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Re: (ET) Curtis controller mod



In case anyone wants a long-winded explanation of the physics behind why 
field weakening lets the tractor go faster....

When I first learned that the Elec-Trak achieves its highest speeds by 
weakening the field (which I had never heard of a motor doing), I was 
confused about how it worked. The torque on a loop of wire of area A 
carrying current I in a magnetic field B is IABsin(wt), where w is the 
angular frequency that the motor is spinning at. So the torque would be 
maximum when sin(wt) is +/- 1, so the max torque would be IAB. So, the 
torque is proportional to the field strength.

So it seemed odd that  weakening the field would allow the motor to spin 
faster, if there is less torque. So, back when I first heard about this, I 
had to did a little more thinking about it. In case anyone is interested, 
here's my explanation of why it does this.

It all has to do with the induced current. The  magnetic "flux" through a 
loop of wire is the amount of magnetic field passing through the loop - an 
analogy would be holding a hula hoop outside in the rain, we could speak 
of the "rain flux" through the hoop. The rain flux would depend on how 
hard it's raining (R), the area of the loop (A), and the angle between 
them (cos(theta), where theta is measured between the rain and a vector 
perpendicular to the hoop - so the rain flux is maximum when the hoop is 
held horizontal), RAcos(theta).  The magnetic flux would similarly be 
BAcos(theta). If the loop is spinning at a rate w, then theta would be wt, 
so the flux is BAcos(wt).

If you change the flux through a loop of wire, it induces a current in the 
wire. You could alternatively think of it as inducing a voltage across the 
loop (called "back EMF"), which is equal to the number of loops (n) 
multiplied by the change in flux, which would be the derivative of the 
flux, thus the back EMF is nwBAsin(wt). 

Notice the w that is now part of the stuff in front of the trig function. 
So the maximum back EMF is nwBA, thus proportional to the magnetic field 
strength (B) and the angular velocity the loop (armature) is spinning at. 
As a motor spins faster, that back EMF gets bigger, opposing the battery 
voltage - and that is what ultimately sets a limit on how fast the motor 
can spin. So since that back EMF is proportional to both w (speed) and B 
(field), if you make the field smaller, it will allow the motor to spin 
faster before the back EMF gets high enough to keep it from going any 
faster.

The problem is that the field strength is reduced by just throwing a 
resistor in series with the coil - and any time you toss a resistor in 
series with the stuff you want to power, you are wasting some power across 
that resistor, accomplishing nothing other than producing heat. So, it's 
less efficient. 

If the field strength could be reduced without just wasting energy across 
a resistor, then it shouldn't be any less efficient.

Mike




________________________________
Michael S. Briggs, PhD
UNH Physics Department
(603) 862-2828
________________________________

________________________________________
From: Robert Troll <roberttroll hotmail com>
Sent: Thursday, April 28, 2016 11:12 PM
To: elec-trak cosmos phy tufts edu
Subject: Re: (ET) Curtis controller mod

So ideally the field weakening should only be used occasionally, not when 
doing active things (mowing, etc.).

Mike
________________________________

My understanding, and i think it is stated in the manual, is that field 
weakening is only to be used occasionally when torque is not required 
(working) as a short burst of speed. As weakening the field causes the 
motor to spin faster, use more power, loose torque, and generate more 
heat. It does say that "whenever possible the speed control should be 
maintained in the recommended DRIVE position for most efficient 
operation". Drive position is straight 36v, non weakened field.

It is a extra feature, not something intended to be used as a normal 
operating mode.


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