On the significance of equivalent chip thickness
Citation for published version (APA):
Bus, C., Touwen, N. A. L., Veenstra, P. C., & van der Wolf, A. C. H. (1970). On the significance of equivalent chip thickness. (TH Eindhoven. Afd. Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0241). Technische Hogeschool Eindhoven.
Document status and date: Published: 01/01/1970
Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page numbers.
Link to publication
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:
www.tue.nl/taverne Take down policy
If you believe that this document breaches copyright please contact us at: openaccess@tue.nl
providing details and we will investigate your claim.
WT-Rapport no.0241 Code : P.7.b.3
Q'l' THE SIGNIFICANCE OF ::lCY-IVALENT CHI~ TIUCl\1\TESS
by
C. BUS~
N.A.L.
TOUWEN,
P.C. VEENS11'\l\ ,A.C.H. i!
m
DER WOLP.Eindhoven" Universi r.y of Technology) the Netherlands
..
Paper to be presented to the Genel'aZ Assemb ly of the C,I.R.P . .> Tori-no., 1970.
•
rapport no.0241
SLMv1ARY.
In this article, the technological importance of the equivalent
chip thickness and equivalent chip width is shmm. Both quantities are defined with the aid of the total length of engaged cutting edge and the true area of undeformed chip section.
In the Htboratory of Production Engineering at the Eindhoven University of Technology computer programs have been developed in order to calculate these quantities in dependence on different
geometrical conditions. •
~ relevrult exrunple concerning cutting forces is given.
1
Aus der vorliegenden Arbeit ist die grosse techndlogische Bedeutung der 'Begriffe 'Vergleichsspandicke" und 'Vcrgleichssprulbrci te"
ersichtlich. Beide Grossen werden definiert in Abhangigkeit von der beteiligten Gesrulltlange der Sc1meidkante und dem unverfonnten
Spanqu~rschnitt. Zwecks rechnerischer Ennittlung dieser Grossen flir'unterschiedliche geometrische Verhaltnisse sind im Institut flir Fertigungstechnik der Tec1mischen Hochschule Eindhoven Computer-Programme entwickelt worden. Beispiclsweise wird der Rechnungsgang schliesslich an Hand die Meisselkraft naher erHi.utert.
RESUM.B.
Dans cet article l'in~ortance technologique de l'equivalent epaisseur
du copeau et l'equivalent largeur du .copeau est indiquee. Les deux . grandeurs sont determinees au moyen de la longueur 'totale de la levre
de coupe concernante et l'airc effective de la' section du copeau undeformee.
AlJ L~b(\r8t(\ire de la Tec!-..nologio H6c:.~ique
a
l'Univ-cl"site Technique: d'Eindhoven,·des computer-programmes sont developpes pour calculerles grandeurs susdites en cormexion de conditions geometriques differentes. Une exelnple considerable concernant des forces de coupe est ajoute.
rapport no:0241
,In common practice) both in the workshop and in metal cutting research the quantities depth of cut, and \vidth of cut or even feed are considered being primary variables independently control-ling important technological phenomena like cutting force and lite time of tools.
From this way of thinking, generalised cutting force relations' and life time relations arise of a nature as proposed by
Kronenberg {1}.
Typically~ the process is described by, both a specific quantity which is arbi,trarily chosen and the, exponents of depth of cut and . width of cut,
.. !he spec;ific quantity being specific cutting force or specific cutting speed accounts for the influence of materials properties', Hovi'ever) the e}.1?onents are still affected by the latter,
Obviously, in the relations mentioned the variables chosen are of
a geometrical nature rather th~n being technological. It can be
assumed that they do not act seperately in th~ technological
process. On the contrary, depth of cut and width of cut are
constituents of two basic technological quantities being the total
length of engaged cutting edge or equivalent chip width be on the one, hand and the surface area A of ui1deformed chip cross section on the other--{2},
From these a third tedmological quantity is derived being the equivalent chip thickness
or rather A h ::: 1)-e .. 1)-e A h ' e :: ,-e
t;
(1 )where Ae r~presents the true area of undeformed chip section. Thus
accolllting for the influence of the nose radius as shO'\\111 in Fig, 1.
Clearly the introduction of equivalent chip thic1mess allmvs for
replacing the actual cutting geometry b;T an equivalent model
containing all the parameters of geometlY but for the rake angle.
It is remarked that by the very definition of equivalent chip
rapport no.0241
thi~kness
a
variety ~f different geometry renders the same value of the quantity in question.Now, a point of major interest appears as experimental investigation shows that cutting force and tool temperature are merely controlled by equivalent chip thickness irrespective of the seperate values of the geometry parameters involved.
'This proves that the equivalent model of cutting geometry must not be considered being a ·conception of purely academic value. Actually, the mode1·revea1s the basic technological quantities governing the metal cutting process.
By this time, restricting ourselves to forces in turning op~rations, .
. it appeqrs that the reduced cutting force, being the cutting force .
"
per unit length. of engaged cutting edge, is a strictlinear function
of the equivalent chip thickness" as shmm in Figs. 2a and zb.
TIle reduced feed and thrust force are linear functions of the equivalent cllip thickness too.
Hence, Kronenberg's relations can be replace~ by an expression of the
type
(2)
From this follows for the specific cutting force or the specific cutting energy F k =-.-! =6+ s
A
e h' e (3)It is concluded that application of the equivalent model reduces the amount of data involved in transfer of infonnation regarding
cutting forces to only two, being the "material's constants" a and
s.
With an eye to teclmo10gy transfer the common geometrical data must be translated in tenns of equivalent chip width ffild equivalent chip thickness. The relevant relation available" {3} has only limited value as its application is restricted to the region of feed ,vhere the minor cutting edge is not engaged in cutting.
rapport no.0241
be distinguished in order t'o calculate the equivalent functions. It follows analytically: case: (1) (2) b e
=
(3) (4) a - r (1-cos (K)) r £; + { K + arcsinCzr)}
s e2
sin (K) e a - r (1-COS(K)) r be = sin (K) e: + { K'+ K'}2
e: + + _ arcsin (s sin(K') r . £; .a - r (1-COS(K)) b - e: e - sin (K) , 5 sin (K) - {1 - sin(2 -
1t. K - K'l} +---=.--~---=.---cosCI -
K - K').* cOt~(K) + cos' {K - arcsin (s ~in (K2 - 1))*' .
e: . { . (s sin (K) 1) _S_ill _ _ K_-_a_r_c_sD_l. _ _
--=-___
-__
}
l
+ 'Z'~
. arcsin (_5 _5_i_n-.cC",-K..<...2 . 1)-
}
2 - l~-rapport no.0241
. z{·
1 _, cot (K) f 7f (3) A = s a - r e E Sln . (K) 2 + tan (~ ) - ...:.. + 4 arcsin' { 1 s sin (K I) } r + E' + 2sin' { 1T Kf - arCSln (1 - s sin (KI))}
r
}+
...
E 2 sin (K)~
{s 1 t } 2 •- r
{sin (K) - cot (K) + tan (r)} ,~ 2 { cot (K I) + cot (K) }
{
1
t}2
s - r { - cot(K)
+ tan (K2 )} ______ ~E~ _ _ sin~)~ _______________ ~~~ cot(K'
+ cot(K)}
In order to make these fonnulas practically useful, 'they have been
numerically evaluated by means of an AJJ30L-60 program.
Table't shows the typical res.ult referring to Fig. 3. The general program is available on request.
To a limited extent, it is also possible to ask for numerical data connected with a particular case of chip geometry.
REFERENCES:
{1 } 'Nachining Science and Application"
by M. Kronenberg, Pergamom Press, 1966.
-rapport no.0241
{2} "Wirtschaftlich' Zerspanen"
von W. Leyensetter,. Westell11ruID Verlag, 1953.
, .
{3} "A wear Relationship for Turning, Milling and
Grinding; Machining Economics" by B.N. Colding, Stockholm, 1959.
. 6
-•
rapport no.0241
Fig. 1. The true area of undefol'med ahip seation A •
e
-- 8 rapport no~Q241 " 1400 N/mm 1300 ,
y
reduced cutting force
Fv
V
be
A
1200 / AI
I
..
tooltip : P20A/' .
'-V
material: C45N-XI
-.. f, , ,~ t. 1100 1000 900 /. ,21.
gABOO
700 100 •6//
~~
, 6!
reduced feedFf
/-~
forceb
<>.:;----e ... <5'~-)
V
<> ~ ,--<>---~ ~ <> <>---<
<> (> .--<>~
Q~(>~
~~
p
<> ¢ ~ v .,.v ____~
t-v . ~ . . v~, 'Ii . ~ V . .. - - - -. __ .. _p-_ .. _---ct7-v~~"
FpL.-!-;
"V"'- \l V reduced thrust force -T~.---:1
'V v J 1 I De . 600 500 300 200o
0:4 O.~ 0.6 0.7 Iequivalent chip thickness he (mm)
O.i 0.2 0.3
Fig. 2a• Reduced cutting forces versus equivalent chip thickness for a cutting speed v
=
1 m/s.\
.
! rapport no.021+1 1400'----···--~---~---T---~----~---N/mm13001---~----~---r·----~---I
1200 - - - --.-.--~- ---'-re-d+~u-c~-e-d~c-u-tl--t··-jn-g-f-o-r-lcl-e-~-~--i-/-'."---t
1100~--~--4Uo--l-ti-'P-.-:+P-2--0----r-I----~~--~--~~-7~r----.~
1000- materia : 1 C SN 4 /V
9001---~---~---+---_+---+---~~---~----_,.. l./
8001- - - + - -... --I...-:..---+---=r-c-/-.. - - - t - - - + - - - tl{
i
AA/
700~----~----~~---+~~~+---~---~-~--_;/
6001--·---~----~---A7~~/----~----~---r----'
.1
500~---+---+--~-4---~~-~1---_+---_t/0
,4001- - - -l'
F · t-g. '2b • 0.1 0.2 0.3 . 0.'1 0.5 OJ) 0.7 equivalent chip thickness h~ (mm)Reduced cutting forces versus equivaZent chip thickness for a cutting speed v = 3
mls.
rapport no .0241
Fig. 3. "Different geometrical conditions for a depth of cut of 1 mm and a corner radius of o.~ mm.
feed •
I
r 0,7 mm/rev K' :: 601) 10rapport no. 0241
EQUIV AlENT CHIP THICKNESS, PROGI~. A - 2403 - 9
a depth of cut
[mm)
A area of the chip section [rom2)
e
b equivalent chip width [mffi]
e h f
e equivalent chip thickness [ram]
K major cutting edge angle [0 ]
"
K' minor cutting edge angle
r' ]
r corner radius [ram]
E
B feed per revolution [mm/rJ
a
=
1.00 ram a ::::: 1.00 inmK == 60 0
Ii: == 30 0
k.' ::::: 30 0 K'
=
60 0r
=
,,!~O rom r '" .ltO rom£, £, s b e .1 1.3928 .2 1.4437 .3 1.4964 .4 1.5521 .5 1.6143 .6 1.6844 .7 1. 7614 .8 1.8Lt49 .9 1.9315 1.0 2.0181 1 • 1 2. , oh7 1.2 2.1913 . 1.3 2.2779 1 .It 2.3645 1.5 2.4511 Table 1. A h f case 'b A h i case e e e e e .0999 .071'7
,
2.1524 .0999 .0~~64 1 .1992 .1379 1 2.2033 .1992 .090!~ 1 .2971 .1986 1 2.2560. .2911 .1317 1 .3931 .2532 1 2.3117 .3931 .1700 1 .4806 .2977 3 2.3723 .4862 .. 2049 2 .5739 .3407 3 2.11-11-15 .5760 .2359 2 .6617 .3756 3 2.5284 .6621 .2619 2 .7442 .h03h 3 2.7306 .7442 .2726 2 .8221 .4256 4 2.5711 .8221 .3197 4 .8956 .4438 4 2.6211 .8956 .3hi7 4 .9647 .l~584 h 2.6711 .9647 .3612 4 1.0296 .4699 t~ 2.7211 1.0296 .3784 It 1.0901 .4786 4 2.7711 1.0901 .3931+ 4 1. 1463 .4848 il- 2.8211 1.1 !f63 .4063 Il-1.1981 .1+88-3 4 2.8711 1. 1981 .4173 hTypical result of the ALGOL-cO progranl referring to Fig. J.
