# Force produced by current carrying coil to the sludge(Steel rod).

#### rvb53

Joined Apr 21, 2008
28
hi everyone,

I have a problem, if U see the photo I have coil which carries current of rectified ac waveform through it. I have sludge(Steel rod of weight 20#) which has to be moved till the centre of the coil.

If the current in coil induces magnetic field to sludge to move upward, then what will be the force with which th sludge is gonna move and I need the lift (or) displacement from its initial position to final position.

If possible, I need the equation for the lift of the sludge and which should depend on the current which flows in the coil.

If anybody wants the value of the current, I can give it.....
pls do help me....I am struck in this problem from many days.....

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#### scubasteve_911

Joined Dec 27, 2007
1,203
The current needed isn't constant, but variable. Higher if the iron is further out of the core, and less when it is inside. This is due to the classic r^2 losses in electromagnetics..

Steve

#### mik3

Joined Feb 4, 2008
4,843
The force applied to the sludge equals

F=0.5*(((dL/dx)*i^2)+L*((d(i^2))/dx))

L=(A*μ*N^2)/x where x is the distance the sludge moves into the coil

substitute dL/dx into the previous equation:

F=F=0.5*((((-μ*A*N^2)/x^2)*i^2)+L*((d(i^2))/dx))

find the derivative of your current i and substitute in the above equation to get the final answer.

#### rvb53

Joined Apr 21, 2008
28
hi mik3,
I do not know the force which the sludge got from the current and regarding current flowing in the coil halfwave rectified AC i.e. always +ve and I have discrete values with me ,so how can I find derivative of constant number which is gonna be zero.
can U define what is A and 'N' is no of turns of the coil.is that?

#### rvb53

Joined Apr 21, 2008
28
hi mik3,
I need the equation for the lift of the sludge and I think which goona depend on current in the coil + some losess..

#### mik3

Joined Feb 4, 2008
4,843
hi mik3,
I do not know the force which the sludge got from the current and regarding current flowing in the coil halfwave rectified AC i.e. always +ve and I have discrete values with me ,so how can I find derivative of constant number which is gonna be zero.
can U define what is A and 'N' is no of turns of the coil.is that?
If your half wave rectifier is filtered and gives a nice smooth voltage, then you can ignore this part of the equation L*((d(i^2))/dx). If your current is not pure dc then things get more complicated.

The equation i told you gives a good result if your sludge is fitting exactly inside the coil otherwise things are complicated.

A=cross sectional area of the sludge
N=turns of the coil

#### rvb53

Joined Apr 21, 2008
28
hi mik3,
thanx once again for ur reply and the information.
when I am trying to solve the equation U gave, I am ending up with two unknowns i.e. force(F) and displacement of slug(dx).Is there any way to find the value of force?
I need the displacement of the slug.
I have attached the waveforms of the current and voltage.
pls do help me ....

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#### mik3

Joined Feb 4, 2008
4,843
hi mik3,
thanx once again for ur reply and the information.
when I am trying to solve the equation U gave, I am ending up with two unknowns i.e. force(F) and displacement of slug(dx).Is there any way to find the value of force?
I need the displacement of the slug.
I have attached the waveforms of the current and voltage.
pls do help me ....
dx is not a variable and is not included on the final equation. Your current is almost constant thus assume that this part of the equation equals zero L*((d(i^2))/dx)

#### rvb53

Joined Apr 21, 2008
28
hi mik3,
my final equation is

x=-{[0.5*U*A*(N^2)*(I^2)]/F}

where I do not know the value of F.
can U help me here?

#### thingmaker3

Joined May 16, 2005
5,083
x=-{[0.5*U*A*(N^2)*(I^2)]/F}
Please forgive my intrusion. I've been following this topic closely as I've had a similar problem nagging me for years.

Does the "U" in the above equation mean "$$\mu$$" (permeability)?

And is "A" the cross sectional area of the interior of the coil?

#### rvb53

Joined Apr 21, 2008
28
hi thingmaker3,
ya, U is the relative permeabilty and A is cross-scetional area of the slug which moves in the coil due to the magnetic filed caused by current flowing in the coil..
I am also struck at this problem from weeks and try to get some help...
Is there anyway U can help me?

#### thingmaker3

Joined May 16, 2005
5,083
I suggest plotting F versus x on a graph. Since the slug weight is 20#, any force greater than 88.964 Newton should pull the slug into the coil if the slug need travel no further than x.

Do you know what type of steel the slug is made from? I might be able to find an accurate value for $$\mu$$.

#### mik3

Joined Feb 4, 2008
4,843
hi mik3,
my final equation is

x=-{[0.5*U*A*(N^2)*(I^2)]/F}

where I do not know the value of F.
can U help me here?
If you lift the sludge with the magnetic field then the force should equal the sludge's mass times g (acceleration of gravity, approximately 10 m/s^2) when the sludges is in a stationary position. If the sludge moves in the center of the coil then you cant say that because you dont know exactly the value of the force. The sludge will balance in the center if the force at this position is equal or greater than the mass of the sludge times g, so you dont know the value of the force.

#### rvb53

Joined Apr 21, 2008
28
hi thingmaker3,
I know that the slug is made of steel and I think that relative permeability is 50(min) and 100(max) values for stell.
So,
$image=http://forum.allaboutcircuits.com/mimetex.cgi?\mu&hash=5e0c16136b139187a74fbe4a83c9267c$
= 50*4*pi*10^-7.
Is that true ?

#### rvb53

Joined Apr 21, 2008
28
hi mik3,
I tried to calculate the force F= [(Imax^2)*(Inductance of the coil)]/[2*Lift of slug]. Is that right?
ya mik3, I do not know the value of the force.
If I find anyway to solve for force then I am done with the problem.
Initially the slug gets pulled by the magnetic force(F) of the coil and keeps moving upward untill the centre of coil and after that the magnetic force is removed, so due the remaining force, it(slug) moves further upwards and due to gravity returns back and hits the anvil at bottom.

Any suggestions are appreciated...

Last edited:

#### mik3

Joined Feb 4, 2008
4,843
hi thingmaker3,
I know that the slug is made of steel and I think that relative permeability is 50(min) and 100(max) values for stell.
So,
$image=http://forum.allaboutcircuits.com/mimetex.cgi?\mu&hash=5e0c16136b139187a74fbe4a83c9267c$
= 50*4*pi*10^-7.
Is that true ?
I am not sure about the permeability of steel but you are right about the way you find μ.

#### thingmaker3

Joined May 16, 2005
5,083
Relative permeability of steel can run from as low as 1.01 to more than 850, depending on composition.

$image=http://forum.allaboutcircuits.com/mimetex.cgi?\mu&hash=5e0c16136b139187a74fbe4a83c9267c$