-------- Original Message --------
Subject: Re: Predicted forces on E614 coils
Date: Sun, 03 Jun 2001 09:15:33 -0700
From: Michael Barnes 
Organization: TRIUMF
To: nathan.rodning@ualberta.ca
CC: John Macdonald , Ewart Blackmore
,drgill@triumf.ca, Gary Wait 
References: <3B197CEC.66C139BA@triumf.ca>
<3B1A558C.3802C98B@phys.ualberta.ca>

Hi Nate,

I am out of the office for the next 3 weeks. But to try and answer your
questions:
I would expect the forces to be a maximum AT full current. The force in
the Z
direction on an individual coil (Fz) is given by the cross product of
the
radial component of flux density (Br) and the circumferential component
of
current density (Jc) [Fz=Br*Jc]. Br, in the force calculation, is the
radial
flux density that intersects the coil of interest. The component Jc is
proportional to the coil current. In addition Br is dependent upon the Z
component of field (Bz "returns"  in the radial direction as Br). A
previous
Opera3D simulation (long_half_sym), carried out at 113.85A, showed that
Bz at
the centre of the solenoid at 113.85A was only 1.4% greater than the Bz
predicted at 245A*113.85A/245A, i.e. Bz is almost directly proportional
to
current.

As the steel saturates more radial field may pass through the coil,
rather than
through the end plates (however the Bz will not increase in proportion
to
current as the steel saturates). So it is expected that the force, as a
function of current, levels off at higher current. But since the Bz is
almost
directly proportional to current between 113.85A and 245A I would not
expect
any nasty surprises.

Please note that some safety margin should be allowed for when
interpreting the
force predictions: the net force is the difference of some large
numbers, e.g.
for a +0.5cm displacement in Zm the net force on the assembly of 12
coils is
4720N. However coil 11 has a predicted force in the Z direction of
-210.3 kN,
and coil 12 a predicted force of +212.3 kN !, i.e; the net force in the
Z
direction is approximately 2% of the largest forces on two coils.

Hope this addresses your concerns for the time being.

Best regards,
Mike

Nathan Rodning wrote:

> Hi Mike-
>         is it possible that the forces may reach a maximum before the steel
> saturates?  Even though it takes a lot of cpu, perhaps it would be
> worthwhile to repeat the calculations at 1/4 current (57A?), 3/4
> current, and full current.
>
> thanks-
>                 nate
>
> Michael Barnes wrote:
> >
> > John,
> >
> > The results of force calculations that both Dennis and I previously
> > carried out on the coils were incorrect -- the finite element mesh were
> > not fine enough to accurately determine these forces.
> > After talking to the authors of the code, Vector Fields, I have carried
> > out some further Post Processing of the simulation results. The Post
> > Processing takes a lot of CPU time, i.e. approximately 25 hours CPU per
> > simulation -- but the results should be considerably more accurate.
> >
> > Here are the results of force calculations for the assembly of 12 coils,
> > carried out as a function of displacement (dZ) of the coils:
> > dZ         Force in Z direction
> > +0.0             0
> > +0.1cm        +943 N (96 kg) -> 960 kg/cm
> > +0.5cm        +4717 N (480 kg) -> 960 kg/cm
> > +3.0cm        +28278 N (2890 kg) ->960 kg/cm
> >
> > The force calculation now gives a predicted force which is monotonic
> > (this was previously not the case), and is approximately 960 kg/cm
> > displacement in Z, at a current of 114 A.
> >
> > The force is positive, for a positive displacement in Z. Hence, when the
> > coils are centered in the iron this point is an unstable equilibrium.
> >
> > Please note that the above forces are for a current of just under 114A.
> > At a (full) current of 245A I would anticipate the force on the assembly
> > of 12 coils would be approximately 4.7 (i.e. [245/113.85]^2) times
> > higher than shown above, i.e. 4500 kg/cm displacement in Z.
> >
> > Best regards,
> > Mike Barnes
>
> --
>
> Nathan Rodning
> Professor of Physics
> (780) 492-3518  /  Fax:  (780) 492-0714
> http://www.thehungersite.com/

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