DC and AC Electrical Machines

Introduction

Electrical machines convert energy between electrical and mechanical forms. Motors convert electrical energy into mechanical torque; generators convert mechanical energy into electrical power. Transformers transfer electrical energy between circuits without mechanical motion, but rotating machines are especially important in mechatronics because they provide controlled motion for conveyors, robots, pumps, machine tools, vehicles, and actuators.

This chapter examines DC machines, induction motors, synchronous machines, stepper motors, and brushless motors. Their construction, operating principles, characteristics, starting methods, speed control, losses, and selection criteria are compared from both theoretical and engineering perspectives.

Learning Objectives

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

1. Explain the construction and operating principles of major electrical machines.
2. Use fundamental torque, back-emf, slip, speed, and power equations.
3. Describe starting and speed-control methods.
4. Identify machine losses, efficiency limitations, and operating characteristics.
5. Select an appropriate motor for a mechatronic application.
6. Recognize safety, control, maintenance, and sustainability considerations.

1. Electromechanical Energy Conversion

A current-carrying conductor in a magnetic field experiences force. For a conductor of active length l carrying current I in a magnetic flux density B, the force magnitude is:

Here, θ is the angle between the conductor and magnetic field. The expression applies to a straight conductor in a approximately uniform magnetic field. In a rotating machine, many conductors experience forces whose combined effect produces torque.

Electromagnetic torque is related to mechanical power by:

where P_mech is mechanical power in watts, T is torque in newton-metres, and ω_m is angular speed in radians per second. Since ω_m = 2πn/60 for speed n in revolutions per minute, an often-used engineering form is:

The ideal energy-conversion relationship is reversible. Real machines have copper, magnetic, mechanical, and stray-load losses, so output power is less than input power in motor operation.

2. Classification and Construction

Machines may be classified according to supply and commutation:

A rotating machine commonly contains a stator, rotor, air gap, magnetic core, windings or permanent magnets, bearings, frame, shaft, and cooling system. The air gap is kept small to reduce magnetizing current while allowing mechanical clearance. Laminated steel cores reduce eddy-current loss.

Figure: Simplified cross-section of a rotating electrical machine.

3. DC Machines

Construction and principle

A DC machine has a stationary field system and a rotating armature. The field may be produced by shunt, series, compound, or permanent-magnet excitation. The armature winding lies in rotor slots. A commutator mechanically reverses coil connections so that torque remains unidirectional in motor operation and the generated voltage is rectified at the brushes in generator operation.

The generated or back emf is:

where E is emf in volts, k_e is a machine constant, Φ is flux per pole in webers, and ω_m is angular speed. For a motor, the terminal voltage equation is:

where E_b is back emf, I_a armature current, R_a armature resistance, and V_br brush voltage drop. Neglecting brush drop gives E_b ≈ V − I_aR_a. The electromagnetic torque is:

For a consistent SI model, the torque constant and emf constant have compatible numerical values when angular speed is expressed in radians per second. These equations assume a linear magnetic circuit and neglect saturation and armature reaction.

Characteristics

For a separately excited or shunt motor, flux is approximately constant; therefore torque is approximately proportional to armature current and speed decreases moderately as load increases. A series motor has high starting torque because field flux increases with armature current, but it must not be operated unloaded because speed can rise dangerously. A compound motor combines series starting torque with shunt-like speed regulation.

Starting and speed control

At standstill, E_b = 0, so direct connection would produce approximately I_a = V/R_a, which may be many times rated current. Starters or electronic drives limit current during acceleration. Methods include a series starting resistor, three-point or four-point starter, controlled rectifier, and DC chopper.

For constant flux, speed is approximately:

Thus armature-voltage control provides speeds below base speed. Field weakening reduces Φ and provides speeds above base speed, but torque capability decreases. Regenerative braking returns energy to the supply; dynamic braking dissipates energy in a resistor, and plugging reverses torque but causes substantial current and stress.

Losses and applications

Losses include armature and field copper losses, brush-contact loss, core hysteresis and eddy-current losses, friction, windage, and stray-load loss. Efficiency is:

DC motors remain useful where simple torque control or very high starting torque is required, although brushes require maintenance and create electrical noise.

4. Three-Phase Induction Motors

Construction and rotating field

A three-phase stator winding supplied by balanced currents produces a rotating magnetic field. Synchronous speed is:

where f is supply frequency in hertz and P is the number of poles. The rotor rotates slightly below synchronous speed in motoring operation. Slip is:

where n_r is rotor speed. Slip is dimensionless and is often expressed as a percentage. Rotor frequency is f_r = sf. At standstill, slip is one; near rated load, slip is usually only a few percent for a standard motor.

The squirrel-cage rotor uses conducting bars short-circuited by end rings. It is rugged and inexpensive. A wound rotor has a three-phase winding connected through slip rings, allowing external resistance for starting or speed control.

Torque and characteristics

Induced rotor currents interact with the rotating field to produce torque. At small slip, torque is approximately proportional to slip. As slip increases, torque reaches a maximum (breakdown torque), then falls. A simplified equivalent-circuit torque expression is:

Here, V_th, R_th, and X_th are Thevenin-equivalent stator quantities referred to the rotor, R₂' and X₂' are rotor resistance and leakage reactance referred to the stator, and ω_s is synchronous angular speed. This equation is based on a per-phase equivalent circuit and steady-state sinusoidal operation. It is useful for analysis but rated performance should be obtained from manufacturer data.

The motor draws magnetizing current even at no load, has a lagging power factor, and experiences voltage-dependent starting current. Reduced voltage lowers starting torque approximately with the square of voltage for a fixed-frequency induction motor.

Starting and speed control

Direct-on-line starting is simple but produces high current. Star-delta starting reduces applied phase voltage during starting, reducing current and torque. Autotransformer starters and soft starters provide controlled voltage ramping. Rotor-resistance starting applies only to wound-rotor motors.

The most effective modern method is a variable-frequency drive (VFD). Below base speed, the controller maintains approximately constant V/f, preserving air-gap flux. Above base speed, voltage is limited and frequency increases, producing field weakening and an approximately constant-power region. VFDs improve process control but can cause harmonic currents, bearing currents, electromagnetic interference, and motor insulation stress unless correctly specified.

Losses and applications

Losses consist of stator and rotor copper losses, core losses, friction and windage, and stray-load losses. Rotor copper loss represents the slip portion of air-gap power; the remainder is converted to mechanical power, apart from mechanical losses. Induction motors are preferred for pumps, compressors, fans, conveyors, and machine tools because they are robust, low-cost, and nearly maintenance-free.

5. Synchronous Machines

A synchronous machine has a stator, usually with a three-phase winding, and a rotor that produces a magnetic field using DC excitation, permanent magnets, or salient-pole reluctance. In steady operation, rotor speed equals synchronous speed:

Unlike an induction motor, an ordinary synchronous motor is not inherently self-starting because it develops no average starting torque when the stationary rotor sees a rapidly alternating field. Starting may use damper bars, a pony motor, or an inverter that gradually increases frequency.

The rotor locks to the rotating field when synchronism is achieved. The power angle δ is the electrical angle between internal emf and terminal voltage. For a simplified cylindrical-rotor model neglecting resistance:

Here, V is phase voltage, E is internal phase emf, X_s is synchronous reactance, and δ is the power angle. The equation assumes balanced sinusoidal steady state and neglects resistance and saturation. The theoretical maximum of this simplified expression occurs at δ = 90°, but stable practical operation uses a lower angle.

Changing field excitation changes reactive-power exchange. Under-excitation generally causes lagging power factor; over-excitation can produce leading power factor. Synchronous motors therefore provide constant speed and may improve system power factor, but they require excitation and synchronization equipment.

Synchronous generators are widely used in utility plants and renewable-energy systems. Important losses are field and armature copper losses, core losses, mechanical losses, stray losses, and excitation-system losses.

6. Stepper Motors

A stepper motor converts a sequence of electrical pulses into discrete angular movements. A permanent-magnet, variable-reluctance, or hybrid rotor aligns successively with energized stator phases. If a motor has N_s steps per revolution, its step angle is:

For a command pulse frequency f_p, the ideal stepping speed is:

These relationships assume every pulse produces one valid step and that no steps are lost. In practice, acceleration, load torque, resonance, supply voltage, and drive current impose limits.

Full-step, half-step, and microstepping drives alter resolution and smoothness. A stepper motor can hold position without feedback, but open-loop operation cannot detect missed steps. Its torque decreases as speed rises because winding current cannot change instantaneously. Current-regulated chopper drives improve high-speed performance and reduce heating.

Applications include printers, 3D printers, valve actuators, camera mechanisms, and low-cost positioning systems. Closed-loop stepper systems add encoders and can detect following error.

7. Brushless DC Motors and Permanent-Magnet Synchronous Motors

A brushless DC (BLDC) motor uses permanent magnets on the rotor and electronically switched stator windings. Hall sensors, encoders, or sensorless back-emf estimation provide rotor-position information. The inverter replaces the mechanical commutator.

BLDC motors commonly use trapezoidal back emf and six-step commutation, whereas permanent-magnet synchronous motors (PMSMs) commonly use sinusoidal currents and field-oriented control. The distinction is partly based on waveform and control strategy; both are electronically commutated permanent-magnet machines.

Advantages include high efficiency, high power density, quiet operation, and low maintenance. Limitations include inverter cost, magnet temperature sensitivity, demagnetization risk, control complexity, and electromagnetic compatibility concerns. Regenerative braking is readily implemented when the drive and energy-storage system can accept returned power.

8. Losses, Thermal Limits, and Efficiency

Electrical machines are thermally limited. Copper loss is:

where I is rms current and R is winding resistance at the relevant temperature. Core loss includes hysteresis and eddy-current components and depends on frequency, flux density, and material. Mechanical loss includes bearing friction and windage. Stray-load loss results from leakage flux and nonuniform current distribution.

Temperature rise depends on loss, cooling, enclosure, ambient temperature, altitude, and duty cycle. Insulation classes specify permissible winding temperature limits, while service factors and thermal protection must not be treated as substitutes for correct sizing. Overload relays, thermistors, circuit breakers, grounding, and emergency isolation are essential safeguards.

9. Selection of a Machine

Selection begins with the load, not with the motor catalogue. Determine:

• required torque, speed range, acceleration, and duty cycle;
• starting, braking, reversing, and regeneration requirements;
• position accuracy, repeatability, and allowable overshoot;
• supply voltage, frequency, drive compatibility, and environment;
• enclosure, cooling, noise, maintenance, and safety requirements;
• efficiency, lifecycle cost, spare parts, and controls expertise.

The load torque may be classified as constant torque, variable torque, or constant power. Fans and centrifugal pumps approximately follow variable-torque behavior, while conveyors often require approximately constant torque. For acceleration, the net torque is:

and angular acceleration is:

where J is total reflected inertia in kilogram-metres squared. These equations assume torque and inertia are expressed at the same shaft and neglect torsional compliance.

A DC motor may suit legacy variable-speed equipment; an induction motor with VFD is a strong general-purpose choice; a synchronous or PMSM drive suits high efficiency and precise control; a stepper suits modest-speed incremental positioning; and a BLDC or servo system suits compact, dynamic, electronically controlled motion.

10. Illustrative Case: Conveyor Drive Selection

Background

An automated packaging conveyor requires 1.5 kW at 1,440 rpm, frequent starts, moderate speed adjustment, and reliable operation in a dusty factory.

Problem analysis

The machine requires continuous rotation rather than discrete positioning. Frequent starts increase thermal stress, while dust favors a totally enclosed motor. A brushed DC motor would require brush maintenance. A stepper motor would be inefficient and would provide unnecessary discrete positioning.

Approach and solution

A three-phase squirrel-cage induction motor with an appropriately rated VFD is selected. The VFD provides controlled acceleration, reducing mechanical shock and starting current. The motor is selected with suitable enclosure and thermal protection. The approximate rated torque is:

where P_kW is power in kilowatts and n is speed in rpm. Thus:

The selected motor must provide this continuous torque plus the required acceleration torque and service margin. The VFD must be compatible with motor insulation, braking requirements, cable length, and electromagnetic compatibility practices.

Outcome and learning points

The induction motor offers ruggedness and low maintenance, while the VFD supplies the required speed control. The case demonstrates that motor selection depends on load profile, environment, control requirements, and lifecycle considerations—not merely rated power.

11. Contemporary Developments and Professional Practice

Modern drives combine power electronics, digital control, communication networks, condition monitoring, and model-based diagnostics. Encoders and current sensors enable servo control, while machine-learning algorithms can identify abnormal vibration, bearing degradation, or insulation problems. Such tools support predictive maintenance but do not eliminate the need for calibrated sensors, validated models, cybersecurity, and qualified engineering judgment.

Energy regulations increasingly encourage high-efficiency motors and variable-speed operation. Engineers should follow applicable electrical codes, machinery-safety standards, lockout procedures, grounding rules, and electromagnetic-compatibility requirements. Permanent-magnet machines also require responsible sourcing and end-of-life recycling strategies. Safe design must address unexpected restart, stored energy in DC-link capacitors, rotating inertia, and regenerative voltage.

Chapter Summary

Electrical machines use magnetic fields to convert electrical and mechanical energy. DC machines use brushes and commutators and provide convenient voltage and field-based speed control, but require maintenance. Induction motors use slip-induced rotor currents and are rugged, economical, and widely used; VFDs provide efficient speed control. Synchronous machines operate at synchronous speed and can exchange reactive power, but require starting and excitation arrangements. Stepper motors provide discrete motion and useful holding torque but may lose synchronism. BLDC and PMSM drives replace mechanical commutation with electronic switching and offer high efficiency and power density.

Machine performance is governed by torque, speed, emf, slip, losses, thermal limits, and control strategy. Correct selection requires analysis of load torque, inertia, duty cycle, environment, safety, efficiency, and total lifecycle cost.

Key Terms

Electromagnetic torque: Torque produced by interaction between magnetic field and current.

Back emf: Voltage induced in a motor opposing the applied voltage.

Commutator: Mechanical switching device in a DC machine.

Armature: Machine winding in which operating current or generated emf is present.

Slip: Relative difference between synchronous speed and rotor speed in an induction motor.

Synchronous speed: Speed of the rotating magnetic field.

VFD: Variable-frequency drive used to control AC-motor voltage and frequency.

Breakdown torque: Maximum torque developed by an induction motor before torque falls.

Power angle: Angle relating internal emf and terminal voltage in a synchronous machine.

Excitation: Production of a machine’s magnetic field.

Stepper motor: Motor that advances in discrete angular steps.

Microstepping: Drive technique that divides a full step into smaller commanded movements.

BLDC motor: Permanent-magnet motor with electronic commutation.

PMSM: Permanent-magnet synchronous motor.

Copper loss: Resistive winding loss equal to I²R.

Core loss: Magnetic loss caused principally by hysteresis and eddy currents.

Duty cycle: Time pattern of loading and rest in machine operation.

Regenerative braking: Braking method that returns mechanical energy to an electrical system.

Field weakening: Speed increase obtained by reducing magnetic flux above base speed.

Service factor: Permitted additional loading under specified conditions.

Review Questions

5 Short Answer Questions

1. Why is a DC motor fitted with a starter or current-limiting controller?
2. Define slip in an induction motor.
3. State one important advantage and one limitation of a stepper motor.
4. Why is an ordinary synchronous motor not self-starting?
5. List four major categories of losses in electrical machines.

5 Long Answer Questions

1. Explain the construction, emf equation, torque equation, characteristics, and speed-control methods of a shunt DC motor.
2. Describe the operation of a three-phase induction motor, including rotating-field speed, slip, torque production, and VFD control.
3. Compare induction and synchronous motors in construction, starting, speed regulation, power factor, and applications.
4. Explain the operation and practical limitations of stepper and brushless motors in mechatronic systems.
5. Discuss how electrical, mechanical, magnetic, and thermal losses affect efficiency and machine rating.

3 Analytical / Application Questions

1. A 50 Hz, four-pole induction motor runs at 1,440 rpm. Calculate synchronous speed and slip, and explain the physical meaning of the result.
2. A positioning system needs 0.9° commanded steps at 600 pulses per second. Determine the ideal steps per revolution and speed in rpm. State practical factors that may prevent this ideal result.
3. Select and justify a motor and drive for a dusty conveyor requiring variable speed, frequent starts, and continuous operation. Address torque, thermal protection, enclosure, maintenance, and safety.

Multiple Choice Questions with Answers

Question 1

Which equation gives the synchronous speed of an AC machine?

A. n_s = 120f/P

B. n_s = 60P/f

C. n_s = P/(120f)

D. n_s = 2πfP

Correct Answer: A. n_s = 120f/P

Question 2

At standstill, the back emf of a DC motor is approximately:

A. Equal to supply voltage

B. Zero

C. Equal to rated torque

D. Infinite

Correct Answer: B. Zero

Question 3

A four-pole, 50 Hz induction motor has a synchronous speed of:

A. 750 rpm

B. 1,000 rpm

C. 1,500 rpm

D. 3,000 rpm

Correct Answer: C. 1,500 rpm

Question 4

The rotor of an induction motor must have slip in motoring operation because slip:

A. Eliminates stator copper loss

B. Creates the relative motion needed to induce rotor current

C. Makes rotor speed greater than synchronous speed

D. Prevents magnetic-field rotation

Correct Answer: B. Creates the relative motion needed to induce rotor current

Question 5

Which motor is normally associated with discrete commanded angular movements?

A. Stepper motor

B. Squirrel-cage induction motor

C. Series transformer

D. Synchronous generator

Correct Answer: A. Stepper motor

Question 6

A motor delivers 2 kW at 1,000 rpm. Its approximate shaft torque is:

A. 1.91 N·m

B. 9.55 N·m

C. 19.1 N·m

D. 191 N·m

Correct Answer: C. 19.1 N·m

Question 7

For a constant-flux DC motor, increasing armature voltage primarily:

A. Reduces speed

B. Increases speed below the base-speed region

C. Eliminates torque

D. Reverses the magnetic field automatically

Correct Answer: B. Increases speed below the base-speed region

Question 8

Which feature distinguishes a brushless DC motor from a conventional brushed DC motor?

A. It has no magnetic field

B. It uses electronic rather than mechanical commutation

C. It cannot produce torque at low speed

D. It operates only from a single-phase supply

Correct Answer: B. It uses electronic rather than mechanical commutation

Question 9

The ideal step angle of a stepper motor with 400 steps per revolution is:

A. 0.45°

B. 0.9°

C. 1.8°

D. 90°

Correct Answer: A. 0.45°

Question 10

Which loss is directly represented by I²R?

A. Windage loss

B. Hysteresis loss

C. Copper loss

D. Stray-load loss

Correct Answer: C. Copper loss