Design Notes for Various shape

8/9/2019 Design Notes for Various shape

1/34

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


2/34

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


3/34

Common Modes of Loading


4/34

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


5/34

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

--

-


6/34

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


7/34

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:


9/34

Shape #actors: #ail$re(Strength

BENDING

π

π

//

-


10/34

Shape #actors: #ail$re(Strength

Please Note!

T)e s)a*e 7actors 7or 7ailure


11/34

Comparison of Si*e and Shape

Rectan"#lar sections

I$sections

SIDE


12/34

Shape #actors

SectionS)a*e Sti77ness Failure


13/34

Shape #actors cont+d

SectionS)a*e Sti77ness Failure


14/34

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


15/34


-


16/34


ELASTIC TORSION

π

φ π φ

-lo9lo9-lo9G

--

e

T e

T AK A

K +==

TORSIONAL STRENGT

π

φ π φ

-lo9lo9

-2

lo9G-

-


17/34

,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:

-


18/34

,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


19/34

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 -


20/34

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


21/34

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


22/34

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==


23/34

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


24/34

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

--

/

-


25/34

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.


26/34

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 ,

⋅⋅=

⋅⋅=

⋅⋅=⋅⋅=


27/34

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 = -


28/34

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


29/34

M$ltiple Constraints: !raphical


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


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.


30/34

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


31/34


,+7 β α λ µ

L

i ' f o=T)e 7iel6 +weber


32/34


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 '


33/34


Material

) y

+(Pa

-

+(9


34/34

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


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

Design Notes for Various shape

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