### Basic Equation of DC Motor

= V – I

_{a}R_{a }…….….(1)
OR

Mechanical power
= E

_{b}I_{a}……….(4)
= Tω

Angular speed ω
= 2πN / 60

Where

E

_{b}= Back emf
I

_{a}= Armature current
V = Armature voltage

R

_{a}= Resistance of armature
Ф = Flux per pole

Ф

_{a}= Armature flux
T

_{a}= Armature torque
ω = Angular speed

N = Speed ( RPM )

- The speed control of DC motor is done by armature control or flux control.

### Constant Horse Power

- The speed of the motor can be changed by changing flux of the motor if the supply voltage is kept constant.
- The torque of the DC motor depends upon flux if the armature current is kept constant.
- The speed of the DC motor can be increased by decreasing flux of the motor.

T α Ф

_{a}I_{a}
T α Ф

_{a}( if armature current is kept constant )…….(5)
Horse Power α Tω

- The torque decreases if the speed of the motor increases as per equation (5).
- As the speed increases and torque decreases by changing decreasing field flux, the horse power of the DC motor remains constant it is called as constant HP operation.

N α 1 / ω

- This method is applicable when the speed of the motor requires above the normal speed.

### Constant torque

- The armature torque in the DC motor is directly proportional to flux per pole and armature current.

T α Ф

_{a}I_{a}- If the field current is kept constant, the armature torque is directly proportional to the armature current.
- Therefore the maximum armature torque depends upon maximum armature current. The armature torque always kept constant in any speed therefore it is called as constant torque operation.

HP α Tω

- The output of the DC motor is directly proportional to speed if the torque is kept constant. Therefore the output power is not kept constant at any speed.

#### Speed control of DC Series Motor

- The speed control of DC series motor by half wave circuit is shown in the figure A.
- The DC motor armature gets supply when SCR is turned on by gate pulse during positive half cycle of alternating supply.

- The charging of capacitor is done through variable resistor R.
- When the voltage across capacitor is equal to back emf of armature and break over voltage of diac, the SCR receives gate pulse through gate – cathode circuit.
- As soon as the SCR turns on, the current passes through field winding and armature winding.
- The variable resistor R determines the charging rate of the capacitor C. The voltage across armature is due to only residual flux in the negative half cycle of the alternating supply.
- The firing angle of the SCR is adjusted by changing variable resistor R. This will result in speed of the motor changes.

- The speed of the motor decreases as the load on it increases for a given value of variable resistor R.
- As the back emf is directly proportional to speed , the back emf decreases due to decrease the speed of the motor.
- The voltage across armature decreases as the speed decreases therefore the voltage across capacitor decreases during next half cycle.

V

_{c}= V_{a}+ V_{br}
V

_{br}= Break over voltage of Diac
V

_{a}= Voltage across armature and
V

_{c}= Voltage across capacitor- The firing angle of SCR decreases as the SCR fires earlier during positive half cycle.
- The average voltage across armature increases as the firing angle of SCR decreases. This will result in speed of motor increases.

### Speed Control of DC Shunt Motor

- The power circuit diagram for speed control of the DC Shunt Motor is shown in the figure E.

- The function of the bridge rectifier is to converter alternating voltage in to direct voltage.
- The zener diode clips the voltage and provides constant voltage.
- The field winding of the DC shunt motor is connected across supply voltage.
- The SCR is connected in series with the armature winding of the DC shunt motor.
- The charging of capacitor is done through variable resistor R.
- When the voltage across capacitor becomes equal to peak point voltage, the UJT turns on.
- The discharging of capacitor is done through path C – EB1 – Primary of pulse transformer – C.
- As soon as the pulse transformer primary energies, the SCR gets pulse through pulse transformer secondary.
- Now the current passes through the armature winding of the DC motor.
- The charging rate of the capacitor depends upon variable resistor R.
- If the value of variable R is set minimum, the charging of capacitor done faster resulting UJT turns on in short time.
- This will resulting the firing angle of the SCR decreases and DC motor speed increases.
- If the value of resistor R set at maximum, the firing angle of SCR increases and DC motor speed decreases.
- As the field winding gets constant voltage, the motor speed is directly proportional to back emf.
- If the armature winding drop is neglected, the speed of the DC motor is directly proportional to armature voltage.
- The speed of the DC motor is adjusted by the firing angle of the SCR.
- When the UJT turns on, the diode D2 forward biases and diode D1 reverse biased therefore the charging of capacitor is done only through variable resistor R.
- The diode D1 reverse biases when current passes through the armature winding.
- As soon as the current passes through the armature winding becomes zero, the stored energy of armature winding dissipates through diode D1.

### Speed Regulation

- As the motor speed increases, the back emf also increases and diode D2 becomes forward biased in this condition.
- As the charging path of capacitor and resistor R2 becomes parallel, the charging current of capacitor decreases and firing angle of SCR increases.
- This will result the speed of motor decreases. If the motor speed decreases by any chance, the back emf decreases.
- This will result in small current passes through shunt resistor R2 and firing angle of SCR decreases due to charging rate of capacitor increases.
- The DC shunt motor speed increases due to decrease of firing angle.

### Speed Control of Separately Excited DC Motor

- The power circuit diagram for speed control of separately excited DC motor is shown in the figure A.

- The armature of DC motor is connected to the semi converter.
- The DC supply to the field winding is given by controlled or uncontrolled rectifier.
- When the semi converter is used, the power flows from supply to load side.
- As the power flows from load to supply is not possible, the DC motor regenerative action is not possible.
- The operation of semi converter due to flow of armature current is possible in the following modes.

### Continuous mode

- The armature current becomes continuous as shown in the figure G.
- The SCR T1 and SCR T2 turns on at firing angle of α and π + α during positive and negative half cycle of alternating supply.
- The DC motor gets supply through SCR T1 and diode D1 through path P – SCR T1 – R – L – Armature – D1 – N during α < ωt < π.
- The energy stored
in the inductor gets dissipated through diode D
_{fw}during negative half cycle of alternating supply during π < ωt < π + α . The voltage across armature becomes zero during π < ωt < π + α. - The SCR T2 and diode D2 conducts during negative half cycle of alternating supply and load current flows through path N – SCR T2 – R – L – Armature – D2 – P path during π + α < ωt < 2π.
- The power flows through supply to load during both positive and negative half cycles. The armature current becomes continuous when the firing angle becomes small.

### Discontinuous mode

- When the firing angle becomes large, the armature current becomes discontinuous due to high speed and low torque operation.
- The speed regulation becomes poor when the no load speed of DC motor becomes high and operation of DC motor armature in the discontinuous mode.
- Therefore the operation of the DC motor is always done in the continuous conduction mode.
- The waveform of the discontinuous armature current is shown in the figure G.
- The DC motor gets supply through SCR T1 and diode D1 during 0 < ωt < π. The armature short circuited through freewheeling diode after positive half cycle of alternating supply.
- The armature current becomes zero at angle β before SCR T2 is turned on.

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