- Email: [email protected]
The applicability of the binomial law to the process of friction in the cutting of metals
274
THE APPLICABILITY OF THE BINOMIAL FRICTION IN THE CUTTING OF METALS*
LAW TO THE
PROCESS
OF
M. B. GORDON Frunze Textile Institute, Ivanovo (U.S.S.R.) (Received
July 7, 1966)
SUMMARY
On the basis of the systematic experimental data obtained with the “split cutting tool” device constructed by the author and the graphico-analytical treatment of these data, it is shown that when cutting metals, in conditions where excrescence is absent, friction has a molecular-mechanical nature and is governed by the binomial law, in which, as in DERYAGUIN'S law, the adhesion component has a variable value. Changing the conditions of cutting, including the external medium, influences the adhesion component of friction fundamentally. Effective media partially or completely prevent adhesion and convert heterogeneous behaviour of friction into homogeneous, which is described by the one-term law (Amontons’). The conceptions developed in the article make it possible to explain the basic laws of friction observable in dry cutting and with various media and to construct a representation of the nature of the contact. INTRODUCTION
Among specialists engaged in the study of friction, a united opinion concerning the nature and laws of this process has not, as yet, emerged. At the same time, there is in technical literature1 a classification of the basic types of friction, and it is noted that “all the enormous variety of processes and phenomena of external friction of solid bodies experimentally observable are confined within the range between friction of “juvenile” surfaces and hydrodynamic friction”. For every type of friction there are definite peculiarities : the definite physical nature of the friction forces, characteristic values of the coefficient of friction and the law of friction establishing the functional dependence of the friction forces on the basic parameters determining its value. Great scientific and practical interest attaches to the elucidation of the question concerning what types of friction take place during metal cutting without cooling, what laws of friction obtain in this process, and how the character, behaviour and laws of friction change during the process of cutting in different artificially introduced media. The experimental data given below and the results obtained from their treatment permit an approach to the solution of these questions. * Condensed by the editor. Wear, IO (1967) z74--2go
PROCESS OF FRICTION IN CUTTING OF METALS
275
THE STATUS OF THE PROBLEM AND METHODS OF INVESTIGATION
During the process of cutting metals, independently of the character of the strained state, the forces applied to the working surfaces of the cutting tool may be represented as normal and friction forces distributed according to definite laws on the nominal contact areas of the back surface of the tool with the article being processed (S,’ = bL’; b is the width of cut) and the front surface of the tool with the chip (SN = bL). Replacing these forces with their resultants in the case of rectangular free cutting, we find that normal force N and friction force F act upon the front surface of the tool (Fig. I). Correspondingly, forces N’ and F’ act upon the back surface, in which case F =,uN, and F’=p’ N’, where ,u and p’ are the mean friction coefficients on the front and back surfaces of the tool.
Fig. I. The system of forces acting on the tool during the process of free cutting. L = length of contact area on the front surface of the cutting tool; L’ = length of contact area on the back surface of the cutting tool; y = front angle of the cutting tool; a = thickness of cut.
In the course of the last twenty years, many attempts have been made to distinguish the forces acting on the back surface of the tool and to obtain forces F and N separately on the front surface of the tool. The most widespread method is that of extrapolation of the force dependencies P, (u) and Pz (u) on a zero thickness of cut213. Pg and P, are, respectively, the projections of forces on the radial and tangential directions; a is thickness of cut. The basis of this method, as is known, is the assumption, the reliability of which remains to be proved, that forces F’ and N’ on the back surface of the tool are independent of the thickness of the cut. Simultaneously with the method of extrapolation, the study of friction is being carried out with the help of a device based on the principle of the “split cutting tool”, which was introduced by the author in 1948495. On this basis, there appeared, for the first time, the possibility of experimental research also on the nature of the distribution of contact stresses on the front surface of the tool, side by side with investigation of friction forces and the mean coefficients of friction. Later on, some researchers turned their attention to the method of photoelasticityG-8. Some well-known research has been carried out with cutting tools made wholly of plexiglass in the conditions of polarized light; in consequence, the optical Wear,
IO
(1967)z74-zgo
M. 13. CORDOK
276
picture characterizing the state of stress in the tool appears as a summary action of the stresses applied both to the investigated front surface and to the back surface as well. Hence, and also because of the concentration of plastic deformations near the cutting edge, the curves of stress distribution in this area are greatly distorted. Practically, the experimental determination of the forces and stresses acting separately on the front and back surfaces of the tool is, at the moment, possible only by means of the split cutting tool. The idea of the split cutting tool is used by many specialists in the field of metal cutting 9- 12. This idea has penetrated even into an adjacent field : devices based on the use of split tools are now employed also in research work on friction during the processing of metals under pressureia,i4. At the same time, it has been established that data previously obtained5 with the help of such tools are only the first approximation. In the course of further investigationi5Ti6 it became clear that the accuracy of work with split tool devices depends upon many factors which had not been taken into consideration, including some which, at first glance, seem to be immaterial. METHODS AND CONDITIONS OF CONDUCTING INVESTIGATIONS
Presented below are the results of the systematic research carried out with the help of the analytico-experimental method based on the use of the “split tool” device. The working principle of this device (Fig. 2) is based on the division of the front and back surfaces of the cutting tool, with a part of the front surface executed in the form of a separate movable plate which is set in motion by the action of the friction forces. The construction of the device has been described in detail elsewhere4,5915,i6.
\ Bock
plate
Fig. 2. Scheme of the “split cutting tool” device for measuring the force of friction and the length of contact between the chip and the front surface of the tool. Fig. 3, Scheme of the installation of the front and back plates on the “split cutting tool” device. Wear, IO (‘967) 274-290
PROCESS
OF FRICTION
IN CUTTING
277
OF METALS
On the basis of special investigations, we formulated the basic requirements, the fulfillment of which permits reducing to a minimum possible experimental errors in determining the length of the contact area, the friction forces and contact stresses on the front surface of the too115,16. The optimum variant method for determining these parameters consists of the following steps (Fig. 3). (I) From preliminary experiments the maximum value of forces (frictional and normal), and correspondingly the maximum thickness of cut a,.,, are determined with which the device shows stable, reproducible results. (2) A set of back plates is prepared, usually amounting to n= 1~3,. . ., to< IO, with sizes of working surfaces Ii>12 > . . . I, > . . . lk. Length 11is equivalent to the length of contact during the process of cutting with a maximum thickness of cut tolerance amax. (3) In the first experiment, the first pair of plates is installed: “back plate with length 11 and front plate”, and thickness of cut alXamax is determined. The value of a is selected in such a way that all the chip is distributed on section 11; then the friction force on front plate Fl is equal to zero (in practice FI E 3-5 N). (4) Plates 12,. . ., I,, . .., lk are installed consecutively in the device, and one experiment is carried out with each pair of plates, with a constant thickness of cut al. Since, in this case, the length of contact lo= L =const., and lo> 12> . . . 1, > . . . IL, then in each experiment, including the first, friction force FIZO, F2,. . ., F,, . . ., Ft is measured, acting correspondingly on the contact area with length I1=11-11=0 72=11-12 I, L.1; -1, r; =‘1; 11;
where ii, t2, . . ., I,, . . ., ik is the length of contact between the chip and the movable (front) plate. As Fig. 3 shows, for any number 12,plates i,, + 1, = 11. It is necessary to measure the friction forces in the order of increase of value of i, i.e., in the order of gradual approach to the cutting edge. Also, it is necessary to note that the minimum length tolerance of the area on back plate (It) must be within 0.05-o.r mm. With smaller values, the reliability of the device’s performance is uncertain. The full force of friction F on the whole length of contact is located by extrapolation of curves F (1) at value IX= o, i.e., on the cutting edge (Fig. 4). Tangential stresses on different contact areas of the chip with the front surface of the tool are determined by the formula:
AF, t=3z=
Fn - Fn-I
(I)
b(ln-ln-1)
During the experiments, the feed (thickness of cut), cutting speed, front angle of the tool and the external medium were varied. The cutting process was carried out with high-speed and hard alloy cutting tools without lubrication, with compressed air for blowing, with lubrication by a 1.5% emulsion and “industrialnoye 20" (pouring and spraying) oil, and in a medium of carbon tetrachloride. Different metals were Wear,
IO (1967) z74-zgo
M. B. GORDOlU
278
lfmm)
l(mm)
Nmm)
Fig. 4. Curves of increments of friction force on the front surface of the tool when cutting steel 40X. (v = 0.017 m/set) (a)y = -oo.175rad, ~:a = o.ramm, 0 : a = 0.07 mm, + : a = 0.034 mm, 0 : a = 0.0195 mm. (b)y=o, A:a=o.r56mm, o:a=o.og5mm,+:a=o.o57mm, O:a=o.o34mm. (c) y = 0.26 rad, A : a = 0.208 mm, q:a=o.r8mm,+:a=o.o78mm, o:a=o.o43mm.
worked on, i.e., steel 40X, stainless steel rXr8HgT, cast iron, titanium alloy BT4, copper and lead. In experiments with steel I x r8HgT, b = 2 mm ; in the others, b=jmm. As is well known, practically no excrescence is formed when cutting alloy BT4, lead and copper. In order to prevent the formation of excrescences in experiments with steel 40X and steel rXr8HgT, they were machined at low cutting speeds (before excrescence formation) and at higher speeds (after excrescence formation).
a,(mm)
0
0.1
0.2
0.3 0.4 a, (mm)
CM
0.6
0.7
a41
0
I 0.05
I 01 a,(mm)
I 015
Fig. 5. Dependence of the mean friction coefficient on the thickness of cut and the front angle. (a) Steel 40X, v = 0.017 mJsec; (b) steel rXr8HgT. IJ = 0.014 m/set; (c) lead, v = 0.00%0.2 m/set; (d) alloy BT4, v = 0.017 m/set; O:y=-o.r75rad,+:y=o, a:~=o.s6rad. Wear, IO (1967) 274-sgo
279
PROCESS OF FRICTION IN CUTTING OF METALS RESULTS
The diagrams (Figs. 5 and 6) show the dependence of the mean friction coefficient ~1on thickness of cut a and front angle y; Figs. 7 and 8 show the dependence of ,u upon the mean normal stress during dry machining; dependence p (a, y) during machining in artificially introduced media is shown in Fig. 9.
a, (mm)
a,(mm)
Fie. 6. Deoendence of the mean friction coefficient on the thickness of cut and the front angle. (a)-Coppep, v = 0.27 m/set; (b) cast iron, v = 0.125 m/set. o: y = -o.r75rad, +: y = o, A: y = 0.26 rad.
0.4 600
urn,, (MN/m*)
700 U,,,
a00 (MN/m*)
SO0
Fig. 7. Connection between the mean friction coefficient and the mean normal stress. (a) Steel 40X. v = 0.017 m/set; (b) lead, v = 0.00%0.2 m/set; (c) alloy BTq, v = 0.017 m/set. o: y = -0.175rad, +:y = 0, A:y = o.z6rad. 0.85
c1 0.8 0.75 0.6
0.7 0.65
0.65
0.6
/J 0.6
0.55
0.55
0.5 200
300 b,,,
400 (MN/m*)
0.5 300
IJ 0.5
600 400 500 Urnmean (MN/m*)
Fig. 8. Connection between the mean friction coefficient IXr8HgT, v = 0.014 m/set; (b) copper, v = 0.27 m/set; -0.175 rad, + : y = o, A : y = 0.26 rad.
a4 400
600 000 Umean (MN/m*)
and the mean normal stress. (a) Steel (c) cast iron, v = 0.125 m/set. o : y =
These and other experimental data we obtained proved to be so different in character that at first glance it seemed impossible to discover any general laws which could serve as a basis for carrying out a qualitative, not to mention a quantitative, analysis of the process of friction in different cutting conditions. Thus, when cutting Wear, 10 (1967) 274-290
at low speeds (up to 0.017 mjsec) without cooling, some materials (steel 405, steel xx18HgT, lead and alloy RT4), we established a law of dependence of the mean friction coefficient on the front surface of the cutting tool upon the thickness of cut and the front angle (Fig. 5) ; in experiments with copper and grey cast iron (at v = 0.27 and 0.125 m/set) practically no influence of a and y on ,u was detected (Fig. 6). In some working conditions a connection is observed between friction coefficient p and mean normal stress omean (Fig. 7), and in others (Fig. 8) there is no such connection. Increasing the cutting speed changes friction qualitatively in experiments Fig. g
Fig.
I"
t’
I_
0.6
I
I
I
Fig. 9. Dependence of the mean friction coefficient on the thickness of cut and the front angle when cutting in various media. (a) Steel rXr8HgT, II = o.or4 mjsec. y = 0.26 rad. (b) lead, v = 0.008 m/see. o: without coohng, y = o. 8): pouring 1.5% emuision, y = 0.25 rad., v: m a medium of CCL y = 0.26 rad. Fig. IO. Dependence of friction force on normal force. (a) Steel 40X, v = o.or7 m/set; (b) steel rXr8HgT, ZI = 0.014 m/set; (c) lead, B = 0.0080.2 mjsec; (d) ahoy BT4, v = 0.017 mjsec. 0: y= --o_175rad,-t_:y=o,~:Y=o.z6rad. Wear, IO (1967)
274-290
PROCESS OF FRICTION IN CUTTING OF METALS
281
with steel 40X, dependence ,~(a, y) is lost, and when cutting steel IXI~H~T and alloy BTq, it remains practically unchanged. Using some kinds of artificially-introduced media when machining steels and lead at low speeds practically eliminates the dependence of ~1on a and y ; the use of others does not change it (Fig. 9). The same liquid (CCL) applied to steel IXI~H~T (Fig. g(a)) reduces friction and changes the laws governing it during the cutting process without cooling; when applied to lead, on the other hand, it increases friction without changing it qualitatively (Fig. o(b)). Increasing the cutting speed in some cases weakens the lubricating action of external media, and in others strengthens it. METHODS OF TREATMENT
OF EXPERIMENTAL
DATA
A physical interpretation of the experimental data obtained proved to be possible by means of graphico-analytical treatment based on the graphic method, well known in the theory of friction, of separating the adhesion component from the total friction force. It should be noted that the idea of separating the adhesion component of friction as an independent term in the basic law of friction made its appearance long ago. As far back as the 18th. century, Coulomb, confirming Amonton’s one term law of friction, introduced in it for the first time the constant quantity A, which expresses the adhesive interaction of surfaces. At the present time, the development of the basic law of friction is connected with the work of DERYAGUIN, which is based on the mechanics of the molecular interaction of abrading surface+-20. The molecular theory of friction leads to the binomial law of friction in the form F =,LJo(N+ No)
(2)
Here ~0 is the “true” friction coefficient in conditions where adhesion is equal to zero, depending on the molecular-atomic roughness of surfaces, NO= P&O is the resultant of the forces of molecular attraction between the two bodies and PO is the force of molecular attraction acting upon the unit of true area of contact SO. In contrast to Coulomb’s law (F = Fo+ A), where the adhesion (tangential) component of friction A is a constant value independent of the true area of contact, and consequently not dependent on the normal load, in DERYAGUIN’Slaw the normal adhesion force is a variable value, the function of the true area of contact. In connection with the great difficulties of measuring the force of adhesion directly, even in the simplest friction pairs, it is usually determined by the method of extrapolation of graphs expressing the dependence of the friction force on the normal load (Fig. IO) at value N =o (to find the tangential force of adhesion A) or at value F = o (to find the normal force of adhesion NO). In our work we used the idea and graphic method of extracting the adhesion component from the total friction force, and the law itself, describing friction in the cutting of various metals in the given experimental conditions, was obtained as a result of analytical treatment of experimental curves of dependence of friction forces upon the normal force F(N). WecZT,IO (1967) 274-290
hf. H. GORDON
282 BEHAVIOUR AND LAW OF FRICTION DURING CUTTING WITHOUT COOLING
At low qbeeds “up to excrescence” The analysis IXI8HgT, with
lead
of the diagrams
and
assurance,
correspondingly
BT4,
shows
be broken
down
into two
in the zone of greater
In the extrapolation the force
in Fig.
alloy
of friction which
every
sections:
of the rectilinear
is not
converted
is obviously
experimental
conditioned
cutting
a group
assumed
that
At coincide,
time
with
friction The
force
same
straight
line
analytical
of adhesion and normal
or with
consequently,
of experimental
A is a variable
equal force
and as a result,
the
during
the process
of one form
straight
ac (Fig.
of by
line bc, occurring
during
the
of
law.
IO) does
process
not
as the
of cutting
law or by Coulomb’s
F(N) function
curves
is a binomial
binomial of the
one, in
law of friction, true
area
the
(length)
of
force.
F=Fo+A(L,N)=p,N+A(L,N) The data obtained parameters
to
(ac), it may be
by one general
curve
DERYAGUIN’S
value,
value
is the greatest
is governed
experimental
by Amonton’s
with
a definite
tenacity,
by curves
law;
expression
kc
F (N) curves at value N = o,
F (N), obtained
either
correspondence
ak and rectilinear force.
conditions,
friction
that
Fo=,uoN,
binomial
is not governed,
in complete
contact
conditions
and
of the tool.
is expressed
it is clear
of
aquires
by molecular
dependence
metals,
in experimental
the
of Coulomb’s
metals, which,
of different
either
diagram
as experimental
but
steels 40X
F (N) curve may,
curvilinear
section
to zero,
the local grasp of the chip on the front surface Inasmuch
when cutting
experimental
and lesser value of normal
A max. The value of Amax, in definite adhesion
IO, obtained
that
of friction
(3)
and their
treatment
and adhesion.
Thus,
make
friction
it possible coefficient
to calculate
the basic
,u0 is determined
from
eqn. (4).
F-Am, N
PO= or directly
from
(4)
F(N) diagrams
(see Fig. IO).
po=tanolo The value of the adhesion
force is calculated
as the difference
(5)
A=F-Fo The mean be determined
The
coefficient
by dividing
ratio
of forces
of friction
A/N
stresses, and then it is possible
p=po+2tT.2E Cmean
Wear.
IO (1967)
z74-zgo
p at the front
both parts of eqn.(g)
in eqn.
surface
by the normal
(6) is expediently
of the cutting
tool may
force N.
replaced
by
the ratio
of
to record (7)
PROCESS OF FRICTION IN CUTTING OF METALS
283
where: qmean= A/bL is the mean stress creating the force of adhesion (or specific force of adhesion) and amean= N/bL is the mean normal contact stress. Designating qmean/umean=,u~, we obtain: /J’IuO-?-PA,
(8)
is the adhesion component of the friction coefficient. Equation (8) shows that the friction coefficient during the cutting process consists of two quantities: a constant (,uo), which we will call conditionally the mechanical quantity, and a variable, the adhesion quantity (PA), which is the function of two variables (qmean and omesn). According to these formulae and the experimental data, we obtained the values of friction force Fo, the coefficients of friction p, ~0 and ,UA,the force of adhesion, the stress created by the force of adhesion and other parameters. Since ,UOis a constant value of the abrading pair, the dependence of the mean friction coefficient ,u on the adhesion component PA, in conformity with eqn. (8), is expressed by a straight line with the initial ordinate ,UO(Fig. II).
where
0
PA
0.04
0.08
0.12
al6
0.2
0.24 pA
Fig. I I. Dependence of the mean friction coefficient on the adhesion component. (a) Steel 40X, v = 0.017 m/set, 0: y = -0.175 rad, + :y = o, A :y = 0.26 rad, steel IXISHgT, v = o.o~qm/sec, q:y = o,O:r = 0.26rad:lead,v = 0.008-o.2m/sec, 0:~ = o, +:y = 6.26 rad. (b) AlloyBTq,v = o.o17m/sec, o:y = -0.175rad; +:y = o.
The full force of adhesion A (Fig. 12) with extension of the length of contact from very small values (small thickness of cut and a great front angle) grows from Amin to A,,, and further remains constant. Inasmuch as the rate of growth of the force of adhesion is much smaller than the rate of growth of the length of contact L, specific force of adhesion q mean, on the other hand, diminishes from qmeanmax to qmean mia, asymptomatically approaching zero at L-xo. The analysis of the curves of distribution of adhesion stresses along the length of contact of the chip with the front surface of the tool q (1) shows that, for example, in the case of dry cutting of lead (Fig. 13), the adhesion stresses, and consequently the adhesion component of friction is observed, not on the whole investigated length of Wear, IO (1967) z74-2go
M. B. GORI)OS
284
contact, but only on the section of length from 0.5 to 0.7 mm from the cutting edge. In principle it is possible to draw the same conclusion on the basis of an analysis of F(N) graphs in Fig. IO (and others not presented here), where the increase of the force of adhesion on the curvilinear section gradually diminishes to zero. It is obvious that precisely at point k, where it is equal to zero, the rectilinear section (kc), which
L,fmm)
L,(mm)
Fig. I 2. Dependence of full force A and (a) Steel 40X, v = 0.017 mjsec 0:y -= -o.175 rad +:y=o A(L) A: y = 0.26 rad 1 (b) Steel I Xr8HgT, v = 0.014 mjsec .+ : y = 0 ) A(L) A : y = 0.26 rad (c) Lead, v = o.o08-0.2 mjscc + :y = 0 .4(L) n : y = 0.26 rad 1 (d) Alloy RT4, v = o.oq mjsec 0: y == --o.r7j rad A (Lf +:y=o I
specific force ~,MW of adhesion on the length of contact. and
uz y = -0.175 r&d qmeaa(L) 0: y = o i 0: y = 0.26 rad
and
clm=&)
and
@=a&)
and
qmesaW (i:
1%:;
f
z t,26
o:y=o O: y = o.26 rad
--ax?5 wd c z o
Fig. 13. Distribution of specific forces of adhesion and the friction of the cutting toot when cutting lead. v = o.o08-0.2 mlsec, o : y Fig. 14. Scheme of contact W&W, IO (1967) 274-290
rad
coefficient
on the front surface
= o, 0: y = o and 0.26 rad.
sections on the front surface of the cuttingtool.
PROCESS OF FRICTION IN CUTTING OF METALS
285
characterizes the homogeneous transient* behaviour of friction without noticeable adhesion, begins. The data obtained thus permits the whole area of contact to be divided in the direction of movement of the chip into three sections (Fig. 14): first, the section of “juvenile” (adhesion) friction; second, the mixed section (“juvenile” plus transient friction) ; and the third section, homogeneous transient friction. The analysis of the accumulated experimental material shows that in the investigated cutting conditions, when practically no excrescence is formed, the adherence of the chip to the front surface of the cutting tool in consequence of the action of molecular forces of attraction (adhesion) has a local character (takes place in separate centres) and the contact area consists of two or only one zone of friction (the second and third or the second). In the first case, the behaviour of friction on the section of contact close to the cutting edge is heterogeneous (mixed) and on the remaining part, homogeneous (transient) ; in the second case, it is mixed on the whole length of contact. According to AKHMATOV’S classification 1, both these behaviours of friction may be attributed to the friction of oxidized physico-chemically clean surfaces. It may be assumed that the existence of sections with different behaviours of friction is conditioned, in the first place, by the fact that on the front surface of the tool there is contact with elements of the chip with different physico-chemical consistency, from newly formed to the last on the complete path of friction with length L, and hence differently oxidized by the atmospheric air**; and in the second place, it is conditioned by uneven distribution of normal stresses. For this reason, a physical parameter such as the coefficient of friction acquires a variable value along the length of contact as shown in diagram p(Z)*** (Fig. 13) and becomes dependent on the thickness of cut, the front angle and other factors which, without changing the physico-chemical nature and character of the contact, only increase or decrease the length of the contact. In this case, the adhesion component of the coefficient of friction changes correspondingly, and the mean coefficient changes in the same degree. This explains, what is usually observable, especially with small thicknesses of cut and large front angles, the high values (greater than I) of the mean coefficient of friction and the greater value of the coefficient of friction on the back surface of the tool than on the front. It is necessary to stress that precisely these circumstances (dependence of ,u on a and y, and value ,u 21) served as the basic reason for the departure of many specialists from the classical conception of the process and laws of friction during the cutting of metals. This idea is most clearly formulated by FINNIE AND %-IAWa4.
Thus, in dry cutting the basic parameters of friction, i.e. the force of friction, the coefficient of friction and the contact stresses, consist of two components, mechanical, which is constant, and adhesion, which is variable. For one and the same * Transient friction is a behaviour of friction in which the abrading surfaces are covered with thin films, the properties of which are within the range of influence of the solid bodies. ** The influence of atmospheric air on friction, adhesion, the projection of cutting force and other parameters of the cutting process is proved by direct experiments carried out in a vacuuma1pa2. *** The method of obtaining the computed dependence ~(2) is presented below; the experimental dependence has already been describedas. Wear,
IO
(1967) 274-290
286
31. 13. GORDOS
abrading factors
pair,
the latter
(length
components
depends
of contact).
of friction
on the thickness
The correlation
changes
within
of cut, the front
between
angle
the mechanical
very wide limits,
depending
and other
and the adhesion upon the conditions
of work.
At increased
“after excrescence”
speeds
Changing
the
and length
of contact,
the contact
surfaces,
influencing
cutting
speed,
their
mechanical
to one result, of cutting
friction
to homogeneous,
because
vanishing
there
speed,
and other
II 2 I m/set).
oxidation,
(2) Diminution ,!,&Ais constant
diminution
of both
important
On the whole,
essentially
coefficient
time state
of
characteristics
from
when
coefficient
,uo when
IXI8HgT).
(3)
steel
(~0 and ,&I) when
fact
(A, N) approaches
the
cutting
steel
by
of
the
cutting
(cutting
the
behaviour
conditioned
component
is established
variants
(I) With
heterogeneous
apparently
the adhesion
different
of friction.
of the friction
components may
three
behaviour,
(such a phenomenon
coefficient
disclosed
of the mean
transient
component 21to I m/set.
were
there is a transformation
of intensive
point
friction
the temperature,
upon the physico-chemical
firmness
i.e. diminution
increase that,
as it changes
way
friction.
In our experiments, leading
inasmuch
acts in a complicated
40X
at speed
the value
of adhesion
Simultaneous
negligible
alloy
BT4
at an increase
of
a slight
(within
the limits
of IO-ZO~/~) diminution
of the
be observed
within
the range
of alteration
speed
of cutting
we investigated. These of friction mation
data,
with
from
hand,
theory,
they
agree
according
when very
changes
steel 40X
(transfor-
and the purely
cutting
well
to which
qualitative
with
law of friction),
in speed on friction
on the other
of DERYAGUIN’S
temperature
the above-mentioned
speed in experiments
to the one-term
of the increase
and lead;
corollary
in cutting
the binomial
ive influence BT4
on the one hand, explain
an increase
quantitat-
steel IXI~H~T,
with
the highly
~0 depends
very
alloy
important
little
upon the
of the contact*.
INFLUENCE
OF THE EXTERNAL
MEDIUM ON THE BEHAVIOUR
AND LAW OF FRICTION
Cutting at low speeds From concrete
the point
conditions
ineffective
of view
or even harmful
media
To the first group and to the second fluence tive
which
the adhesion in dry cutting,
those which partially
on the behaviour carbon
qualitative
component friction
and (2) effective
which
arise during
of friction
changes
and the mean parameters is described
by the binomial
upon
into two groups,
adhesion
eliminate
are essentially when
in the behaviour it only
in dependence
(I)
media.
do not eliminate
tetrachloride
dry cutting:
developed
conditionally
or completely
* In experiments with steels, the highest cutting alloy BTq, up to 1300°C. Wear, IO (1967) 274-290
being
may be divided
belong
(for example,
does not introduce as those
those
of these media
medium
of the conception
of use, all media
cutting
it, in-
different.
An ineffeca steel tool)
and its laws, such
in one degree
of friction.
The
lead with
of friction
increases,
or increase
adhesion.
of another,
In these conditions,
as
law.
temperature
reached up to 600-7ooT;
with
PROCESS OF FRICTION IN CUTTING OF METALS
287
Thus, the result is that the nature of adhesion (molecular attraction of clean metals or films has practically no influence on the law of friction. When cutting lead in a medium of CCL, PbCla films are found on the chip2iJ5. An effective lubricating and cooling medium prevents adhesion (No=0 and A = o) ; e.g. the same carbon tetrachloride with respect to steel IXI~H~T, converts a heterogeneous behaviour of friction into a transient (homogeneous) behaviour. This, according to eqns. (2) and (3), eliminates the main cause of the dependence of the mean coefficient of friction on the front angle and the thickness of cut, the inequality of the friction coefficients on the front and back surfaces of the tool, and the high values ,u ( >I). The coefficient of friction is lowered, as a rule, and acquires an approximately constant value (~0) on all the contact surfaces. Friction with such a behaviour (sometimes with a negligible deflection) is described satisfactorily by the one term law (Fig. IS). (b)
F,(N)
0” N,fNf
N,(N)
i 40
80 12o 200 N,@J1
/
Fig. 15. Dependence of friction force on normal force when cutting in various media: (a) Steel 40x, v = 0.017 m/set, 1.5% emulsion; (b) steel IXISHQT, II = o.or4 m/set, (I) 1.5% emulsion, (&CC%;
(c) lead, v = 0.008 m/set, 1.5% emulsion;
o: y = -0.175
rad, +: y = o; A: 7 = 0.26
CMting at imcreasing speeds In principle, the law established with respect to low speed cutting also applies to high speed cutting. With the increase of cutting speed, the lubricating effect diminishes, disappears, or sometimes, on the contrary, increases. It is known that with the increase of cutting speed, the time of contact decreases, and consequently, the time of the medium’s action. However, as a result of the augmentation of the contact temperature, there is, simultaneously, a rapid increase of the chemical reaction. When there is constant shrinkage of the chip, the area of the chip increases in direct proportion to the speed, and the contact area also increases along the back surface of the tool, which interacts with the medium in a unit of time. The result of these competing changes may be either a weakening, or a strengthening of the lubricating effect. In our experiments with increase in cutting speed, we observed, as a rule, a weakening of the lubricating action of the emulsion, which is expressed in the increase of the adhesion component of friction. When cutting lead in a chemically active medium /fCCQ, an increase of cutting speed from 0.008 to 0.2 mjsec, i.e. 24 times, augments the adhesion component of friction approximately 1.4 times (Fig. 16). The latter may be considered a result of the appearance of the first (adhesion) section Wear, x0 (1967) 274-290
288
RI. B. GORRON
of contact (about 0.05 mm in length) and the augmentation of the length of the mixed (second) contact section (see Fig. 14), which in turn is obviously conditioned by
the
increase
of
the
number
of
contact
centres
of
adhesion
and
the
true
area
of
contact.
I
f
0
40 Normal
Dependence v = 0.008 mjsec, + Fig.
16.
LUBRICATING
I
80 force,
120
d 2 ‘00
160
N,(N)
of friction
force on normal
force when
cutting lead in a medium of CC&. (a)
: y = o; (b) u = o.z m/set, A : y = 0.26 rad.
ACTION
OF TI-IE EXTERNAL
MEDIUM
ON DIFFERENT
SECTIONS
OF CONTACT
The treatment of the experimental data shows that one and the same medium reacts selectively upon different contact sections. What is common to all the investigated media is that their conditional lubricating action, i.e. the increase or decrease of friction force on the relative length of contact x, is manifested more extensively on the sections of contact where the value of the adhesion component of friction is greater (near the cutting edge). Relative contact length x is defined as the ratio x=hlL, where 1, is the distance from the cutting edge to the point under consideration. When I, =o, x=o is the point on the cutting edge; when I,= L, Wear, IO (1967) 274-290
PROCESS OF FRICTION IN CUTTING OF METALS
289
x = I is the terminal point of contact. The influence of the medium on the mechanical component of friction in sections remote from the cutting edge may be more or less strong, depending upon the properties of the medium and the material being processed, but it is always lower than the influence on the adhesion component. This situation is illustrated by graph c (x) which represents the lubricating action of the medium on a relative contact length (Fig. 17).
V.5’ 0
0.2
0.4
Y
0.6
0.8
I 1.0
I.
Fig. I 7. Distribution of the coefficient characterizing the lubricating action of the emulsion on a relative length of contact when cutting steel 40X. Y = 0.017 m,/sec; (a) y = --0.175 rad, @: Q = 0.121 mm, 0: ca= 0.07 mm; + : tl = 0.045 mm; (b) y = o,@ : a = 0.104 mm, 0: @= 0.065 mm;(c)y=o.26rad,Q:a=o.r3mm, o:a=o.o78mm.
It is to be noted that, inasmuch as C= AF with lubrication/AF without lubrication, the more the lubricant lowers the force of friction AF on the elementary contact section AX, the smaller coefficient C and the higher the lubricating action of the medium. As the c(x) curve steadily increases, the lubricating action of the medium steadily diminishes according to the measure of removal from the cutting edge. A combined consideration of these data with the distribution curves of normal stress along the contact length in different conditions of cutting shows that the influence of the medium on the force (and coefficient) of friction does not depend, in practice, on the character of the distribution of normal stresses on the contact surface. It is obvious that in the conditions of heterogeneous behaviour of friction complicated by adhesion, a varying degree of activity of the contact sections is a stronger factor than a varying value of normal pressure. This situation conforms with the results of an investigation26, where it is established that iodic liquids react weakly with titanium, stainless steel, lead, nickel and cobalt, the surfaces of which are usually covered with a thin film of oxides. However, liquids of just this class, on coming in contact with clean surfaces formed during cutting and friction, create on them a layer of crystalline structure (film), which acquires anti-friction properties. Wear, IO (1967) 274-290
M. H. GORDOX
290 ACKNOWLEDGEMENTS The author wishes to express for
his
valuable
consideration present
advice
during
of the results,
his profound the
long
gratitude
period
and to B. V. DERYAGUIN
of
to Professor
experimental for his scientific
M. I. KLUSHIN work
and
editing
the
of the
work.
REFERENCES A. S. AKHMATOV, The Moleczllar Physics of Transient Friction, F&math, Moscow, 1963. A. M. ROSENBERG, The Dynamics of Milling, Sovietskaya Nauka, Moscow, 1945. N. N. ZORYEV, The Normal Forces and the Forces of Friction in Oblique Angle Free Cutting, Mashgiz, Moscow, 1948, p. 5. (Vol. 15. Central Scientific Institute.) M. B. GORDON, A device for determining the friction forces appearing during the cutting of metals, Bull. of Inventions No. I, 1951, p. 49. (Author’s Certificate No. 88039.) M. B. GORDON, The distribution of the friction forces on the front edge of the cutting tool in the zone of contact with the chip, Vestn. Mashinostr., 33 (5) (1953) 53. W. KATTWINKEL, Untersuchungen an Schneiden spanender Werkzeuge mit Hilfe der Spannungsoptik, Ind.-Anzeiger, 36 (73) (1957) 29. 7 G. S. ANDREYEV, An investigation of stresses in the working part of the cutting tool on a polarized optical installation with the implementation of a motion picture camera, Vest%.
Mashinostr., 38 (5) (1958) 54. method, IZV. 8 M. F. POLETIKA. Investigation of the cutting Process bv the optical-polarization - _ _ _ _ Tomsk. Politekn..Inst., 112 (1964) 157. 9 D. T. VASILIEV, The forces on the cutting surfaces of the tool, Stanki i Instr., zg (4) (1954) I.
D. T. VASILIEV, The physical conditions of the zone of deformation and the contact surface of the cutting tool as a factor in increasing the efficiency of the cutting tool, Material; Seminara No. 3, Moscow House of Scientific and Technical Propaganda, Moscow, 1963. 10 L. F. KAMSKOV, Simultaneous use of the force of friction and the force of normal pressure on the front edge of the cutting tool, Vestn. Mashinostr., 38 (6) (1958) 52. II A. N. REZNIKOV, The Temperature and Cooling of Cutting Tools, Kuibishevskoye Knignoe Isdat., Kuibishev, 1959. I2 V. F. BOBROV, On the distribution of specific normal forces and friction forces on the front surface of the tool, in The Machining of Metals by Cutting and Pressure, Mashinostroyenia,
Moscow, 1965, p. 57. ‘3 I. M. PAVLOV AND Du DEH YUAN, A compound measuring device for the contact forces of friction, Sci. Refits. of Higher Schools Metallurgy No. 2, 1958, p. 147. I4 A. A. PRESNYAKOV AND A. A. VIKNITZSKI, A device with a split puncheon for determining the coefficient of external friction with sedimentation, Zavodsk. Lab., 25 (4) (1959) 487. I5 M. B. GORDON, A device for measuring friction forces in metal cutting, Stanki i Instr., 36 (7) (1965) 24. 16
I7 18 I9 20 21
22
23
M. B. GORDON, The method and results of an investigation of the law of distribution of friction forces and tangential stresses on the length of contact of the chip with the front surface of the cutting tool, in M. I. KLUSHIN (ed.), Q uestions Concerning the Use of Lubricating and Cooling Liquids in Metal Cutting, Upper Volga Publ. House, Ivanovo, 1965, p. 64. B. V. DERYAGUIN, 2. Physik, 88 (1934) 661. B. V. DERYAGUIN, Wear, I (1958) 277. B. V. DERYAGIJIN,J. Phys. Chem., 5 (9) (1934) 1165. R. V. DERYAGUIN, What is Friction?, Acad. Sci. U.S.S.R., Moscow, 1963. N. G. ABULADZE, The influence of the medium on adhesion in metal cutting, Tr. Gruzinsk. Politekhn. Inst., 8 (60) (1~58) No. 3. G. W. ROWE AND E. E. SMART, The importance of oxygen in dry machining of metal on a lathe, Brit. J. A#. Phys., 14 (12) (1~63) 924. M. B. GORDON, Parameters of the process of friction in metal cutting, Stanki i Instr., 37 (6) (1966) 31.
24 I. FINNIE AND M. C. SHAW, The friction process in metal cutting, Trans. ASME 78 (3) (1956) 1649. 25 M. MERCIIANT, The influence of lubricating and cooling liquids on the wear of the cutting instrument, in A. I. PETRUSYEVICH (ed.), Intern. Conf. Lzlbrication and Wear of Machines, Moscow, 1962, p. 4~9. 26 Iodine lubricants smooth the way for broader use of titanium,
Wear, IO (1967) 274-290
Iron Age, rg6 (22) (1965) 68-6~.
THE APPLICABILITY OF THE BINOMIAL FRICTION IN THE CUTTING OF METALS*
LAW TO THE
PROCESS
OF
M. B. GORDON Frunze Textile Institute, Ivanovo (U.S.S.R.) (Received
July 7, 1966)
SUMMARY
On the basis of the systematic experimental data obtained with the “split cutting tool” device constructed by the author and the graphico-analytical treatment of these data, it is shown that when cutting metals, in conditions where excrescence is absent, friction has a molecular-mechanical nature and is governed by the binomial law, in which, as in DERYAGUIN'S law, the adhesion component has a variable value. Changing the conditions of cutting, including the external medium, influences the adhesion component of friction fundamentally. Effective media partially or completely prevent adhesion and convert heterogeneous behaviour of friction into homogeneous, which is described by the one-term law (Amontons’). The conceptions developed in the article make it possible to explain the basic laws of friction observable in dry cutting and with various media and to construct a representation of the nature of the contact. INTRODUCTION
Among specialists engaged in the study of friction, a united opinion concerning the nature and laws of this process has not, as yet, emerged. At the same time, there is in technical literature1 a classification of the basic types of friction, and it is noted that “all the enormous variety of processes and phenomena of external friction of solid bodies experimentally observable are confined within the range between friction of “juvenile” surfaces and hydrodynamic friction”. For every type of friction there are definite peculiarities : the definite physical nature of the friction forces, characteristic values of the coefficient of friction and the law of friction establishing the functional dependence of the friction forces on the basic parameters determining its value. Great scientific and practical interest attaches to the elucidation of the question concerning what types of friction take place during metal cutting without cooling, what laws of friction obtain in this process, and how the character, behaviour and laws of friction change during the process of cutting in different artificially introduced media. The experimental data given below and the results obtained from their treatment permit an approach to the solution of these questions. * Condensed by the editor. Wear, IO (1967) z74--2go
PROCESS OF FRICTION IN CUTTING OF METALS
275
THE STATUS OF THE PROBLEM AND METHODS OF INVESTIGATION
During the process of cutting metals, independently of the character of the strained state, the forces applied to the working surfaces of the cutting tool may be represented as normal and friction forces distributed according to definite laws on the nominal contact areas of the back surface of the tool with the article being processed (S,’ = bL’; b is the width of cut) and the front surface of the tool with the chip (SN = bL). Replacing these forces with their resultants in the case of rectangular free cutting, we find that normal force N and friction force F act upon the front surface of the tool (Fig. I). Correspondingly, forces N’ and F’ act upon the back surface, in which case F =,uN, and F’=p’ N’, where ,u and p’ are the mean friction coefficients on the front and back surfaces of the tool.
Fig. I. The system of forces acting on the tool during the process of free cutting. L = length of contact area on the front surface of the cutting tool; L’ = length of contact area on the back surface of the cutting tool; y = front angle of the cutting tool; a = thickness of cut.
In the course of the last twenty years, many attempts have been made to distinguish the forces acting on the back surface of the tool and to obtain forces F and N separately on the front surface of the tool. The most widespread method is that of extrapolation of the force dependencies P, (u) and Pz (u) on a zero thickness of cut213. Pg and P, are, respectively, the projections of forces on the radial and tangential directions; a is thickness of cut. The basis of this method, as is known, is the assumption, the reliability of which remains to be proved, that forces F’ and N’ on the back surface of the tool are independent of the thickness of the cut. Simultaneously with the method of extrapolation, the study of friction is being carried out with the help of a device based on the principle of the “split cutting tool”, which was introduced by the author in 1948495. On this basis, there appeared, for the first time, the possibility of experimental research also on the nature of the distribution of contact stresses on the front surface of the tool, side by side with investigation of friction forces and the mean coefficients of friction. Later on, some researchers turned their attention to the method of photoelasticityG-8. Some well-known research has been carried out with cutting tools made wholly of plexiglass in the conditions of polarized light; in consequence, the optical Wear,
IO
(1967)z74-zgo
M. 13. CORDOK
276
picture characterizing the state of stress in the tool appears as a summary action of the stresses applied both to the investigated front surface and to the back surface as well. Hence, and also because of the concentration of plastic deformations near the cutting edge, the curves of stress distribution in this area are greatly distorted. Practically, the experimental determination of the forces and stresses acting separately on the front and back surfaces of the tool is, at the moment, possible only by means of the split cutting tool. The idea of the split cutting tool is used by many specialists in the field of metal cutting 9- 12. This idea has penetrated even into an adjacent field : devices based on the use of split tools are now employed also in research work on friction during the processing of metals under pressureia,i4. At the same time, it has been established that data previously obtained5 with the help of such tools are only the first approximation. In the course of further investigationi5Ti6 it became clear that the accuracy of work with split tool devices depends upon many factors which had not been taken into consideration, including some which, at first glance, seem to be immaterial. METHODS AND CONDITIONS OF CONDUCTING INVESTIGATIONS
Presented below are the results of the systematic research carried out with the help of the analytico-experimental method based on the use of the “split tool” device. The working principle of this device (Fig. 2) is based on the division of the front and back surfaces of the cutting tool, with a part of the front surface executed in the form of a separate movable plate which is set in motion by the action of the friction forces. The construction of the device has been described in detail elsewhere4,5915,i6.
\ Bock
plate
Fig. 2. Scheme of the “split cutting tool” device for measuring the force of friction and the length of contact between the chip and the front surface of the tool. Fig. 3, Scheme of the installation of the front and back plates on the “split cutting tool” device. Wear, IO (‘967) 274-290
PROCESS
OF FRICTION
IN CUTTING
277
OF METALS
On the basis of special investigations, we formulated the basic requirements, the fulfillment of which permits reducing to a minimum possible experimental errors in determining the length of the contact area, the friction forces and contact stresses on the front surface of the too115,16. The optimum variant method for determining these parameters consists of the following steps (Fig. 3). (I) From preliminary experiments the maximum value of forces (frictional and normal), and correspondingly the maximum thickness of cut a,.,, are determined with which the device shows stable, reproducible results. (2) A set of back plates is prepared, usually amounting to n= 1~3,. . ., to< IO, with sizes of working surfaces Ii>12 > . . . I, > . . . lk. Length 11is equivalent to the length of contact during the process of cutting with a maximum thickness of cut tolerance amax. (3) In the first experiment, the first pair of plates is installed: “back plate with length 11 and front plate”, and thickness of cut alXamax is determined. The value of a is selected in such a way that all the chip is distributed on section 11; then the friction force on front plate Fl is equal to zero (in practice FI E 3-5 N). (4) Plates 12,. . ., I,, . .., lk are installed consecutively in the device, and one experiment is carried out with each pair of plates, with a constant thickness of cut al. Since, in this case, the length of contact lo= L =const., and lo> 12> . . . 1, > . . . IL, then in each experiment, including the first, friction force FIZO, F2,. . ., F,, . . ., Ft is measured, acting correspondingly on the contact area with length I1=11-11=0 72=11-12 I, L.1; -1, r; =‘1; 11;
where ii, t2, . . ., I,, . . ., ik is the length of contact between the chip and the movable (front) plate. As Fig. 3 shows, for any number 12,plates i,, + 1, = 11. It is necessary to measure the friction forces in the order of increase of value of i, i.e., in the order of gradual approach to the cutting edge. Also, it is necessary to note that the minimum length tolerance of the area on back plate (It) must be within 0.05-o.r mm. With smaller values, the reliability of the device’s performance is uncertain. The full force of friction F on the whole length of contact is located by extrapolation of curves F (1) at value IX= o, i.e., on the cutting edge (Fig. 4). Tangential stresses on different contact areas of the chip with the front surface of the tool are determined by the formula:
AF, t=3z=
Fn - Fn-I
(I)
b(ln-ln-1)
During the experiments, the feed (thickness of cut), cutting speed, front angle of the tool and the external medium were varied. The cutting process was carried out with high-speed and hard alloy cutting tools without lubrication, with compressed air for blowing, with lubrication by a 1.5% emulsion and “industrialnoye 20" (pouring and spraying) oil, and in a medium of carbon tetrachloride. Different metals were Wear,
IO (1967) z74-zgo
M. B. GORDOlU
278
lfmm)
l(mm)
Nmm)
Fig. 4. Curves of increments of friction force on the front surface of the tool when cutting steel 40X. (v = 0.017 m/set) (a)y = -oo.175rad, ~:a = o.ramm, 0 : a = 0.07 mm, + : a = 0.034 mm, 0 : a = 0.0195 mm. (b)y=o, A:a=o.r56mm, o:a=o.og5mm,+:a=o.o57mm, O:a=o.o34mm. (c) y = 0.26 rad, A : a = 0.208 mm, q:a=o.r8mm,+:a=o.o78mm, o:a=o.o43mm.
worked on, i.e., steel 40X, stainless steel rXr8HgT, cast iron, titanium alloy BT4, copper and lead. In experiments with steel I x r8HgT, b = 2 mm ; in the others, b=jmm. As is well known, practically no excrescence is formed when cutting alloy BT4, lead and copper. In order to prevent the formation of excrescences in experiments with steel 40X and steel rXr8HgT, they were machined at low cutting speeds (before excrescence formation) and at higher speeds (after excrescence formation).
a,(mm)
0
0.1
0.2
0.3 0.4 a, (mm)
CM
0.6
0.7
a41
0
I 0.05
I 01 a,(mm)
I 015
Fig. 5. Dependence of the mean friction coefficient on the thickness of cut and the front angle. (a) Steel 40X, v = 0.017 mJsec; (b) steel rXr8HgT. IJ = 0.014 m/set; (c) lead, v = 0.00%0.2 m/set; (d) alloy BT4, v = 0.017 m/set; O:y=-o.r75rad,+:y=o, a:~=o.s6rad. Wear, IO (1967) 274-sgo
279
PROCESS OF FRICTION IN CUTTING OF METALS RESULTS
The diagrams (Figs. 5 and 6) show the dependence of the mean friction coefficient ~1on thickness of cut a and front angle y; Figs. 7 and 8 show the dependence of ,u upon the mean normal stress during dry machining; dependence p (a, y) during machining in artificially introduced media is shown in Fig. 9.
a, (mm)
a,(mm)
Fie. 6. Deoendence of the mean friction coefficient on the thickness of cut and the front angle. (a)-Coppep, v = 0.27 m/set; (b) cast iron, v = 0.125 m/set. o: y = -o.r75rad, +: y = o, A: y = 0.26 rad.
0.4 600
urn,, (MN/m*)
700 U,,,
a00 (MN/m*)
SO0
Fig. 7. Connection between the mean friction coefficient and the mean normal stress. (a) Steel 40X. v = 0.017 m/set; (b) lead, v = 0.00%0.2 m/set; (c) alloy BTq, v = 0.017 m/set. o: y = -0.175rad, +:y = 0, A:y = o.z6rad. 0.85
c1 0.8 0.75 0.6
0.7 0.65
0.65
0.6
/J 0.6
0.55
0.55
0.5 200
300 b,,,
400 (MN/m*)
0.5 300
IJ 0.5
600 400 500 Urnmean (MN/m*)
Fig. 8. Connection between the mean friction coefficient IXr8HgT, v = 0.014 m/set; (b) copper, v = 0.27 m/set; -0.175 rad, + : y = o, A : y = 0.26 rad.
a4 400
600 000 Umean (MN/m*)
and the mean normal stress. (a) Steel (c) cast iron, v = 0.125 m/set. o : y =
These and other experimental data we obtained proved to be so different in character that at first glance it seemed impossible to discover any general laws which could serve as a basis for carrying out a qualitative, not to mention a quantitative, analysis of the process of friction in different cutting conditions. Thus, when cutting Wear, 10 (1967) 274-290
at low speeds (up to 0.017 mjsec) without cooling, some materials (steel 405, steel xx18HgT, lead and alloy RT4), we established a law of dependence of the mean friction coefficient on the front surface of the cutting tool upon the thickness of cut and the front angle (Fig. 5) ; in experiments with copper and grey cast iron (at v = 0.27 and 0.125 m/set) practically no influence of a and y on ,u was detected (Fig. 6). In some working conditions a connection is observed between friction coefficient p and mean normal stress omean (Fig. 7), and in others (Fig. 8) there is no such connection. Increasing the cutting speed changes friction qualitatively in experiments Fig. g
Fig.
I"
t’
I_
0.6
I
I
I
Fig. 9. Dependence of the mean friction coefficient on the thickness of cut and the front angle when cutting in various media. (a) Steel rXr8HgT, II = o.or4 mjsec. y = 0.26 rad. (b) lead, v = 0.008 m/see. o: without coohng, y = o. 8): pouring 1.5% emuision, y = 0.25 rad., v: m a medium of CCL y = 0.26 rad. Fig. IO. Dependence of friction force on normal force. (a) Steel 40X, v = o.or7 m/set; (b) steel rXr8HgT, ZI = 0.014 m/set; (c) lead, B = 0.0080.2 mjsec; (d) ahoy BT4, v = 0.017 mjsec. 0: y= --o_175rad,-t_:y=o,~:Y=o.z6rad. Wear, IO (1967)
274-290
PROCESS OF FRICTION IN CUTTING OF METALS
281
with steel 40X, dependence ,~(a, y) is lost, and when cutting steel IXI~H~T and alloy BTq, it remains practically unchanged. Using some kinds of artificially-introduced media when machining steels and lead at low speeds practically eliminates the dependence of ~1on a and y ; the use of others does not change it (Fig. 9). The same liquid (CCL) applied to steel IXI~H~T (Fig. g(a)) reduces friction and changes the laws governing it during the cutting process without cooling; when applied to lead, on the other hand, it increases friction without changing it qualitatively (Fig. o(b)). Increasing the cutting speed in some cases weakens the lubricating action of external media, and in others strengthens it. METHODS OF TREATMENT
OF EXPERIMENTAL
DATA
A physical interpretation of the experimental data obtained proved to be possible by means of graphico-analytical treatment based on the graphic method, well known in the theory of friction, of separating the adhesion component from the total friction force. It should be noted that the idea of separating the adhesion component of friction as an independent term in the basic law of friction made its appearance long ago. As far back as the 18th. century, Coulomb, confirming Amonton’s one term law of friction, introduced in it for the first time the constant quantity A, which expresses the adhesive interaction of surfaces. At the present time, the development of the basic law of friction is connected with the work of DERYAGUIN, which is based on the mechanics of the molecular interaction of abrading surface+-20. The molecular theory of friction leads to the binomial law of friction in the form F =,LJo(N+ No)
(2)
Here ~0 is the “true” friction coefficient in conditions where adhesion is equal to zero, depending on the molecular-atomic roughness of surfaces, NO= P&O is the resultant of the forces of molecular attraction between the two bodies and PO is the force of molecular attraction acting upon the unit of true area of contact SO. In contrast to Coulomb’s law (F = Fo+ A), where the adhesion (tangential) component of friction A is a constant value independent of the true area of contact, and consequently not dependent on the normal load, in DERYAGUIN’Slaw the normal adhesion force is a variable value, the function of the true area of contact. In connection with the great difficulties of measuring the force of adhesion directly, even in the simplest friction pairs, it is usually determined by the method of extrapolation of graphs expressing the dependence of the friction force on the normal load (Fig. IO) at value N =o (to find the tangential force of adhesion A) or at value F = o (to find the normal force of adhesion NO). In our work we used the idea and graphic method of extracting the adhesion component from the total friction force, and the law itself, describing friction in the cutting of various metals in the given experimental conditions, was obtained as a result of analytical treatment of experimental curves of dependence of friction forces upon the normal force F(N). WecZT,IO (1967) 274-290
hf. H. GORDON
282 BEHAVIOUR AND LAW OF FRICTION DURING CUTTING WITHOUT COOLING
At low qbeeds “up to excrescence” The analysis IXI8HgT, with
lead
of the diagrams
and
assurance,
correspondingly
BT4,
shows
be broken
down
into two
in the zone of greater
In the extrapolation the force
in Fig.
alloy
of friction which
every
sections:
of the rectilinear
is not
converted
is obviously
experimental
conditioned
cutting
a group
assumed
that
At coincide,
time
with
friction The
force
same
straight
line
analytical
of adhesion and normal
or with
consequently,
of experimental
A is a variable
equal force
and as a result,
the
during
the process
of one form
straight
ac (Fig.
of by
line bc, occurring
during
the
of
law.
IO) does
process
not
as the
of cutting
law or by Coulomb’s
F(N) function
curves
is a binomial
binomial of the
one, in
law of friction, true
area
the
(length)
of
force.
F=Fo+A(L,N)=p,N+A(L,N) The data obtained parameters
to
(ac), it may be
by one general
curve
DERYAGUIN’S
value,
value
is the greatest
is governed
experimental
by Amonton’s
with
a definite
tenacity,
by curves
law;
expression
kc
F (N) curves at value N = o,
F (N), obtained
either
correspondence
ak and rectilinear force.
conditions,
friction
that
Fo=,uoN,
binomial
is not governed,
in complete
contact
conditions
and
of the tool.
is expressed
it is clear
of
aquires
by molecular
dependence
metals,
in experimental
the
of Coulomb’s
metals, which,
of different
either
diagram
as experimental
but
steels 40X
F (N) curve may,
curvilinear
section
to zero,
the local grasp of the chip on the front surface Inasmuch
when cutting
experimental
and lesser value of normal
A max. The value of Amax, in definite adhesion
IO, obtained
that
of friction
(3)
and their
treatment
and adhesion.
Thus,
make
friction
it possible coefficient
to calculate
the basic
,u0 is determined
from
eqn. (4).
F-Am, N
PO= or directly
from
(4)
F(N) diagrams
(see Fig. IO).
po=tanolo The value of the adhesion
force is calculated
as the difference
(5)
A=F-Fo The mean be determined
The
coefficient
by dividing
ratio
of forces
of friction
A/N
stresses, and then it is possible
p=po+2tT.2E Cmean
Wear.
IO (1967)
z74-zgo
p at the front
both parts of eqn.(g)
in eqn.
surface
by the normal
(6) is expediently
of the cutting
tool may
force N.
replaced
by
the ratio
of
to record (7)
PROCESS OF FRICTION IN CUTTING OF METALS
283
where: qmean= A/bL is the mean stress creating the force of adhesion (or specific force of adhesion) and amean= N/bL is the mean normal contact stress. Designating qmean/umean=,u~, we obtain: /J’IuO-?-PA,
(8)
is the adhesion component of the friction coefficient. Equation (8) shows that the friction coefficient during the cutting process consists of two quantities: a constant (,uo), which we will call conditionally the mechanical quantity, and a variable, the adhesion quantity (PA), which is the function of two variables (qmean and omesn). According to these formulae and the experimental data, we obtained the values of friction force Fo, the coefficients of friction p, ~0 and ,UA,the force of adhesion, the stress created by the force of adhesion and other parameters. Since ,UOis a constant value of the abrading pair, the dependence of the mean friction coefficient ,u on the adhesion component PA, in conformity with eqn. (8), is expressed by a straight line with the initial ordinate ,UO(Fig. II).
where
0
PA
0.04
0.08
0.12
al6
0.2
0.24 pA
Fig. I I. Dependence of the mean friction coefficient on the adhesion component. (a) Steel 40X, v = 0.017 m/set, 0: y = -0.175 rad, + :y = o, A :y = 0.26 rad, steel IXISHgT, v = o.o~qm/sec, q:y = o,O:r = 0.26rad:lead,v = 0.008-o.2m/sec, 0:~ = o, +:y = 6.26 rad. (b) AlloyBTq,v = o.o17m/sec, o:y = -0.175rad; +:y = o.
The full force of adhesion A (Fig. 12) with extension of the length of contact from very small values (small thickness of cut and a great front angle) grows from Amin to A,,, and further remains constant. Inasmuch as the rate of growth of the force of adhesion is much smaller than the rate of growth of the length of contact L, specific force of adhesion q mean, on the other hand, diminishes from qmeanmax to qmean mia, asymptomatically approaching zero at L-xo. The analysis of the curves of distribution of adhesion stresses along the length of contact of the chip with the front surface of the tool q (1) shows that, for example, in the case of dry cutting of lead (Fig. 13), the adhesion stresses, and consequently the adhesion component of friction is observed, not on the whole investigated length of Wear, IO (1967) z74-2go
M. B. GORI)OS
284
contact, but only on the section of length from 0.5 to 0.7 mm from the cutting edge. In principle it is possible to draw the same conclusion on the basis of an analysis of F(N) graphs in Fig. IO (and others not presented here), where the increase of the force of adhesion on the curvilinear section gradually diminishes to zero. It is obvious that precisely at point k, where it is equal to zero, the rectilinear section (kc), which
L,fmm)
L,(mm)
Fig. I 2. Dependence of full force A and (a) Steel 40X, v = 0.017 mjsec 0:y -= -o.175 rad +:y=o A(L) A: y = 0.26 rad 1 (b) Steel I Xr8HgT, v = 0.014 mjsec .+ : y = 0 ) A(L) A : y = 0.26 rad (c) Lead, v = o.o08-0.2 mjscc + :y = 0 .4(L) n : y = 0.26 rad 1 (d) Alloy RT4, v = o.oq mjsec 0: y == --o.r7j rad A (Lf +:y=o I
specific force ~,MW of adhesion on the length of contact. and
uz y = -0.175 r&d qmeaa(L) 0: y = o i 0: y = 0.26 rad
and
clm=&)
and
@=a&)
and
qmesaW (i:
1%:;
f
z t,26
o:y=o O: y = o.26 rad
--ax?5 wd c z o
Fig. 13. Distribution of specific forces of adhesion and the friction of the cutting toot when cutting lead. v = o.o08-0.2 mlsec, o : y Fig. 14. Scheme of contact W&W, IO (1967) 274-290
rad
coefficient
on the front surface
= o, 0: y = o and 0.26 rad.
sections on the front surface of the cuttingtool.
PROCESS OF FRICTION IN CUTTING OF METALS
285
characterizes the homogeneous transient* behaviour of friction without noticeable adhesion, begins. The data obtained thus permits the whole area of contact to be divided in the direction of movement of the chip into three sections (Fig. 14): first, the section of “juvenile” (adhesion) friction; second, the mixed section (“juvenile” plus transient friction) ; and the third section, homogeneous transient friction. The analysis of the accumulated experimental material shows that in the investigated cutting conditions, when practically no excrescence is formed, the adherence of the chip to the front surface of the cutting tool in consequence of the action of molecular forces of attraction (adhesion) has a local character (takes place in separate centres) and the contact area consists of two or only one zone of friction (the second and third or the second). In the first case, the behaviour of friction on the section of contact close to the cutting edge is heterogeneous (mixed) and on the remaining part, homogeneous (transient) ; in the second case, it is mixed on the whole length of contact. According to AKHMATOV’S classification 1, both these behaviours of friction may be attributed to the friction of oxidized physico-chemically clean surfaces. It may be assumed that the existence of sections with different behaviours of friction is conditioned, in the first place, by the fact that on the front surface of the tool there is contact with elements of the chip with different physico-chemical consistency, from newly formed to the last on the complete path of friction with length L, and hence differently oxidized by the atmospheric air**; and in the second place, it is conditioned by uneven distribution of normal stresses. For this reason, a physical parameter such as the coefficient of friction acquires a variable value along the length of contact as shown in diagram p(Z)*** (Fig. 13) and becomes dependent on the thickness of cut, the front angle and other factors which, without changing the physico-chemical nature and character of the contact, only increase or decrease the length of the contact. In this case, the adhesion component of the coefficient of friction changes correspondingly, and the mean coefficient changes in the same degree. This explains, what is usually observable, especially with small thicknesses of cut and large front angles, the high values (greater than I) of the mean coefficient of friction and the greater value of the coefficient of friction on the back surface of the tool than on the front. It is necessary to stress that precisely these circumstances (dependence of ,u on a and y, and value ,u 21) served as the basic reason for the departure of many specialists from the classical conception of the process and laws of friction during the cutting of metals. This idea is most clearly formulated by FINNIE AND %-IAWa4.
Thus, in dry cutting the basic parameters of friction, i.e. the force of friction, the coefficient of friction and the contact stresses, consist of two components, mechanical, which is constant, and adhesion, which is variable. For one and the same * Transient friction is a behaviour of friction in which the abrading surfaces are covered with thin films, the properties of which are within the range of influence of the solid bodies. ** The influence of atmospheric air on friction, adhesion, the projection of cutting force and other parameters of the cutting process is proved by direct experiments carried out in a vacuuma1pa2. *** The method of obtaining the computed dependence ~(2) is presented below; the experimental dependence has already been describedas. Wear,
IO
(1967) 274-290
286
31. 13. GORDOS
abrading factors
pair,
the latter
(length
components
depends
of contact).
of friction
on the thickness
The correlation
changes
within
of cut, the front
between
angle
the mechanical
very wide limits,
depending
and other
and the adhesion upon the conditions
of work.
At increased
“after excrescence”
speeds
Changing
the
and length
of contact,
the contact
surfaces,
influencing
cutting
speed,
their
mechanical
to one result, of cutting
friction
to homogeneous,
because
vanishing
there
speed,
and other
II 2 I m/set).
oxidation,
(2) Diminution ,!,&Ais constant
diminution
of both
important
On the whole,
essentially
coefficient
time state
of
characteristics
from
when
coefficient
,uo when
IXI8HgT).
(3)
steel
(~0 and ,&I) when
fact
(A, N) approaches
the
cutting
steel
by
of
the
cutting
(cutting
the
behaviour
conditioned
component
is established
variants
(I) With
heterogeneous
apparently
the adhesion
different
of friction.
of the friction
components may
three
behaviour,
(such a phenomenon
coefficient
disclosed
of the mean
transient
component 21to I m/set.
were
there is a transformation
of intensive
point
friction
the temperature,
upon the physico-chemical
firmness
i.e. diminution
increase that,
as it changes
way
friction.
In our experiments, leading
inasmuch
acts in a complicated
40X
at speed
the value
of adhesion
Simultaneous
negligible
alloy
BT4
at an increase
of
a slight
(within
the limits
of IO-ZO~/~) diminution
of the
be observed
within
the range
of alteration
speed
of cutting
we investigated. These of friction mation
data,
with
from
hand,
theory,
they
agree
according
when very
changes
steel 40X
(transfor-
and the purely
cutting
well
to which
qualitative
with
law of friction),
in speed on friction
on the other
of DERYAGUIN’S
temperature
the above-mentioned
speed in experiments
to the one-term
of the increase
and lead;
corollary
in cutting
the binomial
ive influence BT4
on the one hand, explain
an increase
quantitat-
steel IXI~H~T,
with
the highly
~0 depends
very
alloy
important
little
upon the
of the contact*.
INFLUENCE
OF THE EXTERNAL
MEDIUM ON THE BEHAVIOUR
AND LAW OF FRICTION
Cutting at low speeds From concrete
the point
conditions
ineffective
of view
or even harmful
media
To the first group and to the second fluence tive
which
the adhesion in dry cutting,
those which partially
on the behaviour carbon
qualitative
component friction
and (2) effective
which
arise during
of friction
changes
and the mean parameters is described
by the binomial
upon
into two groups,
adhesion
eliminate
are essentially when
in the behaviour it only
in dependence
(I)
media.
do not eliminate
tetrachloride
dry cutting:
developed
conditionally
or completely
* In experiments with steels, the highest cutting alloy BTq, up to 1300°C. Wear, IO (1967) 274-290
being
may be divided
belong
(for example,
does not introduce as those
those
of these media
medium
of the conception
of use, all media
cutting
it, in-
different.
An ineffeca steel tool)
and its laws, such
in one degree
of friction.
The
lead with
of friction
increases,
or increase
adhesion.
of another,
In these conditions,
as
law.
temperature
reached up to 600-7ooT;
with
PROCESS OF FRICTION IN CUTTING OF METALS
287
Thus, the result is that the nature of adhesion (molecular attraction of clean metals or films has practically no influence on the law of friction. When cutting lead in a medium of CCL, PbCla films are found on the chip2iJ5. An effective lubricating and cooling medium prevents adhesion (No=0 and A = o) ; e.g. the same carbon tetrachloride with respect to steel IXI~H~T, converts a heterogeneous behaviour of friction into a transient (homogeneous) behaviour. This, according to eqns. (2) and (3), eliminates the main cause of the dependence of the mean coefficient of friction on the front angle and the thickness of cut, the inequality of the friction coefficients on the front and back surfaces of the tool, and the high values ,u ( >I). The coefficient of friction is lowered, as a rule, and acquires an approximately constant value (~0) on all the contact surfaces. Friction with such a behaviour (sometimes with a negligible deflection) is described satisfactorily by the one term law (Fig. IS). (b)
F,(N)
0” N,fNf
N,(N)
i 40
80 12o 200 N,@J1
/
Fig. 15. Dependence of friction force on normal force when cutting in various media: (a) Steel 40x, v = 0.017 m/set, 1.5% emulsion; (b) steel IXISHQT, II = o.or4 m/set, (I) 1.5% emulsion, (&CC%;
(c) lead, v = 0.008 m/set, 1.5% emulsion;
o: y = -0.175
rad, +: y = o; A: 7 = 0.26
CMting at imcreasing speeds In principle, the law established with respect to low speed cutting also applies to high speed cutting. With the increase of cutting speed, the lubricating effect diminishes, disappears, or sometimes, on the contrary, increases. It is known that with the increase of cutting speed, the time of contact decreases, and consequently, the time of the medium’s action. However, as a result of the augmentation of the contact temperature, there is, simultaneously, a rapid increase of the chemical reaction. When there is constant shrinkage of the chip, the area of the chip increases in direct proportion to the speed, and the contact area also increases along the back surface of the tool, which interacts with the medium in a unit of time. The result of these competing changes may be either a weakening, or a strengthening of the lubricating effect. In our experiments with increase in cutting speed, we observed, as a rule, a weakening of the lubricating action of the emulsion, which is expressed in the increase of the adhesion component of friction. When cutting lead in a chemically active medium /fCCQ, an increase of cutting speed from 0.008 to 0.2 mjsec, i.e. 24 times, augments the adhesion component of friction approximately 1.4 times (Fig. 16). The latter may be considered a result of the appearance of the first (adhesion) section Wear, x0 (1967) 274-290
288
RI. B. GORRON
of contact (about 0.05 mm in length) and the augmentation of the length of the mixed (second) contact section (see Fig. 14), which in turn is obviously conditioned by
the
increase
of
the
number
of
contact
centres
of
adhesion
and
the
true
area
of
contact.
I
f
0
40 Normal
Dependence v = 0.008 mjsec, + Fig.
16.
LUBRICATING
I
80 force,
120
d 2 ‘00
160
N,(N)
of friction
force on normal
force when
cutting lead in a medium of CC&. (a)
: y = o; (b) u = o.z m/set, A : y = 0.26 rad.
ACTION
OF TI-IE EXTERNAL
MEDIUM
ON DIFFERENT
SECTIONS
OF CONTACT
The treatment of the experimental data shows that one and the same medium reacts selectively upon different contact sections. What is common to all the investigated media is that their conditional lubricating action, i.e. the increase or decrease of friction force on the relative length of contact x, is manifested more extensively on the sections of contact where the value of the adhesion component of friction is greater (near the cutting edge). Relative contact length x is defined as the ratio x=hlL, where 1, is the distance from the cutting edge to the point under consideration. When I, =o, x=o is the point on the cutting edge; when I,= L, Wear, IO (1967) 274-290
PROCESS OF FRICTION IN CUTTING OF METALS
289
x = I is the terminal point of contact. The influence of the medium on the mechanical component of friction in sections remote from the cutting edge may be more or less strong, depending upon the properties of the medium and the material being processed, but it is always lower than the influence on the adhesion component. This situation is illustrated by graph c (x) which represents the lubricating action of the medium on a relative contact length (Fig. 17).
V.5’ 0
0.2
0.4
Y
0.6
0.8
I 1.0
I.
Fig. I 7. Distribution of the coefficient characterizing the lubricating action of the emulsion on a relative length of contact when cutting steel 40X. Y = 0.017 m,/sec; (a) y = --0.175 rad, @: Q = 0.121 mm, 0: ca= 0.07 mm; + : tl = 0.045 mm; (b) y = o,@ : a = 0.104 mm, 0: @= 0.065 mm;(c)y=o.26rad,Q:a=o.r3mm, o:a=o.o78mm.
It is to be noted that, inasmuch as C= AF with lubrication/AF without lubrication, the more the lubricant lowers the force of friction AF on the elementary contact section AX, the smaller coefficient C and the higher the lubricating action of the medium. As the c(x) curve steadily increases, the lubricating action of the medium steadily diminishes according to the measure of removal from the cutting edge. A combined consideration of these data with the distribution curves of normal stress along the contact length in different conditions of cutting shows that the influence of the medium on the force (and coefficient) of friction does not depend, in practice, on the character of the distribution of normal stresses on the contact surface. It is obvious that in the conditions of heterogeneous behaviour of friction complicated by adhesion, a varying degree of activity of the contact sections is a stronger factor than a varying value of normal pressure. This situation conforms with the results of an investigation26, where it is established that iodic liquids react weakly with titanium, stainless steel, lead, nickel and cobalt, the surfaces of which are usually covered with a thin film of oxides. However, liquids of just this class, on coming in contact with clean surfaces formed during cutting and friction, create on them a layer of crystalline structure (film), which acquires anti-friction properties. Wear, IO (1967) 274-290
M. H. GORDOX
290 ACKNOWLEDGEMENTS The author wishes to express for
his
valuable
consideration present
advice
during
of the results,
his profound the
long
gratitude
period
and to B. V. DERYAGUIN
of
to Professor
experimental for his scientific
M. I. KLUSHIN work
and
editing
the
of the
work.
REFERENCES A. S. AKHMATOV, The Moleczllar Physics of Transient Friction, F&math, Moscow, 1963. A. M. ROSENBERG, The Dynamics of Milling, Sovietskaya Nauka, Moscow, 1945. N. N. ZORYEV, The Normal Forces and the Forces of Friction in Oblique Angle Free Cutting, Mashgiz, Moscow, 1948, p. 5. (Vol. 15. Central Scientific Institute.) M. B. GORDON, A device for determining the friction forces appearing during the cutting of metals, Bull. of Inventions No. I, 1951, p. 49. (Author’s Certificate No. 88039.) M. B. GORDON, The distribution of the friction forces on the front edge of the cutting tool in the zone of contact with the chip, Vestn. Mashinostr., 33 (5) (1953) 53. W. KATTWINKEL, Untersuchungen an Schneiden spanender Werkzeuge mit Hilfe der Spannungsoptik, Ind.-Anzeiger, 36 (73) (1957) 29. 7 G. S. ANDREYEV, An investigation of stresses in the working part of the cutting tool on a polarized optical installation with the implementation of a motion picture camera, Vest%.
Mashinostr., 38 (5) (1958) 54. method, IZV. 8 M. F. POLETIKA. Investigation of the cutting Process bv the optical-polarization - _ _ _ _ Tomsk. Politekn..Inst., 112 (1964) 157. 9 D. T. VASILIEV, The forces on the cutting surfaces of the tool, Stanki i Instr., zg (4) (1954) I.
D. T. VASILIEV, The physical conditions of the zone of deformation and the contact surface of the cutting tool as a factor in increasing the efficiency of the cutting tool, Material; Seminara No. 3, Moscow House of Scientific and Technical Propaganda, Moscow, 1963. 10 L. F. KAMSKOV, Simultaneous use of the force of friction and the force of normal pressure on the front edge of the cutting tool, Vestn. Mashinostr., 38 (6) (1958) 52. II A. N. REZNIKOV, The Temperature and Cooling of Cutting Tools, Kuibishevskoye Knignoe Isdat., Kuibishev, 1959. I2 V. F. BOBROV, On the distribution of specific normal forces and friction forces on the front surface of the tool, in The Machining of Metals by Cutting and Pressure, Mashinostroyenia,
Moscow, 1965, p. 57. ‘3 I. M. PAVLOV AND Du DEH YUAN, A compound measuring device for the contact forces of friction, Sci. Refits. of Higher Schools Metallurgy No. 2, 1958, p. 147. I4 A. A. PRESNYAKOV AND A. A. VIKNITZSKI, A device with a split puncheon for determining the coefficient of external friction with sedimentation, Zavodsk. Lab., 25 (4) (1959) 487. I5 M. B. GORDON, A device for measuring friction forces in metal cutting, Stanki i Instr., 36 (7) (1965) 24. 16
I7 18 I9 20 21
22
23
M. B. GORDON, The method and results of an investigation of the law of distribution of friction forces and tangential stresses on the length of contact of the chip with the front surface of the cutting tool, in M. I. KLUSHIN (ed.), Q uestions Concerning the Use of Lubricating and Cooling Liquids in Metal Cutting, Upper Volga Publ. House, Ivanovo, 1965, p. 64. B. V. DERYAGUIN, 2. Physik, 88 (1934) 661. B. V. DERYAGUIN, Wear, I (1958) 277. B. V. DERYAGIJIN,J. Phys. Chem., 5 (9) (1934) 1165. R. V. DERYAGUIN, What is Friction?, Acad. Sci. U.S.S.R., Moscow, 1963. N. G. ABULADZE, The influence of the medium on adhesion in metal cutting, Tr. Gruzinsk. Politekhn. Inst., 8 (60) (1~58) No. 3. G. W. ROWE AND E. E. SMART, The importance of oxygen in dry machining of metal on a lathe, Brit. J. A#. Phys., 14 (12) (1~63) 924. M. B. GORDON, Parameters of the process of friction in metal cutting, Stanki i Instr., 37 (6) (1966) 31.
24 I. FINNIE AND M. C. SHAW, The friction process in metal cutting, Trans. ASME 78 (3) (1956) 1649. 25 M. MERCIIANT, The influence of lubricating and cooling liquids on the wear of the cutting instrument, in A. I. PETRUSYEVICH (ed.), Intern. Conf. Lzlbrication and Wear of Machines, Moscow, 1962, p. 4~9. 26 Iodine lubricants smooth the way for broader use of titanium,
Wear, IO (1967) 274-290
Iron Age, rg6 (22) (1965) 68-6~.