Hi,I have a project where I have to try and get the maximum force/weight ratio for a magnetic actuator within a set of constraints. I am working on the calculations for the force but I need to know if I am on the right track so I need some help
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:
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:
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
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:
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:
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