Lecture 8:
A Design Example An Electromagnet
Objective
„
Use a genetic algorithm to solve an engineering
design example
2
The Problem
„
Design an electromagnet to lift a mass.
i
rb
vb
Battery
f
M
3
Specifications
„
Mass
… 10
kG
… 10 cm by 10 cm area
… Magnetic material should not overlap mass
… Must lift from distance of 5 mm
… Gravity is on surface of Earth (G=9.8 m/s2)
„
Battery
… vb
= 12 V
… rb = 0.5 Ω
… Current should not exceed 6 A
4
Specifications (Continued)
„
Winding
… Should
not exceed packing factor of 0.7
… May use Aluminum (Al) or Copper (Cu)
… Aluminum
Density (ρw) = 2701 Kg/m3
„ Conductivity (σw) = 35.4 1 1/(μmΩ)
„ Current Density (jmax) = 6.14 MA/m2
„
… Copper
Density (ρw) = 8900 Kg/m3
„ Conductivity (σw) = 58.0 1/(μmΩ)
„ Current Density (jmax) = 7.62 MA/m2
„
5
Specifications (Continued)
„
Magnetic Material
… Microsil
„
Bsat = 1.4 T, μ = 15000 μ0 , ρm = 7064 Kg/m3
… Superperm
„
Bsat = 0.7 T, μ = 6000 μ0 , ρm = 8069 Kg/m3
… Superperm
„
80
49
Bsat = 1.2 T, μ = 3500 μ0 , ρm = 7892 Kg/m3
6
Specifications (Continued Again)
„
Size (Mass)
… Total
mass of electromagnet should be as small as
possible
7
Electromagnet Dimensions
ww
wb
Depth into
page = d
dw
ds
g
wi
we
ws
we
8
Design Variables
„
Wire
… Material
„
Type mw
1=Cu, 2=A)
… Conductor
Cross Section ac
… Number of Turns N
„
Magnetic Material
… Material
„
Type mm
1=Microsil, 2=Superperm 80, 3=Superperm 49)
9
Design Variables (Continued)
„
Core
… Slot
width ws
… Wire window width ww
… Slot depth ds
… Wire window depth dw
… End width we
… I-core width wi
… Back width wb
… Depth d
10
Parameter Vector
⎡ mw ⎤
⎢a ⎥
⎢ w⎥
⎢N ⎥
⎢ ⎥
⎢ mm ⎥
⎢ ws ⎥
⎢ ⎥
⎢rww ⎥
θ =⎢ ⎥
d
⎢ s⎥
⎢ rdw ⎥
⎢ ⎥
⎢ we ⎥
⎢ rwi ⎥
⎢ ⎥
⎢ rwb ⎥
⎢ d ⎥
⎣ ⎦
ww = rww ws
d w = rdw d s
wi = rwi we
wb = rwb we
11
Data Vector
⎡ M ⎤
⎢ G ⎥
⎥
⎢
⎢ g ⎥
⎥
⎢
ρ
⎢ w ⎥
⎢ ρm ⎥
⎥
⎢
Ψ = ⎢ σw ⎥
⎥
⎢ B
⎢ sat ⎥
⎢ imax ⎥
⎥
⎢
J
⎢ max ⎥
⎢ l max ⎥
⎥
⎢
⎢⎣ p f ,max ⎥⎦
12
Electrical Analysis
„
Goal
⎡pf
⎢ j
⎢
⎢⎣ i
„
⎤
⎥ = F (θ, Ψ)
elec
⎥
⎥⎦
Matlab m-file: Electrical_Analysis.m
13
Electrical Analysis
„
Packing factor
ac N
pf =
ww d w
„
Winding volume (conductor)
(
v w = p f ww d w (2d + 2 wb ) + πd w2 ww
„
Winding length
)
vw
lw =
ac
14
Electrical Analysis (Cont.)
„
Winding resistance
rw =
„
Current
„
Current Density
lw
a cσ w
vb
i=
rb + rw
i
j=
ac
15
Magnetic Analysis
„
Goal
⎡ B0,1 ⎤
⎢B ⎥
⎢ 1, 2 ⎥
⎢ B2,3 ⎥ = Fmag (θ, i, Ψ )
⎢
⎥
⎢ B 4,5 ⎥
⎢ fe ⎥
⎣
⎦
„
Matlab m-file: Magnetic_Analysis.m
16
Magnetic Equivalent Circuit
ww
N0
dw
N1
N7
N2
N6
N3
N4
N5
we
ws
we
wb
ds
g
wi
17
Magnetic Equivalent Circuit (Cont)
Pe
Pvl
Ni
Φ 0 ,1
N0
Φ1,2
P0 ,1
P0 ,7
N1
P1, 2
N2
Φ 2 ,3
N7
Phl
P6 ,7
P2, 3
N3
N6
P6, 3
P5, 6
P3 ,4
N5
P4 ,5
Φ 4 ,5
N4
18
Review: Magnetic Equivalent Circuits
19
Magnetic Material Permeances
P0,1
wb dμ
=
ws + we
P1, 2 = P0,7
P2,3 = P6,7
P4,5
ww
2 we dμ
=
wb + d w
we dμ
=
ds − dw / 2
wi dμ
=
ws + we
N0
dw
N1
N7
N2
N6
N3
N4
N5
we
ws
wb
ds
g
wi
we
20
Air Gap Permeances
P6,3
(d s − d w )dμ 0 2 μ 0 (d s − d w ) ⎛ πwe
ln⎜⎜1 +
=
+
ws
ws
π
⎝
ww
⎞
⎟⎟
⎠
N0
P3, 4 = P5,6 =
we dμ 0 μ 0 d ⎛ πwi ⎞
⎟⎟ +
ln⎜⎜1 +
+
g
g
π
123 144⎝2443⎠
main face
N7
N2
N6
N3
wb
ds
outer face
2μ 0 d
⎛ π min(ws , d s ) ⎞ 2μ 0 we ⎛ πwi ⎞
⎟⎟
⎟⎟ +
ln⎜⎜1 +
ln⎜⎜1 +
π
π
4g
⎝ 44g4
⎝4
1444
4244444
3⎠ 14442
3⎠
inner face
dw
N1
g
N4
N5
wi
front / back faces
we
ws
we
21
Hor. And Vert. Leakage Permeances
ww
1 μ 0 d w d 2 μ 0 d w ⎛ πwe
ln⎜⎜1 +
+
Phl =
3 ws
3π
ws
⎝
Pvl =
⎞
⎟⎟
⎠
N0
N1
1 μ 0 dww
6 ds + g
dw
N7
N2
N6
N3
N4
N5
we
ws
we
wb
ds
g
wi
22
End Leakage Permeance
ww
wt = d s − d w
Pe1 =
μ 0 wt wb (d + 2we )
wt + wb
1
ww +
k1 = d w − 2 ww
⎧ 2 ww
⎪
k2 = ⎨ d w
⎪ 2
⎩
(2d w + wt + wb ) wt wb
wt + wb
d w > 2 ww
dw
d w ≤ 2 ww
1 2 2
⎡ 4
3
+
+
k
2
k
k
k1 k 2
1 2
⎢ 2
4
μ 0 (d + 2we ) ⎢
Pe 2 =
4
8ww2 d w2 ⎢− 2 k 3 k + k1 ln⎛⎜1 + 2 2 k 2
⎢
1 2
k1
8
16 ⎜⎝
⎢⎣
Pe = Pe1 + Pe 2
⎤
⎥
⎥
⎞⎥
⎟⎥
⎟
⎠⎥⎦
N0
N1
N7
N2
N6
N3
ds
g
N4
N5
we
wb
ws
wi
we
23
Nodal Equations
Pe
(F1 − Ni )P0,1 + F1 Pe + (F1 − F2 )P1,2 = 0
Pvl
(F2 − F1 )P1,2 + (F2 − F7 )Phl + (F2 − F3 )P2,3 = 0
(F3 − F6 )P6,3 + (F3 − F4 )P3,4 + (F3 − F2 )P2,3 = 0
(F4 − F3 )P3,4 + (F4 − F5 )P4,5 = 0
(F5 − F4 )P4,5 + (F5 − F6 )P5,6 = 0
(F6 − F7 )P6,7 + (F6 − F5 )P5,6 + (F6 − F3 )P6,3 = 0
F7 P0,7 + (F7 − F2 )Phl + (F7 − F6 )P6,7 = 0
Ni
Φ 0 ,1
N0
Φ1,2
P0 ,1
P0 ,7
N1
P1, 2
N2
Φ 2 ,3
N7
Phl
P6 ,7
P2, 3
N3
N6
P6, 3
P5, 6
P3 ,4
N5
P4 ,5
Φ 4 ,5
N4
24
Nodal Equations (Cont)
⎡ P0,1 + Pe + P1, 2
⎢
− P1, 2
⎢
⎢
0
⎢
0
P=⎢
⎢
0
⎢
0
⎢
⎢
0
⎣
P1, 2
− P1, 2
+ Phl + P2,3
0
− P2,3
0
0
0
0
0
0
− P2,3
0
0
P6,3 + P3, 4 + P2,3
− P3, 4
0
− P3, 4
P3, 4 + P4,5
− P4,5
0
− P4,5
P4,5 + P5,6
− P6,3
0
− P5,6
0
− Phl
− P6,3
0
0
0
− P5,6
0
P6,7 + P5,6 + P6,3
− P6,7
F = NiP0,1 P −1
[F1
F2
F3
F4
F5
1st
⎤
⎥
⎥
⎥
0
⎥
0
⎥
⎥
0
⎥
− P6,7
⎥
+ Phl + P6,7 ⎥⎦
0
− Phl
P0,7
column
F6
F7 ] = F T
25
Fluxes
Pe
Φ 0,1 = ( Ni − F1 ) P0,1
Pvl
Φ1, 2 = ( F1 − F2 ) P1, 2
Ni
Φ 2,3 = ( F2 − F3 ) P2,3
Φ 3, 4 = ( F3 − F4 ) P3, 4
Φ 4,5 = (F4 − F5 )P4,5
Φ 5,6 = ( F5 − F6 ) P5,6
Φ 6,7 = ( F6 − F7 ) P6,7
Φ 0,7 = F7 P0,7
Φ 0 ,1 N
1
N0
Φ1,2
P0 ,1
P0 ,7
P1, 2
N2
Φ 2 ,3
N7
Phl
P6 ,7
P2, 3
N3
N6
P6, 3
P5, 6
P3 ,4
N5
P4 ,5
Φ 4 ,5
N4
26
Flux Densities
B0,1 =
B1, 2 =
B2,3 =
B4,5 =
ww
Φ 0,1
wb d
N0
N1
Φ1, 2
we d
Φ 2, 3
dw
N7
N2
N6
N3
wb
ds
we d
Φ 4,5
wi d
N4
N5
we
ws
g
wi
we
27
Force
„
Using co-energy techniques and assuming
magnetic linearity it can be shown
∂P3, 4
∂g
=
∂P5,6
∂g
=−
we dμ 0
g2
2μ 0 d min(ws , d s )
μ 0 dwi
2μ 0 dwe wi
−
−
−
g (g + πwi ) 4 g (4 g + π min(ws , d s )) g (g + πwi )
∂Pvl
1 μ 0 dww
=−
∂g
6 (d s + g )2
28
Force (Cont.)
⎡0
⎢0
⎢
⎢0
⎢
⎢
∂P ⎢0
=⎢
∂g ⎢
⎢0
⎢
⎢
⎢0
⎢
⎢⎣0
0
0
0
0
∂P3, 4
0
0 −
∂g
∂P3, 4
0
−
0
∂P3, 4
∂g
∂P3, 4
∂g
∂g
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
∂P5,6
−
∂g
∂P5,6
∂g
0
−
∂P5,6
∂g
∂P5,6
∂g
0
0⎤
0⎥⎥
0⎥
⎥
⎥
0⎥
⎥
⎥
0⎥
⎥
⎥
0⎥
⎥
0⎥⎦
29
Force (Continued)
[ ]
∂L
= N 2 P012 P −1
∂g
1st row
[ ]
∂P −1
P
∂g
∂Pvl
+N
1st column
∂g
2
1 ∂L 2
fe = −
i
2 ∂g
30
Setting Up Constraints
„
Less than function
1
⎧
⎪⎪
1
ltne( x, xmax , Δx) = ⎨
x
−x
⎪1 + max
⎪⎩
Δx
x ≤ xmax
x > xmax
31
Setting Up Constraints
„
Greater than function
1
⎧
⎪⎪
1
gtne( x, x min , Δx) = ⎨
x −x
⎪1 + min
⎪⎩
Δx
x ≥ x min
x < x min
32
Geometrical Constraints
„
Recall, magnetic material should not overlap
mass
c1 = ltne( ws + 2we , lmax ,0.1lmax )
c2 = ltne(d , lmax ,0.1lmax )
33
Electrical Constraints
„
Packing Factor c3 = ltne( p f , p f ,max ,0.1 p f ,max )
„
Current Density c4 = ltne( j, jmax ,0.1J max )
„
Current
c5 = ltne(i, imax ,0.1imax )
34
Flux Density Constraints
„
Back of U-Core c6 = ltne( B0,1 , Bsat ,0.01Bsat )
„
Back of Legs
c7 = ltne( B1, 2 , Bsat ,0.01Bsat )
„
Front of Legs
c8 = ltne( B2,3 , Bsat ,0.01Bsat )
„
I-Core
c9 = ltne( B4,5 , Bsat ,0.01Bsat )
35
Force Constraints
„
We must lift mass (and I-core)
f req = ( M + wi d ( ws + 2we ) ρ m )G
c10 = gtne( f e , f req ,0.01 f req )
36
Performance Metrics
„
ww
Total mass
m1 =
(2d s we d + ( ws + 2we )( wb + wi )d )ρ m +
p f (ww d w (2d + 2 wb ) + πd w2 ww )ρ w
wb
Depth into
page = d
dw
ds
g
wi
we
ws
we
37
Fitness Function
„
Combined constraint
c = min(c1 , c2 ,L c10 )
„
Fitness Function
1
⎧
c =1
⎪⎪ m + ε
f = ⎨ 10 1
⎪ ∑ ci − 10 c < 1
⎪⎩c =1
38
Code Organization
„
Design Codes
…Electromagnet_Design.m
„ GOSET
…Electromagnet_Fitness.m
ƒ Electrical_Analysis.m
ƒ Magnetic_Analysis.m
39
Code Organization (Cont)
„
Supporting Routines
… Electromagnet_Drawing1
… Electromagnet_Drawing2
… Electromagnet_Design_Review
… Electromagnet_Design_Multirun
… Electromagnet_Design_Multrun_Review
40
Electromagnet_Design.m (1/3)
%
%
%
%
%
%
%
%
Electromagnet Design
Written by:
Ricky Chan for S.D. Sudhoff
School of Electrical and Computer Engineering
1285 Electrical Engineering Building
West Lafayette, IN 47907-1285
E-mail: [email protected]
% Set Up Population
GAP
= gapdefault;
GAP.fp_ngen = 2500;
GAP.fp_ipop = 500;
GAP.fp_npop = 500;
GAP.mc_alg = 4.0;
GAP.dt_alg = 3;
% Set Up Migrations
GAP.mg_nreg=5;
GAP.mg_tmig=100;
GAP.mg_pmig=0.05;
% Units
mm=1.0e-3;
cm=1.0e-2;
% number of regions
% mean time between migrations
% probability of a individual migrating
41
Electromagnet_Design.m (2/3)
% Problem Requirement Data
Psi.M
= 10;
Psi.G
= 9.8;
Psi.g
= 0.5*cm;
Psi.rhow
= [
8900;
2701];
Psi.sigmaw = [
58.0;
35.4]*1e6;
Psi.jmaxw = [
7.62;
6.14]*1e6;
Psi.descw = ['Copper '; 'Aluminum'];
Psi.bmaxm = [
1.4;
0.7;
Psi.rhom
= [7064.1;
8069.4;
Psi.myum
= [ 15000;
6000;
Psi.descm = ['Microsil
'; ...
'Superperm 80'; ...
'Superperm 49'];
Psi.imax
= 6;
Psi.lmax
= 10e-2;
Psi.pfmax = 0.7;
Psi.vb
= 12;
Psi.rb
= 0.5;
1.2];
7892.1];
3500];
%
%
%
%
%
%
%
%
%
%
Mass of object (Kg)
Gravity (m/s2)
Gap Width (m)
Wire - Kg/m3
Wire - A/Ohm
Wire - A/m2
Wire - Description
Steel - Bsat, T
Steel - Density Kg/m3
Steel - Perm., (relative)
%
%
%
%
%
%
Steel Maximum
Maximum
Maximum
Battery
Battery
Description
current, A
length
packing factor
Voltage
Resistance
42
Electromagnet_Design.m (3/3)
% Genetic Mapping
%
mw
GAP.gd_min = [ 1
GAP.gd_max = [ 2
GAP.gd_type = [ 1
GAP.gd_cid = [ 1
ac
1e-8
1e-4
3
1
N
10
1e3
3
1
mm
1
3
1
1
ws
1*cm
10*cm
3
1
rww
0.1
1.0
3
1
ds
1*mm
20*cm
3
1
rdw
0.1
1.0
3
1
we
1*mm
5*cm
3
1
rwi
0.2
2.0
3
1
rwb
d
0.2 1*mm];
2.0 10*cm];
3
3 ];
1
1 ];
% Solve Problem
[fP,GAS]= gaoptimize(@Electromagnet_Fitness,GAP,Psi,[],[],[]);
% Get Final Answer and Plot
final_parameters = GAS.bestgenes(:,end);
f = Electromagnet_Fitness(final_parameters,Psi,23);
% Save run
s=input('Type 1 to Save Run ');
if (s==1)
save samplerun
end
43
Electromagnet_Fitness.m (1/7)
function fitness = Electromagnet_Fitness(param,Psi,figNum)
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
ELECTROMAGNET_FITNESS
fitness = Electromagnet_Fitness(param,Psi,x)
Inputs:
param
Psi
x
= design parameters
= data vectors
= optional input to print out extra information
Outputs:
fitness
= fitness value
Written by:
Ricky Chan for S.D. Sudhoff
School of Electrical and Computer Engineering
1285 Electrical Engineering Building
West Lafayette, IN 47907-1285
E-mail: [email protected]
44
Electromagnet_Fitness.m (2/7)
% Map to nicer variable names
mw
= param(1);
ac
= param(2);
N
= round(param(3));
mm
= param(4);
ws
= param(5);
rww
= param(6);
ds
= param(7);
rdw
= param(8);
we
= param(9);
rwi
= param(10);
rwb
= param(11);
d
= param(12);
45
Electromagnet_Fitness.m (3/7)
% Computing the width of winding (ww), depth of winding (dw), width of the
% I core (wi), and the width of the back of the U core (wb)
ww = rww*ws;
dw = rdw*ds;
wi = rwi*we;
wb = rwb*we;
% Electrical Circuit Analysis
[pf, j, i] = Electrical_Analysis(param,Psi);
% Magnetic Analysis
[B01, B12, B23, B45, fe] = Magnetic_Analysis(param,Psi,i);
% Constraints
lmax = Psi.lmax;
pfmax = Psi.pfmax;
jmaxw = Psi.jmaxw(mw);
imax = Psi.imax;
bmax = Psi.bmaxm(mm);
rhom = Psi.rhom(mm);
rhow = Psi.rhow(mw);
46
Electromagnet_Fitness.m (4/7)
c1 =
c2 =
c3 =
c4 =
c5 =
c6 =
c7 =
c8 =
c9 =
f_req
c10 =
ltne(ws+2*we,lmax,0.1*lmax);
ltne(d,lmax,0.1*lmax);
ltne(pf,pfmax,0.1*pfmax);
ltne(j,jmaxw,0.1*jmaxw);
ltne(i,imax,0.1*imax);
ltne(B01,bmax,0.01*bmax);
ltne(B12,bmax,0.01*bmax);
ltne(B23,bmax,0.01*bmax);
ltne(B45,bmax,0.01*bmax);
= (Psi.M + wi*d*(ws+2*we)*rhom)*Psi.G;
gtne(fe,f_req,0.01*f_req);
% find the aggregrate constraint
c = [c1 c2 c3 c4 c5 c6 c7 c8 c9 c10];
cmin = min(c);
% design objective
m1 = (2*ds*we*d + (ws+2*we)*(wb+wi)*d)*rhom + ...
pf*(ww*dw*(2*d+2*wb)+pi*dw^2*ww)*rhow;
% compute the fitness
if (cmin == 1)
fitness = 1/(m1+1e-6);
else
fitness = sum(c)-length(c);
end
47
Electromagnet_Fitness.m (5/7)
% if more than 3 arguments, plot the result
% and write a report
if nargin >= 3
format short g
disp('Parameters');
disp(['Parameter 1: Wire type ',Psi.descw(mw,:)]);
disp(['Parameter 2: Wire cross section is ', num2str(ac), ' m^2']);
disp(['Parameter 3: Number of turns is ', num2str(N)]);
disp(['Parameter 4: Magnetic material is ', Psi.descm(mm,:)]);
disp(['Parameter 5: Slot width is ',num2str(ws*100),' cm']);
disp(['Parameter 6: Winding width is ',num2str(rww*100),'% slot width']);
disp(['Parameter 7: Slot depth is ',num2str(ds*100),' cm']);
disp(['Parameter 8: Winding depth is ',num2str(rdw*100),'% slot depth']);
disp(['Parameter 9: End width is ',num2str(we*100),' cm']);
disp(['Parameter 10: I width is ',num2str(rwi*100),'% end width']);
disp(['Parameter 11: Base width is ',num2str(rwb*100),'% end width']);
disp(['Parameter 12: Depth is ',num2str(d*100),' cm']);
disp(' ');
48
Electromagnet_Fitness.m (6/7)
disp('Constraints');
disp(['Overall width is ',num2str(100*(ws+2*we)/lmax),'% allowed']);
disp(['Overall depth is ',num2str(100*d/lmax),'% allowed']);
disp(['Packing factors is ',num2str(100*pf/pfmax),'% allowed']);
disp(['Current density is ',num2str(100*j/jmaxw),'% allowed']);
disp(['Current is ',num2str(100*i/imax),'% allowed']);
disp(['Back core flux density is ',num2str(100*B01/bmax),'% allowed']);
disp(['Back end core flux density is ',num2str(100*B12/bmax),'% allowed']);
disp(['Front end core flux density is ',num2str(100*B23/bmax),'% allowed']);
disp(['I core flux density is ',num2str(100*B45/bmax),'% allowed']);
disp(['Force required is ',num2str(f_req),' N']);
disp(['Force produced is ',num2str(100*fe/f_req), '% required']);
disp(' ');
disp('Metrics');
disp(['Mass is ',num2str(m1),' Kg']);
figure(figNum);
clf;
Electromagnet_Drawing1(param,Psi);
figure(figNum+1)
Electromagnet_Drawing2(param,Psi);
end
49
Electromagnet_Fitness.m (7/7)
function p = ltne(x,xmax,delta)
if x <= xmax
p = 1;
else
p = 1./(1+abs((xmax-x)./delta));
end
function p = gtne(x,xmin,delta)
if x >= xmin
p = 1;
else
p = 1./(1+abs((xmin-x)./delta));
end
50
Sample Evolution
Normalized Value
1
0.5
0
1
2
3
4
5
6
7
8
Parameter Number
9
10
11
12
f:B(b) Md(g) Mn(r)
2
0
-2
-4
-6
500
1000
1500
Generation
2000
2500
51
Evolution – Best Fit Individual
„
(Matlab Demo)
52
Parameters
„
„
„
„
„
„
„
„
„
„
„
„
Parameter 1: Wire type Copper
Parameter 2: Wire cross section is 7.8519e-007 m^2
Parameter 3: Number of turns is 585
Parameter 4: Magnetic material is Microsil
Parameter 5: Slot width is 7.1906 cm
Parameter 6: Winding width is 97.7656% slot width
Parameter 7: Slot depth is 0.96031 cm
Parameter 8: Winding depth is 97.8117% slot depth
Parameter 9: End width is 1.2104 cm
Parameter 10: I width is 49.2545% end width
Parameter 11: Base width is 52.2008% end width
53
Parameter 12: Depth is 3.7947 cm
Constraints
„
„
„
„
„
„
„
„
„
„
„
Overall width is 96.1141% allowed
Overall depth is 37.9474% allowed
Packing factors is 99.3753% allowed
Current density is 99.4713% allowed
Current is 99.1917% allowed
Back core flux density is 99.442% allowed
Back end core flux density is 50.9116% allowed
Front end core flux density is 49.215% allowed
I core flux density is 99.6887% allowed
Force required is 99.5053 N
Force produced is 100.3524% required
54
Metrics
„
Mass is 0.86127 Kg
55
0.15
Profile View
0.15
0.1
0.1
0.05
0.05
0
0
-0.05
-0.05
-0.1
-0.1
-0.15
-0.15
-0.1
-0.05
0
0.05
0.1
-0.1
-0.05
0
0.05
0.1
56
3-D View
0.02
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
0.02
0
-0.05
-0.02
0
0.05
57
Design Repeatability
„
Repeat design 25 times:
Parameter
Min/Mn
Max/Mn
Std/Mn
mw
100.00
100.00
0
aw
95.26
102.05
1.46
N
93.95
106.16
3.48
mn
100.00
100.00
0
58
Design Repeatability
Parameter
Min/Mn
Max/Mn
Std/Mn
ws
88.44
110.01
5.06
rww
97.93
100.72
0.57
ds
92.18
105.86
4.07
rdw
96.46
101.94
1.46
59
Design Repeatability
Parameter
Min/Mn
Max/Mn
Std/Mn
we
88.55
109.82
5.93
rwi
90.00
109.26
5.06
rwb
89.55
108.78
5.17
d
83.18
118.91
9.02
Fitness
97.55
102.00
1.09
60