Re: Lua sample of line integral

[jim271@xxxxxxxxxxx]

Hello Dave,

Thank you for explaining that detail about the Lorentz force. I've 
only been using it with a simple coil-plunger combination, so I was 
lucky :-)

One problem I've had with the stress tensor around a contour is 
having to use a high mesh density in the region where the contour is 
drawn. If I want a very small air gap, this requires a very large 
number of meshes and long execution time. 

I'm wondering if by using the volume integral for coenergy and taking 
the derivative, you actually get more accurate results (compared to 
the stress tensor) with relatively few meshes in the narrow air gap, 
as long as the mesh density is much smaller than the plunger step 
size? That is, since there is no contour in the air gap, is the mesh 
density critical there?

Also, how do you keep data from one iteration of the lua script to 
pass on to the next iteration so it can calculate the derivative?

Thanks again.

-- Jim

===================================================================


--- In femm@xxxx, dcm3c@xxxx wrote:
> In a message dated 8/16/01 11:01:41 AM Eastern Daylight Time, 
> jim271@xxxx 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
> <A 
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