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Engineering model for wear
ENGINEERING R. G. BAYER, IBM
MODEL
1%‘.(‘. CLINTON,
FOR
C. W. NELSON
AND
WEAR
R. A. SCHUMACHER
General Products Division, Development Laboratory, Endicott, N.Y. (U.S.A.) (Received
June 2, 1962)
SUMMARY The wear produced between two metallic bodies sliding relative to each other has been correlated with stress. The results of 1,200 tests for various combinations of materials and lubricants have shown that wear can be eliminated for a given amount of time if the shear stress is kept below a certain fraction of the yield point in shear of the weaker of the two metals. It has been shown that this fraction is a function of the materials and the lubricant used. Values of this fraction have been determined for a large number of combinations of materials. INTRODUCTION
Until now, there has been no model to relate stress to wear. The work reported here correlates shear stress with the wear occurring when two metallic surfaces slide in contact with each other, and develops a criterion for eliminating wear on this basis. This study was conducted by sliding a ball against a plane at specified loads for a given number of passes. It involved examining IZO different combinations of materials in conjunction with four different lubricants. The exact experimental procedure used and the analysis performed in relation to the model are discussed. EXPERIMENTAL
METHODS AND MATERIALS
Apparatus Two different
Fig.
I.
wear and friction
machines,
Friction apparatus converted Norton surface grinder.
modeled
Fig.
after the well-known
z. Wear
_-.-._.__--
apparatus miller.
Bowden-
I.~-,._,_“._.--
converted
Elgin
Wear, 5 (1962) 378-391
ENGINEERING MODEL FOR WEAR
379
Leben apparatusl, are used in the experiments. They are capable of measuring friction and accumulating wear at controlled speeds and applied loads. One machine (Fig. I) is built around a Norton surface grinder, and the other machine (Fig. 2) around an Elgin miniature milling machine. The Norton machine is used exclusively for measuring friction at very slow sliding velocities, while the Elgin machine is used to accumulate wear by making multiple traverses at a moderate rate of longitudinal oscillatory movement. The longitudinal movement of the table on the Norton machine is achieved hydraulically by using a Graham variable speed transmission and a Zenith gear pump. This unit is located a distance of ten feet from the apparatus so that pump vibrations are sufficiently damped through long pressure lines. The well-known “stick-slip” movement exhibited at slow sliding velocities by most surface grinders is eliminated by supporting the table hydrostatically, using a Pesco gear pump also located ten feet away. This machine has a uniform, minimum sliding velocity of 0.0005 cm/set and a maximum of 0.5 cm/set. The longitudinal oscillatory movement of the Elgin machine is achieved by using a Graham variable speed transmission and a rocker arm borne by a rockshaft. The rocker arm is coupled to a carriage mounted on two bearing shafts that slide in ball bushings. The entire assembly of transmission, rocker arm, and carriage are mounted on the table of the Elgin milling machine. This machine has a maximum useful oscillatory motion of 600 cycles/min and a minimum of 25 cycles/min. The machines are operated in a controlled environment maintained at a relative humidity of 10%. Simply, they are two convenient means for holding, loading, and providing relative motion between a spherical surface and a plane. The spherical surface (called a slider) is a 4 in. ball, and the plane (called a platen) is a I$ x I x i in. block. The slider, which is locked immovably in a ball-holder, is attached to a twisted cantilever beam rigidly mounted in the spindle head of each machine. On the Norton machine, the spindle head is lowered to make contact between the slider and the platen, while, on the Elgin machine, the table is raised to establish contact between the slider and the platen. The identical twisted cantilever beams (called relaxation oscillators) on each machine are designed to measure the applied load and to monitor the tangential force at the sliding area of contact. Figure 3 shows one’s general appearance in detail. It consists of two independent vibratory planes milled 90~ apart from a single bar of 4140
Fig. 3. rwisted cantilever
beam with ball-holder
and ball. Wear, 5 (1962) 378-391
Ii. G. BAYER,
380
W. (‘. CLINTON,
c‘. W. NELSON,
R. A. SCHUMACHER
steel hardened to RC30. The natural resonant frequency of each plane is approximately I80 cycles/set. Separate Wheatstone bridge circuits comprised of four strain gages each are cemented to each plane -two gages on the near face and two gages on the far face of each plane. With the Norton machine, electrical unbalance of the two bridge circuits is monitored by a Sanborn six-chamiel 350 recorder; whereas, two Brush BL-520 Universal Amplifiers are used with the Elgin machine. Test specimens
and their preparation
The wear and friction characteristics of 40 different metals were studied in sliding contact with 52100 high carbon steel balls, 302 stainless steel balls, and yellow brass
TABLE SPECIMEN
Steel stainless 302-A4 303-EZ 321 347 A ISI steels
wrought
DESIGNATION
I AND
SOURCE
Carpenter Allegheny Ludlum Allegheny Ludlum Allegheny Ludlum
410 410-1AC 416-EZ 440
Allegheny Ludlum Carpenter Allegheny Ludlum Carpenter
Raw stores IBM Raw stores IBM Wm. S. Hacker Precision Metals Wm. J. Hacker Raw stores IBM
4150 4620-A 5130 8214 8620 52100
Raw stores IBM Precision Metals Raw stores IBM Wm. J. Hacker Precision Metals Raw stores IBM
356 Special alloys Hymu 80AHycc
Precision Metals Precision Metals Precision Metals
43-774 112-184 195-2933
Alcoa Alcoa Alcoa
Carpenter Wm. J. Hacker
Wm. J. Hacker Carpenter
Hycc
Precision Metals
Ketos
Wm. J. Hacker
Invar 36
Carpenter
Rexaa Hampden Steel Oil Wear Carpenter No. I I Water Hardened Star Zenith Red Wear Nitralloy G
1018
Hardened 1055
1045
1060 1085 4140
Copper alloys &pro-nickel 30% Phosphor-bronze 8% grd. C Beryllium copper Aluminum alloys 220 355
Raw stores IBM Raw stores IBM Precision Metals
Carpenter Carpenter Copper Weld
balls. Table I lists the identification, source, composition, hardness, and other pertinent data for the platens. Table I also lists similar information for the balls. Platen preparation First, each platen was always reground before any experiment to remove any work-hardened material generated from prior experiments. After grinding to a V-r2 finish, they were polished successively with wet 350A, 4ooA, SOOA,and 6ooA “WetorWear, 5 (1962) 378-391
ENGINEERING
MODEL FOR WEAR
381
Dry” Tri-Mite silicon carbide paper. The RlU scratches produced by abrasion were perpendicular to the direction of sliding in the friction and wear machines. Then, the wet specimens were dried with CP acetone and immediately refluxed for 30 min in a CP benzene vapor chamber. After refluxing, they were mounted immediately in a friction and wear machine and an experiment was started. Ball preparation The 52100 steel balls and the 302 stainless steel balls were degreased six times in boiling CP benzene. They were then refluxed in a benzene vapor chamber for 30 min. After refluxing, they were immediately locked in a degreased ball-holder, which was mounted in a friction and wear machine, and an experiment was started. The commercial brass balls were also degreased six times in boiling benzene. After drying, they were abraded with wet 6ooA grid silicon carbide paper and dried with CP acetone. They were then refluxed for 30 min in a benzene vapor chamber. After refluxing, they were immediately locked in a degreased ball holder, which was mounted in a friction and wear machine; then an experiment was started. Early experiments were not reproducible with brass balls. It was found necessary to remove by abrasion the heavy oxide layer residing on the balls when purchased. This was not found to be true of the 52100 steel balls nor of the 302 stainless steel balls. The lubricants Four different lubricants were used in the experiments. Three of the lubricants are commercially available, and their designation and other pertinent data are shown TABLE PROPERTIES
Oil designation
TvPe
of
stock
Flask
@int
oJ5encull,
POW
pJint
(“F)
(“F)
435
--I5
II
OF LUBRICANTS
Gravity
Viscosity index
23.1
77
(A PII
Neutraliza&m no.
TY@ additive
of
Oxidation A
Napthenic
0.03
and tackiness Oxidation
B
Paraffin
40.5
20
33.0
105
0.05
and corrosion Oxidation-
Specific C
Paraffin
200
-75
20/20°c 0.859
188
0.20
V.I. improveranti-wear
in Table II. The viscosity-temperature characteristics of these three lubricantsare shown in Fig. 4. The fourth lubricant is oil “B” which has been doped with 0.2% of Eastman’s white label grade stearic acid. Wear, 5 (1962) 378-391
382
H. 1;. BAYER,
W. C’. CLIKTON,
1‘. W. NELSON,
Ii. A. SCHIJBIACHER
1
..,.,
1””
61”
TEMPERATURE, DEDREES FAH~E#HElT
Fig. 4. Kinematic
viscosity versus temperature for three lubricants.
Procedure Two types of experiments were performed with the three different balls and the forty different platens. The first type of experiment was withclean, dry test specimens. The second type of experiment was made with lubricated balls and platens. (I) Dry ex@eriments. First, the coefficient of friction was measured on the Norton machine for a single traverse of each kind of ball on each platen. The normal load was always 800 g and the sliding velocity was 0.005 cm/see. Second, photomicrographs were made of the scar on the ball and a portion of the track’ worn on the platen. Third, a trace of the wear track contour was made with a Talysurf** profilometer. The direction of travel was perpendicular to the direction of sliding. Occasionally, a profile trace of the ball was also made. (2) Lubricated experiments. These experiments were made at two different normal loads with each sliding combination. These normal loads were calculated from data pertaining to the elastic properties of the two metals in contact. Consequently, both loads calculated for a given sliding combination generally were different from those calculated for other sliding combinations. The test sequence followed was always identical at each of the two normal loads calculated for each pair of sliding metals. First, the clean, dry platen and ball were flooded with one of the four different lubricants and the coefficient of friction was measured in the Norton machine. A single * Total sliding distance was one cm for both the dry and lubricated experiments. ** Tradename, Taylor-Hobson, Inc. Wear, 5 (1962) 378-39x
ENGINEERING MODEL FOR WEAR
383
traverse was made at one of the calculated normal loads P and at a sliding velocity of 0.005 cm/set. Second, the platen and the ball, which remained securely locked in a ballholder, were transferred to the Elgin machine. In this machine, the platen was oscillated in sliding contact with the ball at a normal load equal to that applied previously in the Norton machine. After 2,000 traverses at the rate of 75 traverses/min, observations were made to determine the amount of debris generated and to detect any evidence of fretting corrosion. Third, the ball and platen were returned to the Norton machine, and the coefficient of friction was measured. A single traverse was made with the ball sliding in the wear track, which was worn on the platen by the ball during the 2,000 traverses on the Elgin machine. The normal load was equal to that applied when TRACK WIDTH
.I
Fig. 5. Diagram of wear track defining track width, VAVO,and
VPER.
making the first friction measurement, and the sliding velocity was 0.005 cm/set. Fourth, photomicrographs were made of the wear track on the platen and of the wear scar on the ball. Afterwards, a profile trace of the contour across the width of the wear track was made with a Talysurf profilometer. In some instances, a profile trace of the wear scar on the ball was made along the major axis of wear. MODEL
In the model for wear between two surfaces sliding relative to one another, it has been postulated that wear can occur in several ways. One type of wear is that which occurs when the material in the vicinity of the gross contact region is subjected to a stress system which causes plastic flow and results in some movement of material away from the contact region. This mechanism is called gross plowing. An example of this type of wear is given in Fig. 6. The same type of wear mechanism involved in gross plowing can occur on a local scale as a result of surface asperities. This type is called local plowing. Another way in which wear can occur is by transfer, or exchange of material between the two contacting surfaces (Fig. 7). Note that transfer can produce a change in the geometry, either on a gross scale (Fig. 7) or on a local scale. In either event, the stress system caused by the new geometry can produce plowing. The above mechanisms can produce debris. This debris can then produce an abrasive action, which is the final type of wear. If the abrasive action is caused by debris in oxide form, it is called fretting corrosion; otherwise, it is called fretting (Fig. 8). Wear, 5 (1962) 378-391
I-L G. HAYER, \I’. (‘. (‘I>lNTOS, C. XV. NELSON, R. A. SCHUMACHER
384
V I
\
,
Fig. 6. Top: Profilometer trace and photomicrograph of 52100 ball. Bottom: Profilometer trace with ball profile indicated and photomicrograph of 1055 platen. One pass: lubrication: dry; ty (platen) = 58 103 p.s.i.; ty (ball) := Ijo 103 p.s.i.; tmsx = 97.5 103p.s.i.
‘aJ ‘. .
I
\
I
\
I
/
I / I
Fig. 7. Top: Profilometer trace and photomicrograph of 52100 ball. Bottom: Profilometer trace with ball profile indicated and photomicrograph of 410 (A-L) platen. One pass; lubrication: dry; load: 800 g. Wear, 5 (I@)
378-391
ENGINEERING
MODEL
FOR WEAR
3%
The model states that wear can be reduced to a minimum, or eliminated, by keeping the stress in the vicinity of the region of contact below a certain value. This value is a function of the materials and lubricants used and the lifetime.
Fig. 8. Top: Photomicrogrqhs of gzroo ball and 303 EZ platen, respectively. Bottom: Profilometer trace with ball profile indicated of 303 EZ. 2,000 passes; Iubrication: oil “A”; q, (platen) = 63 . 101psi.; T* (ball) = ISO * 108psi.; r= 12.5 = IO* pa.i.
The maximum shear stress theory of failure states that, if the maximum shear stress occurring in a body is greater than the yield stress in shear, plastic flowing will occur. Consequently, to eliminate gross plowing, the following condition must be observed: ty > Zmex
(If
where tY is the yield point in shear of the weaker of the two materials in contact, and tmax is the maximum value of the shear stress experienced. This maximum value must be determined for each particular contact problem. For a large number of cases, the results of Hertz’s contact stress problem are applicable. Wear produced by transfer and local plowing can be eliminated for one pass by keeping the stress beIow a certain fraction of the yield point in shear; that is: zmax i cay, a < I
121
One pass is defined as that relative displacement sufficient to just unload the original contact region.
#G
I<. (;. JMYEK,
1s’. (‘. CLINTOX,
(‘. \\:. NELSON,
Ii. A. SCHUMACHER
LiTear produced by transfer, local plowing, fretting corrosion, and fretting can be eliminated for a given number of passes by keeping the stress below a fraction of the yield point in shear, or :
Tmax< pt!/, p < x
(3)
011 the basis of existing information, the present model for wear also postulates that for wear less than or equal to the surface roughness, the wear is the same for two sets of conditions of stress and number of passes as predicted by the following equation : )9Nz, (Tm*)~N1 = (TlmXZ
zooo<
A’,
rr6,ooo
(4)
where tmaxl and Nr are the values of t maxand the number of passes for one set of conditions, respectively, and t maxZand Nz are the values for the other set of conditions. This equation is a modified form of Palmgren’s equation* for ball bearings, relating load to lifetime. ANALYSIS
The model for wear was verified by correlating the maximum shear stress in the vicinity of the contact region with the amount of wear produced on the platen. Qualitative examination of the ball for wear was also considered. Note that the ball experiences many more passes than the platen in any given experiment. This occurs because the diameter of the circle of contact is much smaller than the length of the track, that is, the overall sliding distance. In this paper, the number of passes is always specified with respect to the platen. As stated when describing the experimental procedures, the wear in these tests was measured by means of a profilometer trace across the wear track on the platen. The cross-sectional area of the wear scar was used as a measure of wear. Two areas were measured. The first, VAVG, is the average area appearing underneath the width of the track. (The width was determined by means of photomicrographs.) The second, VPER, is the sum of the perturbations on the average area. These two areas are shown in Fig. 5. When the track could not be distinguished from the surface roughness, there was said to be zero wear, that is, VAVG= o and V~EH.= O. The contact stress problem between a sphere and a plane pressed together by a normal load is covered by the Hertz contact problem. If sliding is introduced into the Hertz contact stress problem, it is found that the two possible maximum shear stresses occurring for the sphere-plane geometry are :
where ~1is the coefficient of friction, v is Poisson’s ratio, and QO is the maximum contact pressure as defined in the Hertz problem (eqn. (6)). Also, && occurs on the surface of the contact, and tdmzxoccurs at a certain distance underneath the surface of contact. These two expressions involve two additional assumptions beyond those *Palmgren’s equation for roller bearings is P13N1 = P23Nz where the P’s are the loads and the N’sthe life time. For roller bearings P is proportional Therefore in terms of stress, the equation is t19N1 = tzQN*
to x3.
Wear, j (1902) 378-391
ENGINEERING
MODEL
FOR
WEAR
387
contained in the original Hertz contact problem. One is that the local coefficient of friction is equal to the coefficient of friction as measured. The second is that the effect of the frictional force on the &ear underneath the surface can be ignored. This assumption is based on the results of a crude analysis which indicates that, when the coefficient of friction becomes large enough to influence the shear underneath the surface, the maximum shear occurs on the surfaces. Since only the maximum shear is of interest, eqn. (5) is satisfactory. The maximum contact pressure 40 for the sphere-plane geometry is: 6P $74 =
I ~I__
VI?
113
$_ I ___
v23 ES
El
= Rz I
(6) 1
where P is the normal load, R is the radius of the sphere; ~1 and El are Poisson’s ratio and Young’s modulus, respectively, for the material of the sphere ; and uz and EZZare those for the material of the plane. Note that the model does not solely apply to Hertz contact problems, but rather to any problem for which a value of the stress occurring can be determined. For the particular geometry used in the tests, the Hertz contact problem was applicable. The analysis of the wear scar on the platen in terms of wear mechanisms was performed by comparing and considering several things. The profile of the scar was compared to a ball profile. Depending on the fit, one or more wear mechanisms could be postulated to have occurred (Fig. 6-8). Optical examination of the scar then gave additional information concerning the type of wear occurring. This was particularly helpful in determining if fretting or fretting corrosion had occurred. Information could also be obtained on transfer and local plowing- Finally, an examination of the friction trace would aid in the identification of transfers. This technique for identification was found to be excellent in determining the major types of wear occurring in a particular experiment, In several cases, the conclusion reached by such an analysis was confirmed by additional examination. Figures 6 and 7 show the results of such a confirmation. The scar shown in Fig. 6 was determined to be caused by gross plowingt and that in Fig. 7s by transfer and plowing. The Talysurf profilometer traces of the ball in both cases confirm these conclusions. The elimination of wear by reducing the stress to below a certain value was demonstrated in the following manner. For several different combinations of lubricant and material, an average value of cxwas determined experimentally. #lwas determined for 2,000 passes. Then, by using the yield point in shear of the weaker of the two materials involved in a given test and using the above values of CTand /3,allowable maximum shear stresses were computed. Then, the corresponding loads were determined by using eqns. (5) and (6). The wear produced after 2,000 passes for each combination of lubricant and materials was measured and identified. Equation (4) and the interpretation were verified by experiments for 12 different combinations of materials. Equation (4) was used to predict the stress required to produce the same wear at z16,ooo passes that was produced at 2,000 passes. RESULTS
Table III lists the results of a representative
portion of approximately
1,200
tests.
% I+
%?
5 $
p _(n
1018 1018
52100 52100 52100
33 33 33
7 show that wear can be eliminated 1018 52100 33
Lines 8 through 33 show that wear can be eliminated 8 8620 302 40 8620 302 40 9 IO 8620 302 40 8620 II 302 40 8620 I2 302 40 8620 302 I3 40 52100 50 I4 347 52100 50 347 I5 52100 16 50 347 52100 50 I7 347 gzroo 18 50 347 52100 I9 50 347 Brass 58 IO55 Brass “2’: 58 IO55 Brass 22 55 IO55 Brass 55 IO55 Brass 55 IO55 23 24 Brass 55 IO55 25 112 Alum 26 52100 I5 52~00 112 Alum I5 28 27 52100 112 Alum I5 52100 II2 Alum 29 15 106 30 302 ‘045 106 302 IO45 3’ 82.5 414oLL 302 32 82.5 4140LL 33 302
2 7
Lines 4 through 4
III
dry dry dry
ON STRESS
132.8 77.3 60.2
58 55 55 58 55 58 I50 I50 I5o 150 I50 I50 17.9 17.9 17.9 17.9 17.9 17.9 150 I50 I5o 150 55 55 58 55
for 2,000
I5o 150 I50
B B
31.4 25.4 17.8
0 0
0
14.8 0 0
passes when tmax is reduced to j?rfy (eqn. (3)) B .21.45 10.6 2,000 7.9; B 0 2,000 A 0 2,000 21.45 A 0 2,000 7.91 C 2,000 21.45 7.6 C 0 2,000 7.91 B 26.81 2,000 2.4 0 B 9.88 2,000 A 1.0 26.81 2,000 0 A 9.88 2,000 C 26.81 2,000 4.0 C 9.88 0 2,000 0 B 9.66 2,000 5.28 0 B 2,000 A 9.66 0 2,000 0 A 5.28 2,000 0 c 9.66 2,000 0 C 5.28 2,000 B 8.04 2,000 5.2 2.96 0 B 2,000 A 8.04 2,000 7.6 0 A 2.96 2,000 31.10 B 2,000 3.0 11.46 0 2,000 B C 31.10 2.8 2,000 0 C 11.46 2,000
I I
for one pass when the rmSx is reduced to LX~‘~ (eqn. (2)) I50 I B 32.0
(eqn. (I)) I I I
OF WEAR
TABLE
Lines I through 3 show that wear is produced when rmax exceeds t’# I 321 52100 40 150 2 IO45 52100 106 I50 3 IO55 Brass 55 17.9
DEPENDENCY
0.3 0 0 0 0.6 0 2.6 0 2.2 0 0 0 0.36 0
0 0 2.8 0 2.6 0 0.12 0 0 0 0.8 0
0.35 0.30 0
0.50
5.26 0 1.80
0.54 0.20
o-54 0.20
0.54 0.20
0.54 0.20
0.54 0.23
0.54 0.23
0.54 0.23
0.54 0.20
0.54 0.20
0.54 0.20
0.54 0.20
0.54 0.20
0.54 0.20
0.97 0.95 0.77 0.54
3.34 0.73 3.36
4’50 4x50 4’50 4150 4150 4’50 302 302
65 65 58
58
Brass Brass
52 100
302 58
150
17.9 17.9
58
58
58 58 150 I50 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000
B B B B B B
B C C B B+St.a.* B B A B B B B B B B B
17.79 10.58 21.45 7.91 4.71
49.86
31.1 31.1 11.46 14.48 ‘4.48 9.65 3.56 9.65 34.85 12.85 31.10 11.46 9.66 5.28 11.46 11.46
7.6 0 0 2.0 0 0
0 20.0 0 7.6 0 6.0 0 0 15.0 0 0 0 0 0 5.0 0
1.76 0 0 3.0 0 0
2.6 0 0 0 0.5 0 0.4 0
0
0.2 0 0.6 0
0
0
0
0.54 0.54 0.20 0.54 0.54 0.54 0.20 0.54 0.54 0.20 0.54 0.20 0.54 0.23 0.20 0.20
of the two yield points in shear. occurring in the text (Fig. 5.) zero for one pass or to p if V A”G and VPER equal zero after either 2,000 or 216,000 passes. (eqns.
of /l on the number of passes (eqn. (4)) 90 I50 2,000 90 I50 2,000 90 I50 216,000 40 150 2,000 40 I5O 2,000 40 I50 216,000
65
302
the dependency G 52100 G 52Ioo G 52100 52100 52100 52100
65
302
52100 52100
18 18 65 65
of B on materials and lubricants. 63 58 2,000 63 58 2,000 63 58 2,000 27 58 2,000 27 58 2,000 18 58 2,000
* ty is the yield point in shear; rly is the smaller b tmax is the maximum value of the shear stress c VavG and Vp~a are indices of wear as defined fl tm&‘u is equal to oc if VAVC and VPEB equal (3) and (4)) * Stearic acid
Lines 50 through 55 show 50 Nitralloy 51 Nitralloy 52 Nitralloy 53 Monel C 54 Monel C 55 Monel C
42 43 44 45 46 47 48 49
Lines 34 through 49 show the dependency 34 303 302 35 303 302 36 303 302 37 Phos. Bronze 302 38 Phos. Bronze 302 39 220 Alum 302 40 220 Alum 302 4= 220 Alum 302
E
8
g
390
Ii. G. BAYER, IV. (‘. (‘LIN’W?\‘, C. W. NELSON, R. A. SCHUMACHER
In general, all the tests performed agreed with the model proposed. These results were obtained for the following surface roughnesses (peak to peak) 5 to 15 $4. for steels; IO to 35 pin. for aluminums; and 5 to 40 pin. for the remaining materials. The data obtained for one pass under dry conditions and a load of 800 g showed, in general, that, whenever the yield point in shear was exceeded, wear occurred (rows I through 3, Table III). In these runs, the occurrence of plowing and/or transfer, especially on a large scale, could usually be identified quite easily (Figs. 6 and 7). It was found that, in general, the platen material transferred to the 302 stainless ball under these conditions. In the brass series, it was found that the brass transferred to the platen. In the case of the szroo steel balls, transfer did occur, but not as frequently as in the other cases. The value of LXwas found for lubricated conditions to be 0.54, and appears to be independent of lubricant and materials (rows 4 through 7, Table III). Since, under lubricated conditions, the amount of transfer occurring in one pass is quite small, 01 may be interpreted as a mechanical factor, x/a being analogous to a stress concentration factor. Rows 8 through 4g of Table III show a typical series of experimental results. It was found that @ varied between 0.54 and 0.~0. The data indicated that B was a function of the materials and lubricants used (rows 34 to 49, Table III). There appeared to be no correlation with viscosity. However, if oil “B” was doped with 0.20/h stearic acid, the value of sy rose from 0.20 to 0.34 in most cases (rows 37 and 38). It is felt that the variation of /? is the result of variation in the tendency for various combinations of materials to form debris. Because of the behavior of p with the doped oil, transfer is considered to be a major c~)ntributor in the formation of debris.
Fig. 9, Top: Profilometer trace and photomicrograph, respectively, of Monel C platen after z,ooo passes, rmax= 7.91 ros psi. Bottom: After 216,000 passes, t ,,,sx= 4.71 103p.s.;., 52100 ball; lubrication: oil “B”. Wear, 5 (1962) 378-391
ENGlNEERING
MODEL FOR WEAR
39*
Consequently, ,!I is considered to be mainly a function of the ability of the oil to prevent transfer from occurring. In approximately 90% of the cases tested, it was found that a suitable value for fi was either 0.20 or 0.54,0.54 being the value of !X determined in the tests. All of the 12 experiments performed to verify eqn. (4) reproduced the wear conditions obtained for 2,000 passes. The results of two of these tests are given in rows 50 to 55, Table III (Fig. 9 also)*. Qualitatively, in most cases, there was little or no wear on the balls when wear was eliminated on the platen, except in the case of the brass balls. However, because of the limits of the experimental equipment, the brass balls could not be run at the low load specified by /I = 0.20 (rows rg through 25). Therefore, some wear on the brass ball should be anticipated. The authors believe that this model correlates wear quite satisfactorily with load, geometry, materials, and lubricants in such a way that the results of simple wear tests may be applied satisfactorily to other geometries, materials, and loads not specifically tested. Further, it has been demonstrated that wear can be eliminated by keeping the stress under a certain value, &,, where p is a function of the materials and lubricants used and the lifetime. ACKNOWLEDGEMENTS
The authors thank Dr. C. W. MACGREGOR for his interest, guidance, and encouragement in this work. They also thank Mr. J, E. BROPHY for indicating this problem and for suggesting how to treat it. Their appreciation is due to Dr. T. C. Ku for his stimulating discussions on this work. Special appreciation is also due to Miss BETTY DEYO, J. 2. DEVINE, and J. L. SIRICO for their help in obtaining and compiling the data. The authors also thank the following companies for supplying them with samples: Allegheny Ludlum Steel Corporation, Aluminum Company of America, Carpenter Steel Company, Copperweld Steel Company, Precision Metals Company, and William J. Hacker and Company, Inc. REFERENCES F. P. BOWDEN AND D. TABOR, The Friction and Lubrication of Solids,OxfordUniversityPress, 19508 pp. 73-75. M.C. SHAW AND E.F. MACKS, Analysis and Lubrication of Bearings, McGraw-Hill Book Co., New York, 1949, p. 411. See ref. r, pp. 78-82. * A few test results not covered by this paper show that the experimentally determined constant wear line for a specific small amount of wear, when plotted in a log-log graph of tmsa versus N, is not exactly the straight line indicated by eqn. (4). These test results indicate that eqn. (4) is too safe for N greater than 216,000. The experimental constant-wear curve departs radically upward from the line given by eqn. (4) in their range of N. wear, 5 (1962) 37g-39r
MODEL
1%‘.(‘. CLINTON,
FOR
C. W. NELSON
AND
WEAR
R. A. SCHUMACHER
General Products Division, Development Laboratory, Endicott, N.Y. (U.S.A.) (Received
June 2, 1962)
SUMMARY The wear produced between two metallic bodies sliding relative to each other has been correlated with stress. The results of 1,200 tests for various combinations of materials and lubricants have shown that wear can be eliminated for a given amount of time if the shear stress is kept below a certain fraction of the yield point in shear of the weaker of the two metals. It has been shown that this fraction is a function of the materials and the lubricant used. Values of this fraction have been determined for a large number of combinations of materials. INTRODUCTION
Until now, there has been no model to relate stress to wear. The work reported here correlates shear stress with the wear occurring when two metallic surfaces slide in contact with each other, and develops a criterion for eliminating wear on this basis. This study was conducted by sliding a ball against a plane at specified loads for a given number of passes. It involved examining IZO different combinations of materials in conjunction with four different lubricants. The exact experimental procedure used and the analysis performed in relation to the model are discussed. EXPERIMENTAL
METHODS AND MATERIALS
Apparatus Two different
Fig.
I.
wear and friction
machines,
Friction apparatus converted Norton surface grinder.
modeled
Fig.
after the well-known
z. Wear
_-.-._.__--
apparatus miller.
Bowden-
I.~-,._,_“._.--
converted
Elgin
Wear, 5 (1962) 378-391
ENGINEERING MODEL FOR WEAR
379
Leben apparatusl, are used in the experiments. They are capable of measuring friction and accumulating wear at controlled speeds and applied loads. One machine (Fig. I) is built around a Norton surface grinder, and the other machine (Fig. 2) around an Elgin miniature milling machine. The Norton machine is used exclusively for measuring friction at very slow sliding velocities, while the Elgin machine is used to accumulate wear by making multiple traverses at a moderate rate of longitudinal oscillatory movement. The longitudinal movement of the table on the Norton machine is achieved hydraulically by using a Graham variable speed transmission and a Zenith gear pump. This unit is located a distance of ten feet from the apparatus so that pump vibrations are sufficiently damped through long pressure lines. The well-known “stick-slip” movement exhibited at slow sliding velocities by most surface grinders is eliminated by supporting the table hydrostatically, using a Pesco gear pump also located ten feet away. This machine has a uniform, minimum sliding velocity of 0.0005 cm/set and a maximum of 0.5 cm/set. The longitudinal oscillatory movement of the Elgin machine is achieved by using a Graham variable speed transmission and a rocker arm borne by a rockshaft. The rocker arm is coupled to a carriage mounted on two bearing shafts that slide in ball bushings. The entire assembly of transmission, rocker arm, and carriage are mounted on the table of the Elgin milling machine. This machine has a maximum useful oscillatory motion of 600 cycles/min and a minimum of 25 cycles/min. The machines are operated in a controlled environment maintained at a relative humidity of 10%. Simply, they are two convenient means for holding, loading, and providing relative motion between a spherical surface and a plane. The spherical surface (called a slider) is a 4 in. ball, and the plane (called a platen) is a I$ x I x i in. block. The slider, which is locked immovably in a ball-holder, is attached to a twisted cantilever beam rigidly mounted in the spindle head of each machine. On the Norton machine, the spindle head is lowered to make contact between the slider and the platen, while, on the Elgin machine, the table is raised to establish contact between the slider and the platen. The identical twisted cantilever beams (called relaxation oscillators) on each machine are designed to measure the applied load and to monitor the tangential force at the sliding area of contact. Figure 3 shows one’s general appearance in detail. It consists of two independent vibratory planes milled 90~ apart from a single bar of 4140
Fig. 3. rwisted cantilever
beam with ball-holder
and ball. Wear, 5 (1962) 378-391
Ii. G. BAYER,
380
W. (‘. CLINTON,
c‘. W. NELSON,
R. A. SCHUMACHER
steel hardened to RC30. The natural resonant frequency of each plane is approximately I80 cycles/set. Separate Wheatstone bridge circuits comprised of four strain gages each are cemented to each plane -two gages on the near face and two gages on the far face of each plane. With the Norton machine, electrical unbalance of the two bridge circuits is monitored by a Sanborn six-chamiel 350 recorder; whereas, two Brush BL-520 Universal Amplifiers are used with the Elgin machine. Test specimens
and their preparation
The wear and friction characteristics of 40 different metals were studied in sliding contact with 52100 high carbon steel balls, 302 stainless steel balls, and yellow brass
TABLE SPECIMEN
Steel stainless 302-A4 303-EZ 321 347 A ISI steels
wrought
DESIGNATION
I AND
SOURCE
Carpenter Allegheny Ludlum Allegheny Ludlum Allegheny Ludlum
410 410-1AC 416-EZ 440
Allegheny Ludlum Carpenter Allegheny Ludlum Carpenter
Raw stores IBM Raw stores IBM Wm. S. Hacker Precision Metals Wm. J. Hacker Raw stores IBM
4150 4620-A 5130 8214 8620 52100
Raw stores IBM Precision Metals Raw stores IBM Wm. J. Hacker Precision Metals Raw stores IBM
356 Special alloys Hymu 80AHycc
Precision Metals Precision Metals Precision Metals
43-774 112-184 195-2933
Alcoa Alcoa Alcoa
Carpenter Wm. J. Hacker
Wm. J. Hacker Carpenter
Hycc
Precision Metals
Ketos
Wm. J. Hacker
Invar 36
Carpenter
Rexaa Hampden Steel Oil Wear Carpenter No. I I Water Hardened Star Zenith Red Wear Nitralloy G
1018
Hardened 1055
1045
1060 1085 4140
Copper alloys &pro-nickel 30% Phosphor-bronze 8% grd. C Beryllium copper Aluminum alloys 220 355
Raw stores IBM Raw stores IBM Precision Metals
Carpenter Carpenter Copper Weld
balls. Table I lists the identification, source, composition, hardness, and other pertinent data for the platens. Table I also lists similar information for the balls. Platen preparation First, each platen was always reground before any experiment to remove any work-hardened material generated from prior experiments. After grinding to a V-r2 finish, they were polished successively with wet 350A, 4ooA, SOOA,and 6ooA “WetorWear, 5 (1962) 378-391
ENGINEERING
MODEL FOR WEAR
381
Dry” Tri-Mite silicon carbide paper. The RlU scratches produced by abrasion were perpendicular to the direction of sliding in the friction and wear machines. Then, the wet specimens were dried with CP acetone and immediately refluxed for 30 min in a CP benzene vapor chamber. After refluxing, they were mounted immediately in a friction and wear machine and an experiment was started. Ball preparation The 52100 steel balls and the 302 stainless steel balls were degreased six times in boiling CP benzene. They were then refluxed in a benzene vapor chamber for 30 min. After refluxing, they were immediately locked in a degreased ball-holder, which was mounted in a friction and wear machine, and an experiment was started. The commercial brass balls were also degreased six times in boiling benzene. After drying, they were abraded with wet 6ooA grid silicon carbide paper and dried with CP acetone. They were then refluxed for 30 min in a benzene vapor chamber. After refluxing, they were immediately locked in a degreased ball holder, which was mounted in a friction and wear machine; then an experiment was started. Early experiments were not reproducible with brass balls. It was found necessary to remove by abrasion the heavy oxide layer residing on the balls when purchased. This was not found to be true of the 52100 steel balls nor of the 302 stainless steel balls. The lubricants Four different lubricants were used in the experiments. Three of the lubricants are commercially available, and their designation and other pertinent data are shown TABLE PROPERTIES
Oil designation
TvPe
of
stock
Flask
@int
oJ5encull,
POW
pJint
(“F)
(“F)
435
--I5
II
OF LUBRICANTS
Gravity
Viscosity index
23.1
77
(A PII
Neutraliza&m no.
TY@ additive
of
Oxidation A
Napthenic
0.03
and tackiness Oxidation
B
Paraffin
40.5
20
33.0
105
0.05
and corrosion Oxidation-
Specific C
Paraffin
200
-75
20/20°c 0.859
188
0.20
V.I. improveranti-wear
in Table II. The viscosity-temperature characteristics of these three lubricantsare shown in Fig. 4. The fourth lubricant is oil “B” which has been doped with 0.2% of Eastman’s white label grade stearic acid. Wear, 5 (1962) 378-391
382
H. 1;. BAYER,
W. C’. CLIKTON,
1‘. W. NELSON,
Ii. A. SCHIJBIACHER
1
..,.,
1””
61”
TEMPERATURE, DEDREES FAH~E#HElT
Fig. 4. Kinematic
viscosity versus temperature for three lubricants.
Procedure Two types of experiments were performed with the three different balls and the forty different platens. The first type of experiment was withclean, dry test specimens. The second type of experiment was made with lubricated balls and platens. (I) Dry ex@eriments. First, the coefficient of friction was measured on the Norton machine for a single traverse of each kind of ball on each platen. The normal load was always 800 g and the sliding velocity was 0.005 cm/see. Second, photomicrographs were made of the scar on the ball and a portion of the track’ worn on the platen. Third, a trace of the wear track contour was made with a Talysurf** profilometer. The direction of travel was perpendicular to the direction of sliding. Occasionally, a profile trace of the ball was also made. (2) Lubricated experiments. These experiments were made at two different normal loads with each sliding combination. These normal loads were calculated from data pertaining to the elastic properties of the two metals in contact. Consequently, both loads calculated for a given sliding combination generally were different from those calculated for other sliding combinations. The test sequence followed was always identical at each of the two normal loads calculated for each pair of sliding metals. First, the clean, dry platen and ball were flooded with one of the four different lubricants and the coefficient of friction was measured in the Norton machine. A single * Total sliding distance was one cm for both the dry and lubricated experiments. ** Tradename, Taylor-Hobson, Inc. Wear, 5 (1962) 378-39x
ENGINEERING MODEL FOR WEAR
383
traverse was made at one of the calculated normal loads P and at a sliding velocity of 0.005 cm/set. Second, the platen and the ball, which remained securely locked in a ballholder, were transferred to the Elgin machine. In this machine, the platen was oscillated in sliding contact with the ball at a normal load equal to that applied previously in the Norton machine. After 2,000 traverses at the rate of 75 traverses/min, observations were made to determine the amount of debris generated and to detect any evidence of fretting corrosion. Third, the ball and platen were returned to the Norton machine, and the coefficient of friction was measured. A single traverse was made with the ball sliding in the wear track, which was worn on the platen by the ball during the 2,000 traverses on the Elgin machine. The normal load was equal to that applied when TRACK WIDTH
.I
Fig. 5. Diagram of wear track defining track width, VAVO,and
VPER.
making the first friction measurement, and the sliding velocity was 0.005 cm/set. Fourth, photomicrographs were made of the wear track on the platen and of the wear scar on the ball. Afterwards, a profile trace of the contour across the width of the wear track was made with a Talysurf profilometer. In some instances, a profile trace of the wear scar on the ball was made along the major axis of wear. MODEL
In the model for wear between two surfaces sliding relative to one another, it has been postulated that wear can occur in several ways. One type of wear is that which occurs when the material in the vicinity of the gross contact region is subjected to a stress system which causes plastic flow and results in some movement of material away from the contact region. This mechanism is called gross plowing. An example of this type of wear is given in Fig. 6. The same type of wear mechanism involved in gross plowing can occur on a local scale as a result of surface asperities. This type is called local plowing. Another way in which wear can occur is by transfer, or exchange of material between the two contacting surfaces (Fig. 7). Note that transfer can produce a change in the geometry, either on a gross scale (Fig. 7) or on a local scale. In either event, the stress system caused by the new geometry can produce plowing. The above mechanisms can produce debris. This debris can then produce an abrasive action, which is the final type of wear. If the abrasive action is caused by debris in oxide form, it is called fretting corrosion; otherwise, it is called fretting (Fig. 8). Wear, 5 (1962) 378-391
I-L G. HAYER, \I’. (‘. (‘I>lNTOS, C. XV. NELSON, R. A. SCHUMACHER
384
V I
\
,
Fig. 6. Top: Profilometer trace and photomicrograph of 52100 ball. Bottom: Profilometer trace with ball profile indicated and photomicrograph of 1055 platen. One pass: lubrication: dry; ty (platen) = 58 103 p.s.i.; ty (ball) := Ijo 103 p.s.i.; tmsx = 97.5 103p.s.i.
‘aJ ‘. .
I
\
I
\
I
/
I / I
Fig. 7. Top: Profilometer trace and photomicrograph of 52100 ball. Bottom: Profilometer trace with ball profile indicated and photomicrograph of 410 (A-L) platen. One pass; lubrication: dry; load: 800 g. Wear, 5 (I@)
378-391
ENGINEERING
MODEL
FOR WEAR
3%
The model states that wear can be reduced to a minimum, or eliminated, by keeping the stress in the vicinity of the region of contact below a certain value. This value is a function of the materials and lubricants used and the lifetime.
Fig. 8. Top: Photomicrogrqhs of gzroo ball and 303 EZ platen, respectively. Bottom: Profilometer trace with ball profile indicated of 303 EZ. 2,000 passes; Iubrication: oil “A”; q, (platen) = 63 . 101psi.; T* (ball) = ISO * 108psi.; r= 12.5 = IO* pa.i.
The maximum shear stress theory of failure states that, if the maximum shear stress occurring in a body is greater than the yield stress in shear, plastic flowing will occur. Consequently, to eliminate gross plowing, the following condition must be observed: ty > Zmex
(If
where tY is the yield point in shear of the weaker of the two materials in contact, and tmax is the maximum value of the shear stress experienced. This maximum value must be determined for each particular contact problem. For a large number of cases, the results of Hertz’s contact stress problem are applicable. Wear produced by transfer and local plowing can be eliminated for one pass by keeping the stress beIow a certain fraction of the yield point in shear; that is: zmax i cay, a < I
121
One pass is defined as that relative displacement sufficient to just unload the original contact region.
#G
I<. (;. JMYEK,
1s’. (‘. CLINTOX,
(‘. \\:. NELSON,
Ii. A. SCHUMACHER
LiTear produced by transfer, local plowing, fretting corrosion, and fretting can be eliminated for a given number of passes by keeping the stress below a fraction of the yield point in shear, or :
Tmax< pt!/, p < x
(3)
011 the basis of existing information, the present model for wear also postulates that for wear less than or equal to the surface roughness, the wear is the same for two sets of conditions of stress and number of passes as predicted by the following equation : )9Nz, (Tm*)~N1 = (TlmXZ
zooo<
A’,
rr6,ooo
(4)
where tmaxl and Nr are the values of t maxand the number of passes for one set of conditions, respectively, and t maxZand Nz are the values for the other set of conditions. This equation is a modified form of Palmgren’s equation* for ball bearings, relating load to lifetime. ANALYSIS
The model for wear was verified by correlating the maximum shear stress in the vicinity of the contact region with the amount of wear produced on the platen. Qualitative examination of the ball for wear was also considered. Note that the ball experiences many more passes than the platen in any given experiment. This occurs because the diameter of the circle of contact is much smaller than the length of the track, that is, the overall sliding distance. In this paper, the number of passes is always specified with respect to the platen. As stated when describing the experimental procedures, the wear in these tests was measured by means of a profilometer trace across the wear track on the platen. The cross-sectional area of the wear scar was used as a measure of wear. Two areas were measured. The first, VAVG, is the average area appearing underneath the width of the track. (The width was determined by means of photomicrographs.) The second, VPER, is the sum of the perturbations on the average area. These two areas are shown in Fig. 5. When the track could not be distinguished from the surface roughness, there was said to be zero wear, that is, VAVG= o and V~EH.= O. The contact stress problem between a sphere and a plane pressed together by a normal load is covered by the Hertz contact problem. If sliding is introduced into the Hertz contact stress problem, it is found that the two possible maximum shear stresses occurring for the sphere-plane geometry are :
where ~1is the coefficient of friction, v is Poisson’s ratio, and QO is the maximum contact pressure as defined in the Hertz problem (eqn. (6)). Also, && occurs on the surface of the contact, and tdmzxoccurs at a certain distance underneath the surface of contact. These two expressions involve two additional assumptions beyond those *Palmgren’s equation for roller bearings is P13N1 = P23Nz where the P’s are the loads and the N’sthe life time. For roller bearings P is proportional Therefore in terms of stress, the equation is t19N1 = tzQN*
to x3.
Wear, j (1902) 378-391
ENGINEERING
MODEL
FOR
WEAR
387
contained in the original Hertz contact problem. One is that the local coefficient of friction is equal to the coefficient of friction as measured. The second is that the effect of the frictional force on the &ear underneath the surface can be ignored. This assumption is based on the results of a crude analysis which indicates that, when the coefficient of friction becomes large enough to influence the shear underneath the surface, the maximum shear occurs on the surfaces. Since only the maximum shear is of interest, eqn. (5) is satisfactory. The maximum contact pressure 40 for the sphere-plane geometry is: 6P $74 =
I ~I__
VI?
113
$_ I ___
v23 ES
El
= Rz I
(6) 1
where P is the normal load, R is the radius of the sphere; ~1 and El are Poisson’s ratio and Young’s modulus, respectively, for the material of the sphere ; and uz and EZZare those for the material of the plane. Note that the model does not solely apply to Hertz contact problems, but rather to any problem for which a value of the stress occurring can be determined. For the particular geometry used in the tests, the Hertz contact problem was applicable. The analysis of the wear scar on the platen in terms of wear mechanisms was performed by comparing and considering several things. The profile of the scar was compared to a ball profile. Depending on the fit, one or more wear mechanisms could be postulated to have occurred (Fig. 6-8). Optical examination of the scar then gave additional information concerning the type of wear occurring. This was particularly helpful in determining if fretting or fretting corrosion had occurred. Information could also be obtained on transfer and local plowing- Finally, an examination of the friction trace would aid in the identification of transfers. This technique for identification was found to be excellent in determining the major types of wear occurring in a particular experiment, In several cases, the conclusion reached by such an analysis was confirmed by additional examination. Figures 6 and 7 show the results of such a confirmation. The scar shown in Fig. 6 was determined to be caused by gross plowingt and that in Fig. 7s by transfer and plowing. The Talysurf profilometer traces of the ball in both cases confirm these conclusions. The elimination of wear by reducing the stress to below a certain value was demonstrated in the following manner. For several different combinations of lubricant and material, an average value of cxwas determined experimentally. #lwas determined for 2,000 passes. Then, by using the yield point in shear of the weaker of the two materials involved in a given test and using the above values of CTand /3,allowable maximum shear stresses were computed. Then, the corresponding loads were determined by using eqns. (5) and (6). The wear produced after 2,000 passes for each combination of lubricant and materials was measured and identified. Equation (4) and the interpretation were verified by experiments for 12 different combinations of materials. Equation (4) was used to predict the stress required to produce the same wear at z16,ooo passes that was produced at 2,000 passes. RESULTS
Table III lists the results of a representative
portion of approximately
1,200
tests.
% I+
%?
5 $
p _(n
1018 1018
52100 52100 52100
33 33 33
7 show that wear can be eliminated 1018 52100 33
Lines 8 through 33 show that wear can be eliminated 8 8620 302 40 8620 302 40 9 IO 8620 302 40 8620 II 302 40 8620 I2 302 40 8620 302 I3 40 52100 50 I4 347 52100 50 347 I5 52100 16 50 347 52100 50 I7 347 gzroo 18 50 347 52100 I9 50 347 Brass 58 IO55 Brass “2’: 58 IO55 Brass 22 55 IO55 Brass 55 IO55 Brass 55 IO55 23 24 Brass 55 IO55 25 112 Alum 26 52100 I5 52~00 112 Alum I5 28 27 52100 112 Alum I5 52100 II2 Alum 29 15 106 30 302 ‘045 106 302 IO45 3’ 82.5 414oLL 302 32 82.5 4140LL 33 302
2 7
Lines 4 through 4
III
dry dry dry
ON STRESS
132.8 77.3 60.2
58 55 55 58 55 58 I50 I50 I5o 150 I50 I50 17.9 17.9 17.9 17.9 17.9 17.9 150 I50 I5o 150 55 55 58 55
for 2,000
I5o 150 I50
B B
31.4 25.4 17.8
0 0
0
14.8 0 0
passes when tmax is reduced to j?rfy (eqn. (3)) B .21.45 10.6 2,000 7.9; B 0 2,000 A 0 2,000 21.45 A 0 2,000 7.91 C 2,000 21.45 7.6 C 0 2,000 7.91 B 26.81 2,000 2.4 0 B 9.88 2,000 A 1.0 26.81 2,000 0 A 9.88 2,000 C 26.81 2,000 4.0 C 9.88 0 2,000 0 B 9.66 2,000 5.28 0 B 2,000 A 9.66 0 2,000 0 A 5.28 2,000 0 c 9.66 2,000 0 C 5.28 2,000 B 8.04 2,000 5.2 2.96 0 B 2,000 A 8.04 2,000 7.6 0 A 2.96 2,000 31.10 B 2,000 3.0 11.46 0 2,000 B C 31.10 2.8 2,000 0 C 11.46 2,000
I I
for one pass when the rmSx is reduced to LX~‘~ (eqn. (2)) I50 I B 32.0
(eqn. (I)) I I I
OF WEAR
TABLE
Lines I through 3 show that wear is produced when rmax exceeds t’# I 321 52100 40 150 2 IO45 52100 106 I50 3 IO55 Brass 55 17.9
DEPENDENCY
0.3 0 0 0 0.6 0 2.6 0 2.2 0 0 0 0.36 0
0 0 2.8 0 2.6 0 0.12 0 0 0 0.8 0
0.35 0.30 0
0.50
5.26 0 1.80
0.54 0.20
o-54 0.20
0.54 0.20
0.54 0.20
0.54 0.23
0.54 0.23
0.54 0.23
0.54 0.20
0.54 0.20
0.54 0.20
0.54 0.20
0.54 0.20
0.54 0.20
0.97 0.95 0.77 0.54
3.34 0.73 3.36
4’50 4x50 4’50 4150 4150 4’50 302 302
65 65 58
58
Brass Brass
52 100
302 58
150
17.9 17.9
58
58
58 58 150 I50 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000 2,000
B B B B B B
B C C B B+St.a.* B B A B B B B B B B B
17.79 10.58 21.45 7.91 4.71
49.86
31.1 31.1 11.46 14.48 ‘4.48 9.65 3.56 9.65 34.85 12.85 31.10 11.46 9.66 5.28 11.46 11.46
7.6 0 0 2.0 0 0
0 20.0 0 7.6 0 6.0 0 0 15.0 0 0 0 0 0 5.0 0
1.76 0 0 3.0 0 0
2.6 0 0 0 0.5 0 0.4 0
0
0.2 0 0.6 0
0
0
0
0.54 0.54 0.20 0.54 0.54 0.54 0.20 0.54 0.54 0.20 0.54 0.20 0.54 0.23 0.20 0.20
of the two yield points in shear. occurring in the text (Fig. 5.) zero for one pass or to p if V A”G and VPER equal zero after either 2,000 or 216,000 passes. (eqns.
of /l on the number of passes (eqn. (4)) 90 I50 2,000 90 I50 2,000 90 I50 216,000 40 150 2,000 40 I5O 2,000 40 I50 216,000
65
302
the dependency G 52100 G 52Ioo G 52100 52100 52100 52100
65
302
52100 52100
18 18 65 65
of B on materials and lubricants. 63 58 2,000 63 58 2,000 63 58 2,000 27 58 2,000 27 58 2,000 18 58 2,000
* ty is the yield point in shear; rly is the smaller b tmax is the maximum value of the shear stress c VavG and Vp~a are indices of wear as defined fl tm&‘u is equal to oc if VAVC and VPEB equal (3) and (4)) * Stearic acid
Lines 50 through 55 show 50 Nitralloy 51 Nitralloy 52 Nitralloy 53 Monel C 54 Monel C 55 Monel C
42 43 44 45 46 47 48 49
Lines 34 through 49 show the dependency 34 303 302 35 303 302 36 303 302 37 Phos. Bronze 302 38 Phos. Bronze 302 39 220 Alum 302 40 220 Alum 302 4= 220 Alum 302
E
8
g
390
Ii. G. BAYER, IV. (‘. (‘LIN’W?\‘, C. W. NELSON, R. A. SCHUMACHER
In general, all the tests performed agreed with the model proposed. These results were obtained for the following surface roughnesses (peak to peak) 5 to 15 $4. for steels; IO to 35 pin. for aluminums; and 5 to 40 pin. for the remaining materials. The data obtained for one pass under dry conditions and a load of 800 g showed, in general, that, whenever the yield point in shear was exceeded, wear occurred (rows I through 3, Table III). In these runs, the occurrence of plowing and/or transfer, especially on a large scale, could usually be identified quite easily (Figs. 6 and 7). It was found that, in general, the platen material transferred to the 302 stainless ball under these conditions. In the brass series, it was found that the brass transferred to the platen. In the case of the szroo steel balls, transfer did occur, but not as frequently as in the other cases. The value of LXwas found for lubricated conditions to be 0.54, and appears to be independent of lubricant and materials (rows 4 through 7, Table III). Since, under lubricated conditions, the amount of transfer occurring in one pass is quite small, 01 may be interpreted as a mechanical factor, x/a being analogous to a stress concentration factor. Rows 8 through 4g of Table III show a typical series of experimental results. It was found that @ varied between 0.54 and 0.~0. The data indicated that B was a function of the materials and lubricants used (rows 34 to 49, Table III). There appeared to be no correlation with viscosity. However, if oil “B” was doped with 0.20/h stearic acid, the value of sy rose from 0.20 to 0.34 in most cases (rows 37 and 38). It is felt that the variation of /? is the result of variation in the tendency for various combinations of materials to form debris. Because of the behavior of p with the doped oil, transfer is considered to be a major c~)ntributor in the formation of debris.
Fig. 9, Top: Profilometer trace and photomicrograph, respectively, of Monel C platen after z,ooo passes, rmax= 7.91 ros psi. Bottom: After 216,000 passes, t ,,,sx= 4.71 103p.s.;., 52100 ball; lubrication: oil “B”. Wear, 5 (1962) 378-391
ENGlNEERING
MODEL FOR WEAR
39*
Consequently, ,!I is considered to be mainly a function of the ability of the oil to prevent transfer from occurring. In approximately 90% of the cases tested, it was found that a suitable value for fi was either 0.20 or 0.54,0.54 being the value of !X determined in the tests. All of the 12 experiments performed to verify eqn. (4) reproduced the wear conditions obtained for 2,000 passes. The results of two of these tests are given in rows 50 to 55, Table III (Fig. 9 also)*. Qualitatively, in most cases, there was little or no wear on the balls when wear was eliminated on the platen, except in the case of the brass balls. However, because of the limits of the experimental equipment, the brass balls could not be run at the low load specified by /I = 0.20 (rows rg through 25). Therefore, some wear on the brass ball should be anticipated. The authors believe that this model correlates wear quite satisfactorily with load, geometry, materials, and lubricants in such a way that the results of simple wear tests may be applied satisfactorily to other geometries, materials, and loads not specifically tested. Further, it has been demonstrated that wear can be eliminated by keeping the stress under a certain value, &,, where p is a function of the materials and lubricants used and the lifetime. ACKNOWLEDGEMENTS
The authors thank Dr. C. W. MACGREGOR for his interest, guidance, and encouragement in this work. They also thank Mr. J, E. BROPHY for indicating this problem and for suggesting how to treat it. Their appreciation is due to Dr. T. C. Ku for his stimulating discussions on this work. Special appreciation is also due to Miss BETTY DEYO, J. 2. DEVINE, and J. L. SIRICO for their help in obtaining and compiling the data. The authors also thank the following companies for supplying them with samples: Allegheny Ludlum Steel Corporation, Aluminum Company of America, Carpenter Steel Company, Copperweld Steel Company, Precision Metals Company, and William J. Hacker and Company, Inc. REFERENCES F. P. BOWDEN AND D. TABOR, The Friction and Lubrication of Solids,OxfordUniversityPress, 19508 pp. 73-75. M.C. SHAW AND E.F. MACKS, Analysis and Lubrication of Bearings, McGraw-Hill Book Co., New York, 1949, p. 411. See ref. r, pp. 78-82. * A few test results not covered by this paper show that the experimentally determined constant wear line for a specific small amount of wear, when plotted in a log-log graph of tmsa versus N, is not exactly the straight line indicated by eqn. (4). These test results indicate that eqn. (4) is too safe for N greater than 216,000. The experimental constant-wear curve departs radically upward from the line given by eqn. (4) in their range of N. wear, 5 (1962) 37g-39r