Actuator:

Equivalent Circuit:

Lamination details:

Dimensions:

**These are the constraints:**

12V dc input supply

Current not to exceed 1A in the coil

Maximum depth of core is 16 mm

Lamination type, hot rolled silicon steel

**Parameters under my control:**

Number of turns on coil

Area of the core

Top air gap width

All dimensions are in mm. The 0.5mm is the thickness per lamination.

__I will show some of my work here what iv'e done so far:__

__The first thing is to calculate the current in the coil:__

Using,

**R**= p*length of wire/Area of wire ,

**p**= resistivity of copper wire

**Length wire**= Number of turns*Perimeter of bobbin ,

**Perimeter of bobbin**= 74mm

**Area of wire**= (pi*d^2)/4,

**where d is diameter of wire**= 0.32 mm

__I am thinking I should be aiming for maximum current in the coil to get maximum mmf ?__

__So I chose as a start:__

**Number of turns**= 775

Using

**V**= IR, where

**V**= 12V (fixed)

**I**= 0.97 A

So,

**Total mmf**= NI

= 775*0.97

= 751.75 At

__For the air gap, I am thinking I should make it small so as to get a higher H value ?__

So I chose as a start:

So I chose as a start:

**Top air gap**= 0.5 mm

__Using similar triangles:__

lgt/40 = lgc/20 where

**lgt**= top air gap (0.5mm) and

**lgc**= centre air gap

**lgc**= 0.25mm

__I can now calculate the air gap reluctances, as follows:__

**Rgt**= Lgt/u*Agt

**Rgc**= Lgc/u*Agc

where Rgt and Rgc are the top and centre air gap reluctances

__For the area, i'm not too sure. If I add too many laminations the mass will increase__

So I chose as a start:

So I chose as a start:

16 laminations*0.5mm thickness = 8mm depth

So,

**Agt**= 8*8 = 64 mm^2

**Agc**= 16*8 = 128 mm^2

__Substituting I get:__

**Rgc**= 1.55*10^6 At/Wb

**Rgt**= 6.22*10^6 At/Wb

The next part I need to estimate the mmf drops in the air gap, so I estimated 90% drop in the combined Rgt and Rgc. This part I am not sure off but I know that mmf will be greatest in the air gap

So, 0.9*751.75 (Total mmf) = 676.575 At for

**Rgt**and

**Rgc**

__I then divided that mmf individually between Rgt and Rgc using the ratio:__

20:80 , ie 20% for Rgc and 80% for Rgt. I am also not too sure about this part

So, 0.2*676.575 = 135.315 =

**mmf of Rgc (Fgc)**

and 0.8*676.575 = 541.26 =

**mmf of Rgt (Fgt)**

Now, I found B using the formula

**Bgc**= Fgc*u/lgc

**Bgt**= Fgt*u/lgt

Substituting I get

**Bgc**= 0.68 T = magnetic field of

**RcoreAB**because area and flux is same

and,

**Bgt**= 1.36 T = magnetic field of

**RcoreBCDA**because area and flux is same

Using the BH curve for hot rolled silicon steel, I get

**Hgt**= 660 At/m

**Hgc**= 40 At/m

Now using the formula

**F**= HL, I can find the remaining mmf core drops

I hope that wasn't too long, can you please see if i did it correctly, thanks