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Magnetic Forces
Radial forces
The forces between a coil and some ferromagnetic material is
highly depending on the distance from the magnet.
An approximation of the stray field (for large r)
B = Bo * r ^ (-3)
and the field gradient is
dB/dr = - 3 Bo * r ^ (-4)
The force is proportional to the product of the induced field in
the ferromagnet and the field gradient. The induced field is proportional
to the stray field, for low fields, but gets constant when the ferromagnet
saturates. Therefore the force between the coil and a ferromagnetic piece
is proportional to the power of -4 of the distance in high fields
F ~ r ^ (-4)
and proportional to the power of -7 of the distance in low fields.
When the distance is kept constant, the relation between the force
and the central field is quadratic for low fields, and gets linear
for higher fields.
Taking the torque into account
In general, the forces or not only radial but also tangential,
inducing a torque onto the magnet. For estimating the forces
on the fixation, we need to take into account the distance of
the fixation points from the coil center.
For MA7, with a mean coil radius of about 100 m and fixation points
at about 150 mm from the coil center, we get the following:
Ro: object distance (mm)
phi: angle (deg) between field direction and direction of object, for maximum force on fixation
Fp: force when object on magnet axis (in field direction)
Ft: maximum total force on fixation
Ro | phi | Ft / Fp |
<600 | 0 | 1.0 |
800 | 20 | 1.04 |
1000 | 27 | 1.13 |
1200 | 32 | 1.25 |
This particular version was published on 11-Nov-2011 08:16:01 UTC by MarkusZolliker.
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