Basic Equation of DC Motor
Back emf Eb =
ZNP / 60A
= V – IaRa …….….(1)
OR
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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