DC Machines Cheatsheet

Cheatsheet Content

DC Machine Fundamentals Principle: Converts electrical energy to mechanical energy (motor) or mechanical to electrical (generator). Components: Stator (field winding), Rotor (armature winding), Commutator, Brushes. EMF Equation: $E_a = \frac{P \Phi Z N}{60 A}$ $P$: Number of poles $\Phi$: Flux per pole (Wb) $Z$: Total number of armature conductors $N$: Speed (rpm) $A$: Number of parallel paths Torque Equation: $T_a = \frac{P \Phi Z I_a}{2 \pi A}$ or $T_a = K_a \Phi I_a$ $I_a$: Armature current $K_a = \frac{P Z}{2 \pi A}$: Armature constant Voltage Equation (Motor): $V_t = E_a + I_a R_a$ Voltage Equation (Generator): $E_a = V_t + I_a R_a$ Separately Excited DC Machine Circuit Diagram Field winding is supplied by an independent DC source. Arm Motor Field $V_f$ $V_t$ Field Current: $I_f = V_f / R_f$ (independent of armature circuit) Motoring Mode: $V_t = E_a + I_a R_a$ Speed-Torque: $N \propto \frac{V_t - I_a R_a}{\Phi}$ and $T_a \propto \Phi I_a$ Characteristics: Relatively constant speed for varying load if flux is constant. Generating Mode: $E_a = V_t + I_a R_a$ Output voltage $V_t$ depends on speed and field current. Characteristics: Good voltage regulation if field current is controlled. Shunt DC Machine Circuit Diagram Field winding is connected in parallel with the armature across the supply. Arm Field Motor $V_t$ Current Relations: $I_L = I_a + I_f$ (Motor), $I_a = I_L + I_f$ (Generator) Field Current: $I_f = V_t / R_f$ Motoring Mode: $V_t = E_a + I_a R_a$ Characteristics: Relatively constant speed due to constant field flux. Slight drop due to $I_a R_a$ drop. Speed-Torque: $N \approx \frac{V_t}{\Phi K_n} - \frac{R_a}{(K_n \Phi)^2} T_a$. Speed drops slightly with load. Generating Mode: $E_a = V_t + I_a R_a$ Self-excitation is possible if residual magnetism exists. Characteristics: Terminal voltage drops with increasing load current due to $I_a R_a$ drop and armature reaction. Series DC Machine Circuit Diagram Field winding is connected in series with the armature. Arm Field Motor $V_t$ Current Relations: $I_L = I_a = I_{se}$ (series field current) Motoring Mode: $V_t = E_a + I_a (R_a + R_{se})$ $\Phi \propto I_a$ (in unsaturated region) Speed-Torque: $N \propto \frac{V_t - I_a (R_a + R_{se})}{I_a}$. Speed is inversely proportional to torque. Characteristics: High starting torque, speed varies widely with load (runs away at no-load). Applications: Cranes, traction, hoists. Generating Mode: $E_a = V_t + I_a (R_a + R_{se})$ Characteristics: Poor voltage regulation, requires load to build up voltage. Not commonly used as a generator. Comparison of DC Motors (Motoring) Characteristic Separately Excited Shunt Series Speed Regulation Excellent Good Poor (runs away at no-load) Starting Torque Good Good Excellent (very high) Load Impact on Speed Least affected Slightly affected Highly affected Flux control Independent Dependent on $V_t$ Dependent on $I_a$ Speed Control of DC Motors Speed equation: $N \propto \frac{V_t - I_a R_a}{\Phi}$ 1. Armature Voltage Control ($V_t$ control) Method: Vary the supply voltage $V_t$ to the armature while keeping field current constant (constant flux). Effect: Speed is directly proportional to $V_t$. Effective for speeds below rated speed. Application: Separately excited and shunt motors. Often done using choppers or controlled rectifiers. 2. Field Flux Control ($\Phi$ control) Method: Vary the field current $I_f$ (and thus flux $\Phi$) while keeping $V_t$ constant. Effect: Speed is inversely proportional to $\Phi$. Increasing $R_f$ reduces $I_f$, reduces $\Phi$, and increases speed. Effective for speeds above rated speed. Application: Separately excited and shunt motors. Not suitable for series motors as flux is load-dependent. Caution: Weakening field too much can lead to commutation problems and unstable operation. 3. Armature Resistance Control ($R_a$ control) Method: Insert an external resistance $R_{ext}$ in series with the armature. Effect: Increases the total armature circuit resistance $R_a' = R_a + R_{ext}$. This increases the voltage drop $I_a R_a'$ for a given load, reducing $E_a$ and thus speed. Application: All DC motors. Provides speeds below rated speed. Disadvantages: Power loss in $R_{ext}$ (low efficiency), speed varies with load (poor regulation).