MODULE 2 — DC Machines
2.1 DC Machine Construction
Hover over diagram parts
Explore the internal construction of a DC Machine to learn about its components.
2.2 EMF Equation
$$ E = \frac{P \phi N Z}{60 A} $$
$P$ = Poles, $\phi$ = Flux per pole (Wb), $N$ = Speed (RPM)
$Z$ = Total conductors, $A$ = Parallel paths ($P$ for lap, $2$ for wave).
$Z$ = Total conductors, $A$ = Parallel paths ($P$ for lap, $2$ for wave).
0 V
2.3 Torque Equation
$$ T = \frac{P \phi Z I_a}{2\pi A} \quad \Rightarrow \quad T \propto
\phi I_a $$
$$ E_b = V - I_a R_a \quad \text{(Motor Back EMF)} $$
$$ P_{dev} = E_b I_a = T \omega $$
2.4 Armature Winding
LAP WINDING
$$ A = P $$
High Current, Low Voltage
WAVE WINDING
$$ A = 2 $$
High Voltage, Low Current
2.5 Commutator Action
$$ \text{AC (Armature)} \xrightarrow{\text{Commutator}} \text{DC
(External)} $$
2.6 Types of DC Generators
Series Generator
$$ V_t = E - I_a (R_a + R_{se}) $$
$$ I_a = I_L = I_{se} $$
Shunt Generator
$$ V_t = E - I_a R_a $$
$$ I_a = I_L + I_{sh} $$
$$ I_{sh} = V_t / R_{sh} $$
Compound (Long)
$$ I_a = I_L + I_{sh} $$
$$ V_t = E - I_a(R_a + R_{se}) $$
2.7 Speed Control of Motor
$$ N \propto \frac{E_b}{\phi} = \frac{V - I_a R_a}{\phi} $$
Base speed achieved by varying armature voltage $V$. speeds above
base
achieved by weakening field flux $\phi$.
2.8 DC Machine Testing
Swinburne's Test (No-Load)
$$ \eta = \frac{V I_L}{V I_L + W_c + I_a^2
R_a} $$
$W_c$ = Constant losses found at no-load.
Hopkinson's Test (Back-to-Back)
$$ \eta_{motor} = \frac{V I_2 -
\frac{W_s}{2}}{V I_1} $$
$$ \eta_{max} \text{ when } W_c = I_a^2 R_a $$