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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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