Greg Watson wrote: > > From: dcm3c@xxxxxxx > > To: femm@xxxxxxxxxxx > > Sent: Tuesday, January 02, 2001 6:42 AM > > Subject: Re: [femm] Re: Incorrect force direction > > > > The program is doing the right thing--the force generated by your > > configuration is just really close to zero. > > Not so......... > > Hi Dave, > > I have attached a Qfield (Ver 3.4, 500 nodes max) screen shot of approx the same > sim which shows a force of 29.574 N @ -1.497 deg (to the right). Note the flux > distortion of the magnet's field is also to the right. > > Here in Oz a Newton of force is worth about 100 g of pressure, so if the model > had a real depth of say, 10 cm we should expect to see about 290 g of force > pushing the magnet into the horizontal centre of the parallel bars according to > the Qfield result. Well, Quickfield uses exactly the same technique to obtain forces as femm does--evaluating Maxwell's stress tensor along a line. As such, it is subject to all of the same caveats as femm with respect to force calculations. In your problem, you could split the stress tensor integration into two parts--one for the left side of the magnet, and one for the right side. If you did this, you'd find that each result is a rather large number, and that both sides have nearly the same magnitude, but different signs. The total force is then obtained by adding the two results. This is basically subtracting two large numbers to get a small number, which isn't a very well-conditioned problem. You could think of it as the stress tensor on a path around the magnet has a large RMS value, but a nearly zero average value. Here, the Quickfield Student Version's 500 node limit isn't adequate to deliver an accurate result. For other problems (i.e. where RMS of stress tensor and average of stress tensor are on the same order), the 500 nodes may be perfectly fine. Their magn1.pbm is a good example of where you can get an OK model out of a limited number of nodes. > Actual duplication of the setup in reality does show a good generation of a > centring force on the magnet. If the rig matches the problem description, you shouldn't see a centering force once the magnet gets between the iron bars. However, just like the numerical problem, I'd expect the actual experimental rig to be pretty sensitive to perturbations. Very strong vertical forces are cancelled out due to the magnet being exactly centered between the bars. Small misalignments can cause these forces not to cancel, and depending on how the magnet is mounted, react some of this force onto the horizontal direction. For example, if the iron bars aren't exactly straight and parallel, I'd expect that to translate into lateral forces. To test how the rig performs, the magnet would have to ride on some sort of linear bearing. That bearing would have to be aligned straight with respect to the bars. In addition, the support for the magnet has be be relatively rigid--if you supported the magnet with, say, a thin aluminum spoke, the bowing of the support would be an asymmetry that would yield lateral forces. These are just some possibilities--you could probably think of others. Anyhow, I modeled your problem on Amperes by IES, which is a rather expensive commercial 3-D magnetostatic solver based on boundary elements, rather than finite elements. This ought to give a good idea of how things would run in a real 3-D test rig, assuming everything is carefully aligned. I arbitrarily made the machine 1" deep in the "into the page" direction, for the purposes of making a 3-D geometry. I chose a relatively fine density for the surface elements, and then set it to evaluate the forces on the magnet at a bunch of different axial positions. What it predicts is that the centering force peaks when the front edge of the magnet is just past the iron, with the centering force dropping to near zero when the magnet is completely between the iron bars. femm predicts the same sort of behavior, except that femm predicts the peak force to be more like 15 Newton/inch, rather than 9 N. The force from the 3-D geometry is smaller than in the 2-D model because some of the magnet's flux leaks into the sides of the bars--this is an intrinsically 3-D effect that can't be modeled by a 2-D solver. Anyhow, since it's only about 4K long, I've attached a pdf file that contains a plot of the force versus distance profile predicted by Amperes 4.0. Dave.
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