## 21/08/2017

### Basic Equation of DC Motor

b = ZNP / 60A
= V – IaRa …….….(1)
OR
Speed N α Eb / Ф…................…(2)
Torque T α ФaIa…........….........(3)

Mechanical power = EbIa……….(4)
= Tω
Angular speed ω = 2πN / 60
Where
Eb = Back emf
Ia = Armature current
V = Armature voltage
Ra = Resistance of armature
Ф = Flux per pole
Фa = Armature flux
Ta = 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 ФaIa
T α Фa ( 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 ФaIa
• 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.
Vc = Va + Vbr
Vbr = Break over voltage of Diac
Va = Voltage across armature and
Vc = 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 Dfw 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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