I found an error in my Figure 4! I've redrawn it. I think the green
force vectors were right though, so no harm. I can see why this is
has been so difficult to explain though, and perhaps why no one has
understood my explanations.
Below are links to the two figures, Fig. 3 and Fig. 4, that are
critical to my explanation of the effect.
http://www.mtaonline.net/~hheffner/Fig3BBMM.pdf
http://www.mtaonline.net/~hheffner/Fig4BBMM.pdf
Fig. 3 is simple. It merely shows the H field instantly imposed on
the bearing and inner race as the current i flows through them. It
therefore also shows an M field being generated where the H field
is. It is easiest to imagine Fig. 3 and Fig. 4 showing very short
current pulses i at differing times of the rotation, but from the
point of view of the ball bearing. Fig 4 shows where the M fields in
Fig. 3 move after the ball rotates 90 degrees in its travels. They
stay around for a while because of hysteresis. If the current i is
imposed in Fig. 4 as a sudden pulse, you can see that the i l x mu0 M
forces shown in green will be generated. This also happens even if
the current is continuous, but it is complex to imagine how the
continuous wave of M moves.
That's the whole explanation of why the ball bearing motor works, and
in one short paragraph. I hope it makes sense!
Next to look at back emf and how Lentz' Law applies.
Suppose we have armature material with an "o" field in it and a
current i flowing through it bottom to top. I think this is the case
for the ball bearing race adjacent to the shaft, and shown in Fig. 4.
If the armature material has the "o" field as supposed, and is not
moving, then the current flowing upward through the material will
clearly induce force in the material to the right, as in Fig. 1, and
there will be no back emf.
(-) Current driving polarity
^
| i
|
o|o o
o|o o F ->
o|o o
|
(+)
Fig. 1 - material static
Now, if the material starts moving to the right, due to the i L B
force, or for whatever other reason, it will induce a potential in
the current path that opposes the potentials shown in Fig. 1.
(+) Induced potential
|
o|o o o o o
o|o o o o o => material and field move right
o|o o o o o
|
(-)
Fig. 2 - material in motion, induced potential
The emf induced is in the direction opposed to the driving current.
Everything seems to be working nicely according to Lenz' Law. This
is why I expect a proper back emf, and why at least some back emf has
been observed.
Now, if the armature material is driven to the right at a high speed
by an external added force, the current through the material still
exerts the same i L B force. However, the back emf should increase
due to the increased material (and thus magnetic field) motion, thus
reducing i and thus reducing the energy applied to the armature. The
armature should slow down if the external torque is removed.
The hysteresis effect can make testing the back emf difficult because
(1) it requires time for the M to be induced and (2) the M has to
move into place (the place where i is) without benefit of a
sustaining H. Thus condition (1) requires not moving too fast, and
condition (2) requires not moving too slowly. The relationship
between speed, i, torque, and back emf is therefore complicated.
From experience it appears the ideal speed of the motor is pretty
fast. My motor has not had the opportunity to come up to speed
because I have had to shut it down due to the nichrome resistor
overheating and concerns regarding the battery being overloaded by a
large factor.
I think examining the potential drop across ball bearing motors at
differing speeds and currents will show even more clearly that the
effect is purely ordinary magnetic, and that Lenz' Law applies. Too
bad the motor is so inefficient, because that masks the basic
performance characteristics.
The curious thing is there appears to be no generator equivalent!
Horace
