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On the mechanism of wear between metal surfaces
\OJ.. 1 (19~7~s~)
WEAR
ON THE MECHANISM 01; WEAK BETWEEN
METAL SURFACES
‘l‘he analysis of the mechamsm of \~ear between metal surfaces IS tlcpentlcnt on tile distribution of the real area of contact, LP. the mechanism of contact. Assummg a simple model which represents the profile curve of the metal surfacr, the number and six of the individual areas of contact can be dedncctl theoretically. Considering three types of wear [or steel or cast iron (mechanical wear, Fc,O, film wear. and l’e,O, film wear), the theoretical wear rate concerning each type of wear can also bc clfduced. In general, one of the three types of wear does not occur indiv~duall?;, but two or three types occur together. Moreover, the comhnatwn of three types of wear ma\i-bedepcndentc)n the velocit>r of sliding anti the load between the surfaces. From this relationship between the mechanism of wear and the velocity or the loat1, the colllT~licat~~~variation of the actual wear rate with vclocit~ or IO& is discusseti theo~eticdlly.
iihf,v dm I’cvschlrzssmrchu~ris~~zf~,s m~.scl~eu ~~l~,talobcvfliichcII : Ausgangspunkt bei der Analyse des Vcrschleissmechatlismus zwischen Metaloberfltichen ist die Verteilung der wirklichen Heriihrungsfll.chen, d.h. der ~eriihrun~smechanismus. l;nter tier Annahme eines einfachen Models, tlas die I’rofllkurx~e der Metaloherfl&chc tlarstellt, lassen sich Zahl untl Criisse tier einzelnen Beriihrungspunkte theoretisch ablciten. Fdr Stahl und Eisen werden tlrei I’erschleisstypen (Mechanischer \‘rrschleiss, F‘c,O,-l;ilmverschleiss, ~e,O,-Filmverschleiss) in Hetracht gezogen, urn die theoretischen \Verte des ~erschleiss\,erh%Itnisses hei jedem dieser Vcrschleisstypen berechnen ZLI kbnnen. Im aligemeincn tritt nicht nttr ciner der drei \‘erschleisst?;pen a&in auf, vielmehr verlaufen zwei oder tlrei Typcn neben einandcr, Ferner h%ngttleri~ntrilclerdrci ~erschleisstypenwahrscl~einlich van tier relativen Gleitgcsch~vin(iigk~it ~tntlder Belastungz~~ischcncten Beriihrltngsoberfi~hen ab. Auf Grund dieser Beziehnngen zwischen Verschlpissntechanismus und Gleitgeschwindigkeit oder Belastung we&en the l~(~mpli~ierten ~er~n~it~r~iilgentier wirklichcn \-;errchIeissverhBltnisses mit der f;leitgescll~indigkeit o&r TSrlastung throretisch erijrtrrt.
1. IN’~KOl)LlC?‘I~)N
Jt is generally
acceptctl
that
two nominally
flat metal surfaces
pressed
together
under an applied load are held apart by small asperities and that the real area of contact is composed of these several individual bution
of the individual
formation
areas. A study of the number,
areas, generally
called “junctions”,
as to the nature of the sliding process, in particular,
ed with metal transfer
and wear.
provides
size, and distriimportant
in-
about problems connect-
Assuming
a simple model which represents
the profile curve of metal surface,
relationships between the applied load and the number have been deduced. Making further simple assumptions
the
or size of the individual areas as to the nature of the sliding
process, simple laws for three types of wear have also been deduced: mechanical wear, Fe,O, film wear, and Fe,O, On the basis of these theoretical deductions wear are discussed.
film wear. the influence
of velocity
and load on
II. MECHANISM OF CONTACT z.
~~~~~s~~c~~~~~~~s~s of surface ~~~*~~~~~~~~~~s
When the distribution curve that is obtained in Fig. I has LInormal distribution, we have
where
from the profile curve of the surface
f(a) =
probability density, IL = deviation from the median o = standard deviation.
Profile
Abbott’s
cut-w Fig.
Then the number
I.
line of the profile curve,
bearing
CUPW
Method of drawing distribution
” Distribution curve
Distribution hiotogmm
curve from profile curve.
of surface units1 between M = ;I and u - p + df4 (Fig. z) is given by ~~~~~~~~~,
where N = total number
of surface units contained
within measured
length L. Hence
c,. YOSHIMOTO,
474
T, TSUKIZOE
VOL. 1 (1957~5~)
the number of intersections of the profile curve on the parallel line 24 = !6 will be ~‘&L+n, where F(T= projection of one surface unit. When many asperities on the profile curve have an equal base angle 0, we obtain .I’FO-= 1,tant?. And so the number of asperities crossed by the parallel line IP = ~6is
When a parallel line is brought close to the profile curve, consider the beginning of contact where $5.= Eu (corresponding to the z coordinate z = o in Fig. 3), Then consider Jf asperities into contact resulting from the movement of the parallel line through unit distance. In other words, :If is the number of asperities per unit depth, and from the above analysis Jl is given by
where 1 is dependent on N, and on L. Hence
(1)
where H is the maximum height of asperities given by 1-f = icr (i is dependent on the measured length L used for measuring N).
(a) C&act hetzueen th.e metal surface and the ideal flat swface. We assume that the metal surface has the same profile curve in any direction, the number of asperities per unit depth ~11is given by
where L,L, = area of the metal surface (apparent contact area between two surfaces), Nlr = total number of surface units contained within measured length L,, NY = total number within L,. KefPrenc&T p.
490
VOL. 1 (1957/58)
=
MECHANISM0F WEAR BETWEEN METAL SURFACES
+y-~‘) {exp(;-&j-I)
+ 1) x 5gtan2e.
(exp(+&j
(b) Contact between two metal surfaces. In this
475
H = dH,2
case substituting
(2)
+ H,Z
in eqn. (z)“, we obtain
tan2e,
where H,, H, = maximum heights When H, is equal to H,,
of asperities
(3)
of two surfaces.
izI = _____ p exp (-- I”) 167s
(4)
We can deduce j = 5.0 when the maximum the following values of measured length L: L = 0.3 mm for
using
H < 0.8 ,u ,
L=
rmm for 0.8
H is measured
height of asperities
6.251 -1 HI2j
tip, 25 ,u (ref.2).
area L,L,
I
X exp rI.6+6.251 1 I (
is in the order of
X LXL,
HI21
+ I __ tana& 1 HI2
(5)
Fig. 3. (‘ontact model between the profde curve and the ideal flat surface (c = 0). 2. The rtumber and size of the ilzdiuidztal ayeas of co&act
The model which represents the profile curve of metal surface is shown in Fig. 3. In this modelit is assumed that the surface contains a large number of conical asperities References p. 490
of equal base angle 8, and that the asperities are evenly distributed in depth (the z direction) ; i.e., there is one asperity at each of the z coordinates z = o, I?, zh, :jh, . . . , etc. Thus, there are M asperities per unit depth, where
When an ideal flat surface is pressed against the model surface under a load II’, consider the movement of the ideal surface through a distance z = &z (n asperities into contact) (Fig. 4). Since we may assume plastic deformation of the metal occurring at the contact3, the flow pressure fi, should be constant under any load. In this case
Hence the theoretical number of the individual areas ?zis given by
Size of the individ~lal areas can be written as
Substituting eqn. (a) in eqns. (h) and (7), we can estimate the theoretical number and size of the individual areas of contact between the metal surface and the ideal flat surface. Also, the total contact area A is given by
VOL.
1 ~195~~5~)
M~CKA~ISM
OF WEAR
BETWEEN
METAL
SURFACES
477
The distance through which the ideal flat surface moves into the model surface under the applied load 11’ is given by (9)
Fig. 5. Contact model between two profile cnrves (z = ~~12).
In the case of contact written as
between
two metal
surfaces
(Fig. 5), 72, SVZ~~,and nh can be
where M is given by eqn. (3) or (4).
3.
The electrical cimtact resistame
In Fig. 5 the electrical contact resistance X resulting surface through a distance z = ?zJacan be written as
from the movement
where 2 = specific conductivity of two metals (assumed equal), Q = resistance per unit area due to the metal surface films (assumed constant thickness on each surface). Hence in eqn. (13)
is the spreading
resistance
is the film resistance*~5. References p. 490
and
of the
to be
478
G. ~~~SHIMOTO, T. TSUKIZOE
Then
where
For large value2 of n
Hence
~on~bining this equation with eqn. (IO) we obtain
Then, if the contact resistance is mainly metallic, the resistance being the spreading resistance,
Also, if the contact resistance is mainly due to the surface films, the spreading resistance being negligible, I - -I tip. hf _
PiI’.
(IfA
The theoretical resistance can be estimated with eqns. (x4), (rg) or (16). 4. Discussion Assuming a simple model which represents the profile curve of the metal surface, the number and size of the individual areas of contact can be deduced theoretically. These theoretical deductions are discussed in the light of experimental evidence; for example, the deduced relationships between the applied load and the electrical contact resistance or the distance through which the one surface cuts into the other surface
VOL. 1 (1957158) are
compared
experiment
MECHANIST
OF WEAR BETWEEN
with the results of experiments. and theory
METAL SURFACES
It is seen that the agreement
479
between
is quite good2r6.
III. MECHANISM OF WEAR I. Three types of wear In this section we shall consider the wear produced by the continual formation and shearing of metallic junctions between sliding surfaces. When metallic junctions are formed between similar metal surfaces the shearing may occur in two different ways. If the junctions are formed in the absence ot the oxide film, metal-to-metal contact, shearing will rarely occur at the interface itself but will take place within the bulk of the metal, because the process of deformation and welding produced by the intense pressurein the region of contact will work-harden the junctions and appreciably increase their shearing strength, In this case there will be considerable removal of metal and metallic wear particles. If the junctions are formed in the presence of the oxide film which is not broken up by the deformation of the underlying metal, shearing willoccur at theinterface between the oxide film and the bulk of the metal. Under these conditions the amount of oxide removed will be very small in comparison with the metallic wear particles, and for steel or cast iron the oxide wear particles produced are largely of the composition Fe,O, When the sliding velocity and the load are raised, we may expect that a local melting of the metal at the points of contact will be caused and that the composition of the oxide will be Fe,O,.
Consequently,
for steel or cast iron three types of wear may be considered: mechanical wear (metallic wear particles), Fe,O, film wear (Fe,O, wear particles), Fe,O, film wear (Fe,O, wear particles). It is the principal aim of this report to deduce theoretically the wear rate relative
to each type of wear.
2. Tkory
of mechanical
wear
Making simple assumptions as to the nature of the sliding process, simple laws of mechanical wear have been deduced. The assumptions that are made in deducing the theory are as follows: (a) Size alzd distributiort of the total area of contact. As shown in Section II. 2, the number n and the size naYa of the individual areas of contact are given by eqns. (IO) and (II). (b) Process ef ~0~~~~~~~~o~~~t~o~ alzd shearing of metallic ~~nct~o~s. We employ the simplifying assumptions, which are essentially those previously used by RABINOWHX? The location of the two areas forming a fully established circular contact of radius ay
$30
(;. YOSHIMOTCJ,
‘I‘. TSlKIZOE
VOL.
(Iq_j7/5X)
1
at zero time is shown in Fig. 6 at (a), while the position a short time later, after a sliding distance x, is shown at (b). After sliding a distance eration
has been reduced
24,
the contact areaunder
to zero (Fig. 6 (c)) ; in addition,
moment a new similar contact area of radius a, has just been fully established in the surface, since the total area of contact is directly proportional (c) The shape of the wear fiurticles. junctions
is of the type indicated
be made regarding
the volume
where vj is a constant.
consid-
it is assumed that at this elsewhere
to the applied load.
Assuming that the process of shearing of metallic
in Fig. 6, there are two simple assumptions
that can
,!l B of a given wear particle.
This implies that the depth of the material
This type of wear is shown, for example,
removed is constant.
when oxide film wear occurs.
1H -~ y’u,“,
where y is a constant. proportional
This implies that the depth to which the material
to the radius of the contact
particles is independent radius as the contact
(18)
area, i.e., statistically
of their size. Assuming hemispherical areas, the constant
is torn is
the shape of the wear
wear particles of the same
y is given by
y, = t,.
(191
3
Assuming conical wear particles with the base of the same radius as the contact
areas
and with the base angle 0, y is given by y
For the mechanical the conical particles. l~rfeIWLc_rs p. jyo
+tanu.
wear the most probable
(20)
shape of the wear particles
is that of
This is suggested by the profile curve of the metal surfaces where
VOL. 1 (1957~5~)
MECHANIST
the wear
process
following
expression
remains
OF WEAR BETWEEN
of the steady-state
for the volume
11B
METAL SURFACES
type.
Consequently,
48I this case
gives the
: (21)
From
assumptions
per unit sliding
(a), (b) and (c), the wear rate Qi, i.e. the total
distance
for the whole n-
8%=
I
eqns.
(IO),
(II)
can be written
-- f tane 6 LBr
c
and (22) it follows
g,
mechanical
wear
as
n--r
.I5
1= 0 From
surface,
2
?l&2.
I=0
that
_;E+.
(23)
m
This is similar ARCHARD’S The
main
(a} The
to the equation
concept
conclusions
wear
wear
that are derived
rate is proportional
particles from
wear
rate is independent
of the apparent
wear
rate is independent
of the velocity
Theory of Fe&
asperity volume is given
area of contact. of sliding.
model of the process of oxide film wear in sliding surfaces.
diagrammatically
of the upper
is considered
but on the surface
are:
film wear
7 illustrates
an asperity
by replacing
ones.
lc’.
(c) The
Fig.
essentially
by conical
the theory
to the load
{b) The
Fig. 7. Idealized 3.
of ARCHARD~ and is obtained
of hemispherical
surface
to expose
the process
moving
over
clean metal
of the clean metal
A B of a given wear particle,
of the oxide
the lower
surface
when the shearing
a thin layer of metal i.e. the amount
oxide
film wear
produced
on
at a velocity
1’. This
of the junction
occurs,
will form rapidly.
of oxide removed
The
from this asperity
by .fB
= ni@d
d
(24)
G. YOSHIMOTO,
482 where d = the thickness
T. TSUKIZOE
VOL. 1 (Igjp/jS)
of the oxide film formed in time t during which this asperity
moves a distance
s (Fig. 7).
Then
/ _= Q_. The empirical
relation
CL51
for the initial stage of oxidation
of a clean iron surface
is
given by9
‘t d =- ‘, log, - i 1 I cT i where 7 and t are constants.
(261
As the value of the constant
z for oxidation
of iron runs
from 2.6 to 10.4 secg, t/t is much smaller than unity in the case of the sliding process. The thickness
of the oxide film d, therefore,
is approximated
by
and
Substituting
eqn. (27) in eqn. (24) ‘I s; (Cl2 113-= x -TI
Assuming that the process of continual
formation
and shearing of metallic junctions
is similar to that for the mechanical
wear (Fig. O), the wear rate Qz, i.r. the total Fe&),
film wear per unit sliding distance
for the whole surface,
The average distance s between two neighbouring ?z individual
areas of contact
where L,yL, = the apparent IL, ! E di 1 ?
contact
it follows that
Refevences p. 490
asperities
as
on a plane upon which
(eqn. (IO)) exist is given by
contact
area between
= the number of the individual
and the summation
can be written
two surfaces,
areas along one edge L,r of the apparent
area, is carried out for the individual 16 -1
areas along L,r. From
eqn.
(II)
VOL. 1
(1957~58) ~~ECH~4NISM OF WEAR BETWEEN METAL SURFACES
483
Hence
When I., is equal to I,,, L n $=..-.-;--_ 2/n 2M tan0 Substituting
(29)
eqn. (zg) in eqn. (28) n-r
n
Qe =
2MtanB
1
2
n a7
=
y
(+a ‘L
711
--
n 2M
tan B
I==0
=
Combining
this equation
iz
---
rJ
8 t
1
n2
---
1--
1’
T
I
V
i
L EaX"
49f tan B
s -
1
2M2tan%
n3
1.
with eqn. (10) we obtain
This is similar to the equation of UHI,IG~ and is obtained essentially by replacing UHLIG’S contact model between the metal surface and the ideal flat surface by contact model between two metal surfaces. The main conclusions that are derived from the theory are: (a) The wear rate is approximately proportional to a square root of the load TV&, since the first term is generally larger than the second term in eqn. (30). (b) The wear rate is approximately proportional to the length of one edge of the apparent contact area. (c) The wear rate is inversely proportional to the velocity of sliding V. 4. Theory of Fe@,
film
mar
Similarly, the wear rate Qs, i.e. the total Fe,O, can be written as
where constant q’ is different from the constant constants are dependent on the temperature. 5.
film wear per unit sliding distance,
7 for the Fe,O, film wear, since these
Discussion
The experimental evidence for the theory will be considered. In Table I, the experimental values of the mechanical and the Fe,O, film wear given by some workers are compared with the theoretical expressions calculated from their data using eqns. (23) and (30). The following comments may be made : R&eferences
p. 490
4%
G. YOSHIMOTO,
EXPERIMENTAL
T. TSUKIZOE
VOL.
ANIl THEORliTIChL WEAR
1 (19j7ij8)
RITES
J.oall
I
L
0.690,)
I .6kg/cm”
Carbon steel 2 Cast iron
46.3 kg/cm2
3 Mild steel
rkg
0.1-j mjscc
Q = 0.00$ x 2 g/cm2~~oo m = o.131.10-Bcm3/cm
0.4
(1’~ 3.4 x rgjcmz~~Oom =.- 8r.3”0-~crdjCm Q :r: 15 pg/cm = f .g2‘10-6cm3jcm
mjsec
-. - .-.-.-.* The experimental
values
-.
Q,-
X..+w33.9~10-6cm3/cm
Q1 = 18.1 N72.j*10-6cm3/cm $& = 0.78w3.~q’0-~cm+Xl
._ ___-. _
fur No. 1, No. 2, and No. 4 were given
Iii.~ni~owcz AND TABOR~. ** The several values in eqns. (23) and (30) are as follows: L. = 1 cm, pnl = I..? B = riu8degree (H, = rw1op).
x
by OICOSHI~“, and for No. 3 by
101
kg/cm”,
rl ; _= 150 .A/sec.
{a) In the results for Ko. 2 and No. 3, there are fairly good agreements between the theoretical and the experimental values. (b) For No. I and No. 4, the experimental differ from the theoretical values. This difference may be largely due to the intermixture of two types of wear ; i.e. in the experiment for the mechanical wear (No. I) the Fe,O, film wear also occurs, and in the experiment for the Fe,O, film wear (No. 4) the mechanical wear is also produced. IV. INFLUENCE
OF VELOCITY
AND LOAD ON WEAR
In general, none of the three types of wear occurs indi~lidL~all~,but two or three types occur together. Moreover, the combination of three types of wear may be dependent on the velocity of sliding and the load between the surfaces. Weshalldeduce theoretically the relationships between the combination of three types of wear and the velocity or the load. Factors that will influence the combination of three types of wear are as follows: (a) Size of the junctions. The individual areas of contact are not of the same size, but have the size distribution. If there are n junctions for any thickness of the surface oxide film, then large junctions are formed, breaking through the film owing to the deformation of the underlying metal, and small ones are formed in the presence of the film. Consequently, in the former mechanical wear will be produced and in the latter Fe,& film wear or Fe,O, film wear. lirjevewvs
p. 490
VOL.
1 (1957/58)
MECHANISM
OF WEAR
BETWEEN
METAL SURFACES
(b) Thickness of the surface oxide film. The thicker numerous
are the junctions
that produce
Fe,O,
485
the oxide film becomes,
film wear or Fe,O,
the more
film wear.
(c) Local tewqberature rise at the points of contact. For the oxide film wear, the wear particles
produced
are generally
of the composition
the load are raised we may expect contact
2.
Fe,O,,
that a local melting
will be caused and the composition
but when the velocity
and
of the metal at the points of
of the oxide will be Fe,O,.
Size of the junctions As shown in Section
are given by eqns.
II. z and II. I, the number n and the size rcav2 of the junctions
(IO),
(II)
and (4). In eqn. (4) th e size of the unit depth for estimation
of :I1 must be similar to the amount moves into the another strictly speaking,
through
which the one surface
under the applied load W, the distance of invasion.
M is dependent
the size of the junctions eqn.
of the distance
Therefore,
on the load 1%‘.Hence the strict relationships
between
and the applied load can not be deduced merely by combining
with eqn. (4).
(II)
Assuming invasion,
that the size of the unit depth is equal to the amount
our mechanism
of contact
gives the following expression
of the distance
of
for the number and
the size of the junctionsll: (32)
.zar2 =
where TV =
Pm1’148*I’
6.45 . IO“’
I
N
20
Y = 0, I, 2,
(LxLy)o.sas tan6 8
.
, (1%-
I),
(33)
kg
p,
= about
1.5.10~ kg/cm2,
L,L,
= about
IO
mm
x
IO
mm,
H, in ,B, a, in ,u. The relationships stituting
the maximum (za,),
between
the size 7car2 and the load IV can be estimated
eqn. (32) in eqn. (33), but they are very complicated. radius of the junctions
can be written
Combining
by sub-
However, from eqn. (33)
(ar)max and the average diameter of the junctions
as
this equation
with eqn. (32) we obtain (34)
This means that the maximum proportional
radius or the average
to lV”. 142 and is independent
References p. 490
diameter
of the velocity.
of the junctions
is
@h
(i.
TOSHIMOTO,
T.
‘EI~KIZOE
3. Tkickness of tlze surface oxidefilm
As shown in Section
III. 3, the thickness
of the Fe,O, filtn is given by (35)
Substituting
eqns. (32) and (34) in this equation
we obtain
where W is in kg, El, in /J, p, in kg/cm 2, L,
Fig. 8. Idealized model for calculating the local te~l~rature
4.
Locdl tefnperatwe
riseat
the points
In Fig. 8 the force /l1; required
rise at a point of contact.
of contact
to shear a junction
is given by
,.11: = ,zcz”~S, where S z the shearing strength of the metal. The rate at which the shearing energy is expended
138)
will be
E T= 1F II-. If we assumed h’zfe~cmm p. 490
that all of the mechanical
energy associated
(39)
with the shearing
process
VOL.
1
(1957~5~)
MECHANISM
OF WEAR
BETWEEN
METAL
SURFACES
487
is converted into thermal energy, then the amount q of heat developed per unit time per unit area will be (!LL, .rnar2
where J = the mechanical equivalent of heat. Combining this equation with eqns. (38) and (39) 9=i’
s I/
(40)
As the base angle 8 of conical asperities is very small (I’ N 15”j2, this heat 9 can be regarded as a steady-state heat source on the surface of the semi-infinite body, and the mean temperature T in this heat source can be written asi2 ;4 ar
where K = the thermal conductivity, ‘4 = the area factor, To = the room temperature ; the shape of the junction is approxinlated to the square having one edge zaP For the square
A = 0.95.
Then T -
Substituting
T,
= 0.48 F.
eqn. (40) in this equation we obtain
This means that the local temperature rise at the points of contact is proportional to II and a,. As T is generally much larger than T,,, for the maximum point of contact we put a, = (ar)nzax (eqn. (34)) in eqn. (41) and find
where J is in kgm/kcal, K in kcal/m=h.“C, S in kg/mz, V in m/h, Tin “C, H, in ~4,L,L, in mm2, #, in kg/cm2, W in kg. It may be seen that after any raising of the velocity and the load the temperature rise associated with the shearing process comes to the melting-point at the maximum point of contact and production of Fe,O, film wear begins, Rejwmres
p.
490
G.
488
YOSIISMOTO, T. TSUKIZOE
dtB of the melting layer is given by
The thickness
n’,
2K’ . =L .7 --4 (
when we assume that the temperature constant
and the temperature
T”,.,‘.
)*
?‘ across the whole of the shearing
7‘m.p, (melting-point)
between the melting layer and bulk of the metal is constant steady temperature
is
also and that there is a
drop along the depth of the melting layer. Substituting
and (42) in this equation
interface
across the whole of the interface eqns. (40)
we obtain
(43)
when y V?F’0~1*2>Tm,p.. This means that the thickness
of the melting layer increases
with the velocity
and
the load. Equations junctions, of contact)
(34), (36), (37) and (42) can be used to estimate
thickness
three factors
of the surface oxide film, and local temperature
as a function
of the velocity
(size of the
rise at the points
and the load.
d' of oxidt
film th!cknesS
V Fig.
5.
9.
Ikpendcnce
of wear rate on v&city
Inflttence of velocity on the mechmaism
of wenr
Fig. c) shows the ways in which the mechanism Q = Q1 + Q2 -{- Q3 depend on the velocity, and the melting
layer thickness
(theory).
of wear and the total wear rate
The variation
with velocity
of the oxide film thickness
at a constant
load are estimated
eqns. (36), (37) and (43). The term “limit of oxide film thickness” the maximum
limit ; i.e. when the oxide film thickness
film is not broken up by the deformation point of contact
and all junctions
From eqn. (34) the m~imum
rises above that limit the oxide
of the underlying
metal even at the maximum
produce oxide film wear but no mechanical
radius of the junctions
with
is used to denote
increases
wear.
with the load and is
VOL. l(I957~5~)
independent
MEC~ANIS~OF
of the velocity.
dent of the velocity
WEAR
BETWEEN
Consequently,
METALSURFACES
489
the limit of oxide film thickness
is indepen-
(Fig. 9).
In Fig. 9 the ways in which the mechanism are as follows:
of wear changes and the wear rate varies
(I) V
Limit
Fig.IO.Dependenceof wear rate
of oxide
on load
film
thickness
(theory).
Similarly, the ways in which the mechanism of wear and the wear rate depend on the load are shown in Fig. IO. The variation of the oxide film thickness, the melting layer thickness, and the limit of oxide film thickness with load at a constant velocity are estimated with eqns. (36), (37), (43) and (34). 7. Discztssion The experimental evidence for the theory will be considered. Fig. II shows the variation of the wear rate with velocity or with load, which is summarized from many experimental results given by various workers (W. EILENDER AND W. OERTELIO, K. DIES~O,~.KEHLA~DE.SIEBEL lo,1%.OKOSHI~~A~D K. OGAWA~~). Theagreement References p. 490
490
between this summary of experiments and the theory shown in Figs. (1and IO is fairly gaod. We can conclude that by reason of the variation of the mechanism of wear with velocity or load the ways in which tile wear rate depends on the velocity or the load are very complicated (Figs. 9, IO and I I), and that for the same reason the variation of the wear rate with velocity is similar to that with load. In this paper the experimental background is incoml~lete and it is clear that further work is necessary.
WEAR
ON THE MECHANISM 01; WEAK BETWEEN
METAL SURFACES
‘l‘he analysis of the mechamsm of \~ear between metal surfaces IS tlcpentlcnt on tile distribution of the real area of contact, LP. the mechanism of contact. Assummg a simple model which represents the profile curve of the metal surfacr, the number and six of the individual areas of contact can be dedncctl theoretically. Considering three types of wear [or steel or cast iron (mechanical wear, Fc,O, film wear. and l’e,O, film wear), the theoretical wear rate concerning each type of wear can also bc clfduced. In general, one of the three types of wear does not occur indiv~duall?;, but two or three types occur together. Moreover, the comhnatwn of three types of wear ma\i-bedepcndentc)n the velocit>r of sliding anti the load between the surfaces. From this relationship between the mechanism of wear and the velocity or the loat1, the colllT~licat~~~variation of the actual wear rate with vclocit~ or IO& is discusseti theo~eticdlly.
iihf,v dm I’cvschlrzssmrchu~ris~~zf~,s m~.scl~eu ~~l~,talobcvfliichcII : Ausgangspunkt bei der Analyse des Vcrschleissmechatlismus zwischen Metaloberfltichen ist die Verteilung der wirklichen Heriihrungsfll.chen, d.h. der ~eriihrun~smechanismus. l;nter tier Annahme eines einfachen Models, tlas die I’rofllkurx~e der Metaloherfl&chc tlarstellt, lassen sich Zahl untl Criisse tier einzelnen Beriihrungspunkte theoretisch ablciten. Fdr Stahl und Eisen werden tlrei I’erschleisstypen (Mechanischer \‘rrschleiss, F‘c,O,-l;ilmverschleiss, ~e,O,-Filmverschleiss) in Hetracht gezogen, urn die theoretischen \Verte des ~erschleiss\,erh%Itnisses hei jedem dieser Vcrschleisstypen berechnen ZLI kbnnen. Im aligemeincn tritt nicht nttr ciner der drei \‘erschleisst?;pen a&in auf, vielmehr verlaufen zwei oder tlrei Typcn neben einandcr, Ferner h%ngttleri~ntrilclerdrci ~erschleisstypenwahrscl~einlich van tier relativen Gleitgcsch~vin(iigk~it ~tntlder Belastungz~~ischcncten Beriihrltngsoberfi~hen ab. Auf Grund dieser Beziehnngen zwischen Verschlpissntechanismus und Gleitgeschwindigkeit oder Belastung we&en the l~(~mpli~ierten ~er~n~it~r~iilgentier wirklichcn \-;errchIeissverhBltnisses mit der f;leitgescll~indigkeit o&r TSrlastung throretisch erijrtrrt.
1. IN’~KOl)LlC?‘I~)N
Jt is generally
acceptctl
that
two nominally
flat metal surfaces
pressed
together
under an applied load are held apart by small asperities and that the real area of contact is composed of these several individual bution
of the individual
formation
areas. A study of the number,
areas, generally
called “junctions”,
as to the nature of the sliding process, in particular,
ed with metal transfer
and wear.
provides
size, and distriimportant
in-
about problems connect-
Assuming
a simple model which represents
the profile curve of metal surface,
relationships between the applied load and the number have been deduced. Making further simple assumptions
the
or size of the individual areas as to the nature of the sliding
process, simple laws for three types of wear have also been deduced: mechanical wear, Fe,O, film wear, and Fe,O, On the basis of these theoretical deductions wear are discussed.
film wear. the influence
of velocity
and load on
II. MECHANISM OF CONTACT z.
~~~~~s~~c~~~~~~~s~s of surface ~~~*~~~~~~~~~~s
When the distribution curve that is obtained in Fig. I has LInormal distribution, we have
where
from the profile curve of the surface
f(a) =
probability density, IL = deviation from the median o = standard deviation.
Profile
Abbott’s
cut-w Fig.
Then the number
I.
line of the profile curve,
bearing
CUPW
Method of drawing distribution
” Distribution curve
Distribution hiotogmm
curve from profile curve.
of surface units1 between M = ;I and u - p + df4 (Fig. z) is given by ~~~~~~~~~,
where N = total number
of surface units contained
within measured
length L. Hence
c,. YOSHIMOTO,
474
T, TSUKIZOE
VOL. 1 (1957~5~)
the number of intersections of the profile curve on the parallel line 24 = !6 will be ~‘&L+n, where F(T= projection of one surface unit. When many asperities on the profile curve have an equal base angle 0, we obtain .I’FO-= 1,tant?. And so the number of asperities crossed by the parallel line IP = ~6is
When a parallel line is brought close to the profile curve, consider the beginning of contact where $5.= Eu (corresponding to the z coordinate z = o in Fig. 3), Then consider Jf asperities into contact resulting from the movement of the parallel line through unit distance. In other words, :If is the number of asperities per unit depth, and from the above analysis Jl is given by
where 1 is dependent on N, and on L. Hence
(1)
where H is the maximum height of asperities given by 1-f = icr (i is dependent on the measured length L used for measuring N).
(a) C&act hetzueen th.e metal surface and the ideal flat swface. We assume that the metal surface has the same profile curve in any direction, the number of asperities per unit depth ~11is given by
where L,L, = area of the metal surface (apparent contact area between two surfaces), Nlr = total number of surface units contained within measured length L,, NY = total number within L,. KefPrenc&T p.
490
VOL. 1 (1957/58)
=
MECHANISM0F WEAR BETWEEN METAL SURFACES
+y-~‘) {exp(;-&j-I)
+ 1) x 5gtan2e.
(exp(+&j
(b) Contact between two metal surfaces. In this
475
H = dH,2
case substituting
(2)
+ H,Z
in eqn. (z)“, we obtain
tan2e,
where H,, H, = maximum heights When H, is equal to H,,
of asperities
(3)
of two surfaces.
izI = _____ p exp (-- I”) 167s
(4)
We can deduce j = 5.0 when the maximum the following values of measured length L: L = 0.3 mm for
using
H < 0.8 ,u ,
L=
rmm for 0.8
H is measured
height of asperities
6.251 -1 HI2j
tip, 25 ,u (ref.2).
area L,L,
I
X exp rI.6+6.251 1 I (
is in the order of
X LXL,
HI21
+ I __ tana& 1 HI2
(5)
Fig. 3. (‘ontact model between the profde curve and the ideal flat surface (c = 0). 2. The rtumber and size of the ilzdiuidztal ayeas of co&act
The model which represents the profile curve of metal surface is shown in Fig. 3. In this modelit is assumed that the surface contains a large number of conical asperities References p. 490
of equal base angle 8, and that the asperities are evenly distributed in depth (the z direction) ; i.e., there is one asperity at each of the z coordinates z = o, I?, zh, :jh, . . . , etc. Thus, there are M asperities per unit depth, where
When an ideal flat surface is pressed against the model surface under a load II’, consider the movement of the ideal surface through a distance z = &z (n asperities into contact) (Fig. 4). Since we may assume plastic deformation of the metal occurring at the contact3, the flow pressure fi, should be constant under any load. In this case
Hence the theoretical number of the individual areas ?zis given by
Size of the individ~lal areas can be written as
Substituting eqn. (a) in eqns. (h) and (7), we can estimate the theoretical number and size of the individual areas of contact between the metal surface and the ideal flat surface. Also, the total contact area A is given by
VOL.
1 ~195~~5~)
M~CKA~ISM
OF WEAR
BETWEEN
METAL
SURFACES
477
The distance through which the ideal flat surface moves into the model surface under the applied load 11’ is given by (9)
Fig. 5. Contact model between two profile cnrves (z = ~~12).
In the case of contact written as
between
two metal
surfaces
(Fig. 5), 72, SVZ~~,and nh can be
where M is given by eqn. (3) or (4).
3.
The electrical cimtact resistame
In Fig. 5 the electrical contact resistance X resulting surface through a distance z = ?zJacan be written as
from the movement
where 2 = specific conductivity of two metals (assumed equal), Q = resistance per unit area due to the metal surface films (assumed constant thickness on each surface). Hence in eqn. (13)
is the spreading
resistance
is the film resistance*~5. References p. 490
and
of the
to be
478
G. ~~~SHIMOTO, T. TSUKIZOE
Then
where
For large value2 of n
Hence
~on~bining this equation with eqn. (IO) we obtain
Then, if the contact resistance is mainly metallic, the resistance being the spreading resistance,
Also, if the contact resistance is mainly due to the surface films, the spreading resistance being negligible, I - -I tip. hf _
PiI’.
(IfA
The theoretical resistance can be estimated with eqns. (x4), (rg) or (16). 4. Discussion Assuming a simple model which represents the profile curve of the metal surface, the number and size of the individual areas of contact can be deduced theoretically. These theoretical deductions are discussed in the light of experimental evidence; for example, the deduced relationships between the applied load and the electrical contact resistance or the distance through which the one surface cuts into the other surface
VOL. 1 (1957158) are
compared
experiment
MECHANIST
OF WEAR BETWEEN
with the results of experiments. and theory
METAL SURFACES
It is seen that the agreement
479
between
is quite good2r6.
III. MECHANISM OF WEAR I. Three types of wear In this section we shall consider the wear produced by the continual formation and shearing of metallic junctions between sliding surfaces. When metallic junctions are formed between similar metal surfaces the shearing may occur in two different ways. If the junctions are formed in the absence ot the oxide film, metal-to-metal contact, shearing will rarely occur at the interface itself but will take place within the bulk of the metal, because the process of deformation and welding produced by the intense pressurein the region of contact will work-harden the junctions and appreciably increase their shearing strength, In this case there will be considerable removal of metal and metallic wear particles. If the junctions are formed in the presence of the oxide film which is not broken up by the deformation of the underlying metal, shearing willoccur at theinterface between the oxide film and the bulk of the metal. Under these conditions the amount of oxide removed will be very small in comparison with the metallic wear particles, and for steel or cast iron the oxide wear particles produced are largely of the composition Fe,O, When the sliding velocity and the load are raised, we may expect that a local melting of the metal at the points of contact will be caused and that the composition of the oxide will be Fe,O,.
Consequently,
for steel or cast iron three types of wear may be considered: mechanical wear (metallic wear particles), Fe,O, film wear (Fe,O, wear particles), Fe,O, film wear (Fe,O, wear particles). It is the principal aim of this report to deduce theoretically the wear rate relative
to each type of wear.
2. Tkory
of mechanical
wear
Making simple assumptions as to the nature of the sliding process, simple laws of mechanical wear have been deduced. The assumptions that are made in deducing the theory are as follows: (a) Size alzd distributiort of the total area of contact. As shown in Section II. 2, the number n and the size naYa of the individual areas of contact are given by eqns. (IO) and (II). (b) Process ef ~0~~~~~~~~o~~~t~o~ alzd shearing of metallic ~~nct~o~s. We employ the simplifying assumptions, which are essentially those previously used by RABINOWHX? The location of the two areas forming a fully established circular contact of radius ay
$30
(;. YOSHIMOTCJ,
‘I‘. TSlKIZOE
VOL.
(Iq_j7/5X)
1
at zero time is shown in Fig. 6 at (a), while the position a short time later, after a sliding distance x, is shown at (b). After sliding a distance eration
has been reduced
24,
the contact areaunder
to zero (Fig. 6 (c)) ; in addition,
moment a new similar contact area of radius a, has just been fully established in the surface, since the total area of contact is directly proportional (c) The shape of the wear fiurticles. junctions
is of the type indicated
be made regarding
the volume
where vj is a constant.
consid-
it is assumed that at this elsewhere
to the applied load.
Assuming that the process of shearing of metallic
in Fig. 6, there are two simple assumptions
that can
,!l B of a given wear particle.
This implies that the depth of the material
This type of wear is shown, for example,
removed is constant.
when oxide film wear occurs.
1H -~ y’u,“,
where y is a constant. proportional
This implies that the depth to which the material
to the radius of the contact
particles is independent radius as the contact
(18)
area, i.e., statistically
of their size. Assuming hemispherical areas, the constant
is torn is
the shape of the wear
wear particles of the same
y is given by
y, = t,.
(191
3
Assuming conical wear particles with the base of the same radius as the contact
areas
and with the base angle 0, y is given by y
For the mechanical the conical particles. l~rfeIWLc_rs p. jyo
+tanu.
wear the most probable
(20)
shape of the wear particles
is that of
This is suggested by the profile curve of the metal surfaces where
VOL. 1 (1957~5~)
MECHANIST
the wear
process
following
expression
remains
OF WEAR BETWEEN
of the steady-state
for the volume
11B
METAL SURFACES
type.
Consequently,
48I this case
gives the
: (21)
From
assumptions
per unit sliding
(a), (b) and (c), the wear rate Qi, i.e. the total
distance
for the whole n-
8%=
I
eqns.
(IO),
(II)
can be written
-- f tane 6 LBr
c
and (22) it follows
g,
mechanical
wear
as
n--r
.I5
1= 0 From
surface,
2
?l&2.
I=0
that
_;E+.
(23)
m
This is similar ARCHARD’S The
main
(a} The
to the equation
concept
conclusions
wear
wear
that are derived
rate is proportional
particles from
wear
rate is independent
of the apparent
wear
rate is independent
of the velocity
Theory of Fe&
asperity volume is given
area of contact. of sliding.
model of the process of oxide film wear in sliding surfaces.
diagrammatically
of the upper
is considered
but on the surface
are:
film wear
7 illustrates
an asperity
by replacing
ones.
lc’.
(c) The
Fig.
essentially
by conical
the theory
to the load
{b) The
Fig. 7. Idealized 3.
of ARCHARD~ and is obtained
of hemispherical
surface
to expose
the process
moving
over
clean metal
of the clean metal
A B of a given wear particle,
of the oxide
the lower
surface
when the shearing
a thin layer of metal i.e. the amount
oxide
film wear
produced
on
at a velocity
1’. This
of the junction
occurs,
will form rapidly.
of oxide removed
The
from this asperity
by .fB
= ni@d
d
(24)
G. YOSHIMOTO,
482 where d = the thickness
T. TSUKIZOE
VOL. 1 (Igjp/jS)
of the oxide film formed in time t during which this asperity
moves a distance
s (Fig. 7).
Then
/ _= Q_. The empirical
relation
CL51
for the initial stage of oxidation
of a clean iron surface
is
given by9
‘t d =- ‘, log, - i 1 I cT i where 7 and t are constants.
(261
As the value of the constant
z for oxidation
of iron runs
from 2.6 to 10.4 secg, t/t is much smaller than unity in the case of the sliding process. The thickness
of the oxide film d, therefore,
is approximated
by
and
Substituting
eqn. (27) in eqn. (24) ‘I s; (Cl2 113-= x -TI
Assuming that the process of continual
formation
and shearing of metallic junctions
is similar to that for the mechanical
wear (Fig. O), the wear rate Qz, i.r. the total Fe&),
film wear per unit sliding distance
for the whole surface,
The average distance s between two neighbouring ?z individual
areas of contact
where L,yL, = the apparent IL, ! E di 1 ?
contact
it follows that
Refevences p. 490
asperities
as
on a plane upon which
(eqn. (IO)) exist is given by
contact
area between
= the number of the individual
and the summation
can be written
two surfaces,
areas along one edge L,r of the apparent
area, is carried out for the individual 16 -1
areas along L,r. From
eqn.
(II)
VOL. 1
(1957~58) ~~ECH~4NISM OF WEAR BETWEEN METAL SURFACES
483
Hence
When I., is equal to I,,, L n $=..-.-;--_ 2/n 2M tan0 Substituting
(29)
eqn. (zg) in eqn. (28) n-r
n
Qe =
2MtanB
1
2
n a7
=
y
(+a ‘L
711
--
n 2M
tan B
I==0
=
Combining
this equation
iz
---
rJ
8 t
1
n2
---
1--
1’
T
I
V
i
L EaX"
49f tan B
s -
1
2M2tan%
n3
1.
with eqn. (10) we obtain
This is similar to the equation of UHI,IG~ and is obtained essentially by replacing UHLIG’S contact model between the metal surface and the ideal flat surface by contact model between two metal surfaces. The main conclusions that are derived from the theory are: (a) The wear rate is approximately proportional to a square root of the load TV&, since the first term is generally larger than the second term in eqn. (30). (b) The wear rate is approximately proportional to the length of one edge of the apparent contact area. (c) The wear rate is inversely proportional to the velocity of sliding V. 4. Theory of Fe@,
film
mar
Similarly, the wear rate Qs, i.e. the total Fe,O, can be written as
where constant q’ is different from the constant constants are dependent on the temperature. 5.
film wear per unit sliding distance,
7 for the Fe,O, film wear, since these
Discussion
The experimental evidence for the theory will be considered. In Table I, the experimental values of the mechanical and the Fe,O, film wear given by some workers are compared with the theoretical expressions calculated from their data using eqns. (23) and (30). The following comments may be made : R&eferences
p. 490
4%
G. YOSHIMOTO,
EXPERIMENTAL
T. TSUKIZOE
VOL.
ANIl THEORliTIChL WEAR
1 (19j7ij8)
RITES
J.oall
I
L
0.690,)
I .6kg/cm”
Carbon steel 2 Cast iron
46.3 kg/cm2
3 Mild steel
rkg
0.1-j mjscc
Q = 0.00$ x 2 g/cm2~~oo m = o.131.10-Bcm3/cm
0.4
(1’~ 3.4 x rgjcmz~~Oom =.- 8r.3”0-~crdjCm Q :r: 15 pg/cm = f .g2‘10-6cm3jcm
mjsec
-. - .-.-.-.* The experimental
values
-.
Q,-
X..+w33.9~10-6cm3/cm
Q1 = 18.1 N72.j*10-6cm3/cm $& = 0.78w3.~q’0-~cm+Xl
._ ___-. _
fur No. 1, No. 2, and No. 4 were given
Iii.~ni~owcz AND TABOR~. ** The several values in eqns. (23) and (30) are as follows: L. = 1 cm, pnl = I..? B = riu8degree (H, = rw1op).
x
by OICOSHI~“, and for No. 3 by
101
kg/cm”,
rl ; _= 150 .A/sec.
{a) In the results for Ko. 2 and No. 3, there are fairly good agreements between the theoretical and the experimental values. (b) For No. I and No. 4, the experimental differ from the theoretical values. This difference may be largely due to the intermixture of two types of wear ; i.e. in the experiment for the mechanical wear (No. I) the Fe,O, film wear also occurs, and in the experiment for the Fe,O, film wear (No. 4) the mechanical wear is also produced. IV. INFLUENCE
OF VELOCITY
AND LOAD ON WEAR
In general, none of the three types of wear occurs indi~lidL~all~,but two or three types occur together. Moreover, the combination of three types of wear may be dependent on the velocity of sliding and the load between the surfaces. Weshalldeduce theoretically the relationships between the combination of three types of wear and the velocity or the load. Factors that will influence the combination of three types of wear are as follows: (a) Size of the junctions. The individual areas of contact are not of the same size, but have the size distribution. If there are n junctions for any thickness of the surface oxide film, then large junctions are formed, breaking through the film owing to the deformation of the underlying metal, and small ones are formed in the presence of the film. Consequently, in the former mechanical wear will be produced and in the latter Fe,& film wear or Fe,O, film wear. lirjevewvs
p. 490
VOL.
1 (1957/58)
MECHANISM
OF WEAR
BETWEEN
METAL SURFACES
(b) Thickness of the surface oxide film. The thicker numerous
are the junctions
that produce
Fe,O,
485
the oxide film becomes,
film wear or Fe,O,
the more
film wear.
(c) Local tewqberature rise at the points of contact. For the oxide film wear, the wear particles
produced
are generally
of the composition
the load are raised we may expect contact
2.
Fe,O,,
that a local melting
will be caused and the composition
but when the velocity
and
of the metal at the points of
of the oxide will be Fe,O,.
Size of the junctions As shown in Section
are given by eqns.
II. z and II. I, the number n and the size rcav2 of the junctions
(IO),
(II)
and (4). In eqn. (4) th e size of the unit depth for estimation
of :I1 must be similar to the amount moves into the another strictly speaking,
through
which the one surface
under the applied load W, the distance of invasion.
M is dependent
the size of the junctions eqn.
of the distance
Therefore,
on the load 1%‘.Hence the strict relationships
between
and the applied load can not be deduced merely by combining
with eqn. (4).
(II)
Assuming invasion,
that the size of the unit depth is equal to the amount
our mechanism
of contact
gives the following expression
of the distance
of
for the number and
the size of the junctionsll: (32)
.zar2 =
where TV =
Pm1’148*I’
6.45 . IO“’
I
N
20
Y = 0, I, 2,
(LxLy)o.sas tan6 8
.
, (1%-
I),
(33)
kg
p,
= about
1.5.10~ kg/cm2,
L,L,
= about
IO
mm
x
IO
mm,
H, in ,B, a, in ,u. The relationships stituting
the maximum (za,),
between
the size 7car2 and the load IV can be estimated
eqn. (32) in eqn. (33), but they are very complicated. radius of the junctions
can be written
Combining
by sub-
However, from eqn. (33)
(ar)max and the average diameter of the junctions
as
this equation
with eqn. (32) we obtain (34)
This means that the maximum proportional
radius or the average
to lV”. 142 and is independent
References p. 490
diameter
of the velocity.
of the junctions
is
@h
(i.
TOSHIMOTO,
T.
‘EI~KIZOE
3. Tkickness of tlze surface oxidefilm
As shown in Section
III. 3, the thickness
of the Fe,O, filtn is given by (35)
Substituting
eqns. (32) and (34) in this equation
we obtain
where W is in kg, El, in /J, p, in kg/cm 2, L,
Fig. 8. Idealized model for calculating the local te~l~rature
4.
Locdl tefnperatwe
riseat
the points
In Fig. 8 the force /l1; required
rise at a point of contact.
of contact
to shear a junction
is given by
,.11: = ,zcz”~S, where S z the shearing strength of the metal. The rate at which the shearing energy is expended
138)
will be
E T= 1F II-. If we assumed h’zfe~cmm p. 490
that all of the mechanical
energy associated
(39)
with the shearing
process
VOL.
1
(1957~5~)
MECHANISM
OF WEAR
BETWEEN
METAL
SURFACES
487
is converted into thermal energy, then the amount q of heat developed per unit time per unit area will be (!LL, .rnar2
where J = the mechanical equivalent of heat. Combining this equation with eqns. (38) and (39) 9=i’
s I/
(40)
As the base angle 8 of conical asperities is very small (I’ N 15”j2, this heat 9 can be regarded as a steady-state heat source on the surface of the semi-infinite body, and the mean temperature T in this heat source can be written asi2 ;4 ar
where K = the thermal conductivity, ‘4 = the area factor, To = the room temperature ; the shape of the junction is approxinlated to the square having one edge zaP For the square
A = 0.95.
Then T -
Substituting
T,
= 0.48 F.
eqn. (40) in this equation we obtain
This means that the local temperature rise at the points of contact is proportional to II and a,. As T is generally much larger than T,,, for the maximum point of contact we put a, = (ar)nzax (eqn. (34)) in eqn. (41) and find
where J is in kgm/kcal, K in kcal/m=h.“C, S in kg/mz, V in m/h, Tin “C, H, in ~4,L,L, in mm2, #, in kg/cm2, W in kg. It may be seen that after any raising of the velocity and the load the temperature rise associated with the shearing process comes to the melting-point at the maximum point of contact and production of Fe,O, film wear begins, Rejwmres
p.
490
G.
488
YOSIISMOTO, T. TSUKIZOE
dtB of the melting layer is given by
The thickness
n’,
2K’ . =L .7 --4 (
when we assume that the temperature constant
and the temperature
T”,.,‘.
)*
?‘ across the whole of the shearing
7‘m.p, (melting-point)
between the melting layer and bulk of the metal is constant steady temperature
is
also and that there is a
drop along the depth of the melting layer. Substituting
and (42) in this equation
interface
across the whole of the interface eqns. (40)
we obtain
(43)
when y V?F’0~1*2>Tm,p.. This means that the thickness
of the melting layer increases
with the velocity
and
the load. Equations junctions, of contact)
(34), (36), (37) and (42) can be used to estimate
thickness
three factors
of the surface oxide film, and local temperature
as a function
of the velocity
(size of the
rise at the points
and the load.
d' of oxidt
film th!cknesS
V Fig.
5.
9.
Ikpendcnce
of wear rate on v&city
Inflttence of velocity on the mechmaism
of wenr
Fig. c) shows the ways in which the mechanism Q = Q1 + Q2 -{- Q3 depend on the velocity, and the melting
layer thickness
(theory).
of wear and the total wear rate
The variation
with velocity
of the oxide film thickness
at a constant
load are estimated
eqns. (36), (37) and (43). The term “limit of oxide film thickness” the maximum
limit ; i.e. when the oxide film thickness
film is not broken up by the deformation point of contact
and all junctions
From eqn. (34) the m~imum
rises above that limit the oxide
of the underlying
metal even at the maximum
produce oxide film wear but no mechanical
radius of the junctions
with
is used to denote
increases
wear.
with the load and is
VOL. l(I957~5~)
independent
MEC~ANIS~OF
of the velocity.
dent of the velocity
WEAR
BETWEEN
Consequently,
METALSURFACES
489
the limit of oxide film thickness
is indepen-
(Fig. 9).
In Fig. 9 the ways in which the mechanism are as follows:
of wear changes and the wear rate varies
(I) V
Limit
Fig.IO.Dependenceof wear rate
of oxide
on load
film
thickness
(theory).
Similarly, the ways in which the mechanism of wear and the wear rate depend on the load are shown in Fig. IO. The variation of the oxide film thickness, the melting layer thickness, and the limit of oxide film thickness with load at a constant velocity are estimated with eqns. (36), (37), (43) and (34). 7. Discztssion The experimental evidence for the theory will be considered. Fig. II shows the variation of the wear rate with velocity or with load, which is summarized from many experimental results given by various workers (W. EILENDER AND W. OERTELIO, K. DIES~O,~.KEHLA~DE.SIEBEL lo,1%.OKOSHI~~A~D K. OGAWA~~). Theagreement References p. 490
490
between this summary of experiments and the theory shown in Figs. (1and IO is fairly gaod. We can conclude that by reason of the variation of the mechanism of wear with velocity or load the ways in which tile wear rate depends on the velocity or the load are very complicated (Figs. 9, IO and I I), and that for the same reason the variation of the wear rate with velocity is similar to that with load. In this paper the experimental background is incoml~lete and it is clear that further work is necessary.