Terry Blanton wrote:
On 1/22/07, Stephen A. Lawrence <[EMAIL PROTECTED]> wrote:
True; but the energy it takes to get over the bump doesn't depend on the
speed of rotation. It's the same whether you do it fast or slow.
This is the error in your reasoning. Assuming the kick is an EM pulse
generating, say, a 1 Tesla field, the duration of the pulse and
subsequent energy decreases with higher RPM. At the limit (excluding
inductance), the pulse width is zero; hence, Jones post on this
subject.
I don't think you can neglect inductance, though, for a couple reasons.
First, the bigger the kick, the bigger the energy you must put in to
build the field. The shorter the duration, the larger dI/dt must be,
and the higher the voltage needed to build the field. So, a shorter
kick is "pricier".
Second, and more significant, the energy you put in to build the field
comes back out again when the field collapses, _minus_ the part that was
used to drag the load up over the "cliff". _That_ part -- the "true
cost" -- shows up as additional back EMF in the electromagnet, and
_that_ is the part that doesn't depend on the duration of the pulse: it
depends on the field gradient and how far the load moves, but not on how
fast it moves. (Assuming constant coil current during the "kick" (bad
assumption, of course!), back EMF is proportional to load velocity, and
total energy required is back EMF times duration; so, shortening the
time increases the needed power and decreases the duration by equal
factors and the net energy needed is unchanged.)
So, in toto, you actually pay out (and don't receive back) a cost which
is related solely to the size of the "bump" you need to drag the load
over. In addition, you "lend out" (and get back!) an additional "fee"
to set up the field; you get this back when you shut the field off
again. (Of course, you may just get this back in the form of burned
points or a warm power transistor...)
You pay interest on the "loan" in the form of dissipation due to
resistance in the wires of the electromagnet. That "interest" will be
reduced if the "kick" can be made shorter (as the motor goes faster).
But the irreducible energy cost of pulling the load up the cliff won't
actually decrease as a result of higher motor speed.
Higher speed => efficiency of the magnet's action will be higher, due to
reduction of resistive losses. But that just gets you closer to the
ideal state of just putting in the energy you actually need, without any
"extra cost" in the form of waste; it doesn't reduce the amount of
energy you actually need.
Terry
