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# Re: [femm] Re: Lua sample of line integral

- To: femm@yahoogroups.com
- Subject: Re: [femm] Re: Lua sample of line integral
- From: dcm3c@aol.com
- Date: Thu, 16 Aug 2001 13:54:40 EDT

In a message dated 8/16/01 11:01:41 AM Eastern Daylight Time,
jim271@hotmail.com writes:

> There is a sample script file that's distributed with FEMM 3.1
> showing how to do this very thing using the Lorentz force on the
> coil. I've found this to be much easier than drawing a contour to use
> for the stress tensor. Just highlight the object used for the coil
> and then calculate the Lorentz force. The force on the coil is equal
> and opposite (opposite sign) to the force on the plunger.

Well, you have to be a bit careful using Lorentz force with a solenoid. It
works OK in the coilgun example because there are only 2 objects--the coil
and a ball bearing. In that case, the force from on the coil must equal the
force on the ball. However, in the case of a solenoid, there is typically an
iron core wrapped around the coil. The Lorentz force result here would be
equal to the net force on the plunger and the stator iron, whereas one is
probably really interested in just the force on the plunger.
However, there is a volume integral way to get force in the case where there
is an iron core. Instead of integrating Lorentz force over the coil,
integrate magnetic field coenergy over the entire solution domain (i.e.
everywhere). Evaluate this result at intervals along the stroke of the
plunger. The result is a curve of coenergy versus position. You then infer
what the force is on the plunger by from the coenergy by noting that force on
the plunger is the derivative of coenergy with respect to position. You can
approximate the derivative of coenergy with numerical derivatives like
(Wc[n]-Wc[n-1])/(z[n]-z[n-1]) where Wc[n] is the nth coenergy result and z[n]
is the nth plunger position. This result is equal to the average force over
the interval from z[n-1] to z[n]. For this to work right, the mesh density
in the air around the plunger should be smaller than the size of the
steps--otherwise, the force results come out noisy.
Dave.
--
David Meeker
http://members.aol.com/_ht_a/dcm3c

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