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ENB205 Lecture Electrical and Computer Engineering
Linear DC Machines/Motor
Linear DC Machine
Simplest type of DC machine
As soon as the rod starts to move due to the F acting on it,
the rod induces a voltage
According to Lenz’s Law this voltage opposes the flow of
current
Once the rod accelerates to a velocity where induced EMF
€ is equal to input voltage (V), there will be no force on
the rod. In a perfect world without friction the rod would
continue at this velocity for ever
Equivalent circuit of the linear DC machine KVL around the loop gives:
At start up the rod is stationary, so
At terminal velocity,
Applying a load to the machine, slows the motor down (a)
due to Floadin opposite direction of the rod motion. As the
motor slow down the induced voltage reduces, increasing (b)
the current in the rod. (a)
Increase in current in the rod provides more force to (c)
counter the load: (b)
The induced force rises until (c)
Then the rod travels in steady state but at lower speed
Rotational DC Machines
Consider single loop generator:
Voltage induced on length dc:
Voltage induced on length ab :
Total Voltage induced:
Where
1 Week 2 Tuesday, 27 August 2013 ENB205 Lecture Electrical and Computer Engineering
Voltage waveform induced by rotating loop:
To achieve single polarity (DC) output, commutation is
used.
As the output voltage crosses 0V, and the velocity of
the loop wire is parallel to the field, the brushes switch
commutator plates.
The commutator rotates with the loop such that the
brushes continue to alternate commutator plate,
maintaining the polarity of the output voltage.
The voltage in any real machine will depend on:
The flux in machine
Speed of rotation
A constant representing the construction of the
machine
4 Loop DC Machine
4 single loops around a rotor
Each loop can represent more than one turn, however
for simplicity a single turn will be considered.
Output waveform from 4 loop machine
Voltage generated by 4 loop machine is higher, and has a
smaller percent ripple (50%) compared to two loop
(100%).
Higher numbers of loops can provide even less ripple in
the output voltage as only one coil (out of many) is
deactivated and reactivated as the commutator
switches.
2 Week 2 Tuesday, 27 August 2013 ENB205 Lecture Electrical and Computer Engineering
The current in the windings creates a force on the
rotor in reaction to the magnetic field
Forces on the conductors contribute to torque at
the axle. As the machine rotates, a voltage will be
generated in the windings which oppose the flow of
current. This Is called ‘Back EMF’:
In a similar way to the linear machine, the
rotational DC motor will reach a maximum velocity.
Terminal Velocity (v) at: Torque on a 4 loop DC motor
If an external load is applied to motor
Force of the load is in the direction opposite the direction of
the force supplied by the motor F
Small resistance in the windings and back EMF work ind
Finally ind Fload so:
to limit the velocity of the motor A new maximum velocity
These equations are only valid for a 4 loop, 2 pole motor.
Realistic DC Machines
Realisitc DC machines have many loops, to make
calculators easier some terms are defined
Z = number of conductors on rotor
C = number of coils on rotor
N c Number of turns per coil
Some have more than one set of poles:
P = number of poles
Some machines, due to winding structure have multiple Voltage induced in Real DC Generators
current paths Generation voltage depends on
A=Number of

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