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Monday, March 28, 2011

DETERMINATION OF TRANSFER FUNCTION OF AC SERVO MOTOR


Expt. No:                                                                                                        Date:

Determination Of Transfer FUNCTION OF
Ac Servo Motor
AIM:                                                      
To derive the transfer function of the given AC Servomotor.

APPARATUS / INSTRUMENTS REQUIRED:

S. No
Description
Range
Type
Quantity
1.
AC servo motor trainer kit
-

1
2.
AC servo motor


1
3.
Ammeter
(0-1) A
MC
1
(0-100) mA
MI
1
4.
Voltmeter
(0–300) V
MC
1
(0–75) V
MI
1
5.
Patch cords
-

As  required

THEORY:

An AC servo motor is basically a two phase induction motor with some special design features. The stator consists of two pole pairs (A-B and C-D) mounted on the inner periphery of the stator, such that their axes are at an angle of 90o in space. Each pole pair carries a winding, one winding is called reference winding and other is called a control winding. The exciting current in the winding should have a phase displacement of 90o. The supply used to drive the motor is single phase and so a phase advancing capacitor is connected to one of the phase to produce a phase difference of 90o.The rotor construction is usually squirrel cage or drag-cup type. The rotor bars are placed on the slots and short-circuited at both ends by end rings. The diameter of the rotor is kept small in order to reduce inertia and to obtain good accelerating characteristics. The drag cup construction is employed for very low inertia applications. In this type of construction the rotor will be in the form of hollow cylinder made of aluminium. The aluminium cylinder itself acts as short-circuited rotor conductors. Electrically both the types of rotor are identical.
WORKING PRINCIPLE  :
The stator windings are excited by voltages of equal magnitude and 90o phase difference. These results in exciting currents i1 and i2 that are phase displaced by 90o and have equal values. These currents give rise to a rotating magnetic field of constant magnitude. The direction of rotation depends on the phase relationship of the two currents (or voltages). This rotating magnetic field sweeps over the rotor conductors. The rotor conductor experience a change in flux and so voltages are induced rotor conductors. This voltage circulates currents in the short-circuited rotor conductors and currents create rotor flux. Due to the interaction of stator & rotor flux, a mechanical force (or torque) is developed on the rotor and so the rotor starts moving in the same direction as that of rotating magnetic field.

GENERAL SCHEMATIC OF AC SERVOMOTOR:




FORMULAE USED:
Transfer function, Gm (s) = Km / (1+ stm)
                                         
Where

Motor gain constant, Km = K / FO + F
                             
                              K is DT / DC
                            FO is DT / DN
                            Torque, T is 9.81 X R (S1 ~ S2)
                            R is radius of the rotor in m
                            Frictional co-efficient, F = W / (2pN / 60)2
                              Frictional loss, W is 30 % of constant loss in Watts
                              Constant loss in watts = No load input – Copper loss
                               No load i/p = V (IR+IC)
                              V is supply voltage, V
                              IR is current through reference winding, A
                              IC is current through control winding, A
                              Copper loss in watts = IC2 RC
                               RC = 174W
                                     N is rated speed in rpm

Motor time constant, tm = J / FO + F
                                    Moment of inertia J is pd4 L R  ρ / 32
                                    d is diameter of the rotor in m ( Given d =39.5 mm)
                                    LR is length of the rotor in m (Given L R =76 mm)
                                    ρ is density = 7.8 X 102 gm / m



PROCEDURE:

1.         DETERMINATION OF FRICTIONAL CO-EFFICIENT, F

  1. Check whether the MCB is in OFF position.
  2. Patch the circuit using the patching diagram.
  3. Switch ON the MCB
  4. Vary the control pot to apply rated supply voltage
  5. Note the control winding current, reference winding current, supply voltage and speed.
  6. Find the frictional co-efficient using the above values


OBSERVATIONS:


S. No.
Supply Voltage
V
(V)
Control winding  Current  Ic
(A)
Reference Winding Current Ir
(A)
Speed
N
(rpm)









CALCULATIONS:



Determination Of Transfer Function Of AC Servo Motor
PATCHING DIAGRAM TO DETERMINE FRICTIONAL CO-EFFICIENT F:


PROCEDURE:

2.   To determine the motor gain constant Km

 DETERMINATION OF FO FROM TORQUE - SPEED CHARACTERISTICS:

1.      Check whether the MCB is in OFF position.
2.      Patch the circuit using the patching diagram.
3.      Set the control pot in minimum position.
4.      Check whether the motor is in no load condition
5.      Switch ON the MCB
6.      Vary the control pot and apply rated voltage to the reference phase winding and control phase winding.  Note down the no load speed.
7.      Apply load in steps. For each load applied note down the speed and spring balance readings. ( Take 3 or 4 sets of readings)
8.      Reduce the load fully and allow the motor to run at rated speed.
9.      Repeat steps 7 and 8 for 75 % control winding voltage.
10.  Draw the graph between speed and torque, the slope of the graph gives FO.

OBSERVATIONS:

S. No
Control voltage Vc1 =
Control voltage Vc2 =
Speed
N

(rpm)
Spring Balance values
Torque T
(Nm)
Speed
N
(rpm)
Spring Balance values
Torque T

(Nm)
S1
(kg)
S2
(kg)
S1
(kg)
S2
(kg)














































           
MODEL GRAPH: TORQUE - SPEED CHARACTERISTICS

DETERMINATION OF K FROM TORQUE - CONTROL VOLTAGE CHARACTERISTICS:
1.      Check whether the MCB is in OFF position.
2.      Patch the circuit using the patching diagram.
3.      Set the control pot in minimum position.
4.      Check whether the motor is in no load condition
5.   Switch ON the MCB
  6.  Vary the control pot and apply rated voltage to the reference phase winding and         control phase winding.  Note down the no load speed.
7.      Load the motor gradually; the speed of the motor will decrease. Vary the control pot 
        and increase the  control winding voltage till the speed obtained at no load is         reached.  Note down control voltage and spring balance readings.
       8.  Repeat step 7 for various speeds and tabulate. (for 1000 rpm)
        9.   Plot the graph between torque and control winding voltage. The slope of the graph                gives the value of K.

OBSERVATIONS:

S. No
Speed N1 =
Speed N2 =
Control
Voltage
Vc
(V)
Spring Balance values
Torque T

Nm
Speed


rpm
Spring Balance values
Control
Voltage
Vc
V
S1
(kg
S2
kg
S1
Kg
S2
Kg















































MODEL GRAPH: TORQUE - CONTROL VOLTAGE CHARACTERISTICS
Determination Of Transfer Function Of AC Servo Motor
PATCHING DIAGRAM TO DETERMINE MOTOR GAIN CONSTANT KM:

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