Description of a pin-pulling process with aid of dimensional analysis

Description of a pin-pulling process with aid of dimensional

analysis

Citation for published version (APA):

Muller, H. L., Kregting, W. T., Smit, J., & Veenstra, P. C. (1967). Description of a pin-pulling process with aid of dimensional analysis. (TH Eindhoven. Afd. Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0174). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1967

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I~ ~---_...- ..._---..~.- ---- - - --- -- ---~---~-l

I technische hogeschool eindhoven I

~

I.a~~rato~iu",-voor",-~~~~n~~~e_!ec~n_olo~ie e~_""er~~~t.ste-=hniek~'

~

i rapport van de sectie: Werkplaatsteehniek

J

f - - - . ... .

-I

titel: '

Description of a Pin-Pulling process with

I

,

I " aid of dimensional analysis.

i f..- '-' -- ---. auteur(s): Prof.dr.ir. H.L. Muller Ir. W.Th. Kregting Dr. J. Smit .~---",-,..- - - --- ---,-"-- I sectieleider: ~--'~---'-- ---_._-- - _ . -' '

-hoogleraar: Prof .dr.ir. H.L. Muller

samenvatting Summary

F1~~-7bIZ.

I rapport nr. 0174 . f - - - -. I ' I I 1 I codering: II P.6.c.1 UDC:62-13, ~-£21.}85.0}2 trefwoord: Pin-Pulling Process

The total process of pin-pulling consists of two main processes.

1. The thermal behaviour of an electrically heated piece

of wire clamped on both ends.

2. The construction occurring when the wire is overstretched,

and many interrelated effects such as change in dimension because of plastic flow, change in heat intensity resulting in different temperature-time relations at different places.

Direct mathe~tical analysis is very difficult; therefore

an empirical approach is used, whereby the t~st results are

processed for practical application by means of dimensional analysis. The following process-description shows a way to determine the required current, warming-up time and tensile force for different materials.

Though the experimenta have been performed in the sphere of the factory practice and thus could not get that kind of . attention that is usual for laboratory tests, the questioD if it is possible to describe this process with aid of dimensional analysis seeas answered to us quite well in the affirmative. ~ ~ - +... _ -prognose datum: mei 1967 aantal biz. 17 geschikt voor publ icatie in: . "Annals of

the C.1.R.P. "

Presented to the C.l.R.P. conferenoe 1967 by

Prof.dr.p.g. Veenstra.

';

DESCRIPTION OF A PIN-PULLING

PROCESS

WITH AID OF DIMENSIONAL ANALYJIS

by

PROF.

DR.

r~. H.L. MULLER

IR.W.TH.KREGTlNG

DR.J. SMIT

TECHNOLOGICAL UNIVERSITY EINDHOVEN

HOLLAND

Presented to the

C.l.R.P.

conference

1967

1-

rap~ort ~r~--01~~---

-r-~----

---

---O~

Materialien.

biz. van

17

biz.

10 --15 .~ 20 ~-25 30 ~ 35 I AO~ AS SO

~-Obgleich die Versuche unter Betriebaverhlltn1ssen durchgetuhrt wurden, und daher kein. laboralssig. Aufmerkaamkeit in Anapruch

n• .bm.n konnt•• , haben d::.e Aussichten auf eine

dimensiou-analytische Beschreibung dieses Proz.sses SiCA unseres Erachte••

verhI1tnis"ssi« gut bestatigt •

.

SOllUl&1re

Le procede de "pin-pulling" se compose de deux processW!l principals:

1. 1a conduit. therm1que d'uDe piece de fil chauff6e electrique.ent

et fix'. par s.rrag.

a

deux cates.

2. la contraction se pr&sentant en cas que le fil sera aurtend. et beaucoup d'effet. se tenant se produisent, co. .e modificatioD

de diaension en co~equence de fluidite plastique, modification

d'intensit' de chaleur, concentrant en temperature-teaps relations

differente.

a

places differentes.

L'application de 1'analyse math'matique direct. est difficile; pour cette raison une methode empirique est choisie pour 1e. resultats d'essa! app1icabl.s pratique.ent, et bien 1'analyse dillensione11e.

18 procede concernant fait Yoir une voie de fixer le courant requis, 1e temps de chauffage et la force de tension pour des materiaux different••

Bien que les experiences sont faites au millieu de l'organisation

d'atelier, iap1iquant que cela n'appel1e pas l'att.ntion desire.

pour lea resultat., la question de la pos.ibilite de r'soudre ce

procede

a

l'aide de l'analyse dimensionelle doit 'tre repondu

affirmative.nt.

i werkplaatstechniek

L _

I

--- ---

---~-l technische hogeschool eindhoven

rapport nr. 0174 blz. 1 van 11J1z. 5 -10 .20 -25 ~-30 Su-r:

1h. total process of pin-pulling consists of two main process••

1. The thermal behaviour of an electrical17 heated piece of wire

~lamped on both ends.

2. The construction occurring when the wire is overstretcked, and many interrelated effects such as change in dt.eDsion because

of plastic flow, change in heat intensit7 r.sulting in different

te~erature-ti•• relations at diff.rent plac.s.

Direct mathematical analysis is yery difficult; ther.fore an e~irical

approach is used, wh.r.b, the t.stresult. ar. processed for practical

application b1 means

of

d1. .nsion&1 analysis. The following proce.

.-description shows a way to deteraine the required curre.t, waraing -up time and tensile force for difterent materials.

Though the experi. .nts haye been p.rfor.ed in the sphere

ot

the

facto17 practica and thus could not get that kiDd ot attention that

ia usual

tor

laboratorr t.sts, the question if it 18 possible to

~escrib. this process with aid of diaensional analy.is see. . answered to us quite ••11 in the affirmati...e.

Der geaaat. Stift-Ziehproces •• tat etch ausammen aus zwei wichtigen Teil...orglngen,

35

r----I _{1. de. th.raod1namischen Verhalten ein•• elektrisch geh.izten}

DrahtstUckes, dass mit beiden Seiten eingekl. . .t 1st.

2. d.r .~.~.t.ndenE~schnUrungbei stossartig.r Ub.rb.laatung

des DrcD~ und . .hr.r.n damit ausamm.nhangenden Effekten, wie s.B. plaatische Ha.gMnderung und 8rtliche Unterschiede in der

HeizwirkunSt woraue eich yon Ort zu Ort ungleiche

T••peratur-Zeitb.ziehungen ergeben.

liae unaittelbare mathematische Analys. iat mit gro•••n Schwi.rigkeiten .... rbuaden; daher wurde ...ersuchaaM••ig an die Aufgab. heraagetrete••

Di. Versuchaergebnis•• wurd.n mittels Di••naionaa. .

l)8w

ftir praktische

V.rwendung zuglnglich ge. .cht. Die Proaes8b•••hr.ibung ze1gt .1n. Mlglichkeit zur B•• tiaauag.des .rforderlichen Stro.es. der

Erwlrmungadauer un4 4erben6tigten Zugbelastung fUr ....rschiede. .

40

45

50

i

~---~---werkplaatstechniek technische hogeschool eindhoven

biz. 2 van o rapport nr. 0174 ~ ~ ~ ~ ~ ~ - , 17blz. ! 5 15 20 25 30 35 40 45 50 Introduction

In the electronic component industry pins are widely used as parts £or radio tubes and transistors. The pins

vary in diameter £rom 0.2 to 2.0 mm and in length £rom

8 to 72 mm. If they are to be handled by vibratory

hoppers and inserting equipment, the pins must meet the

£ollowing requirements:

- The pin must have pointed ends and a sufficiently

smooth point surface.

- Length variation of the pin must be limited (normal

tolerance ~ 0.2 mm).

Drawing of a pin is shown in fig. 1.

These pins .can be manufactured by various methods such

as cutting, rolling and pulling. Of these three methods

the last will be dealt with more in detail. The machine used for pulling apart the wire, works on the following principle: A length o£ wire is clamped between two

chucks that can be moved in relation to each other. A

current is passed via the chucks through ~he wire as a

result of which its temperature will increase. The heated wire is stretched and separated by moving the

chucks apart. . >

Two d'ifferent processes are involved, viz.

a. The thermal behaviour of an electrically heated piece of wire clamped on both ends.

b. The constric'tion occurring when the wire is over-stretched.

The two processes are interrelated by a number of

effects such as change in dimension because of plastic

flow, change in heat intensity resulting in different

temperature-time relations at different places.

For different products the material and pin dimensions are .given within certain limits.

The practical problen! was to find

1. the bptimal conditions for the process

2. a practical way to bring the machine setting as close as possible to these conditions.

First the stretching process will be stud~ed; the results

will then b~ worked out to dimensionloss numbers. With

help of these numbers the setting of the machine in practical cases can be done more systematically.

werkplaatstec:hniek

_ .._~. . _ _~_~._~~ I

0174 rapport nr.

,---~---.---_.~---;---,

biz., van

17

biz.

I

o

5

10

15

20

The method chosen to solve the problem

As was already outlined above, the total pro~ess

consists of many interrelated effects. Direct

mathematical ,analysis is very difficult; therefore an

empirical approach is used, whereby the testresults

are processed for practical application by means of dimensional analysis.

Readers are referred concerning this method to l i t . 1, 2.

The use of dimensional analysis for a practical problem depends on the hypothesis that its solution can be

expressed in terms of certain variables by means of a homogeneous (dimensional) equation. This hypothesis is based on the trivial fact that physical equations are homogeneous in dimension and that relations can be deduced from these equations and must therefore be

homogeneous in dimension too.

However, if an equation is homogeneous in dimension, i t

can be reduced to a relation between a complete set of dimensionless products (Buckingham theorem). It is obviously necessary that an adequate physical model is used in which all important relevant factors are taken into consideration.

25

30

35

The physical model

Constriction of the wire begins once the stress has exceeded a certain critical value. This stress is temperature dependent and, generally speaking, i t may be said that the required critical stress decreases with increasing temperature. As the temperature reaches

a maximum in the. plane of symmetry, the critical value

will be exceeded first in this plane. The physical quantities determining the temperature at a certain place are:

a. the power suppli~d P

b. the dissipated heat Q

c. the heat ?apacity C

all related to the material element under consideration

will depend on

I~P·l )

---;l"---"1[/4 d2

If we now consider the total length of wire between clamping points and simplify the situation by using

average values of temperature etc., then the power

supplied

50

with ~ • electrical resistivity

II • current

1 • distance between the chucks

d • wire diameter

For the purpose of finding dimensional quantities this simplification may be justified. The wire temperature is considered to be only variab~e with x.and the time t.

I

ra pport nr.

~

o~I I I ~ i I i

5r--~~--~~_. -~-_._-~~-..

_-0174

biz.

It-

van

17

bIz.

~

10

15

20

The dissipated heat for an element in the middle of the wire (Q :: X.A.dT.t) will depend on

dx

1 • A with

>-

₌

heat conductivity

2. T T

₌

temperature .of the middle of the wire

J.

t t ₌ warming-up time

4.

I 1 ₌ distanc~ betwe9-n the chucks

5.

d d ₌ wire diameter The constriction is determined by

1. the deformation energy

I

unit volume E

2. the tensile strength at Toe ~T

E' '-

f

r:

- A • L.

The deformation energy depends on:

25 1. F

2. A

J.

e

with F,= applied force

A

=

surface of a plane, perpendicular on the wire

e

=

strain

30 In considering these simplified equations,we supposed

to have the following variables to be of importance for our dimensional analysis.

1. 12 in W'att.m M.L

-3

.T

-J

35

40

45

I t is permiss! ble to combine I with

fl,

because they are the only variables containing the electrical basic units of charge for current.

Z. E = deformation energy

I

unit volume in Nm/m3

M.L-1.T-2

J.

C

=

heat capacity / unit volume in Nm/m30_C

M.L-1 .T- 2

.e-

1

4.

~

=

heat conductivity in Nm/msecoC

-3

-1

M.L.T .8

5. d

₌

wire diameter in m L

6. I :: distance between the chucks in m _L

7.

T

₌

temperature of' the middle of the wire

e

so 8. t :: warming-up time in sec. T

9.

<T"T- tensile strength of the wire at TOC

M.L-'.T- 2

0174

rapport nr.

, - - - ,

biz.

5

van

11

biz.

I

j---~---.---_____l

o

Table 1. Dimensional matrix of the variables

10 mass length time temperature. E _{f I}2 t T d C A 1 _(JT 1 1 0 0 0 1 1 ·0 1 -1

J

0 0 1 -1 1 1 -1 -2

_-J

1 0 0 -2

-J

0 -2 0 0 0 1 0 -1 -1 0 0 15 20 I

.

25

From these variables the following complete set of dimensionless products· can be formed.

V

A.t

1 • _Cl2 A.T12 V2

=

I'I

2 1· VJ • d 30

The i'ollowing· physical significance can now be given to the dimensionless numbers.

35

v,

= dissipated heat

_/

heat capacity

V

2 = dissipated heat

/

generated heat

V

J

=

geometrical proportion

V

4

=

force applied

/

force required

V

s

= energy supplied / mechanical energy

4S

50

In order to determine the relations between these numbers, i t will be necessary to measure some variables by tests on. the production machines.

From the literature (see l i t . J and l i t . 4) we derive

the following as a function of temperature.

,. the specific electrical resi$tivity

2. the specific heat

J.

the heat conductivity

4.

the tensile strength at temperature T

biz.

0174

The other fo'llowing 1. Nickel

2.

Nickel-Iron

50/50

3.

Nickel plated Iron

4.

Copper + 2

%

Ag

5.

Molybdenum

All with a diameter of 1 mm.

rapport nr.

, . . - - - ' - - - ,

6

van

17

biz.

I

-l

variables are measured at the machine. The five materials are at our disposal.

10 5

o

Tabel 2. Results of measurement

15 20 25 30 35 40 45

Nickel, Nick~l- Nickel- Copper + Molybdenum

Iron Plated

2

%

Ag

50/50

Fe I avo Amp.

_396.

240

297

1131

707

F N

80

70.

70

75

110

.

T

°c

572

607

465

310

705

t sec.

.0.08

0.08

0.08

0.04

0.04

C.

106

Nm/

4.63

4.58

5.02

3.74

.2.78

m30_C

A

Nm/

50.2

21.4

42

369

113

msecoC

11'.108

36.5

m

_11.5

₅₃

₈₈

_23.3

crT.

10

6

.

N/m2

250 .

350

250

88

240

1.103

~ m

2

1.94

1.94

2.0

2.24

50 " werkplaatstechn lek ---~---I

rapport nr. ₀₁₇₄ biz.

7

van 17b1z.

o

10~

15

20

-Dim~llsio)!JL"'~,:;, r,urriJ('r~ that ar", ,'5eflll in practic0

TlH,' d:ll,AP51onle<;,S rllllnbar~ V, to V) incl. a,p '-:alculatE".l

for~h<? five rnat€.rials mentinned above anl1 aj'e s.lj.:>wn

in the table balow.

.

.

Tabl':' J. Val'l'es of thE" Jirnp.r!s\"nles~ tlurrb"'u"

.

v,

_v"

.

v· V,. V_ '- J

.

J :~;j _{0.218 2,0.0 0.!.If,J 0.40 14 •J} XiFe r>. t 0.732 0.51

₅

0.246 19 FA 'J.1 7'3 1

_.58

_0.51

_5.

0.J5h 14 • 1

eu

0.986 12.2

0.:;

1 .08 5.0 No 0.)25 J.~2

o.

'.:~6 0.5) B.1.1

HapresE'nt\~d 0;1 ]og.log papet the relations t;t~per; V and V_ fig.' _J 4 ::> 25 f- V 2 and V_::> fi g. 4 V and V 2 fi.e;~ } 1 are lillHar.

>"t

F A<T:".. .1 30 f -35 40 45 50

Simple sraphical f'H~antl delivpr the ('011owins- I'elations. VII = 5.I! V - t -" :5 _? V"._ :: ~71 V -- 5 V 1 "" O. 1J

v~' ~

Substitution in th<,' E"'luatinnc; l')ads 1.0 t'.~ fnllowing

Axpr0ssicns.

1---~- --.

I

rapport nr.

OL

biz.

8

van 17b1z•

Ttl(' var'ables occurring if tlJ~ ';"~:.{\V8 rE'ldt~'-'[d are:

1 • >..

=

''t

l

( )

.

J ~ ~

c

:;

i~

0 8. M. r::

7l>

4 j:':

*

~

.

S

J.

t-

o 9. F

'

...

0 10. t T 11 • _I

5.

T 0 6. 1

_'*

" 1a r-lS --20 25 '

-As a practical example \..1' the Ilse of PxpHl'imental data

~he following may serve.

The starting point is wi re of a cE·rt.ain .Lameter. what 'Values must the cUT'r"'nt, the warming-up ti.JTl~, t.he

tensile force i'lnd tbe di !':tan0e between the Ch\.lCks have

to obtain the de~ired sJlap~ of. the pointp'l A'nds1 I f WQ

pro~-ped ' fromwir;e with a given diameter, as in our

c~5e, tho magnitudes mal'ked ..d th

*

are given. I f we, moreover, assume that tLe temperatura as measured is the only one at which the process can properly take place, the temperature i . e . tho magnituiAs marked with o are als0 determirHvl.

However, wo s t i l l have three equations and three

unknown variablt'::> , so we can calc ul.ct. te F. t an.i I as a

function of thu diameter. We find; 1 ;:: , ( j '. _from ...~' I }~

=

..

~'i( )

..

t =. t{d) fi g. 6 .fib-~ 7 fif ; . 8 30 ;--The rf;,lsLlll:i,O b~~low •

data "'i i th j :::::; 0,5 are

1 given

3S

\-Table 4. Ii'

,

t ar.l I as a fur;ctio;] ";f the diametel'

. 40 4S 50 I i.n .\:-np. t in oSf~" t f i.[1

:\

;J in f!Jm

I

....

_{428 d}

.-

_•l~ 1 1r;~2 d 92 .12 •• J _I ~iFe 2~.3 d ..,_,

_.9J

_lC,~2 d _I 1 2 I '-,"" -"> _{• )d"} FA )22 .1 2: 10 - ,1 _2J

..

I

·

..,

~2 (;11 1

,

10 .,

,

,J.52 10

.-

j ,.!~

,

'-"

...

'1t) ";"1..;- d ~''~•_{')1 1}')

....

d 10('· .t,." werkplaatstechniek L -.. ~_. _

o~

rapport nr. 0174 biz.

9

van 17biz.

i"rom this limit.:> <l"" ..u·/;. !·':l,,'i;i.surinc; p' ..i:,f-:. ' t 'a!,n:~t

1.-.... f"\xl)C-(,,t-r-.\l tJ'l'dt rn(.~'~ ,~,; r";(·~1.."":~ l)rOr'cr.rti ~.)S \'._"l l~n

1"r",~",1i: 12\ hetv"---""l) '"cle 'J i i f " .<:;1.",'1+-'85 IlU:J)L;"~I-"".

ih.p v t'<.\r~} ~:1 r:~l.l \\~j_z-~ ~~i.! G ()~.-t- $'~.",1 th.4,t

r

t_(irp₀ s ~,~ \.~ u·~ t :"', ~Je

:il~'li t t:-,j :',-, th(~ r,r'.! :~i(j,:-'~ s ~ ,'it-,~"'"

:lo!~~:~vpr"l tl1f~ "~l'"alnps j"nr V 1n t1li? ",'"arlzJlL; t:(~\.'t h(}io)k.:,

10 ~--vdry rath .... r ;-~€'V ;,r t !l ( 1.~.:' '> i mpi~-:,~,"t~jnc'rlt:"'. • : ., 1_{, ... ; rl} t)'I/ . i!, 1.n ct' over t! I:' t I' : d 1 :l .'>r " I )I' ..~ Gi v<'! met \:,.,,1 :,. nIT.'p appliql 15 .- _{I'1-1G t'uCOt;uinG} !t~t (,!'ff.i nf~ ~~: .,~j­ ~\Jnsi1~~ for('('

J i f l , P t : ; i t)~:tl a~::!lys~s )la~ :=t~l··"!·..J--~ U. "~a)­

lnY.,ci od (l~'lr ..."""'~'j,i~li.J..·_lr) ti:t~~ .:..t:i

('.;~" 11C'~'(~'I-'pn';" ::,a+f)!-i~l}"'" ~n ~)Jctn!' tfJ t ~'" 20 -25 • 30-40 ~.-'45~ 50·-I, 1t- t {' l'~p ~' ;.~ the ::d"~( l '1d"" Y ~ ! t~' L:.t d £1,' ..t i 1d \)1;~ .]

r

t. i l l

f d ) \ " , m{lr,~, c>xp''lr<m<>r:,tal wn~.'" t l ? t~'pe if's'; '\-,0·1 h.'is +-l ') ~-"p pC'i-~..c , H~,,' i f: () (~trf~ t ...'t ~~; ~ .•f'1:.~ i ~,~n t a cr:1)r 4" .... { ..~ r~ '5 "11t S ~

1 ,.r t ~)P !. S(1 t

1'1 ';;}j" t';r:l n':! !',:,t I,it', t-f~",,, "-atc>ri'l~5 a ':'-!''''!'ul shrtp,-,

. , ' t ! ,'. p',)i·,t.~,j-",I'" "an also ht, r:\.~tain~d at t;"TT'i"r>ratllre~

, t ~.n r t h :)n t l1 0;";'') .~t W11~coh 1'"'i .''0' {P }:,.'t'1n1'"rl :" S ....1"0,r~e- '1()n2- .

j~r'\wnv:·r. t:li~ ':0111 j Y)Ol : / ' " " t r i P j ,',('tT' tn"l're~ult'"

t"i';cn <"'om the aV:1'labl prr'~l'('tion Ill.tchil, ..•. hflic:h ,,"'as not ,1' ",11 ;ntelljr'; 1

r"'·r

fun 1·.'" ;·~:.,.1.1 {xjJ':lrij,i t:=).

r '1.; l , .":"t ; t;~, ~ t S "'-Jn Hi d j r~:.%J;~,;1 ~ : . S ,"

r

f·~.i :'. .i ~-". ::t11 ) ! '")i'

.,.":, \, .~.l.!;~"n t s " :n;=ty 1.)!t:~, U..-~ ~~f· ... :. ()1 t-! ..j.5 },l ,rf lU~j- ..

o ,-rapport nr. 0174. 1. d.L. La.lIghaal' blz. 10van 5 • 10 -:L,'<,:Lnnald - L ' ) l l L;.' ~f)"":,,)-

.

.. .,.,;,-~ 15 -~ 20 _.-. Ha:-(H·opk ,r ~.tl.· ::>.1~ 1 :'Ii-t t E' 1-i a1s " 25 ~ 30 ---35 _. 40 ;-45 L 50 c-:ctlip, :.ti:" 2(! If,il

d :!:O.2 x j • 11 " d: 1.00m m

Fig.1 Product· drawing.

1.2 mm

Fig 3. The relation between the dimensionless numbers

VI.

and

VS"':'

"~

~--+-+---+--~-+--+--+--+--+-+-+-+ - -

V

5

V

4

"~

1.0 _ I - -h

----I---+--t--~-

C----,u,---t--+-+-+ - + -+_-+---+-_+--+-.+I--+---l

t---I'~+---+- -+---+--f-~~__+_+-I_+_---_+_---+--t---I---+-+-t--+-1 r-+-+-+---+---+---+--,---t-+--+--t--fr'\.M0

~

i

Fe

I

~Fe

' " I O. 1

-j---+----+--If---+--+-I--+--+---i----=t=an:.:-J)_.=:_--+'.~

_ _

f_'>+__t_"'__;>,o__t__+__+I__+___l

I I '\.

I'

.

-~

-H-12 " 1 - - + - 1 - - + - - - _ . - - - - . --+---+

1.0

I 10. I •

Fig

iJ.

The relation between the dimensionless numbers

V

2and

V

s:.-I

I

tt

I ---I-J , I f f f -1.0 I I I i

f-!

-I I II

_I

I

I

I

I .1 I

I

I tan p::-2 I

Fig.5 The relation between the dimensionless numbers V, and ~.:.. "

V,

'C

'At

C./2.

.

~.

ATI

2

~I2

V,

1.0~l

I _ I - -

7rCu_

I - - I V /'

V

~-/ V

/

~MO

l(

I

II

_I

/Y1

;r , i I , _I j

I

I I I f-O.1 Ni-Fe}

V-

I i j

~

tan(X.: 0.81S" I ,

/ '

.

r

/

I

I

[

-...

_~

I 1.0

-,

_r

_I

10_f 14

Fig.

6

The relation between the current

I

and the diameter d. ~

V

CU /

V/

V

Mo 1000

_V

_"/'Ni V / / / _/Fe / /

f-I

in Amp / l/

/

) '

/

l/

/ /

/ N-Fe f

-V

~

V

V/ /

f - - / /

V /v

V

_/V/

f--- /

1/

V V

V

V

V

V

V

_1/

V

~ / / 1..1

/

/

_/

/

~

V

V

Ni 1=428 d

/

_/

Ni-Fe

I:

245 d

/

/

100 _Fe

_I:

_{322 d} / / / --CU

I:

1110 d /

/

,

/ V _Mo

_I:

_{747 d}

r

/ -,

----

--- 1--- . - -_.._.~-- - ---_._..

/

" ~ d in mm. 0.1

_O'f

I I

_I

~

1.0 2.0

I

I

I

Fig

1

The relation between the tensile torse F and the diameter d. lCU I /Mo ,

/

~Ni .

/I!

V

Ni-Fe •

/1/

I

W

I I

I

V

/Fe 100 F in Newton I i f--1-1- II 1/ / 1/

Jl

I

rl

II I ~f--

V

VI Ii

I

!I/

V II

--f

V

_~

I ~

/

1;/

_f/

I

I

I

/

IIIJ

YI

/

~

V

I

1/

V

I I I ₂

~

~

/

Ni-Fe F":77 dNi F: 98 d2 I 2

II

Fe F: 22.3 d2

/

Cu F:141 d 10 - I 2 - -I-- ~~-_._---I----/IJf l l_{I 1/}I Mo 1="":108 d

I II

V·

_I

I'll I

II

' I ! I

/ III

/

t-'

1(//

_/

I

IV

_I

I

V

I

.

I _I I I I I

o.~/

I

...

d in mm 0.1

-

_I

I

I

I

11.

10

2.0

I I

Fig.

9.

The relation between the warming-up time t and the diameter d.

I

" ,Ni-Fe

17

0.1 t in sec. "

J

1/ II III, II

III

II

Nt Fe . I , I '

,

II

. I I

iJ

~/-h

j'---

--+---+---+---+---iI---1 !

II

V/

- - f - - - t - - - l Ni t

=

0..0741

i

I---t---+---+---r,

---+~___hIli',-:..-+-1

)/-J1/L....-- Ni-Fe ,t: 0.0793 ;2

! '

j ,

Vi

Fe. t:0.0725 d I

~,

i,.,

II

t; I Cu t:0.0352 d 2

II

III

Mo t:0.0391

i

!/

r

r(1

i

I

I

I

/ ; I I, _ 0.01+---+---+---Jl-J+-'-+-I-+-t----!+-1+ - '

+-~---+----+---+---+----+--t

' I 1 / ' I : 1/ II i i i f - - - + - - -~,.__-__+____+_____t_---t

II

Iii

1

i I----+ +---lj"w.-

(I

t--+~=t

_

_

- - - t - - - j - i--j-I--+---1

II

!J

I I I ' I ' I I t----+---+---l.~---I-J4 -1I~t-t .

-I

//1

I i '

I

!

II

/I

I

i

~

1_----+----+-+-+--1

)I!

r

o.~

l.p

2.p