induction machines Flashcards
typical effiecncy
> 90%
key components
soft iron core,
3 phase winding,
soft iron rotor
squirrel cage
setup of staor winding
iron stator core in which a three-phase stator winding is incorporated into a series of slots in the core
airgap field produced by phase A
Ba = magnetic flux density in the airgap K = a constant which relates to the dimensions of the iron circuit in the machine N×Ia = phase Ampere-turn
current in each coil a,b ,c
Ia=isin(wt)
Ia=isin(wt-120)
Ia=isin(wt-240)
synchronous speed
Ns=f*60/pole pairs
induction speed in comparison to synchronous speed
an induction machine runs at a speed which is close to, but always
slightly lower than the synchronous speed
equivalent cicuit for one phase
a resisistor and inductor then in parallel an inductor/resistor/back emf
what does each element of the equivalent cicuit represent
R1- stator winding resistance per phase
X1- stator leakage resistance
Rm- eddy cuurent and hysteress(iron losses)
Vp and Ip when star connected
Vp=Vl/sqrt(3)
Ip=Il
Vp and Ip when delta connected
Ip=Il/sqrt(3)
Vp=Vl
slip
S=(Ns-N)/Ns
what happens when the speed reaches synchronous speed
The rotor and stator field move at the same speed. No change in flux linkage, no induced voltage , zero current and therefore zero torque
Power delivered by the stator
Ps=(2piNs/60)*T
Mechanical output from the rotor
Pr=(2piN/60)*T
rotor loss
the difference between stator power and power from the rotor
rotor loss in teerms of power delivered by stator and slip
stator power*slip
rotor equivalent circuit
An inductor and a resistor in series
what do the resistor and inductor represent
R-rotor resistance
L- rotor leakage and inductance (fields that do not couple to the stator)
impedance of the inductor
j2pifL
torque and power
P=Tw
referring voltage uses
E’2=(N1/N2)*E2
turns ratio
referring current and voltage
I’^2R’=I^2R
for referring current
I’2=(N2/N1)*I2
for referring resistance and inductance
R’2=(N1/N2)^2*R2
what is the referred circuit multiplied by
f1/f2
aswell as the referred components what is in equivalent circuit
in parralel and and in parralel to eachother and inductor and resistor
what is the star connected phase voltage
Va=V/sqrt(3)
what side of pull out torque is a machine normally operated
Above the pull out torque
what speed is when current at a maximum and why can’t this be maintained
at 0 speed - it will overheat
slip is an indicator of
rotor thermal losses
what is lagging/power factor
power with a phasor
cos(theta)=x lagging
copper loss equation
I^2*R
output power using torque
P=Tw
f1 to f2 using slip
f1=s*f2
how does a reluctance stepper motor work
the rotor alligns with energised teeth
how can the number of steps in a reluctance stepper be increased
half stepper mode
what is 2 benefits of half stepper mode
the overshoot of the rotor is lower and greater resolution of load positioning
At a high step rate what happens to pul out torque
it goes down
