This notes sheet looks at electric generators and motors, general electric machine properties, motoring graphs and nominal voltages.

## Generators & Motors

### DC Generator

- A torque is applied to the coil, causing it to rotate with angular velocity
- The right-hand rule shows that a current is induced clockwise around the coil
- The emf can be calculated using Faraday’s law

### DC Motor

- There is an anticlockwise current in the coil, as shown
- Fleming’s left hand rule shows that this induces a clockwise torque couple on the coil, due to the magnetic field
- The motor rotates clockwise

A **split-ring commutator** is required where the current and emf is applied to the coil in order to maintain continuous motion (without this, the motor would change direction every half-turn).

The torque varies hugely with the position of the coil, as the Lorentz force depends on angle (it is

maximum when perpendicular, zero when parallel). This is known as the ‘**cogging effect**’, and can

be minimised by adding more coils:

Despite the disadvantages, single coils are usually still used as they are cheaper and lighter.

## Electric Machines

Both generators and motors can be modelled as a Thevenised generic electric machine with

internal (armature) resistance:

- For a generator, the induced emf goes in the same direction as terminal voltage
- For a motor, the induced emf opposes the terminal voltage (it is modelled as a load)

We express Faraday’s Law (see notes sheet on Magnetic Fields & Electromagnetism) in terms of

the angular velocity and a machine constant:

- is the induced emf
- is the machine constant, in Vs/rad
- is the angular velocity, in rad/s

### Generators

The power of the **generator **is given by the mechanical input power minus the power dissipated

in the armature resistance:

- is the mechanical power,
- is the power lost in the armature resistance

for a generator

Therefore, the mechanical torque is:

In a generator, the mechanical torque that is applied, T, is not the same as the mechanical torque

applied to the electrical circuit. This is because some torque – knows as **shaft torque** – is lost as

friction:

- is the torque applied to the circuit
- is the total mechanical torque input
- is the torque lost as friction

### Motors

Meanwhile, the power for a **motor **is the terminal power minus the power lost in the armature

resistance:

for a motor

The mechanical torque is:

In a motor, the mechanical torque output is slightly less than the electrical torque output. This is

again due to friction in the system:

- is the mechanical torque output
- is the torque output from the circuit (Ti in the equations above)
- is the frictional torque

## Electric Motor Graphs

### Torque-Speed Graphs

The relationship between torque and speed for a motor is:

## See derivation for this relationship

- The maximum speed is the
**no load speed**, when there is no torque output, only the frictional shaft torque is overcome. - Stall is when the speed is zero. There output torque here is the stall torque.

### Power-Speed Graphs

- At stall and no load, the power output is zero.

### Efficiency-Speed Graphs

## Nominal Voltage

Electric Machines will have a specified nominal voltage. This is the recommended terminal voltage

they are designed to operate at and does not have to be stuck to.

- Operating a motor above its nominal voltage gives greater performance, but reduced lifespan
- Operating a motor below its nominal voltage reduces performance but increases lifespan.

A motor can operate anywhere in the triangle beneath its torque-speed line. Often, you want to

limit where the motor operates. This can be done in three ways:

### 1. Voltage Regulation

As seen above, reducing or increasing the voltage reduces or increases the area in which the

motor can operate respectively.

### 2. Speed Regulation

This is when a fixed speed is set for a certain voltage range, as torque changes. However, once

the voltage passes the upper limit, the speed follows the torque-speed relation.

### Torque Regulation

This is the opposite: a constant torque is set as speed varies over a voltage rage. Once the voltage

is out of the range, the torque will decrease as speed increases.

- The two basic electric machines are generators and motors:
- An emf is induced in a generator – this can be calculated using Faraday’s Law, and the direction is found with the right-hand rule
- Electric potential is converted to mechanical energy in a motor, and Fleming’s left-hand rule shows the direction of rotation.

- It is easiest to deal with electric machines when thevanised in series with an armature resistance and a terminal p.d.
- Faraday’s law in terms of angular velocity and machine constant:
- For a
**generator:** - For a
**motor:** - All electric machines are specified with a
**nominal voltage**– this is the recommended terminal voltage, and is a balance between lifespan and performance. - The operating point of the machine does not have to be at the nominal voltage, but can be regulated through voltage, speed or torque.