Contribution to the mechanics of machining

Contribution to the mechanics of machining

Citation for published version (APA):

Veenstra, P. C. (1965). Contribution to the mechanics of machining. (TH Eindhoven. Afd. Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0139). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1965 Document Version:

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"

"

",

rechni'sche hogeschool eindhoven

laboratorium voor .... chanisch. t.chnologie en werkplaatstechniek rapport van d. secti.: Verspelflingsonde rzoek

tit.I: aut.ur(s): ,.cti.l.ider: hoogleraar: ,am.nvatting prognos.

Contribution to the t'1echan iea of Machining

Prof. dr. P.C. Veenstra

Chr. BUB

Prof .dr. P .'C. VeenBtra

Uitgaande van het afschuifmodel van Merchant en aannemend dat ar meehanisch evenwieht bestaat

tussen gemiddelde waarden van de spanningen in een toestand van vlakke spanning. wordt een hooIdvergelijking afgeleid 100r te aanvaarden dat. de richting van ,de maximsle rek van het materiaal de richting is van de maximale hoofd-8panning.

Er wordt aangetoond dat npast de Ruber-Rencky voorwaarde v~~r pla8ti~che vloei geen verdere energie voorwaarde noodz8keli~k 115. De opl05sing van de bo~fdvergelijkin~ wordt vastgelegd door de heersende spanningstoestand, die

kan

worden bepaald door de verh(")uding tU6sen de waarde van de maximale schuifspannin, en de plastieiteita-konstante van het mBteriaal. Dit geldt (")ok als

vervormingsverstevigin~ optreedt.

De tbeorie wordt geconfronteerd met experimentele resultaten en een ware 5~anning8-rek kromme,

gebsseerd op de theorie, wordt afgeJeid.

.

, ''\,I...--_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

- - - - J biz. 1 rapport nr.

P.7.a.t

trefwoo,d: dON ... : _" 1 juni

_196'

oontoJ biz. ,"""

49

g.schikt voor publicoti. in:

C.I.R.P.-Aunl!llell. ''it

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Summar~

Based on the t':erchan t &hear plane model and assuming g] obel

mechanical equ~librium between average values of strese in a state of plane .str~G81 a shear angle relation is derived byiden tifying thp di re c tion of maximum strain wi th the directiol'l of l"!8ximum rrincipal stress.

It is shown tha t but the von Hises pla at ici ty condi. ticn no particular assumptior, as to mtnimu!l1 work has to be intro-duced. The shear angle Gol1.!tion i6 f!.xed by the prevalent state of stress,

wn

L:t ean be expressed in terms of the ratio between H,e a'verege value of the maximum shear stress and the pla.st ic i

t:r

eonstan t of the me te rial Machined t which

>I also holds when strain-hardening occurs.

A comparison is made wi th experimental results and a true strain-stress curve of the work-piece material, a6 obtained from the prase nt thf'01'V H3 1"1 vel"!.

werkplaatst.chnl.k technische hogeschool eindhoven

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Resume

Base sur le modele de cisafllement de Merchant et suppose qu'une equilibre globale existera entre valeurs moyennes des' tensions dam; un eas de tension' plan tune relation d'

angle de· cisaillemen t est dedui~ pat' iden titler 18 direction du al1ong.ement maximum contra 1a direction de 18 tensi.on maximum principale.

II es~ demontre que outre Is Mises-Huber-Henckv conditicn de p1asticite aucune surrosition ,",uewonque Lers besoln dtintroduire. La resolution de Pangle de cis:;illement est eompletement fixee par l'etat de tension rreronrierant, ~tant

cale par l'ldee de re18tion rte Ie valeur movenne de 1a ten-• 6ion de cisaillement maximum at Is constante de plastleite du materiel travailJe. Aussi dans Ie domaine de tremper ce

theoreme reste valablp.

Entin un paral1~la ~bt tir6 entre les r6sultate experimen-tals at une courbe I'lllonr,-ement-tension vrai du lltFlteriel de la piece 8 travailler. obter.ue de ·la theorie presente est

montree.

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1 - - - ' ' ' - - - ,

Geg;rundet auf dem Fer"ha.,t'schen Hodell des Schervorgan~s

bei tier Zerspanurllr 11"'(1 mit del" Annahme dasz e1n, Gleiehgewicht zwischen mittlere .Vert'" 1e.r Jrannun,g;en ill ei.Dem ebenen Spann\lngszu-t

staDd bestehe. wird mi ttf.'ls Iden tifizierung del" Richtung der '

Maximaldehnun/f ~p rler- 'eni~e riel" maximalen Hauptspannung im

.system e:ine .3Cherwir.keJ'fleichung ab,creloitet.

Es wird' F!:ezeiF't dpsz auszer di.e von Mi.ses-Huber-Hencky Bedinglm17 keine weitere Vor"ouf1setzung bezuglich 1'I'ie Minimalarbeit

not-wendig ist. '

Die losungen del" ,.:'etn ... "'r-wink,elpo1f>ichung werden vollig bestimmt

'Ii von dem he rrschende n Spannungzusta1:l:l wie fest ge legt durch das

Verhal tnis zwisC'h~~1" l'1en ,Vert del" maxima len 3cherspannung und die FIe st izi tatskonst3 nte des Hate rials. :'uch il':l Gebie te del" Dehnungsverfestigung bewahrt die Theorie seine Gultigk!!it.

Die Voraussage ner :'heori.e wird verglichen mit

Experimental-ergebnisse und el:1P I.iehnunga-5pannungskurve fur das bearbei te te

Material. wie aus dpr Theorie hervor geht. wi.rd dargestellt.

werkplaatstechn lek technische hogeschool eindhoven

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Nomenclature and u~its

--;-""""'--o

a

average prln:ipal stresses in shear zone , 1

a

_x

. 0 . average nor~al stresses in shear zone y

average sh~ar stress in shear plane

biz.

5

van

-2

Nm

biz.

't

max

average max~mum shear stress In shear zone

Nm-2

Nm-

2

Nm-

2

, shear angle

fric tien angle ex rake angle

..

direc tion of

:-naximum

Q direction of rr.ax~mum ,

y _{shear strai ~q tan Y}

F S k plastiC::' t.? constat.

t-o

_true

_tensi.le

c

,otress 20

-crystal elongation rrincipal stress

:: _{tan (", - ex,} heot •

=

kV3

with respect to the shear plane -2 !'<In -2

Nm

g

_a

_{_0} I ~:trebS _parameter f t d TO v

e

t

werkplaatltechniek y. x 't

max

ra t lv f~ l~ tor

-

k feed depth of cut

chip thickness rat. io

cutting

6peed

true strain

natural strain.

=

Pn

(1 +

e)

m/rev -1 me

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6

I. Introduction.

During the past decades a number of theories on the mecha-nics of ma ch in inR' has been publi,shed. Some of them inves-tigate the entire state of stress, while otherwise equi-libri"um between average val ues of stress is assumed to be present in a geometric model of the cutting process. All theories are directed towards the formulation of a shear angle relation. which is an aceessible equation be-tween measurable quantities predicting an unique steady-state configurat ion for 'tool rake-and friction angle.

A hypotheSis of minimum work is generally introduced in order to secure the uniqueness of the shear angle solution.

It even has been shown (1) that the search for uniqueness might considered being fruitless, as a range of steady-state solutions of the Merehant shear-plane type (2) is to be expe'cted wi.thin permissible regions of the characte-ristic angles descriliing the geometry and the meohanics of the cutting process. .

The present author reconsidered extant theories based on the assumption of global equilibrium between !lverage values

of stress. , ' ,

It will be shown that when identifying the direction

ot

maximum strain with the direction of maximum prinCipal stress a shear an gle rela tion can be formulated.

As to this it is not required to introduce any energy con-dition.

However when aiming at a shear angle solution an additional assumption has to be made with regard to the prevalent state of stress t wh ieh wi 11 pr~ve to be equivalent to assuming a value of the maximumlshear stress in the system in the case

the t ma terials };ehavinlf according to the von Mises condition of plasticity are being machined.

As a matter of fact the introduction of the von Mises condi-tion implies accepting an energy condicondi-tion. The latter how-ever, regards exclusively the deformation of the workpiece material and does not refer to the cutting process as a whole.

A treatment of the problem along these lines will pro.e to be able to account for the strain-hardening propertiea of the material.

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The direction of maximum strain

(3)!

and a she-a,r angle

relation.

-

- •. _ , - .

In the present theory the Merchant shear plane geometric

model according

to fig. 1

is accepted. The problem will

be

treated. as a case of plane stress. From

fig. 1

follows

the geometric condi

t ion:

tan (cp ...

f3 -

fl )

·

....

.- (1 )

and hence can be deduced from the Mohr equilibrium

condi-tion as represented

in fig. 2:

tan(

cp ...

f3 -

tl ) =: g

cot

20 (4) (2)

where the parameter

g

defines the state of stress.

As is clear from the figure this parameter can be expressed

in terms of the prevalent stresses:

OP

g :.

MP

""

20 . . l a _0 y :x

Thus

g:. 1

defines a.state

of

pure shear'.

•..•.• 0)

Merchant introduces the angle

I

as the direction of the

maxim.um value of

the crystal

elongation in the chip with

respect to the shear

plane!

which can

be

interpreted as

the direction of the maximum value of strain and henee

in mechanical respect a8 the direction of the maximum

(tensile) prinCipal stress in the system.

This is

exp~essed

by:

, =

0 • • •• •• (4)

Now, as shown in

fig.

3 an element AF of the workpiece

material will be transformed by

the

cutting' prooess into

the

sta

te AF'.

Its

ori~inal

posi

t

ion

if'>

fixed by an angle p rela tive to

the coordinate s:,(stem shown in the figure

t

the position

after deformation

i~

defined

by

the angle q.

The strain

resultin~ fr~m

the deformation amounts:

AF"- AF

""'if -

£.<!.u _

_{eos q} 1

Furthermore follows from fig. 3:

tan q '" ta.n Y " ... tan p

·

...

·

...

(6)

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and hence:

cos p

•••• (7)

Combining eqs. '5 and 7:

1

t

r--·~-

l -

1 •••• (8)

II = - - - -_{cos q}

L

"I .. (tan q - tan y 6) 2

J

The direction of' the maximum strail1""in terms of the angle q by now fa 110ws from:

de

dq ::

o

wbieh renders! tan q' ;::; co t 'f :: e.max

::: t

tan Ys

1l

t

tan'y + •••• (9)

AJ,

from which easily ce,!1 be oerived:

cot 2'9!

=.;

tan Ts Using the eqs. 4 and 2

• • •• (10)

ta n ( " ..

i3 -

a. ) ::

t

g ta nTIS (11 )

Substitution of the explicite expression for the shear

strain in terms of " ar:d a. according to Merchant resu Its in:

tan ( . . . fj -

a

which is a shear angle relation valid in a state

of stress defined by the parameter g.

The value of the maxi~um strain followA from eqs.

9

and

8:

(12 )

e _max

₌

...

_I

₁

i

)i

>+ tanYe

{t

tanT_s +- ('+~

ta"'v}

-

1

Hence:

L .

.

2

11.

(13)

€.

t

In [1 + tan

~

{t

tan

If

+ (1

+

f

tall.

if )

J

S 8 •

By now i t .l6 J!0/::·fn O.le to derive the shear angle re-lation eq.11 in Ii riiret't way fro'll the Mohr equilibrium

diagrl'l!l1 fig.2.

Accordin~ to e05.4 ard 10 the equality holds:

1 - - - -

---.--.--~---.---.--.--.----werkplaatstechn lek technische hogeschool eindhoven

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MP

PQ

co t 2 0 =

t

ta~ y s

and as:

MP

.; PH

follows:

by which a graphical l!'lterpretation is obtained of the relation b~tween the ~he8r 1';train and the charae teristie angle (. cp ..

p -

a ).

From this follows the shear angle rela.t.ion:

,. and hence:

,

OP

tan ( cp ..

p -

ex ) ::

MP

t

tan y

S

OP

g '" ~1P

as already has 'been defined in

eq.3.

Fina 11y is remarked that the' shear strain which in origin

has been defined ml"rely AS a geometric qua.r.tity can be expressed

in terms of stress, as Also can be coneluded from f~g.2: ~~~. Oy

tan y s :: 't S

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r---~.

In the case thA t the va lue of the at ress pa rametel" g 1s known. the shear an~lp relation eq. 12 allows tor a shear angle solution, .t.e. the determination of the shear angle

in dependance of the f1'" ietion angle, wi th the rake angle as a parameter.

As eq.

13

predicts that the strain in the materiai can be expressed merely in terms of the shear strain, and thus

in terms of the ~hear angle • ' this means that an analytical

form~lation will be obtained accounting for the interaction between the frietion on the rake of ..5he tool - whatsoever the physical hackftl'l'ound of this partleulRr nrocese might be -and the deformation of the workpiece material in the shear zone. Thus i. t is important to investigate the physical

meanin~ of the stress parameter g, apart from ita detinition

eq.

3.

The ~neral von Mlses rlasticity condition reducea t~:

0 2 ... 0 2 - 0 a ...

3

'T 2 =

3

k 2 • • •• (14)

x v x

1.

s

in the state of rl~np. stress.

The plastiCity conr;t.8Y't k is considered being Ii function

of the strain & . and hence eq. 14 :r:emains valid when strain-hardeninp occ~rF.

This means that the plasticity elliJ)set when transferred

to the coordinate system of principal stresses:

0 2+ a t _ a a :::

3

k2 t ::l , .3

shows sem~-axes

of

variable magnitude

in

dependance of thp. state of ~train at a given strain rate.

....

The equilibrium condition according to fig.2 requires:

_,

I

a

::: a

-

2. 't f.j cot 2 Q

x y

The geometric cOT'dition as to the stresses has been formulated in eq. '.

....

Now the so luHon of eqa. 1 t 14 and 16 refers to a state of

stress s8tisfyin~ simultaneously the geometric cond~t1on prescrib~d by tt~ shear plane model, the con~ition of

~lobal equilibr:tum and finally the condition of plastieity at the given state of at rain and strain ret e.

{1f»)

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The Be lution is ~

while

°

x can be solvpd from eq,.14.

-The counterpart of eq.16 also goes from fig. 2;

"re :: - 't sin2 0

max and:

2't

_max

:: 0, -

,°

₃

Now two different extreme situations of stress may occur: 1) a state of linear stress:

or 0, ,. 0

In this case fo llows from eq5.

15

and

1P

't

_max

_'" "2 • k..f3

2)

a state of pure oheer 03 . : - 0, I

where follows from the sar,e equations

't ::: k

max

In general thus can be put:

"r ;:: f.k max and : 't S := - f K si n2 Q where ••• (18 ) ••• (19)

From this it is clear that any a priori assumption with regard to the value of the maximum ~hear stress in terms of the plas-ticity constant defines a state of stress.

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In particular the condi tion 't .::; k~ which is quite common

max

in extant theories. dellnes a stAte'of pure sheBr.

~ubstitution of eq. 1q nto

eo.

17 and using eqs. 4 and 10 again leads to a shear angle relAtion:

Compari.son with eq. 11 shows that holds:

1 )

I

t

l

t

tan Y

e ••• (20 )

J

••• (;1)

from which it is cbvious that the state of stress defined in terms of the pa l'amete-r g at a given state of strain he e its physical orig:in in the ratio f between the averap:e· value of the maximum 'shear -stress and the plasticitv constant of the ma teria!.

The positive sign \n eo. 21 implie6:

10yl>ox

the negative sign means:

10 .,

I

< ax

The condition f

= 1 is

compatible with ~

= '.

and defines a state of pure shear, a~ i.s shown before.

I---~ ... -~ ... --.---.. --.---~--..

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

1. _{_ - . . . - . _ _} The case of pure _{"".!I!o~,-i'"_ .... ,_~"''"'~_~~"'} Fhear. _{.. ' ' ' " _}

From the fore!:'"oin,v i~ will be clear that the shear angle relation eq. ?O or ~2 re~uce8 to

tan ( cp ...

f3 -

a

;c

t

r

t;! n ( q) -

a )

-+ co t cp

l

L

J'

from which, car. be solved as a function of

P ,

for

gi~n values of tho rakE" angle

«.

... (22)

The fiolution has teen plotted in fig. 4, wher·e in the usual way of representation the sheer an~le , a~peers as a function of the an .... le

p -

a •

A remarkahle fact is that in the present theor~ the rake angle operElf ~D as R paramt>ter which definitel, influencee

the so luti on obtai ned.

o o'

This is shown fot the va 1 ues a ::

!

30 and

«:=

0 •

As a comparison also the P.1erchant and Lee and Shaffer (5)

solutions haVE" beer t:lot ted.

The present theory rroves to arrive at values intermediate between those predicted by the thworieA ~entioned, as it should do VI'heneverit wquld have a chance to eov~r reality.

It is observed that in the, interv~l 0<., "

t

Jt • th"!

theory apparently dOf'S not allow fnl" tir.hUE! st')lutions. As to deal with thi<:: H is sufficient to remark that the shear strain raSse!'i th!"ou~h a minimum wllue 9S a funetion of the shear angle ~

d tan

_1s

,

1

....

_'" '''''''"'0''-",..,_ •• _'*" .... , - - - - . . - , . , ...

-

; 0

·d ., 2 ( I _{) sin} ?

cos ' cp

-

a

.,

Hence the minimum "~lue of the shear strain is reached at:

••• (23)

where the fri ct ior: anglE' 13 hEl s the val ue zero as can be checked by suhstitutlon of eq.23 into eq. 22.

In this state the cutting process dissipates energy onl:,+,

by deformat ion of the liorkriece l'Mterial in abaenee of friction on the rake of the tool.

It seems obvious th3~ this nev~r can be a physical reality and thus the u~L1ue~e3s of the solution of eq. 22 is

secured by:

••• (24)

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In the figure 4 the reg ion of phYFical significance is restri~ted to :

" =3>00 for

a .. -

)00. to ,

=

450 for

a

= 00 and to

CIt

=

60

0 for a ;: + 30 • o

The solutions ega in l"rove to be unique.

2. The case of ~_.~!?.er~l state of stress.

As disoussed refore the· state of ~eneral stress prevails when:

is

The syste~ governAd by the shear angle relation eq.20. from which after expressing the shear strain in terms of shear angle and rAke angle, shear angle solut~ons can be obtained with both f and a as parameters.

As is shown in fig. 5 the ra t io f has a very strong in-fluence on the course of the shear angle solution, and so it does in particular in the r.egion close to f = 1.

When reading fig.

5

it. should be kept in mind that every value of the parameter f gives to two different shear angle solutions. correspondin~ to the choice of the sign in the eqs. 20 and 2 1 , and hence dependent on the modulus of the ratio between the principal stresses, which can be expressed in terms of g ~ 1 , a s shown before.

Nhen is accepted tha!. the average value of the. maximum shear stress as a resultant of a hypothetic stress dis-tribution might dirf?!' up to about 2% from the plasticity constant of the material machined, quite a number of the observations published in current literature is covered by the present theory.

It even might be thai'. the extreme sensiti.viness of the shear angle solution w~th respect to the stat~ of stress suggests a lack of unique solutions of the problem.

A

more complete ricture gives fi~.

6

where the effect of both of the t::/o parameters is shown simultaneously under the condi tion ~ ') ". as arrears to be usual in a ma .iori

tv

of the practir:al cases investigate~.

I t is observ'?n that the influen.ce of the rakft angle decrea-ses rapidfy as the va 1 ue of f decreases, Le. when the average behaviour of the system moves. out of the state of pure shear.

In conclusion is shown the figurp

7

where experi-men tal data A <5 ust'; d b v Ox 1 ey (6) as an example are compared with the present theory.

o 5 10 IS iO , I

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-A major difficulty in verifyIng 6hear-an~le solutions arises from measuring the sh~ar-angle cp in an accuracy eompara .... le

with which can be obtained when measuring the friction angle ~ by means of dynamometry. As a rule cutting forces

will be reeordednU1"in;~ ,a considerable length of time and hence an average value of the friction angle can be deter-mined with fair precision.

On the contrary deter~inetion of ~he shear-angle depends on measU'ring the chlp-rat in from samples of the ehb,.

A

vast number of samples should be taken in order to arrive at an accuracy cnmFArahle with the one obtained by dynamo-metry.

Now. in a program of investigation of cuttinlZ' temperatures. an extensive study hAS heen made 0' the behaviour of the

chip contact len~th in relation to the cutting conditions

(i).

When machining obliaue ... v an annealed steel C 45 with" a car-bide tool of the ~rade S 2 (1 'SO - P 20)

a def initerela tl.on between feed, s}Jeed and chip ratio proves to exist:

." •• (25)

in the speed

ran~e

1"

v"

5

.B-

1 , in the .feed rs.nge

-3

-3

m/

0,2.10 " t " 1.0. 1 C rev. , and at the depth

of

cut of d

=

3.

10

-3

m.

As eq.25 has been obtained.fromthe study of the average behaviour or' the ch ip .Cbntae t length as recorded in a nat ure 1 way in 'the wear patt~rn on the rake of the tool, the accuracy in de termining the shear-angle from it proves to be about the seml-sirt determining the friction-angle from recordings ob-tained with a sensitive strain-gage dynaMometer (8).

Statistical evaluation shows a relative error of 2% in the shear-angle and a relative error of 2.5% in the angle

P -

« .

The experimental !'€sults have been plotted in fig.

8,

where both values of the shear-angle obtained by use

ot

eq. 25 and those obtained by 1irect measurement of the chip ratio have been used. The 'presene.?: of a systemati.c error is evident. The agreement with tre rref;erd' shear-an gle re lation eq. 22 is pretty good. from wh lch it rnigh t be co ncl uded that the material iF> machined if. An average 8tate of pure shear. /'inti probably behaves ar.cordln~ to the von Mises condition

ot

plasticity.

we,kplaCltstechnlek technische hogeschool eindhoven

, - - - , )1- 51- 11- 51- )1- 51- )1- 5e)

-rapport nr.

₀₁₃₉

biz. 16 van 49 biz. I

A second series of experiments has been performed with a ne gat ive val ue of the 1"F, ke-angle .' The results are shown

irl fig.

9

from which the conclusion mi,ght be the same.

In concl U5 ion it, if) remarked that ,eq. 17 when used in

con-nection with dynl'lmomettic experiments allows for in'1estigation into the plastic tehaviour of the w.orkpiece material un~er machin ing cond i t 1.ons when assuming val idity of the von Mises cond i tion.

~hen' using: cot 2 Q ::

i

tan y _{s_} •

as has been derive,d earlier, the eq. 17 CAn be written like:

C7 C ::

~3

:'

"r

I"

tan2 ( cp ...

~

- ex ) - tan(, +

p -

Cl )tany + tan2Ys+3l

s

L

s J

•••. (26) by which the' true .stressCJ_c is expressed in dynamometric Qua!'!ti-ties and hence can be calculated from num~rical experimental values. 'J'he amoun t of computing work is considerably reduced when io known that the material is machined in a state of pure shear, as in this case eq. 17 reduces to"r

=

k sin 20

s

As derived in eq.

15

the true strain can be calculated from the prevalent. value of the shear strain anli thus a streee-strain relation In t.he rep:ion of machining conditione can be plotted.

This is shown in fi&! •

.,c

as based on the ~eRsurementa of fill'.

8

when machining an a~ne!lled steel C

45.

The. mechanical proper-ties of the material are illustrated in fig. 11, which

represents the true stress-strain relation a!'\ obtained from 8

step by step interrupted tensile test.

.

.

The yield ~oint of the1material is reached at a t:-ue stress

of

3.42.

10 Nm-2 (34.2 kgf/mm2 ) and fraction occ~rs at a vel ue of the st resr' el<,se to 10

9

Nm- 2 (100 kgf/mm ).

In the re~ion hetwpen, the stress-strain curve behaves almost perfectly in ac~ordRnce with the power function:

1 .. c ... ~U 0,22 CJ

e '"

.' (' • ",' e

From fig. 10 it may he concl uded tha t in thl!'! re~don of high I"trai.1 ar.ri straln r,qt .. , RS typical for condi tions of machininP".

apFroximately hOids!

at : 1.56.109

e...

1.32

A simultaneous representation o. u~n of tne two relations is gi ven in f1 p:. 12.

o

5 10 15 !O !5 10 15 10 10

r---.---.~---.---rapport nr.

₀₁₃₉

biz. 17 van 49 biz.

This rreliminary tnvesti~a~ion into the plastic behaviour of the rna tar ia1 under condi t ions of ma'ch ininJf does -not conclude to a Significant influeE e of the cuttin!l' speed and henee of the strain rate on He train hardening. By far the most

important factor in [.traln hardening. refering to the particu-lar material stud 1.ed, Arrears to be· the val ue of the strain.

~o far, nowever. no exo~rlments have been performed in the region of strain which links the ultimate values of the quasi-static tensile test with the minimum values achievable in machining. in order i.O invest.igate wether some continuous

transition from the one re~ion to the other might exist.

-werkplaatstechnl.k _{technische hogeschool eindhoven}

~---. . ---,

rapport nr. 0139

blz.1~

van49 biz.

I

o

References 5 10 15 lO 15 JO 50 1. Hill, R. 2. Merchant,

M.E.

J. HeCll. Fhys. .sol i'ds .J. A pp 1 , Phys •

J. ,\.ppLFhys. J. Arr1.Phys.

3.

Zweekhorst.E.T.~. Metaa ~ewerking

4.

Colding,

B.N.

Thesis. dtockholm 1

959,

p.

39

5.

Lee,

F.H.

and Shaffer, B .N •

6.

¥ Oxley. P.L.B. J. ~Fr1..;V!ech.

-Int.J.Mach.Tool Des.Res. Frod. !::~n;;!:. Oxley. P.L.B. and

Hatton, A. F;. _{Int.J .rle:::h .• 2c5..}

7.

Hulst, A.F.A.J. lab~reAearch report

WT

129~ Eindhoven

8.

Ten Horn,

B.L.

Metaalbewerki.ng and ";ch urmann , R. ~- . :~ctFla 1 bewerking

WT

. 3. (1954 ) 47 11 • (1Q40)

₃₂₃₀

16. (19 4

5)

5 267

16.

(1945 ) 6 318 29. (1964 )22 471

73.

(1951) 4

05

2

( 1962 ) 2

1

₉

43

(1q64 )

₆₀₉

5 (1963)

41

135

(1965 )

24

( 1

958 )

_3.39

24

( 1958)

5,85

rapport nr. 0139 blz.19 van

49

biz.

-The Merchant shear tlEme Monel and the geometric stress condi tion:

a

:c 't tan(/J ..

13.-

(l) y s 1 - - ' " " - - - .--... ~-.... werkplaatstechnlek . -.. -~--... - - -

-technische hogeschool eindhoven ' - - - --.-~ .. --.---.... - -... . '

-rapport nr.0139

TECHNISCHE HOGESCHOOl EINDHOVEN

.

LABORATORIUM VOOR MECHANISCHE TECHHOJ,.OGIE EN WERKPLAATSTECHNIEK

o

5 10 15 20 25 30 35

so

, - - - _ . _ - - - , rapport nr. I •

0139

biz. 21 van 49 biz. I

. I

Fig. 2

-The Mohr equilibriu~ condition and the stress parameter Op

g = -_14F = from which is derived:

ta n ( qI + 13 - a :c g cot 2 0

If the direction Q of the ~aximum principal stress is

iden-tified with the direction of maximum &train, it can be shown that holds!

cot 20

from which follows:

,

-

~ <t Pi\H Y '" s tAn Y s

and hence the hhear angle/equation:

tan (. + 13 - (l) "

~

g 'tan y s :;

i

g [tan (qI - a) + cot.

J .

rapport

nr.0139

di..rczcti.ot')

<S"'3

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK

blz. 22 van 49 bJ.:l,.

o

5 10 15 20 I 2S 30

T

so

rlHIDort nr.

0139

biz.

23

van

1.,9

blz.l

Jetermi~atio~ of th" iire~tion

of mAximum Ftrai~.

An element of material AF is deformed by the cutting proces

into the 3 t b t € Ai' ard _6 thuR strained to the amount

AF'

£ ;:

AF

From the conditiGD m£ximum strain: cot 20 :;06 P_ 1 eos q dt d q Q.

1

tan y s

can be derived the direction of

'cot

2.

rapport nr.0139

...

...

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK

...

_...

bIz. 24 v~n 4~ ~~z.

looL

...

_...

....

_...

o

5 1Q 15 20 25 30 35 40 45

sa

- - -- - - , rapport nr. 0139 blz.25 van 49b1Z.1

Fig. 4

The shear angle solutlC~ ~q. 20 in the ste~e of stress of

pur~ shear, ns 'l~'i"':'d ~,~, the cc>nd.~tion 03 - 0, and hence bv 't '" k cr

• max

Shown i~ the effect of the r~ke 8~gle as a p~rameter.

Ii. comp~ r~ison is rna de Wi t.r, to t~ the r1~ rc:han t ~rd t"1f- J.ee c: rH~

~chaffer solutions.

I

I

. --- --- --- - - - 1

rapport nr.0139

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK

d:-oo

i

10

o

10 15 20 25 30 35

4'

so

rODll:lart nr.

0139

blz.27 van 49 biz.

The shear angle rela1 it.'ln eq. 20 for thE> value of the rake angle ex :: 0 and different. vr:/.l ! .. f:S of the rnt.io

"C max

f --:'

~~,"-~ k: "

Shown is the sensitiveness of the solut10n with respect to minor ehRnges in f in th~ re~ion close to f

=

1.

Both the possible F:olutJ or,s hav-e been plotted accorrlinp, t,(, i:he

value f ::: 0,99. corre:r;rondirIGr with the two possible differer.t states of avera~e stress.

- - - " " - " " - - - " " - - - 1

werkplaatstechn lek technische hogeschool eindhoven

""~~"""---rapport nr.0139

TECHNISCHE HOGESCHOOL EINDHOVEN

2.0

10

d:o

o

10

LA80RATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK \ \ \ \

\

\

\ \ \

,

~~;. ~_d.'=:.lT

\

: 4

\

!

\ i , -t-\ \ blz. \. \.

o

5 10 15 20 30 35

so

r-~---~~~---~~.-~~~~---~-~~~~-~---~--~--~.--~---"---,

.,., ... ,,, ... nr.

₀₁₃₉

_{biz. 29van49 bIz.}

I

li'ig.

6

The shear angle l'Els'ttor. i?Q.2C for different valueR of both the rake angle ex ar:d the !'"b t io f,

Only the solutions corr~stonding wi th the pooitive sign if 1 the eqs. 20 and 21 hay!> been Flotted. as will refer to the majority of the rra~tlc31 ca~@ .

rro be observed is the dE\:reri81flg :mportanee of the" rake angle as the ratio f decrease~ due to the moving of the system out

ot

a state of pur~ shear.

rapijort nr.0139

o

TECHNISCHE HOGESCHOOL EINDHOVEN

10

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK \

\

\

\

\

\

\

\

'-'f+~-d..=

1T

\

4-. 4-. \ \ \ \ \ \

\

\

20 2.~ 30

o

5 1Q 15 20 r---~.--~--.-~--~---.---rapport nr.

0139

biz.

Comparison of a nurnbe r' of f'hear angle va t \leS as used by

Oxley (6) wi th the pred ict ions of the present theory accordin~ to eq. 2C. bIz. 25-30 35 .. 0 50 r - - - -..

rapport nr.0139

'30-20 __ .

10

- . 0

Il.

'"

0

•

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK

c:k=o

. . .

v=

'59~

,.p.

m.

-to

20

40

50

':)A

'E.

4""5$'

RC

_~'5"

~_fk

~Af.. 4<\'&'5

RC_

2.6

~Al:. 44~5

_ QCO

r42ce~"czd.

SAt.

41~S _ o\OoeQ

lcz.d

f

=

O·CJS

1<3)1

f

=-"

o 5 1Q 15 20 25 30 35 50 ,---""---"---"-~----"---~

rapport nr. 0139 biz.

33

van4 biz.

Fig.

8

and fi~:~

Comparison of experimental results with the prediction~ of the

present theory. sq. ~; ~hen ~ach ~in~ an a~nealed steel G 4~

.

~peed range 1 •

5

ma

cut

3

ml'll.

• fee~ rAn~e 0,2 ~ _~ 1,0 mm/r~v. oenth of

• ;:;ip.terrr>1ned ind'ir~i·':..V trornf'hit" '!""Itio relatio'" e". ?c,

x ;:; ~ee8ured dir~ct v fr~m rhip ratio bv samnling.

werkp laatstechn I.k technische

rapport nr.0139

40

e.30

2.0

o

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHAHISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK

10

20

• rapport nr

.0139

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE .. EN WERKPLAATSTECHNIEK

•

•

Ao

Jo

20

40

..

•

•

•

•

o

i I

I

t

! lQ I

I

I

20 ~ 25

+

0139

bl z.}6 van '. ~bl z. Fig.

1..Q

The stress-strain relat.or. of an annealed steel C 45 in metal cutting, accordin~ to ~a5. '3 and 26 a~d based on the measure-me n t 5 0 f' rig.

8.

werkplaatstechn 18k technische hogeschool eindhoven

-rapport nr.0139

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE EN WERKPLAATSTECHNIEK . trUe(. (,tntfa!.

~

& \ (

Ii

9

~

.10 --- --- ----

,

N.m2. . ____ .. __

4

3

---'2

.

.

•••

• . . i· ...

'\ .

....

•

•

•

1d

_{1~---~---~2---~~~----~4~--~~}

\?otu("'Qt $trQ\.t'l

~

o

5 10 15 20 25 30 35 50 • rapport nr.

0139

bl

z.

38

van

49 bl

z.

«<--~-~---<-- <---<---~---; Fig. 11

The stress-strai n relAt i':Or. of an Rnr.ealed steel C

45

as obtained from a stei hv rtep interrupted tensile test. Yield point 3.42 '0' Nm-c _{l3 4 .2 kgf/mm2 ),}

fracture 1C

9

Nm- 2 (·OC ~~!.mrn2).

--~--- ---~---~---_i

rapport nr.0139

9

iO

-5

4

"5-2

TECHNISCHE HOGESCHOOL EINDHOVEN

LABORATORIUM VOOR MECHANISCHE TECHHOLOGIE EN WERKPLAATSTECHNIEK

blz. 39 v~ r. i~(.

~L-

______

~--

__

~--~----~~~---~

0 .. 001 O.OOS 0.01 0.05' 0.1

0."5

I rapport nr. I

l

5 1Q 15 20 25 30 35 .. 0 50 l

0139

biz. 40 van 1.9 biz. I

---.--.-~

I

I

Fig. 12

Comparison of str8i~ hErdenin~ in a tensile test and in the process of metal cutt~~~.

werkplaatstechn lek technische hogeschool eindhoven

-rapport nr.0139

TECHNISCHE HOGESCHOOL EINDHOVEN LABORATORIUM VOOR MECHANISCHE TECHNOLOGIE

EN WERKPLAATSTECHNIEK blz. 41 van 49 blz,

true

~tre~St

crt.

=

'k

J5

1010

N

m'l.

5

4

'3

2

-'S

4

'!

I

2. ...

.:....--~

e:

McztaL/

cutttt')9

/

10

8

O--.O-1~---O-~-5---0-A----~--~O~.~----1~---2~~~~4~5

o i

'I

1Q lS 20 '-2S 30 !-- 3St-

SOl--39

biz. 42 van 49 biz.

conce:r!Jin~ L'.,n;erJ.,;;al valuE's ohtained h~, d:vnA!!'lO~etrv when machining btec~ ~ 45 (a~npBled) with a carbide too 1 gl·l'tdt" f.,~ (F20 )

In these reports the f~lJcwing Rymtols are used: y a

P

y P_A 'r 6 ~ Y

,

~ R C ..,. (I e:

=

:: :: :: = ::: ' :

-=

' : f~ed

main cutting force

force ~n direction of fped, thrust fClrr'8

aver~go st~Ar streR~ in ~hear plane ~nver~e ~~;ue of chjp tbickn~ftR ratio

shear str:l tl

friction A~"'le

The rake en~le is defineri in a plane paRsinR throu~h the dirp~­

tion of the cu·tin", sre~d vector and the direction of the ~or~~l

to the plane rnsehlned.

rake anv,.j,p

clearance angle

side cuttln~ ed~e angle nose rad ,,<.,8 depth of Gut

... 6

0

5°

150 1.? mm

3 mm

Table A2 Table B1

res~lts of calculations rererin~ to nbGerv~ttor' A.

werkplootstechnlek

rake .-;nglp

cl earanl..~e r.t.ngle side ~utt.n~ ed~e

nose rarl i '':'!'; depth of cut;

... 6°

50 angle 00 1,2 mm

3

mm

reSiJ Hs of ca leu lat ions re fering to observa tions

technische hogeschool eindhoven

,

o 5 lQ 15 20 25 35 45 50 .---~----~- ---~---,

rapport nr. 0139 blz.43 van49 biz. I !

7ablp. C, raj< e ardzole

,~10arance angle

:"inf! cuttin .. edp:f> anKle

r'o.:-.;e rad ius

dE'~d h of cu

_ 6

0

17

0 00 1,2 mm

3

mm

re~ultB of alculations referin~ to observation

The machi~e ~onl used is a athe, type A.I.DR 200-special

irp~t power 60/ 0 kW.

o

~

.

5000. continuous control

ra~gp of feed~ 0.0025

7

40

rom/rev., continuous

ccn+.t~d,max.

c tting force 104N (1000 kp"fJ.

The measurements hnve been erformed by the metal eutt~n~

research team under the dir etion of 8hr. Bus, ing. Detailed informa+ion is ",tv r. in the lahoracory report

WT

138

~:v A.ri . • :trouo

and

H r-1unnecom.

r---~---werkplaatltechn I.k technische hogeschool eindhoven

~

aiO

Q13

0,16 0.20

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c·

4~5

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