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The Design Core Market Assessment
Specification
Concept
Design
Detail
Design
Manufacture
Sell
DETAIL
DESIGN
A vast subject. We will concentrate on:
Materials Selection
Process Selection
Cost Breakdown
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Materials Selection with Shape
FUNCTION
MATERIAL
PROCESS
SAPE
SHAPES FOR TENSION,EN!IN", TORSION,
#$%&IN"''''''''''''''''''''
SHAPE FA$TORS''''''''''''''''''''
PERFOR(AN$E IN!I$ES
WITH SHAPE
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Common Modes of Loading
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Moments of Sections: Elastic
SectionS)a*e A
+-I
+/K
+/
-r π /
/ r
π /
- r
π
-b
0-
/b/0/.1 b
abπ ba2
/π
+ --22
ba
ba
+π
bh0-
2bh
+
34.102
2
bh
h
bhb
>
−
-
/2
a22-
/a
412/a
rt
r r i o
π
π
-
+ --
≈
−
t r
r r i o
2
// +/π
π
≈
−
t r
r r i o
2
//
-
+-
π
π
≈
−
A 5 $ross'sectional area
I 5 Secon6 oent o7 area
∫ ∫ == tion y tion y by Ay I sec-
sec
- 66
w)ere y is easure6 verticall8by is t)e section wi6t) at y
K 5 Resistance to twistin9 o7 section+ Polar oent o7 a circular section
∫ = tion r r sec 26-π !TLK θ =w)ere T is t)e tor;ue
L is t)e len9t) o7 t)e s)a7t" is t)e an9le o7 twist! is t)e s)ear o6ulus
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Moments of Sections: Elastic
bt /
t ba + +π
bt
hhb i o
-
+
≈
−
+- bht +
+- bht +
+
-
--
/0
λ
π λ
d t
t b2
2
-
+
a
bt a
20
/
2π
-<
+0-
-
22
o
i o
bth
hhb
≈
−
+
h
bt h
20
=0 2
/+=
-2 bt ht
+
4
-d t λ
/2 0
−
b
t t b
--
-
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Moments of Sections: #ail$re
SectionS)a*e % +2 &+2
2
/ r
π 2
- r
π
=
2b 2-0.1 b
ba-
/π
+-
-
ba
ba
<
π
=
-bh
+
4.02
--
bh
bh
hb
>
+
2-
2a
-1
2a
t r
r r r
i o
o
-
// +/
π
π
≈
−
t r
r r r
i o
o
-
//
-
+-
π
π
≈
−
% 5 Section o6ulusmy
I % =
w)ere
y m is t)e noral 6istance 7ro t)e neutral a>isto t)e outer sur7ace o7 t)e bea carr8in9 t)e)i9)est stress
& 5 Factor in twistin9 siilar to %
τ T & =
w)ere
τ is t)e a>iu sur7ace s)ear stress
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Moments of Sections: #ail$re
SectionS)a*e % +2 &+2
t b-
2
/-
- 0-
−
b
t t b
+a
bt a 20
/
-π
+
+- -
π
( )
o
i o
o
bth
hhh
b
≈
− 22=
+
h
bt h 20
2
-
tbh-
+
b
hbt
/0
2
- -
/+2
-2 bt hh
t + 4+
2
-
hbt
+
+
h
bht
/0
2- -
/d t λ
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Shape #actors: Elastic
BENDING
20
L
EI C S' =
π
π
//
-/ Ar I o ==
en6in9 sti77ness o7 a bea
w)ere C 0 is a constant 6e*en6in9 on t)eloa6in9 6etails, L is t)e len9t) o7 t)e bea,
an6 E is t)e ?oun9@s o6ulus o7 t)e aterial
o'o
'e
' I
I
S
S
==φ
!e7ine structure 7actor as t)e ratio o7 t)esti77ness o7 t)e s)a*e6 bea to t)at o7 asoli6 circular section wit) t)e sae cross'sectional area t)us:
-
/ A
I e'
π φ =so,
TORSION
L
K!ST =Torsional sti77ness o7 a bea
w)ere L is t)e len9t) o7 t)e s)a7t, ! is t)es)ear (o6ulus o7 t)e aterial.
π
π
--
-/ Ar K o == -
- A
K eT
π φ =so,
oTo
T e
T K
K
S
S
==φ
!e7ine structure 7actor as t)e ratio o7 t)etorsional sti77ness o7 t)e s)a*e6 s)a7t to t)ato7 a soli6 circular section wit) t)e saecross'sectional area t)us:
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Shape #actors: #ail$re(Strength
BENDING
π
π
//
-
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Shape #actors: #ail$re(Strength
Please Note!
T)e s)a*e 7actors 7or 7ailure
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Comparison of Si*e and Shape
Rectan"#lar sections
I$sections
SIDE
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Shape #actors
SectionS)a*e Sti77ness Failure
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Shape #actors cont+d
SectionS)a*e Sti77ness Failure
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Efficiency of Standard Sections
-
/ A
I e'
π φ =
ELASTIC BENDING
S)a*e Factor:
π
φ
/lo9lo9-lo9
e
' AI +=
Rearran9e 7or I an6 taCe lo9s:
Plot lo9I a9ainst lo9 A : *arallel lines o7 slo*e -e'φ
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Efficiency of Standard Sections
-
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Efficiency of Standard Sections
ELASTIC TORSION
π
φ π φ
-lo9lo9-lo9G
--
e
T e
T AK A
K +==
TORSIONAL STRENGT
π
φ π φ
-lo9lo9
-2
lo9G-
-
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,erformance Indices with Shape
ELASTIC BENDING
20
L
EI C S' =en6in9 sti77ness o7 a bea:
ELASTIC TORSION
L
K!ST =Torsional sti77ness o7 a s)a7t:
-
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,erformance Indices with Shape
FAILURE IN BENDING
f f % M σ =Failure w)en oent reac)es:
FAILURE IN TORSION
f f &T τ =Failure w)en tor;ue reac)es:
ρ
φ σ 2
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Shape in Materials Selection Maps
En9ineerin9 Allo8s
Pol8erFoas
Woo6s
En9ineerin9Pol8ers
Elastoers
$o*osites
$eraicsSearc%Re"ion
A aterial wit) ?oun9@s o6ulus,E an6 6ensit8, -, wit) a *articular
section acts as a aterial wit) ane77ective ?oun9@s o6ulus
an6 6ensit8
e
'E E φ =∗
e
'φ ρ ρ =∗
Per7orance in6e> 7or elasticben6in9 inclu6in9 s)a*e,
can be written as
ρ
φ -
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Shape in Materials Selection Maps
A aterial wit) stren9t), ) f an66ensit8, -, wit) a *articular
section acts as a aterial wit) ane77ective stren9t)
an6 6ensit8
-+ f 'f f φ σ σ =∗
-+ f 'φ ρ ρ =∗
Per7orance in6e> 7or 7ailure inben6in9 inclu6in9 s)a*e,
can be written as
ρ
σ φ 2
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Micro/Shape #actors
(aterial (icro'S)a*e
K
(acro'S)a*e, 0
K
(acro'S)a*e 7ro(icro'S)a*e6 (aterial,
10
5
#* to now we )ave onl8consi6ere6 t)e role o7acrosco*ic s)a*e on t)e*er7orance o7 7ull8 6ense
aterials.However, aterials can )aveinternal s)a*e, (icro'S)a*eBw)ic) also a77ects t)eir*er7orance,e.9. cellular soli6s, 7oas,)one8cobs.
(icro'S)a*e6 (aterial, 1
5
(icro'S)a*e6 (aterial, 1
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Micro/Shape #actors
Pris*atic cells
Concentric c+lindrical
s%ells wit% ,oa* )etween
Fi)res e*)edded
in a ,oa* *atri-
$onsi6er a soli6 c8lin6rical bea e>*an6e6, at constantass, to a circular bea wit) internal s)a*e +see ri9)t.
Sti77ness o7 t)e soli6 bea: 20
L
I E C S oo'o =
On e>*an6in9 t)e bea, its 6ensit8 7alls 7ro to ,
an6 its ra6ius increases 7ro to
o ρ ρ
oo r r
-is o7 t)e bea t)en
T)e sti77ness o7 t)ee>*an6e6 bea is t)us
==
ρ
ρ oo'
L
EI C
L
EI C S
20
20
S%a.e Factor! ρ
ρ ψ o
o
e
'S
S==
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Function
Tie
ea
$olun
S)a7t
Mats2 Selection: M$ltiple Constraints
Objective
(iniu cost
(iniu wei9)t
(a>iu store6ener98
(iniuenvironental
i*act
$onstraint
Sti77ness
Stren9t)
Fati9ue
"eoetr8(ec)anicalT)eralElectricalL..
In6e>
ρ
-
ρ
σ 2
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Materials for Safe ,ress$re 3essels
DESIGN RE/UIREMENTS
F#nction Pressure vessel 5contain*ressure p
O)0ecti1e (a>iu sa7et8
Constraints +a (ust 8iel6 be7ore breaC+b (ust leaC be7ore breaC
+c Wall t)icCness sall tore6uce ass an6 cost
?iel6 be7ore breaC
-
-
,
≤= f IC
C C
IC K
C aa
CK
σ π π σ
f
IC K M σ
=0
&eaC be7ore breaC
f
IC
IC C
f
K p4 C
t
CK t a
p4
t t
p4
σ
π
π σ
σ σ
--
/
-
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Materials for Safe ,ress$re 3essels
Searc%Re"ion
M2 3 '44 MPa
M' 3 456 *'78
f
IC K M σ
=0f
IC K M σ
-
- =f M σ =2
Material M '9*'78:
M 29MPa:
Co**ent
Tou9) steelsTou9) $u allo8sTou9) Al allo8s
Ti'allo8sHi9) stren9t) Alallo8s"FRP>> 2>>>
Hi9) stren9t),but low sa7et8ar9in. "oo67or li9)tvessels.
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0. E>*ress t)e objective as an e;uation.-. Eliinate t)e 7ree variables usin9 eac) constraint in turn, 9ivin9 a set o7
*er7orance e;uations +objective 7unctions o7 t)e 7or:
w)ere f , g an6 h are e>*ressions containin9t)e 7unctional re;uireents # , 9eoetr8 M
an6 aterials in6ices M .
2. I7 t)e 7irst constraint is t)e ost restrictive +Cnown as t)e acti5e constraint
t)en t)e *er7orance is 9iven b8 , 0, an6 t)is is a>iie6 b8 seeCin9aterials wit) t)e best values o7 M 0. I7 t)e secon6 constraint is t)e activeone t)en t)e *er7orance is 9iven b8 , - an6 t)is is a>iie6 b8 seeCin9aterials wit) t)e best values o7 M -G an6 so on.
N.. For a 9iven Function t)e Active $onstraint will be aterial 6e*en6ent.
M$ltiple Constraints: #ormalised
+++
+++
+++
+++
22222
-----
00000
i i i i i M h!g # f ,
M h!g # f ,
M h!g # f ,
M h!g # f ,
⋅⋅=
⋅⋅=
⋅⋅=⋅⋅=
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M$ltiple Constraints: A Simple Analysis
A LIGT( STIFF( STRONG BEAM T)e object 7unction is ρ ALm =
$onstraint 0: Sti77ness w)ere so,2
0
L
EI C S =
0-
/t I = -
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M$ltiple Constraints: !raphical
lo9 In6e> M 0
l o 9
I n 6 e > M
-
$onstruct a aterials selection a* base6 onPer7orance In6ices instea6 o7 aterials*ro*erties.
T)e selection a* can be 6ivi6e6 into two6oains in eac) o7 w)ic) one constraint is active.
T)e $ou*lin9 &ineB se*arates t)e 6oains an6is calculate6 b8 cou*lin9 t)e Objective Functions:
w)ere C C is t)e $ou*lin9 $onstantB.
------
00000 ++
++M C M
!g # f
!g # f M c ⋅=⋅
=
$ou*lin9 &ineM - 5 C C M 0
M 0 &iite6!oain
M - &iite6!oain
A
(aterials wit) M 6
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M$ltiple Constraints: !raphical
$ou*lin9 &ineM - 5 C C M 0
Searc) Area
$
lo9 In6e> M 0
l o 9
I n 6 e >
M -
M 0 &iite6!oain
M - &iite6!oain
A
$
$
A bo> s)a*e6 Searc) Re9ion is i6enti7ie6 wit) its
corner on t)e $ou*lin9 &ine.Wit)in t)is Searc) Re9ion t)e *er7orance isa>iie6 w)ilst siultaneousl8 satis78in9 bot)constraints. are 9oo6aterials.
M 0 &iite6!oain
M - &iite6!oain
A
$ou*lin9 &ineM - 5 C C M 0
lo9 In6e> M 0
l o 9
I n 6 e >
M -
$
Searc) Area
A $
$)an9in9 t)e 7unctional re;uireents # or 9eoetr8
! c)an9es C C , w)ic) s)i7ts t)e $ou*lin9 &ine, alterst)e Searc) Area, an6 alters t)e sco*e o7 aterialsselection.Now an6 are selectable.
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8indings for 9igh #ield Magnets
DESIGN RE/UIREMENTS
F#nction (a9net win6in9s
O)0ecti1e (a>iie a9netic 7iel6
Constraints +a No ec)anical 7ailure+b Te*erature rise Q031$+c Ra6ius r an6 len9t) L o7
coil s*eci7ie6
-r d d
L Turns$urrent i
'
#**er liits on 7iel6 an6 *ulse 6uration areset b8 t)e coil aterial.Fiel6 too )i9) ⇒ t)e coil 7ails ec)anicall8Pulse too lon9 ⇒ t)e coil over)eats
Classi,ication P#lseD#ration FieldStren"t%
$ontinuous&on9Stan6ar6S)ort#ltra's)ort
0 s ' 011 s'0 s01 ' 011 s01 ' 0111 s1.0 ' 01 s
Q21 T21'=1 T/1'1 T1'41 TM011 T
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8indings for 9igh #ield Magnets
,+7 β α λ µ
L
i ' f o=T)e 7iel6 +weber
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8indings for 9igh #ield Magnets
CONSTRAINT '! O1er%eatin"
So, 'heat is a>iie6b8 a>iiin9
e
pC M Ω
= ρ
-
T)e ener98 o7 t)e *ulse is +4 e 5 avera9e o7 t)e resistance over t)e)eatin9 c8cle, t p$lse 5 len9t) o7 t)e *ulse causes t)e te*erature o7 t)e coil to rise b8
w)ere ?e 5 electrical resistivit8 o7 t)e coil aterialC p 5 s*eci7ic )eat ca*acit8 o7 t)e coil aterial
p$lseet 4 i -≈
ρ µ po
p$lsee
C d
t 'T
--
-Ω
=∆
I7 t)e u**er liit 7or t)e c)an9e in te*eratureis UT ma@ an6 t)e 9eoetric constant o7 t)e coilis inclu6e6 t)en t)e secon6 liit on t)e 7iel6 is ,+7
---
β α ρ µ
Ω
∆≤
e p$lse
po
heat
t
T C d '
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8indings for 9igh #ield Magnets
Material
) y
+(Pa
-
+(9
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Searc) Re9ion:#ltra's)ort *ulse
Searc) Re9ion:lon9 *ulse
Searc) Re9ion:s)ort *ulse
HS&A steels
$u Al'S031.0
$u'/Sn
$u'e'$o'Ni
e'$o**ers
"P co**ers
H$ $o**ers
$u'Nb$u'Al-O2
$u'Dr
8indings for 9igh #ield Magnets
Material Co**ent
Contin$o$s and long p$lseHi9) *urit8 co**ersPure Silver
Short p$lse$u'Al-O2 co*osites
H'$ $u'$6 allo8sH'$ $u'Dr allo8sH'$ $u'$r allo8s!rawn $u'Nb co*@s
ltra short p$lseB$ltra high field $u'e'$o'Ni allo8sHS&A steels
est c)oice 7or low 7iel6,lon9 *ulse a9nets +)eatliite6
est c)oice 7or )i9) 7iel6,s)ort *ulse a9nets +)eatan6 stren9t) liite6
est c)oice 7or )i9) 7iel6,s)ort *ulse a9nets+stren9t) liite6
e
pC M Ω
= ρ
-y M σ =0
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