Why is the motor starting torque vs voltage relation square of the voltage?

[Flicker Index]

The starting current is proportional to voltage, but why is the starting torque square of the voltage?

 

[retirede]

The starting current is proportional to voltage, but why is the starting torque square of the voltage?

It’s a straight line, not square.

 

[synchro]

The magnitude of the stator's current and its magnetic field are proportional to the applied voltage V.
The rotor's magnetic field is created by the currents in the squirrel cage windings that have been induced by the rotating magnetic field of the stator. Therefore the magnitude of the rotor's magnetic field will also be proportional to the applied voltage V.
Torque is produced by the reaction of the rotor's magnetic field against the stator's magnetic field and hence it will be proportional to the product of the magnitudes of these two magnetic fields. Since the magnitude of each of these two magnetic fields is proportional to V, then the torque resulting from their interaction with eachother will be proportional to V².

 

[synchro]

It’s a straight line, not square.

It just looks like a straight line on that graph because the percentage changes are small. Square law would give a +10.25% output change for a +5% input change, and a +21% output change for a +10% input change. I think that's very close to what the graph is showing.

 

[paulengr]

Simpler: power = torque x speed

Power = power factor x v^2 / R (basic ohms law)

Over a short change R and PF are approximately constant.

Either torque or speed needs to decrease when voltage (power) decreases.

 

[WasGSOHM]

And,
"horsepower equals torque multiplied by rpm. H = T x rpm/5252, where H is horsepower, T is pound-feet, rpm is how fast the engine [or motor] is spinning, and 5252 is a constant that makes the units jibe. "

 

[Carultch]

And,
"horsepower equals torque multiplied by rpm. H = T x rpm/5252, where H is horsepower, T is pound-feet, rpm is how fast the engine [or motor] is spinning, and 5252 is a constant that makes the units jibe. "

5252 comes from the HP defined as 550 ft-lbf/sec, 1 minute defined as 60 seconds, and 2*pi radii in a full circumference (i.e. radians per revolution).

5252 = (550 ft-lbf/sec-hp) * (60 sec/min)/ (2*pi rad/rev) = 5252 ft-lbf-sec-rev/hp-min-rad

Put that in the denominator, and it translates ft-lbf-RPM to horsepower.

In the metric system, the equivalent factor is the following, which translates Newton-meter-RPM to kW.
(1000 kW/w)*(60 sec/min)/(2*pi rad/rev) = 30000/pi N-m-RPM/kW = 9549 N-m-RPM/kW

 

[retirede]

It just looks like a straight line on that graph because the percentage changes are small. Square law would give a +10.25% output change for a +5% input change, and a +21% output change for a +10% input change. I think that's very close to what the graph is showing.

True...

 

[Julius Right]

I can start from the definitions of an induction motor and will be a boring long detailing. I'd prefer to start with Steinmetz diagram. Steinmetz considered induction motor as a transformer. Then he used a referring factor of rotor impedance and current to stator-as he did in an actual transformer case. The problem was in induction motor there are two frequencies of currents: one fix in the stator[f1] and one variable in the rotor [f1.s]. So, he used the s[slip] as another factor.
Er/Es=k then I'r/Ir=1/k, R'r=k^2*Rr , s=(rpmsynchron-rpm)/rpmsynchnon [the slip]
The power delivered from stator to rotor through the gap it is then Pg=3.E.I'r.cos(ϕ)=3.I'r^2.R'r/s.
From mechanics it is known P=Tq.ω
ω=2.π.rpm/60=2.π.f1/p p=number of pole pairs.
Tq=Pg/(2.π.f1/p) the motor torque
Tq=3.I'r^2.R'r/s/(2.π.f1/p)
If we neglect the stator impedance then E≈Vs and I'r=Vs/√((R'r/s)^2+X'r^2)
Tq=3.Vs^2.R'r/s/((R'r/s)^2+X'r^2)/(2.π.f1/p)

 

[WasGSOHM]

I think I'm back at school.
Haven't heard that Steinmetz name for a very long time.

BTW, I now have it on good authority that that name means "someone who carves gravestones or does more artistic work with stone."

 

[synchro]

I think I'm back at school.
Haven't heard that Steinmetz name for a very long time.

BTW, I now have it on good authority that that name means "someone who carves gravestones or does more artistic work with stone."

Steinmetz is the short guy in the light suit in the center of the picture at the link below. Albert Einstein is just left of him in the picture, and I believe David Sarnoff is the guy on the left side that's leaning toward the center and with his right hand in his pocket.

https://upload.wikimedia.org/wikipedia/commons/6/6b/Albert_Einstein_with_other_engineers_and_scientists_at_Marconi_RCA_radio_station_1921.jpg