, and the field resistance is below the critical field resistance at the operating speed.

The open-circuit characteristic (OCC) plots generated emf against field current at constant speed. It initially rises approximately linearly and then bends because of magnetic saturation. The external characteristic plots terminal voltage against load current. Series generators can show a rising voltage characteristic over a limited range, while compound generators can be designed for nearly constant terminal voltage.

Voltage regulation of a generator is commonly defined as

Here, voltages are measured at the same speed and field setting, and the sign indicates voltage drop for a typical generator. The definition may vary by convention, so the adopted convention should always be stated.

7. DC Motor Characteristics

Shunt motor

With approximately constant flux, torque is proportional to armature current:

Its speed is nearly constant from no-load to full-load, making it suitable for machine tools, fans, conveyors, and pumps requiring moderate starting torque.

Series motor

Before saturation, flux is approximately proportional to armature current, so

After magnetic saturation, flux is nearly constant and torque becomes approximately proportional to armature current. The series motor is suitable for cranes, hoists, elevators, and traction because of its high starting torque.

Compound motor

A cumulative compound motor combines good starting torque with better speed regulation than a series motor. It is useful where load torque changes substantially but excessive speed variation is undesirable.

8. Starting of DC Motors

At standstill, N=0, so back emf is initially zero. The armature current would therefore be

if no starting resistance were inserted. Since armature resistance is small, this current could be many times rated current and damage the commutator, winding, or supply system.

A starter inserts external resistance in series with the armature and gradually removes it as speed and back emf rise. Three-point and four-point starters also provide no-volt and overload protection. Modern drives use controlled rectifiers or choppers to provide a controlled voltage ramp, current limiting, and electronic protection.

The starting torque is

Consequently, limiting starting current also limits starting torque. The appropriate current limit must be high enough to accelerate the load but low enough to protect the machine.

9. Speed Control

Field control

Reducing field current weakens flux and increases speed according to the speed relation. This method provides speeds above base speed but must respect the maximum permissible speed and commutation limits. Field weakening reduces available torque for a given armature current.

Armature-voltage control

Changing armature voltage gives efficient control below base speed while maintaining approximately constant flux. Ward–Leonard systems historically used a motor-generator set; modern systems use semiconductor converters.

Armature-resistance control

Adding resistance in series with the armature reduces speed, but power is dissipated as heat. It is simple but inefficient and gives poor speed regulation, so it is mainly used for short-duration or low-power applications.

A practical drive normally uses armature-voltage control in the constant-torque region and field weakening in the constant-power region. The transition is constrained by rated current, rated voltage, thermal capacity, commutation, and maximum mechanical speed.

10. Braking

Regenerative braking

During regenerative braking, the machine operates as a generator and returns energy to the supply or DC link. It is efficient when the electrical system can accept the returned energy.

Dynamic or rheostatic braking

The armature is disconnected from the supply and connected to a resistor. Kinetic energy is converted into electrical energy and dissipated as heat. Braking torque decreases as speed falls.

Plugging

The supply polarity or armature connections are reversed while the motor is running, producing a torque opposite to rotation. A resistor must limit current, and the supply must be disconnected near zero speed; otherwise the motor will accelerate in the reverse direction. Plugging is rapid but wasteful and mechanically stressful.

11. Losses, Efficiency, and Heating

Losses are classified as:

• Copper losses: armature, field, and brush-contact losses;
• Core losses: hysteresis and eddy-current losses;
• Mechanical losses: bearing friction, brush friction, and windage;
• Stray-load losses: additional load-dependent losses caused by flux distortion and leakage.

For a motor,

For a generator, efficiency is output electrical power divided by mechanical input power. The exact input and output quantities must be identified before calculating efficiency. Heating limits continuous rating, so a short-time overload may be permissible even though the same current cannot be sustained continuously.

12. Testing of DC Machines

Direct-load test

The machine is operated under load and input, output, speed, current, and temperature are measured. This method gives realistic performance data but requires a suitable load and wastes considerable energy.

Swinburne’s test

A shunt machine is run at no load as a motor. Constant losses are estimated and performance at other loads is predicted. It is economical but less accurate for machines with substantial load-dependent losses and does not reproduce full-load commutation or heating.

Hopkinson’s test

Two similar machines are mechanically coupled, with one operating as a motor and the other as a generator. Most power circulates between the machines, so the supply mainly provides losses. This permits full-load testing with relatively low external power, but it requires two similar machines and careful control.

Retardation test

The machine is allowed to slow down under selected conditions. The rate of deceleration is used to estimate rotational losses. The test is useful for separating mechanical losses from other losses.

13. Worked Example

A separately excited DC motor operates from a 220 V supply. Its armature current is 40 A, armature resistance is 0.30 Ω, and brush drop is 2 V. Determine the back emf and the electrical power converted to mechanical form, neglecting additional brush-contact loss beyond the stated voltage drop.

Using the motor voltage equation,

Therefore,

The converted power is

Thus, the back emf is 206 V and the electromagnetic power conversion is 8.24 kW. This is not necessarily the shaft output because rotational and other losses must still be subtracted.

14. Illustrative Industrial Case: DC Drive for a Rolling-Mill Stand

Background

Consider an illustrative steel-rolling line requiring frequent acceleration, reversal, and rapid speed adjustment. The drive must deliver high torque at low speed and maintain approximately constant power over a higher-speed range.

Problem

A fixed-speed AC motor connected directly to the supply gives limited speed control and produces large mechanical and electrical stresses during repeated reversals. The process also requires controlled braking during deceleration.

Analysis

A separately excited DC motor provides independently controlled armature voltage and field current. Armature-voltage control supplies constant-flux, constant-torque operation below base speed. Above base speed, field weakening provides a constant-power region. A four-quadrant converter permits forward motoring, forward regeneration, reverse motoring, and reverse regeneration.

Approach and solution

The drive system uses a closed-loop speed controller, an inner armature-current controller, current limiting, field-loss detection, thermal monitoring, and regenerative braking into the DC bus. Interpoles and compensating windings reduce commutation problems during rapid load changes. Mechanical guards and emergency isolation are included because stored rotational energy remains hazardous after electrical disconnection.

Outcome

The arrangement provides accurate speed regulation, high starting torque, controlled reversal, and energy recovery during braking. Its disadvantages are brush wear, commutator maintenance, and the need for periodic inspection. In a modern retrofit, a permanent-magnet synchronous or induction motor with a vector-controlled inverter may reduce maintenance, but the DC drive remains technically instructive and may be economically viable where existing equipment is sound.

Learning points

1. Drive selection must consider torque–speed requirements, not only rated power.
2. Regenerative braking can improve energy efficiency but requires an energy-absorbing electrical system.
3. Protection and maintenance are integral parts of machine design.
4. A technically mature machine may still be appropriate when lifecycle cost and existing infrastructure are considered.

15. Limitations, Safety, and Contemporary Practice

Brushes and commutators are wear components and can create electrical noise, sparking, and maintenance requirements. Maximum speed is limited by mechanical stress, commutation, and field-weakening behavior. High humidity, conductive dust, overload, poor ventilation, and incorrect brush setting accelerate failure.

Safe practice includes isolation and lockout/tagout, discharge of stored electrical energy, guarding of rotating parts, correct fuse and overload protection, insulation testing, and verification of field continuity. A series motor must not be run unloaded. Regenerative systems require protection against DC-bus overvoltage.

Modern digital drives use sensors or sensorless estimation, pulse-width modulation, current loops, programmable acceleration ramps, fault logging, and condition monitoring. Data analytics can identify brush wear, bearing defects, abnormal current ripple, and overheating. Artificial intelligence may assist predictive maintenance, but sensor quality, representative failure data, cybersecurity, and human verification remain essential. Automated recommendations should not override electrical safety procedures or manufacturer limits.

Chapter Summary

A DC machine converts energy through electromagnetic interaction between field flux and armature current. Its generated emf is proportional to flux and speed, while electromagnetic torque is proportional to flux and armature current. Constructional elements—including the yoke, poles, laminated armature, winding, commutator, and brushes—determine magnetic performance, cooling, and maintainability.

Excitation may be separate, shunt, series, compound, or permanent-magnet. Armature reaction distorts the main field and affects neutral-plane position and commutation; interpoles and compensating windings reduce these effects. Generator characteristics describe voltage behavior with load, while motor characteristics explain torque, speed, and application suitability.

Because a stationary motor has zero back emf, starting resistance or electronic current control is essential. Speed may be controlled by armature voltage, field weakening, or resistance, with armature-voltage control generally preferred for efficiency. Regenerative, dynamic, and plugging braking provide different compromises among energy recovery, speed, heat, and stress. Loss evaluation, efficiency testing, thermal rating, protection, and maintenance are necessary for safe industrial operation.

Key Terms

DC machine: Electromechanical converter operating as a motor or generator.

Armature: Rotating electrical part in which emf is induced or current produces torque.

Yoke: Outer frame providing mechanical support and magnetic return path.

Field winding: Winding that produces the main magnetic flux.

Commutator: Segmented mechanical rectifier connected to armature coils.

Brush: Stationary sliding electrical contact with the commutator.

Back emf: Motor emf opposing the applied armature voltage.

Armature reaction: Magnetic effect of armature current on the main field.

Commutation: Reversal of current in an armature coil under a brush.

Interpoles: Auxiliary poles that improve commutation.

Lap winding: Winding with approximately one parallel path per pole.

Wave winding: Winding normally having two parallel paths.

Shunt motor: Motor with field winding connected in parallel with the armature.

Series motor: Motor with field winding in series with the armature.

Compound motor: Motor containing both shunt and series field windings.

Regenerative braking: Braking that returns energy to the electrical supply.

Plugging: Braking by reversing the effective torque direction.

Swinburne’s test: No-load test used to estimate machine losses.

Hopkinson’s test: Back-to-back test using two coupled machines.

Voltage regulation: Relative change in terminal voltage between specified load conditions.

Review Questions

Short Answer Questions

1. What are the principal functions of the yoke in a DC machine?
2. Why is the armature core laminated?
3. State the difference between a lap winding and a wave winding.
4. Why is a starter necessary for a DC motor?
5. Name three methods of braking a DC motor.

Long Answer Questions

1. Explain the construction and operating principle of a conventional DC machine.
2. Derive and discuss the generated-emf equation, defining all variables.
3. Explain armature reaction and describe the functions of interpoles and compensating windings.
4. Compare shunt, series, and compound motors in terms of torque, speed, and applications.
5. Describe the major losses in a DC machine and explain two methods of testing.

Analytical / Application Questions

1. A 220 V motor draws 35 A. If armature resistance is 0.25 Ω and brush drop is 2 V, calculate its back emf and converted electromagnetic power.
2. Select a suitable DC motor type for a crane requiring very high starting torque and explain the safety condition that must be observed.
3. An industrial drive requires constant torque below base speed, constant power above base speed, rapid reversal, and energy recovery. Propose a control and braking arrangement and justify it.

Multiple Choice Questions with Answers

Question 1

Which component provides mechanical rectification in a conventional DC machine?

A. Yoke

B. Commutator

C. Bearing

D. Pole shoe

Correct Answer: B. Commutator

Question 2

For a simplex wave winding, the usual number of parallel paths is:

A. 1

B. 2

C. Equal to the number of poles

D. Twice the number of poles

Correct Answer: B. 2

Question 3

A DC motor has V = 220 V, I_a = 20 A, R_a = 0.5 Ω, and a 2 V brush drop. Its back emf is:

A. 208 V

B. 210 V

C. 218 V

D. 232 V

Correct Answer: B. 210 V

Question 4

In a DC motor, electromagnetic torque is proportional to:

A. Φ/I_a

B. I_a/Φ

C. ΦI_a

D. V/I_a

Correct Answer: C. ΦI_a

Question 5

Why must a series motor not be operated at no load?

A. Its field winding becomes open-circuit immediately

B. Its speed can rise to a dangerous value

C. Its armature resistance becomes zero

D. Its commutator stops rotating

Correct Answer: B. Its speed can rise to a dangerous value

Question 6

Which method normally provides efficient speed control below base speed in a separately excited DC motor?

A. Armature-voltage control

B. Permanent insertion of large armature resistance

C. Removing the commutator

D. Opening the field circuit

Correct Answer: A. Armature-voltage control

Question 7

The principal purpose of interpoles is to:

A. Increase bearing friction

B. Improve commutation

C. Reduce shaft diameter

D. Eliminate all copper losses

Correct Answer: B. Improve commutation

Question 8

In regenerative braking, the DC machine:

A. Returns electrical energy to the supply or DC link

B. Operates only with an open armature circuit

C. Dissipates all energy in a series resistor

D. Must be mechanically disconnected from the load

Correct Answer: A. Returns electrical energy to the supply or DC link

Question 9

A motor converts 8 kW of electrical input into 6.8 kW of shaft output. Its efficiency is approximately:

A. 80.0%

B. 85.0%

C. 88.2%

D. 117.6%

Correct Answer: C. 88.2%

Question 10

Which test uses two mechanically coupled similar machines, one acting as a motor and the other as a generator?

A. Swinburne’s test

B. Retardation test

C. Hopkinson’s test

D. Open-circuit test

Correct Answer: C. Hopkinson’s test