ENSC2003 - Lecture 18

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ENSC2003 - Lecture 17
DC Motors - Slides
DC Motors Y12

DC Motors

• Motor converts electrical energy into mechanical energy
• Generator converts mechanical energy to electrical energy

• Rotor $-$ rotating part of motor
  • Carriers wire-wound coils
  • Coils create Lorentz force when energised
• Stator $-$ stationary part of motor
  • Holds magnets that create a fixed field

Circuit Model of DC Motors

The conduction path of the motor looks like:

• Brush -> commutator -> coils -> commutator -> brush

There are only three important properties we need to model:

1. $R_a$ $-$ armature resistance
   • i.e. the wire resistance in the coils
2. $L_a$ $-$ armature inductance
3. $e_b$ $-$ back-EMF
   • Generated by coils spinning in magnetic field
   • Opposes the applied voltage (Lenz’s law)

DC Steady-State

From Lenz’s law:
$e_b=k_{aP}{\omega }_m$

In steady-state, inductor $L_a$ -> short circuit

• Thus, we are left with two equations:
  1. Electrical: $v_a=i_a{R}_a+k_{aP}{\omega }_m$
     • Given by KVL
  2. Mechanical: $k_{TP}\cdot i_a=T_L+b{\omega }_m$
     • From torque equations

For an ideal motor, torque constant and armature constant are equal
$k_{TP}=k_{aP}=k$

Analogue Speed Control

Constant voltage drive

• Motor won’t move below a threshold voltage
  • Minimum voltage: $v_s=\frac{R}{k_{TP}}{T}_L$
  • This is due to static friction
• Then, suddenly jumps to speed above the minimum
  • Thus, some speeds are inaccessible from a stationary start
  • Think of pushing a heavy box in real life

Constant current drive

• Better torque control since $T=k_{TP}\cdot i_a$

Digital Speed Control

Pulse-width modulation (PWM)

• Voltage is either zero or a maximum value $v_{ON}$
  • Ensures voltage is always above threshold value
• Motor drive voltage is periodic
  • On for time $T_{ON}$
  • Off for time $T_{OFF}$
  • Total period is $T=T_{ON}+T_{OFF}$
  • Duty cycle is $\frac{T_{ON}}{T}$
• If $T$ is sufficiently small, motor movement is continuous

PWM is the solution to the static friction problem of constant voltage sources; we can achieve any speed with good control

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End of Unit!