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Extension of the engineering model for wear to plastics, sintered metals, and platings
WEAR
3.54
EXTENSION
OF THE ENGINEERING SINTERED W. C. CLINTON, International (Received
MODEL FOR WEAR
TO PLASTICS,
METALS, AND PLATINGS T. C. KU
AND
R. A. SCHUMACHER
Business Machines Corp., Endicott, N.Y. (U.S.A.) August 20, 1965; revised December
IO,
1965)
SUMMARY The engineering model for wear developed previously for metals’ has been found to be applicable to different plastics, sintered metals and plating% The results of 137 tests for various combinations of sliding materials, with and without lubricants, have shown that wear can be prevented for a given number of cycles if the maximum shear stress is kept below a certain fraction of the yield point in shear of the weaker of the two materials. This fraction is equal to 0.5 for all the plastic-metal combinations that have been investigated under dry and boundary lubricated conditions. However, with respect to the sintered metals and the plated surfaces, this fraction is equal to either 0.5 or 0.2 depending upon the composition of each of the sliding materials as well as the type of lubricant used. INTRODUCTION
The engineering model for wear correlating shear stress with wear has been extended to include metals sliding in contact with plastics, sintered metals, and platings. It is the purpose of this paper to present the new experimental results and to show the correlation of shear stress with wear which was obtained in a study of 31 different combinations of these materials sliding against each other. In order to avoid unnecessary repetition, some familiarity with the earlier paper1 is assumed. An attempt is made in this paper to amplify some of the ideas and concepts postulated previously. A new procedure is described which is used to determine the yield point in shear of the plated surfaces. EXPERIMENTAL
METHODS
The experimental approach was similar to that reported earlier1 in that the geometry involved was a sphere sliding on a plane. Also, the conditions considered were for both dry and boundary lubricated sliding surfaces. The experiments were made for a specific number of passes (N) or (N’) and at different normal loads for each sliding combination. The loads were calculated with the use of the model described by BAYER, et al.1 Apparatus
The friction and wear machine used in the experiments is the same as previously described1 and is built around an Elgin miniature milling machine. The characteristics of this machine and the instrumentation for measuring the normal load and the frictional force have been described in detailr. Wear, 7 (1964) 354-367
ENGINEERING
MODEL FOR WEAR
35.5
Test specimens
Table I lists the compositions of the sliders, the balls, and the platens used in the experiments with each of five different sliding combinations. The plastic platens are identified by both trade name and composition. The sintered metals are identified numerically and by density. The platings are identified numerically and by plating composition. The substrates of four of the plated surfaces are beryllium on which is plated in succession layers of copper, nickel, and chromium. Each plating has been plated at different experimental conditions. The thickness of each plated layer is approximately the same for all four specimens with chromium always the thinnest and copper the thickest. The two specimens with nickel-cobalt plated surfaces differ in their surface structure and hardness. The lubricants
The same three lubricants that were employed in the experiments reported earlier’ were used. These lubricants were flooded on the solid bulk specimens, i.e. plastics and AISI steels. A vacuum pump was used to infiltrate the sintered metals with the respective oils. Platen preparation
Each plastic platen was ground to a V-12 finish and polished successively with wet 350A, 4ooA, 3ooA, and 6ooA silicon carbide paper. Each was dried and stored in a desiccator over anhydrous CaCL. The surfaces of each sintered metal platen were ground to a V-12 finish and then electrolytically etched to expose the porosity. With the use of a vacuum pump, the interstices were infiltrated with distilled water and then with CP acetone. After the acetone was removed by vacuum, the interstices were degreased ten times by the infiltration of fresh, boiling benzene. Afterwards, all traces of benzene were removed by vacuum. For the dry experiments, the sintered metals were then polished successively with the same grades of water-wet silicon carbide paper used with the plastics. For the lubricated experiments, the metals were infiltrated with a given lubricant and then polished with the successive grades of silicon carbide paper wet with the given lubricant. The four AISI metal platens were ground to a V-12 finish and then polished wet with the same successive grades of grit used to polish the plastic platens. After polishing, they were dried with CP acetone and immediately refluxed for 30 min in a CP benzene vapor chamber. The plated specimens were not polished but they were washed with a degreasing detergent, dried with CP acetone, and then refluxed with boiling benzene. Slider and ball fireparation
The Type 302 stainless steel sliders were given a V-32 machine finish and then polished with wet 6ooA silicon carbide paper. After they were dried with CP acetone, they were degreased for 30 min in a boiling benzene vapor chamber. Wear,7
(1964) 354-367
356
w.
c.
CLINTON,
EXPERIMENTAL 302
Stainless steel hemispherical
et al.
MATERIALS
sliders of 2 in. radius sliding on selected plastic platens
Plastic platen designation
Platen composition and identification Molybdenum disulphide-filled nylon FM-10001 Graphite-filled nylon FM-rooor Nylon resin Acetal resin - polymerized formaldehyde Polymerized styrene plastic Tetrafluoroethylene resin Low density - sp. gr. 0.913 Medium density - sp. gr. 0.926 High density - sp. gr. 0.941
Nylatron GS* Nylatron G* Zytel Ior** Delrin 5oo* * Polystyrene Teflon* * Polyethylene I Polyethylene 2 Polyethylene 3
* Registered Trademark, The Polymer Corp., Reading, Pa. ** Registered Trademark, E.I. duPont deNemours & Co. Inc., Wilmington,
Delaware
52100 High carbon steel balls of 114 in. radius sliding on selected sintered metal platens Platen density and composition
Sintered metal platen designation Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered
(glcms)
bronze I bronze 2 brass I brass 2 steel I steel z steel 3 iron-copper iron-copper iron I iron z iron 3
6.4-6.8 - ASTM Bzoz-SST - type II class A 7.0 Min - ASTM B255-61T - type II 7.5 Min - proprietary 7.0-7.5 - proprietary 7.0 Min - stainless AISI type 316L 7.0 Min - proprietary 6.0-6.5 - proprietary 7.1 copper infiltrated 15% 5.8-6.2 high copper - 20% 7.5 Min - proprietary 7.3 Min - proprietary 7.0 Min - proprietary
I 2
Sintered bronze I hemispherical
sliders of 2 in. radius sliding on selected A ISI
Solid metal platen designation
Platen specification
1117 Steel 4140 Steel 8620 Steel
AISI AISI .USI
Sintered steel I hemispherical
slider of 114 in. radius sliding on a selected AISI
Solid metal platen designation 4140
52100
solid steel platens
solid steel platen
Platen specification AISI
Steel
High carbon steel balls of 114 in. radius sliding on selected plated platens
Platen plating designation Chromium plating I Chromium plating 2 Chromium plating 3 Chromium plating 4 Nickel-cobalt plating I Nickel-cobalt plating z
Substrate composition Beryllium Beryllium Beryllium Beryllium Aluminum Brass
1st layer plating Copper Copper Copper Copper None None
2nd layer plating Nickel Nickel Nickel Nickel None None
3rd layer surface plating Chromium Chromium Chromium Chromium Nickel-cobalt Nickel-cobalt
Wear,
7
(1964) 354-367
ENGINEERINGMODEL FOR WEAR
357
The Type 52100 steel balls were washed six times in boiling benzene and then degreased for 30 min in a boiling benzene vapor chamber. The two different sintered metal sliders were prepared in a manner identical with that described for the sintered metal platens. Procedure Two different types of experiments were made in this study. The first type was made with dry, clean surfaces and the second type was made with lubricated surfaces. The first type of experiments were made with all of the platens listed in Table I except the four AISI steel platens. The exceptions were studied only with their surfaces flooded with lubricant B as used by BAYER, et al. Experiments of the second type were made with all of the platens except the six plated platens. These exceptions were studied only with dry, clean surfaces. In the earlier report’ all experiments were made with a 1/4 in.-radius ball. In this report, the experiments with the sintered metal platens and the plated platens were also made with 1/4 in.-radius balls, but the experiments with all other platens were made with sliders which had a 2 in. radius. The values of the yield point in shear, zy, for the plastics and the sintered metals were measured experimentally by conventional methods. The point at which the shear stress-strain curve begins to deviate from a straight line was used as the yield point. The values of tV for the plated surfaces were measured with a Reichert microhardness tester. This instrument was used to measure the variation of hardness with the depth of penetration into the plating. By applying a different small load each time, the average hardness R was obtained up to a depth of penetration, x. The hardness H(x) at any given depth x can be obtained from H(x)
=
E +
(1)
x g
This is illustrated in Figs. I and 2 for the different values of H(x) thus obtained
o!
0
platings. By comparing the with the hardness values measured at comparable small
. . .
I..
fO0
x, DEPTH INTO PLATING,
I,
200
‘,
,I
300
p in.
Fig. I. Microhardness vs. depth of penetration into platings on solid surfaces. 0, Plating plating 2 ; 0, plating 3; A, plating 4.
I ; +,
Wear, 7 (19% 354-367
358
loads (this is to minimize the effect of the variation of the index n, therefore the hardness, with loadz) for the identical or very similar solid metals and alloys for which the values of rV are known, the variation of ry with the depth of penetration into these platings can be determined. The value of ty estimated at the surface of each plating was used for the experiments because the maximum shear stress occurs at the surface of the platings studied in this report. For more general considerations the above criteria, eqns. (I), (a), and (3) given in the earlier paperr, have to be satisfied at the surface and at any point below the surface. In this report it is convenient to designate the yield point of the weaker sliding material as zy’ and that of the stronger as zy”. It was experimentally determined for metals1 that (x = 0.54 for one pass and ,6 was either equal to 0.54 or 0.20 for 2000 passes (N) dependent upon whether or not transfer occurred. For any sliding geometry, one pass is defined as that distance of sliding equal to the dimensions of the contact area, S, measured in the direction of sliding. With the geometry used in this report the value of S is equal to the diameter of the circular area of contact. This is illustrated in Fig. 3. It shows the position of the slider after it has experienced one pass. In addition, it shows that the slider will
Fig. 2. Microhardness US. depth of penetration into platings on solid surfaces. -0--, Nickelcobalt plating, z-brass substrate; -+-,
nickel-cobalt plating, r-aluminium substrate.
Fig. 3. Position of the slider after it has experienced one pass; also shown is the number of passes (N’) made by the slider for one sliding
length (I) or cne pass (,V) on the platen.
experience five passes after sliding a distance I on the platen. The engineering wear model specifies the number of passes with respect to the distance 1 on the platen so that in the illustration one pass on the platen is equal to the distance 1 and it is equivalent to five passes on the slider. This equivalence can be expressed as
where N’ is the number of passes experienced by the slider, and N is the number of passes made on the platen or the sum of the number of times the slider moves backwards and the number of times it moves forwards. In this report, the yield point in shear of the weaker of the two materials involved in a given test was used with the above values of 01 and /l to compute the maximum allowable shear stresses. With the maximum allowable shear stress and using eqns. (5) and (6) from the previous paperi, the corresponding load for a given test was determined. In order U’ew, 7 (1964) 354-367
ENGINEERING MODEL FOR WEAR
359
to verify the validity of the factors 01 and /? additional test loads were detemrined for cases where the maximum shear stress exceeded the allowable shear stress. The wear produced after 2000 passes (N) was measured and identified for each combination of lubricant and material. The experimental sequence followed was identical for all but two tests. First, the ball or the slider was securely locked in a ball holder mounted on the friction and wear apparatus. Second, the platen was oscillated in sliding contact with the ball at a predetermined normal load for 2000 passes (N). Coefficient of friction measurements were made during the first pass and the 2000th pass. Third, photomicrographs were made of the wear track on the platen and of the wear scar on the ball. Afterwards, a Talysurf profile trace was made across the width of the wear track on the platen and along the major axis of wear on the ball. RESULTS
The cross-sectional area of the wear scar on the platen as obtained from a Talysurf trace was used as a measure of wear. Two areas were measured. V,, was the average area appearing underneath the width of the track and Vper was the sum of the perturbations on the average area. A diagram illustrating these two areas was shown in Fig. 5 of the paper by BAYER, et al. 1. When the track was not distinguishable from the surface roughness, there was said to be zero wear, that is V,, = o and Vper = o. Disturbance on the surface up to the magnitude of the surface roughness can occur when Vavg = Vper = o. 302 Stainless steel sliding on selected plastics The amount of wear measured on Nylatron GS after 2000 passes (N) at different stress levels by a 302 stainless steel slider of 2 in. radius is shown in Fig. 4. It shows
g. &
BO-
-16
70-
-14
60-
-1.2
50.
-10 Q. 6s -8 ‘g
40.
.
‘? JO-
-6
6 A! zo-
-4
JO-
-2
% +
o%o a55 a60 a65 a70 0.75 Q~Y) a85 a90 ‘Gclx/q~ 4. The amount of wear expressed as V,. and VW, vs. different ratios of tmsx/ly’. These were obtained with 302 stainless steel sliding for zooo passes (N) on dry Nylatron GS. TV’ = 1.14 + IO* lb/in.* for this plastic. - a-, V.,, ;- IJ--, VP,,. Wear3 7 (1964) 354-367
w. c. CLIN’TQN,et al
360
the amount af wear (I’,,, and Wper)vs. different values of zma.& for the plastic. It is s~g~ifieaut that the value of amrxj.ty’ is o-54 for Nylatron GS when V,, and Pper are equd to zero because this value is identical to that found at Zero wear for each of the other plastics listed in Table 1. This is illustrated in Fig. 5 where the value of tmlLxat zero wear for each plastic is plotted against their respective yield
points, tU’” It is also significant that the value of tfllax/ty‘ at zero wear is still 0.54 for each plastic lubricated in turn with the three test lubricants. A graph illustrating this is not shown because it is identical to Fig. 5. gzroo
Sted ball sliding on mkcted sin&red metal
The experimental sequence followed in this study was identical to that followed in the study of the plastics. The. amomt of wear was measured for different stress Ieveis on each sir&red x&al @atm after moo passes (I%? by a ~~IW bafl af r/s in. radius. %easurements were made on dry surfaces and on m-faces lubricated in turn with the three test lubricants. For brevity, curves showing the decrease in the amount of wear with the decrease in stress level are not presented. Instead, the value of rmaxat zero wear for each dry surface is shown in Fig. 6 plotted against the respective: yield point, -cg’ of each sintered metaf. &ASidentical pi is shcw-n in Fig. 7 for each lubricated surface. The type of lubricant used is indicated with convenient symbols. Sintered bmme-r
sliding on; three diffemnt AISX steel piatelzs
The emphasis in this experiment was on the prevention of wear on the slider when it experienced 2ooo passes (Wj and when its yield point in shear was either less than, equal to, or greater than the yield p&&s of three ~ff~r~~t AIS steel @atens. The sintered bronze-x sli&rs were impregnated with lubricant I31 and the platens were floo&d with the lubricant. Identical tests were made at two different maximum shear stresses with each of the three AISI platens listed in Table I. The experimental
ENGINEERING MODEL FOR WEAR conditions
as well as the results obtained
data in Table because
II. The significance
a running
account
361
can best be explained
of this data is considered
would be identical
by referring to the
only for AISI
steel 1117
for the other two steels.
22
IRON-COPPER-I
dgsTEEL_,
20 /
l8 /6
0
IO
20 r;
40
30
IO
Fig. 6. Experimentally determined values of rmax at zero wear vs. measured values of ty’ for different sintered metals. These metals were in dry sliding contact with 52100 steel for zoo0 passes (N).
Column r
BRONZE-I
Column
a
40
50
Fig. 7. Experimentally determined values of rmax at zero wear vs. measured values of ty’ for different lubricated sintered metals. These metals were in sliding contact with 52100 steel for 2000 passes (N) . - 0 - , lubricant A ; - 0 - , lubricant B; - A - , lubricant C.
TABLE SINTERED
30
20
* IO 31b/n.2
SLIDING
FOR 2000
Column
3
PASSES
(N’)
Column 4
II ON THREE
Column 5
AISI
DIFFERENT
Column 6
METAL
Column 7
PLATENS
Column
Platen AISI no. 1117 4’40 g620
*ti (roYb/in.z) 27 32
40
Number of #asses on platen (N)
tmax (Cblin.2 .
rmsx
108) 7ty
tmax
7 tll
(k2
V BVIl V Per . ro-0) (in.z.10
100 40
17.3 6.4
0.64 0.24
0.54 0.20
-IO
IO0 40
‘7.3 6.4
0.54 0.20
0.54 0.20
-2
100 40
17.3 6.4
0.54 0.20
0.43 0.16
-II
0
0.2 0 0
0 0
0 0.5
0
ry for sintered bronze-r is 32 . 10s lb/in.8 ry’ is the lower value of the two yield points rv” is the higher value of the two yield points Wear, 7 (1964) 354-367
W. C. CLmToN, et al.
362
With AISI steel 1117 (column I) wear occurs on the slider in the form of transferred material or “build-up” on the platen when the maximum shear stress, rmax, is 17.3 * 103 lb/in.2 (column 4). The amount of wear measured is shown in columns 7 and 8 where VIBVg= - IO . IO-* in.2 and Vper = 0.2 . 10-8 in.2. It is convenient to indicate “build-up” with a negative sign preceding the numerical value of the area measured. This amount of wear occurs when the ratio of zmrtX/ry”for the slider is 0.54 (column 6) and the ratio of rmax/ry’ for the platen is 0.64 (column 5). It is important to note that although the wear measurements were made after the slider had moved backwards and forwards over the same path for a combined total of only IOO times (column 3), the number of passes (N’) experienced by the slider is 2000 (eqn. (2)). In order to reduce the amount of wear to zero (see the second row of columns 7 and 8) it is necessary to reduce the ratio of r max/rty”for the slider to 0.20 (column 6). This automatically reduces tmax (column 4) to 6.4 . 103 lb/in.2 and the ratio rmax/ty’ for the platen to 0.24 (column 5). At the reduced stress of 6.4 . 103 lb/in.2 the diameter of the area of contact with a 2 in. radius slider is much smaller so that the slider has now only to move backwards and forwards over the same path for a combined total of 40 times (column 3) in order for the slider to experience 2000 passes (N’). A similar commentary can be made of the results shown for AISI steel 4140 which has a yield point equal to that of the slider. It will be observed that zero wear occurs when the ratios in columns 5 and 6 are both reduced from 0.54 to 0.20. In the case of AISI steel 8620 which has a yield point greater than the slider, zero wear occurs when tmax/ty’ for the slider (column 5) is reduced from 0.54 to 0.20. Sintered steel-r .&ding on AISI
steel 4140
The emphasis in this study was on the prevention of wear on the slider when it experienced more than ooodpasses (N’). The hemispherically ended sliders of 2 in. radius were impregnated with lubricant Bl and the AK1 steel platens were flooded with the same lubricant. Nine separate experiments were made at each of the listed ratios (Table III) of tmax/ty” and for a specified number of passes (N’) to be experienced by the slider. TABLE III Experiment number
Experimental parameters Tmax
I7y
I
2
0.22
0.30
I,
No.ofpasses.104(W)
so
39
3
4
5
6
7
'8
0.36
0.37
0.38
0.47
0.47
0.50
36
3
3'
6
7
3
9 0.54 0.2
A Talysurf trace across the sliding path on the platen and across the contact area on the slider showed that no wear occurred for experiments number I, 2, 4, and g (Table III). However, wear did occur for all other experiments in the form of either “build-up” on the platen, or of a measurable groove on the platen, or of material removed from the contact area on the slider. The two parameters used for each of the nine experiments are plotted against each Wear, 7 (1964) 354-307
ENGINEERING
MODEL
363
FOR WEAR
other in Fig. 8. The significance of this graph is discussed later with respect to the solid line drawn from the point at which rmaxJ’rti” equals 0.54 to the point at which it equals 0.30. 52100 Steel ball sliding on dry elated surfaces The results obtained with nickel-cobalt plating are shown in Fig. 9. In this graph the amount of wear (I’,,) measured after 2000 passes (N) on the plating by a 5~100 steel ball is plotted against the different ratios of tmtsxfry’ used in the experiment. It shows that V,, = o when rmax/ryf = 0.21. An identical type of plot is shown in Fig. IO for nickel-cobalt plating 2. It shows that V,,, = o when tmax/ty’ = 0.51. Similar curves were made with the results obtained for the four chromium plated surfaces. Each of these curves showed that Vavg = o when rmax/ry’ = 0.20.
36 m0-l 80-
l
jz
NICKEL - COBALT PLATING
28
I /
60504030 zo-
IO8-
Fig. 9. The amount of wear expressed as
Vav, vs. different ratios of tmar/‘tv’. These data were obtained with 52 IOOsteel sliding for zooo passes (N) on dry nickel-cobalt plating I. t*’ = 15 . IO* lb/in.2 for this plating. l.6,,4_
a.?-
NN;‘XEL-COEAiTP2
9Q4LQQ2 I
al
1
I
QZ Q3 Q4Q5Q6Q8 / G%9x*/Tyu
Fig. 8. The number of passes (N’) experienced by sintered steel I sliding on AISI steel 4140 vs. different ratios of rms./ry” for sintered steel I.
f
0.50
0.52
Q54
0.56
Q58
0.60
GUXB-; Fig. IO. The amount of wear expressed as V svg vs. different ratios of rma&‘. These data were obtained with 3~100 steel sliding for 2000 passes (N) on dry nickel -cobalt plating 2. tu’ = 26. roalb/in.2 for this plating. Wear. 7 (1964) 354-367
364
W. c. CLINTOX, et d. DISCUSSION
The engineering model for wear1 describes three types of wear: gross plowing, local plowing, and fretting or fretting corrosion. These are depicted by Figs. 6, 7, and 8 in the previous paperl, respectively. In the Talysurf trace of a wear track on a platen (Fig. 6 of the previous paper), the area into which a ball profile fits is the result of gross plowing. It is generally agreed that gross plowing which results from the movement of the material (due to plastic flow) away from the gross-contact region can be eliminated for one pass if tmar < ZY
(3)
The same type of wear mechanism involved in gross plowing can occur on a local scale as a result of surface asperities or roughness, and of transferred material (Fig. 7 of the previous paperi). While gross plowing can be related to the plastic flow of metal on an analytical basis, it has been experimentally determined for the case of metals that local plowing can be eliminated for one pass if tmax< atu
(4)
In the present investigation eqn. (4) has been confirmed for plastics, sintered metals, and platings. The value of 01 for all these materials is approximately equal to 0.5. When wear is caused by the abrasive action of debris, it is called fretting. If the debris is of an oxide form, it is called fretting corrosion. For plastics, sintered metals, and platings it has been found experimentally that if tmax
<
BNty
(5)
wear produced by fretting or fretting corrosion can be prevented for a given number of passes, N. Fig. 4 shows the variation of Vavg and Vper with the ratio rmsx/ty’ for the case of Nylatron GS after 2000 passes (N) on the platen by 302 stainless steel. It clearly shows that when rmax m 0.54 ry’ the magnitude of both Vavg and VP,, is zero, indicating that /I = ,!l~ where N is equal to 2000 passes and its value is approximately equal to 0.54. Figure 9 shows that in the case of nickel-cobalt plating I V avg decreases to zero when the ratio t max/ty’ attains a value of 0.21, indicating that the value of p for this case is approximately equal to 0.21. Similarly, in Fig. IO, a value of 0.51 for /3 is indicated for the case of nickel-cobalt plating 2. Similar curves are obtained for the other plastics, the sintered metals, and the platings. The maximum shear stress, rmax, corresponding to Vavg = VP,, = o is plotted against the yield point in shear for the weaker of the two materials in Figs. 5,6, and 7. This graph is for zero wear with particular sliding combmations. The experimental points all fall on either one or the other of the two straight lines. The slopes of these two lines, corresponding to values for /I, are approximately 0.5 and 0.2, respectively. It is interesting to note that for all the plastics tested, 8~0.5. The reason for this is that plastics are not sensitive to oxidation and fretting. For materials more sensitive to fretting, /Iis approximately equal to 0.2 Comparing Fig. 6 with Fig. 7. it is noted that the value of p for some materials (e.g. sintered steel-3) is approximately equal to 0.2 under dry conditions, and it increases to an approximate value of 0.5 with the proper lubricants while the other Wear, 7 (1964) 354-367
FOR WEAR
ENGINEERINGMODEL
3%
materials do not. From this, it can be concluded that with the appropriate lubrication the value of fi for a particular sliding combination of two materials can be increased from 0.2 to a magnitude of 0.5. This change in the value of ,9 increases the loadcarrying capacity for the particular sliding combination of two materials by a factor of 15 because rmax is approximately proportional to the cube of the load. In the present investigation, the radii of the different size sliders used (1/4in. and z in.) differ by a factor of eight. The values of zy for the different materials cover a range of from 64 p.s.i. (polyethylene I) to 40,000 p.s.i. (sintered steel-r) - nearly three orders of magnitude. The Young’s moduli of the different materials extend over a range of from 2.43 - 104 p.s.i. (polyethylene I) to 3 - IO' p.s.i. (sintered steel-r) different by three orders of magnitude. The loads cover a range of from 4 g for the sintered iron 1-52100 sliding combination to 400 g for the sintered bronze 1-4140 sliding combination - a difference of two orders of magnitude. It is significant to note that in spite of the large variations in magnitude of the above mentioned parameters, experimental results show excellent correlation between zero wear and the maximum shear stress with both dry and lubricated conditions. By correlating zero wear with maximum shear stress, it is possible to explain why a metal-plastic sliding combination (e.g. goz-Nylatron G) can carry as much load as a metal-metal sliding combination of the same geometry (e.g. 52100 sintered steel-r) with /I = 0.20. The ratio of the allowable load for a metal-plastic sliding to that for a metal-metal sliding combination Pmetalcombination, P,,t,lplastto, metal
1s
where ry’piastic and Eplastic are the yield point in shear and Young’s modulus respectively for the plastic. ty’metai and Emeta are the corresponding values for the metal. For example, ty’plast&,‘metal is of the order of 0.025, and Emetai/Eplastic is of the order of 60 for Nylatron G and sintered steel-r. Therefore
It is most significant that the value of OLfound experimentally is approximately equal to 0.5 and that /I is either approximately equal to 0.5 or 0.2 dependent upon whether or not the sliding combination of materials is sensitive to fretting. One possible explanation for this is obtained by regarding 11~4 and r/b as stress concentration factors due to asperities and wear particles, respectively. A pair of asperities in contact can be regarded as a local Hertz contact stress problem (Fig. rra). The ratio of the asperity maximum shear stress (-cmsx**p)to the maximum shear stress (tmax) in the gross contact region is defined as the stress concentration factor k (k > r) tmsx=P
=
hmax
(7)
To prevent local plowing from occurring trnax’~
=
ktmar <
ty
(*I Wear> 7 (1964) 354-367
366
w. c. cLImos,
et al.
Therefore, I
(0)
tmax < - ty k
Hence, I
(10)
k=-5232 a
Similarly, (I//I) = k' can be thought of as a stress concentration factor. For materials not sensitive to fretting corrosion k’ w 2, indicating that the stress concentration may be again associated with the asperities. For materials sensitive to fretting k’ M 5, which can be thought of as a stress concentration factor between wear particles and asperities. The contact between wear particles and asperities can be again regarded as a local Hertz contact stress problem (Fig. orb).
Fig. II. Stress concentration
factors due to asperities and to fretting particles.
It is generally known that to a first order of approximation, the stress concentration factor is practically a constant for different materials if the geometry remains the same. This may offer an explanation of the fact that LXand B have discrete values for all the materials investigated. Palmgren’s equation3 for a rolling-contact bearing is
where PI and PZ are the loads and LI and LZ are bearing life times in revolutions. P is proportional to r,,& and therefore in terms of stress, eqn. (II)becomes (t, 8X1 )QLl = (tmax2)QLz
(12)
The present wear model postulates that, for wear corresponding to the surface roughness, wear is the same for two sets of conditions of stress and of number of passes and the conditions are related by the following modified form of Palmgren’s equation (Tm P.X1 )9Nl =
(7max2)9N2
(13) Wear, 7 (1964) 354-367
ENGINEERING
367
MODEL FOR WEAR
where rmaxl and tmaxZ are the values of the maximum shear stresses and N1 and Nz are the number of passes. Line A in Fig. 8 is drawn according to the relationship indicated by eqn. (13). Points 2 and g fall on this line. The wear on the slider corresponding to these two points is approximately equal to the surface roughness. Points 3, 5,6, 7, and 8 are to the right of this line and there is measurable wear on the slider associated with these five points. The number of passes (N’) in Fig. 8 is indicated with reference to the slider and is determined by eqn. (2). Figure 8 clearly indicates that for a zero wear condition the modified Palmgren’s equation (eqn. (13)) is a sensible criterion for predicting the maximum allowable shear stresses for a given number of passes. It should be pointed out that to maintain the zero wear condition according to eqn. (13), a decrease in rmax by a factor of 2 allows an increase in the number of passes by a factor of 500. It is also worthwhile to mention that the exponent of tmax in eqn. (13) is probably of the order of 8 or 9; the experimental accuracy is not sufficient to pinpoint the exact value. Other experiments4 show that p can have a value of 1.0 under a quasi-hydrodynamic condition. This condition is in contrast to the boundary lubricated condition reported in the present paper. Experimental results show that, for certain sliding combinations of materials, p M 0.5 for 2000 passes (N). At the same time OLM 0.5 foI the same materials for I pass (N). The possible variation in the values of j3 for these materials in the range between I pass (N) and 2000 passes (N) should be investigated further. REFERENCES R. G. BAYER, W. C. CLINTON, C. W. NELSON AND R. A. SCHUMACHER, Engineering model for wear, Wear, 5 (1962) 378-391. B. W. MOTT, Micro-indentation Hardness Testing, Butterworths Sci. Publ., London, 1956. M. C. SHAW AND E. F. MACKS, Analysis and Lubrication of Bearings, McGraw-Hill BookCompany Inc., New York, 1949, 411. A. R. WAYSON, A study of fretting on steel, Wear, 7 (1964) no. 5.
Wear,
7 (1964) 354-367
3.54
EXTENSION
OF THE ENGINEERING SINTERED W. C. CLINTON, International (Received
MODEL FOR WEAR
TO PLASTICS,
METALS, AND PLATINGS T. C. KU
AND
R. A. SCHUMACHER
Business Machines Corp., Endicott, N.Y. (U.S.A.) August 20, 1965; revised December
IO,
1965)
SUMMARY The engineering model for wear developed previously for metals’ has been found to be applicable to different plastics, sintered metals and plating% The results of 137 tests for various combinations of sliding materials, with and without lubricants, have shown that wear can be prevented for a given number of cycles if the maximum shear stress is kept below a certain fraction of the yield point in shear of the weaker of the two materials. This fraction is equal to 0.5 for all the plastic-metal combinations that have been investigated under dry and boundary lubricated conditions. However, with respect to the sintered metals and the plated surfaces, this fraction is equal to either 0.5 or 0.2 depending upon the composition of each of the sliding materials as well as the type of lubricant used. INTRODUCTION
The engineering model for wear correlating shear stress with wear has been extended to include metals sliding in contact with plastics, sintered metals, and platings. It is the purpose of this paper to present the new experimental results and to show the correlation of shear stress with wear which was obtained in a study of 31 different combinations of these materials sliding against each other. In order to avoid unnecessary repetition, some familiarity with the earlier paper1 is assumed. An attempt is made in this paper to amplify some of the ideas and concepts postulated previously. A new procedure is described which is used to determine the yield point in shear of the plated surfaces. EXPERIMENTAL
METHODS
The experimental approach was similar to that reported earlier1 in that the geometry involved was a sphere sliding on a plane. Also, the conditions considered were for both dry and boundary lubricated sliding surfaces. The experiments were made for a specific number of passes (N) or (N’) and at different normal loads for each sliding combination. The loads were calculated with the use of the model described by BAYER, et al.1 Apparatus
The friction and wear machine used in the experiments is the same as previously described1 and is built around an Elgin miniature milling machine. The characteristics of this machine and the instrumentation for measuring the normal load and the frictional force have been described in detailr. Wear, 7 (1964) 354-367
ENGINEERING
MODEL FOR WEAR
35.5
Test specimens
Table I lists the compositions of the sliders, the balls, and the platens used in the experiments with each of five different sliding combinations. The plastic platens are identified by both trade name and composition. The sintered metals are identified numerically and by density. The platings are identified numerically and by plating composition. The substrates of four of the plated surfaces are beryllium on which is plated in succession layers of copper, nickel, and chromium. Each plating has been plated at different experimental conditions. The thickness of each plated layer is approximately the same for all four specimens with chromium always the thinnest and copper the thickest. The two specimens with nickel-cobalt plated surfaces differ in their surface structure and hardness. The lubricants
The same three lubricants that were employed in the experiments reported earlier’ were used. These lubricants were flooded on the solid bulk specimens, i.e. plastics and AISI steels. A vacuum pump was used to infiltrate the sintered metals with the respective oils. Platen preparation
Each plastic platen was ground to a V-12 finish and polished successively with wet 350A, 4ooA, 3ooA, and 6ooA silicon carbide paper. Each was dried and stored in a desiccator over anhydrous CaCL. The surfaces of each sintered metal platen were ground to a V-12 finish and then electrolytically etched to expose the porosity. With the use of a vacuum pump, the interstices were infiltrated with distilled water and then with CP acetone. After the acetone was removed by vacuum, the interstices were degreased ten times by the infiltration of fresh, boiling benzene. Afterwards, all traces of benzene were removed by vacuum. For the dry experiments, the sintered metals were then polished successively with the same grades of water-wet silicon carbide paper used with the plastics. For the lubricated experiments, the metals were infiltrated with a given lubricant and then polished with the successive grades of silicon carbide paper wet with the given lubricant. The four AISI metal platens were ground to a V-12 finish and then polished wet with the same successive grades of grit used to polish the plastic platens. After polishing, they were dried with CP acetone and immediately refluxed for 30 min in a CP benzene vapor chamber. The plated specimens were not polished but they were washed with a degreasing detergent, dried with CP acetone, and then refluxed with boiling benzene. Slider and ball fireparation
The Type 302 stainless steel sliders were given a V-32 machine finish and then polished with wet 6ooA silicon carbide paper. After they were dried with CP acetone, they were degreased for 30 min in a boiling benzene vapor chamber. Wear,7
(1964) 354-367
356
w.
c.
CLINTON,
EXPERIMENTAL 302
Stainless steel hemispherical
et al.
MATERIALS
sliders of 2 in. radius sliding on selected plastic platens
Plastic platen designation
Platen composition and identification Molybdenum disulphide-filled nylon FM-10001 Graphite-filled nylon FM-rooor Nylon resin Acetal resin - polymerized formaldehyde Polymerized styrene plastic Tetrafluoroethylene resin Low density - sp. gr. 0.913 Medium density - sp. gr. 0.926 High density - sp. gr. 0.941
Nylatron GS* Nylatron G* Zytel Ior** Delrin 5oo* * Polystyrene Teflon* * Polyethylene I Polyethylene 2 Polyethylene 3
* Registered Trademark, The Polymer Corp., Reading, Pa. ** Registered Trademark, E.I. duPont deNemours & Co. Inc., Wilmington,
Delaware
52100 High carbon steel balls of 114 in. radius sliding on selected sintered metal platens Platen density and composition
Sintered metal platen designation Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered Sintered
(glcms)
bronze I bronze 2 brass I brass 2 steel I steel z steel 3 iron-copper iron-copper iron I iron z iron 3
6.4-6.8 - ASTM Bzoz-SST - type II class A 7.0 Min - ASTM B255-61T - type II 7.5 Min - proprietary 7.0-7.5 - proprietary 7.0 Min - stainless AISI type 316L 7.0 Min - proprietary 6.0-6.5 - proprietary 7.1 copper infiltrated 15% 5.8-6.2 high copper - 20% 7.5 Min - proprietary 7.3 Min - proprietary 7.0 Min - proprietary
I 2
Sintered bronze I hemispherical
sliders of 2 in. radius sliding on selected A ISI
Solid metal platen designation
Platen specification
1117 Steel 4140 Steel 8620 Steel
AISI AISI .USI
Sintered steel I hemispherical
slider of 114 in. radius sliding on a selected AISI
Solid metal platen designation 4140
52100
solid steel platens
solid steel platen
Platen specification AISI
Steel
High carbon steel balls of 114 in. radius sliding on selected plated platens
Platen plating designation Chromium plating I Chromium plating 2 Chromium plating 3 Chromium plating 4 Nickel-cobalt plating I Nickel-cobalt plating z
Substrate composition Beryllium Beryllium Beryllium Beryllium Aluminum Brass
1st layer plating Copper Copper Copper Copper None None
2nd layer plating Nickel Nickel Nickel Nickel None None
3rd layer surface plating Chromium Chromium Chromium Chromium Nickel-cobalt Nickel-cobalt
Wear,
7
(1964) 354-367
ENGINEERINGMODEL FOR WEAR
357
The Type 52100 steel balls were washed six times in boiling benzene and then degreased for 30 min in a boiling benzene vapor chamber. The two different sintered metal sliders were prepared in a manner identical with that described for the sintered metal platens. Procedure Two different types of experiments were made in this study. The first type was made with dry, clean surfaces and the second type was made with lubricated surfaces. The first type of experiments were made with all of the platens listed in Table I except the four AISI steel platens. The exceptions were studied only with their surfaces flooded with lubricant B as used by BAYER, et al. Experiments of the second type were made with all of the platens except the six plated platens. These exceptions were studied only with dry, clean surfaces. In the earlier report’ all experiments were made with a 1/4 in.-radius ball. In this report, the experiments with the sintered metal platens and the plated platens were also made with 1/4 in.-radius balls, but the experiments with all other platens were made with sliders which had a 2 in. radius. The values of the yield point in shear, zy, for the plastics and the sintered metals were measured experimentally by conventional methods. The point at which the shear stress-strain curve begins to deviate from a straight line was used as the yield point. The values of tV for the plated surfaces were measured with a Reichert microhardness tester. This instrument was used to measure the variation of hardness with the depth of penetration into the plating. By applying a different small load each time, the average hardness R was obtained up to a depth of penetration, x. The hardness H(x) at any given depth x can be obtained from H(x)
=
E +
(1)
x g
This is illustrated in Figs. I and 2 for the different values of H(x) thus obtained
o!
0
platings. By comparing the with the hardness values measured at comparable small
. . .
I..
fO0
x, DEPTH INTO PLATING,
I,
200
‘,
,I
300
p in.
Fig. I. Microhardness vs. depth of penetration into platings on solid surfaces. 0, Plating plating 2 ; 0, plating 3; A, plating 4.
I ; +,
Wear, 7 (19% 354-367
358
loads (this is to minimize the effect of the variation of the index n, therefore the hardness, with loadz) for the identical or very similar solid metals and alloys for which the values of rV are known, the variation of ry with the depth of penetration into these platings can be determined. The value of ty estimated at the surface of each plating was used for the experiments because the maximum shear stress occurs at the surface of the platings studied in this report. For more general considerations the above criteria, eqns. (I), (a), and (3) given in the earlier paperr, have to be satisfied at the surface and at any point below the surface. In this report it is convenient to designate the yield point of the weaker sliding material as zy’ and that of the stronger as zy”. It was experimentally determined for metals1 that (x = 0.54 for one pass and ,6 was either equal to 0.54 or 0.20 for 2000 passes (N) dependent upon whether or not transfer occurred. For any sliding geometry, one pass is defined as that distance of sliding equal to the dimensions of the contact area, S, measured in the direction of sliding. With the geometry used in this report the value of S is equal to the diameter of the circular area of contact. This is illustrated in Fig. 3. It shows the position of the slider after it has experienced one pass. In addition, it shows that the slider will
Fig. 2. Microhardness US. depth of penetration into platings on solid surfaces. -0--, Nickelcobalt plating, z-brass substrate; -+-,
nickel-cobalt plating, r-aluminium substrate.
Fig. 3. Position of the slider after it has experienced one pass; also shown is the number of passes (N’) made by the slider for one sliding
length (I) or cne pass (,V) on the platen.
experience five passes after sliding a distance I on the platen. The engineering wear model specifies the number of passes with respect to the distance 1 on the platen so that in the illustration one pass on the platen is equal to the distance 1 and it is equivalent to five passes on the slider. This equivalence can be expressed as
where N’ is the number of passes experienced by the slider, and N is the number of passes made on the platen or the sum of the number of times the slider moves backwards and the number of times it moves forwards. In this report, the yield point in shear of the weaker of the two materials involved in a given test was used with the above values of 01 and /l to compute the maximum allowable shear stresses. With the maximum allowable shear stress and using eqns. (5) and (6) from the previous paperi, the corresponding load for a given test was determined. In order U’ew, 7 (1964) 354-367
ENGINEERING MODEL FOR WEAR
359
to verify the validity of the factors 01 and /? additional test loads were detemrined for cases where the maximum shear stress exceeded the allowable shear stress. The wear produced after 2000 passes (N) was measured and identified for each combination of lubricant and material. The experimental sequence followed was identical for all but two tests. First, the ball or the slider was securely locked in a ball holder mounted on the friction and wear apparatus. Second, the platen was oscillated in sliding contact with the ball at a predetermined normal load for 2000 passes (N). Coefficient of friction measurements were made during the first pass and the 2000th pass. Third, photomicrographs were made of the wear track on the platen and of the wear scar on the ball. Afterwards, a Talysurf profile trace was made across the width of the wear track on the platen and along the major axis of wear on the ball. RESULTS
The cross-sectional area of the wear scar on the platen as obtained from a Talysurf trace was used as a measure of wear. Two areas were measured. V,, was the average area appearing underneath the width of the track and Vper was the sum of the perturbations on the average area. A diagram illustrating these two areas was shown in Fig. 5 of the paper by BAYER, et al. 1. When the track was not distinguishable from the surface roughness, there was said to be zero wear, that is V,, = o and Vper = o. Disturbance on the surface up to the magnitude of the surface roughness can occur when Vavg = Vper = o. 302 Stainless steel sliding on selected plastics The amount of wear measured on Nylatron GS after 2000 passes (N) at different stress levels by a 302 stainless steel slider of 2 in. radius is shown in Fig. 4. It shows
g. &
BO-
-16
70-
-14
60-
-1.2
50.
-10 Q. 6s -8 ‘g
40.
.
‘? JO-
-6
6 A! zo-
-4
JO-
-2
% +
o%o a55 a60 a65 a70 0.75 Q~Y) a85 a90 ‘Gclx/q~ 4. The amount of wear expressed as V,. and VW, vs. different ratios of tmsx/ly’. These were obtained with 302 stainless steel sliding for zooo passes (N) on dry Nylatron GS. TV’ = 1.14 + IO* lb/in.* for this plastic. - a-, V.,, ;- IJ--, VP,,. Wear3 7 (1964) 354-367
w. c. CLIN’TQN,et al
360
the amount af wear (I’,,, and Wper)vs. different values of zma.& for the plastic. It is s~g~ifieaut that the value of amrxj.ty’ is o-54 for Nylatron GS when V,, and Pper are equd to zero because this value is identical to that found at Zero wear for each of the other plastics listed in Table 1. This is illustrated in Fig. 5 where the value of tmlLxat zero wear for each plastic is plotted against their respective yield
points, tU’” It is also significant that the value of tfllax/ty‘ at zero wear is still 0.54 for each plastic lubricated in turn with the three test lubricants. A graph illustrating this is not shown because it is identical to Fig. 5. gzroo
Sted ball sliding on mkcted sin&red metal
The experimental sequence followed in this study was identical to that followed in the study of the plastics. The. amomt of wear was measured for different stress Ieveis on each sir&red x&al @atm after moo passes (I%? by a ~~IW bafl af r/s in. radius. %easurements were made on dry surfaces and on m-faces lubricated in turn with the three test lubricants. For brevity, curves showing the decrease in the amount of wear with the decrease in stress level are not presented. Instead, the value of rmaxat zero wear for each dry surface is shown in Fig. 6 plotted against the respective: yield point, -cg’ of each sintered metaf. &ASidentical pi is shcw-n in Fig. 7 for each lubricated surface. The type of lubricant used is indicated with convenient symbols. Sintered bmme-r
sliding on; three diffemnt AISX steel piatelzs
The emphasis in this experiment was on the prevention of wear on the slider when it experienced 2ooo passes (Wj and when its yield point in shear was either less than, equal to, or greater than the yield p&&s of three ~ff~r~~t AIS steel @atens. The sintered bronze-x sli&rs were impregnated with lubricant I31 and the platens were floo&d with the lubricant. Identical tests were made at two different maximum shear stresses with each of the three AISI platens listed in Table I. The experimental
ENGINEERING MODEL FOR WEAR conditions
as well as the results obtained
data in Table because
II. The significance
a running
account
361
can best be explained
of this data is considered
would be identical
by referring to the
only for AISI
steel 1117
for the other two steels.
22
IRON-COPPER-I
dgsTEEL_,
20 /
l8 /6
0
IO
20 r;
40
30
IO
Fig. 6. Experimentally determined values of rmax at zero wear vs. measured values of ty’ for different sintered metals. These metals were in dry sliding contact with 52100 steel for zoo0 passes (N).
Column r
BRONZE-I
Column
a
40
50
Fig. 7. Experimentally determined values of rmax at zero wear vs. measured values of ty’ for different lubricated sintered metals. These metals were in sliding contact with 52100 steel for 2000 passes (N) . - 0 - , lubricant A ; - 0 - , lubricant B; - A - , lubricant C.
TABLE SINTERED
30
20
* IO 31b/n.2
SLIDING
FOR 2000
Column
3
PASSES
(N’)
Column 4
II ON THREE
Column 5
AISI
DIFFERENT
Column 6
METAL
Column 7
PLATENS
Column
Platen AISI no. 1117 4’40 g620
*ti (roYb/in.z) 27 32
40
Number of #asses on platen (N)
tmax (Cblin.2 .
rmsx
108) 7ty
tmax
7 tll
(k2
V BVIl V Per . ro-0) (in.z.10
100 40
17.3 6.4
0.64 0.24
0.54 0.20
-IO
IO0 40
‘7.3 6.4
0.54 0.20
0.54 0.20
-2
100 40
17.3 6.4
0.54 0.20
0.43 0.16
-II
0
0.2 0 0
0 0
0 0.5
0
ry for sintered bronze-r is 32 . 10s lb/in.8 ry’ is the lower value of the two yield points rv” is the higher value of the two yield points Wear, 7 (1964) 354-367
W. C. CLmToN, et al.
362
With AISI steel 1117 (column I) wear occurs on the slider in the form of transferred material or “build-up” on the platen when the maximum shear stress, rmax, is 17.3 * 103 lb/in.2 (column 4). The amount of wear measured is shown in columns 7 and 8 where VIBVg= - IO . IO-* in.2 and Vper = 0.2 . 10-8 in.2. It is convenient to indicate “build-up” with a negative sign preceding the numerical value of the area measured. This amount of wear occurs when the ratio of zmrtX/ry”for the slider is 0.54 (column 6) and the ratio of rmax/ry’ for the platen is 0.64 (column 5). It is important to note that although the wear measurements were made after the slider had moved backwards and forwards over the same path for a combined total of only IOO times (column 3), the number of passes (N’) experienced by the slider is 2000 (eqn. (2)). In order to reduce the amount of wear to zero (see the second row of columns 7 and 8) it is necessary to reduce the ratio of r max/rty”for the slider to 0.20 (column 6). This automatically reduces tmax (column 4) to 6.4 . 103 lb/in.2 and the ratio rmax/ty’ for the platen to 0.24 (column 5). At the reduced stress of 6.4 . 103 lb/in.2 the diameter of the area of contact with a 2 in. radius slider is much smaller so that the slider has now only to move backwards and forwards over the same path for a combined total of 40 times (column 3) in order for the slider to experience 2000 passes (N’). A similar commentary can be made of the results shown for AISI steel 4140 which has a yield point equal to that of the slider. It will be observed that zero wear occurs when the ratios in columns 5 and 6 are both reduced from 0.54 to 0.20. In the case of AISI steel 8620 which has a yield point greater than the slider, zero wear occurs when tmax/ty’ for the slider (column 5) is reduced from 0.54 to 0.20. Sintered steel-r .&ding on AISI
steel 4140
The emphasis in this study was on the prevention of wear on the slider when it experienced more than ooodpasses (N’). The hemispherically ended sliders of 2 in. radius were impregnated with lubricant Bl and the AK1 steel platens were flooded with the same lubricant. Nine separate experiments were made at each of the listed ratios (Table III) of tmax/ty” and for a specified number of passes (N’) to be experienced by the slider. TABLE III Experiment number
Experimental parameters Tmax
I7y
I
2
0.22
0.30
I,
No.ofpasses.104(W)
so
39
3
4
5
6
7
'8
0.36
0.37
0.38
0.47
0.47
0.50
36
3
3'
6
7
3
9 0.54 0.2
A Talysurf trace across the sliding path on the platen and across the contact area on the slider showed that no wear occurred for experiments number I, 2, 4, and g (Table III). However, wear did occur for all other experiments in the form of either “build-up” on the platen, or of a measurable groove on the platen, or of material removed from the contact area on the slider. The two parameters used for each of the nine experiments are plotted against each Wear, 7 (1964) 354-307
ENGINEERING
MODEL
363
FOR WEAR
other in Fig. 8. The significance of this graph is discussed later with respect to the solid line drawn from the point at which rmaxJ’rti” equals 0.54 to the point at which it equals 0.30. 52100 Steel ball sliding on dry elated surfaces The results obtained with nickel-cobalt plating are shown in Fig. 9. In this graph the amount of wear (I’,,) measured after 2000 passes (N) on the plating by a 5~100 steel ball is plotted against the different ratios of tmtsxfry’ used in the experiment. It shows that V,, = o when rmax/ryf = 0.21. An identical type of plot is shown in Fig. IO for nickel-cobalt plating 2. It shows that V,,, = o when tmax/ty’ = 0.51. Similar curves were made with the results obtained for the four chromium plated surfaces. Each of these curves showed that Vavg = o when rmax/ry’ = 0.20.
36 m0-l 80-
l
jz
NICKEL - COBALT PLATING
28
I /
60504030 zo-
IO8-
Fig. 9. The amount of wear expressed as
Vav, vs. different ratios of tmar/‘tv’. These data were obtained with 52 IOOsteel sliding for zooo passes (N) on dry nickel-cobalt plating I. t*’ = 15 . IO* lb/in.2 for this plating. l.6,,4_
a.?-
NN;‘XEL-COEAiTP2
9Q4LQQ2 I
al
1
I
QZ Q3 Q4Q5Q6Q8 / G%9x*/Tyu
Fig. 8. The number of passes (N’) experienced by sintered steel I sliding on AISI steel 4140 vs. different ratios of rms./ry” for sintered steel I.
f
0.50
0.52
Q54
0.56
Q58
0.60
GUXB-; Fig. IO. The amount of wear expressed as V svg vs. different ratios of rma&‘. These data were obtained with 3~100 steel sliding for 2000 passes (N) on dry nickel -cobalt plating 2. tu’ = 26. roalb/in.2 for this plating. Wear. 7 (1964) 354-367
364
W. c. CLINTOX, et d. DISCUSSION
The engineering model for wear1 describes three types of wear: gross plowing, local plowing, and fretting or fretting corrosion. These are depicted by Figs. 6, 7, and 8 in the previous paperl, respectively. In the Talysurf trace of a wear track on a platen (Fig. 6 of the previous paper), the area into which a ball profile fits is the result of gross plowing. It is generally agreed that gross plowing which results from the movement of the material (due to plastic flow) away from the gross-contact region can be eliminated for one pass if tmar < ZY
(3)
The same type of wear mechanism involved in gross plowing can occur on a local scale as a result of surface asperities or roughness, and of transferred material (Fig. 7 of the previous paperi). While gross plowing can be related to the plastic flow of metal on an analytical basis, it has been experimentally determined for the case of metals that local plowing can be eliminated for one pass if tmax< atu
(4)
In the present investigation eqn. (4) has been confirmed for plastics, sintered metals, and platings. The value of 01 for all these materials is approximately equal to 0.5. When wear is caused by the abrasive action of debris, it is called fretting. If the debris is of an oxide form, it is called fretting corrosion. For plastics, sintered metals, and platings it has been found experimentally that if tmax
<
BNty
(5)
wear produced by fretting or fretting corrosion can be prevented for a given number of passes, N. Fig. 4 shows the variation of Vavg and Vper with the ratio rmsx/ty’ for the case of Nylatron GS after 2000 passes (N) on the platen by 302 stainless steel. It clearly shows that when rmax m 0.54 ry’ the magnitude of both Vavg and VP,, is zero, indicating that /I = ,!l~ where N is equal to 2000 passes and its value is approximately equal to 0.54. Figure 9 shows that in the case of nickel-cobalt plating I V avg decreases to zero when the ratio t max/ty’ attains a value of 0.21, indicating that the value of p for this case is approximately equal to 0.21. Similarly, in Fig. IO, a value of 0.51 for /3 is indicated for the case of nickel-cobalt plating 2. Similar curves are obtained for the other plastics, the sintered metals, and the platings. The maximum shear stress, rmax, corresponding to Vavg = VP,, = o is plotted against the yield point in shear for the weaker of the two materials in Figs. 5,6, and 7. This graph is for zero wear with particular sliding combmations. The experimental points all fall on either one or the other of the two straight lines. The slopes of these two lines, corresponding to values for /I, are approximately 0.5 and 0.2, respectively. It is interesting to note that for all the plastics tested, 8~0.5. The reason for this is that plastics are not sensitive to oxidation and fretting. For materials more sensitive to fretting, /Iis approximately equal to 0.2 Comparing Fig. 6 with Fig. 7. it is noted that the value of p for some materials (e.g. sintered steel-3) is approximately equal to 0.2 under dry conditions, and it increases to an approximate value of 0.5 with the proper lubricants while the other Wear, 7 (1964) 354-367
FOR WEAR
ENGINEERINGMODEL
3%
materials do not. From this, it can be concluded that with the appropriate lubrication the value of fi for a particular sliding combination of two materials can be increased from 0.2 to a magnitude of 0.5. This change in the value of ,9 increases the loadcarrying capacity for the particular sliding combination of two materials by a factor of 15 because rmax is approximately proportional to the cube of the load. In the present investigation, the radii of the different size sliders used (1/4in. and z in.) differ by a factor of eight. The values of zy for the different materials cover a range of from 64 p.s.i. (polyethylene I) to 40,000 p.s.i. (sintered steel-r) - nearly three orders of magnitude. The Young’s moduli of the different materials extend over a range of from 2.43 - 104 p.s.i. (polyethylene I) to 3 - IO' p.s.i. (sintered steel-r) different by three orders of magnitude. The loads cover a range of from 4 g for the sintered iron 1-52100 sliding combination to 400 g for the sintered bronze 1-4140 sliding combination - a difference of two orders of magnitude. It is significant to note that in spite of the large variations in magnitude of the above mentioned parameters, experimental results show excellent correlation between zero wear and the maximum shear stress with both dry and lubricated conditions. By correlating zero wear with maximum shear stress, it is possible to explain why a metal-plastic sliding combination (e.g. goz-Nylatron G) can carry as much load as a metal-metal sliding combination of the same geometry (e.g. 52100 sintered steel-r) with /I = 0.20. The ratio of the allowable load for a metal-plastic sliding to that for a metal-metal sliding combination Pmetalcombination, P,,t,lplastto, metal
1s
where ry’piastic and Eplastic are the yield point in shear and Young’s modulus respectively for the plastic. ty’metai and Emeta are the corresponding values for the metal. For example, ty’plast&,‘metal is of the order of 0.025, and Emetai/Eplastic is of the order of 60 for Nylatron G and sintered steel-r. Therefore
It is most significant that the value of OLfound experimentally is approximately equal to 0.5 and that /I is either approximately equal to 0.5 or 0.2 dependent upon whether or not the sliding combination of materials is sensitive to fretting. One possible explanation for this is obtained by regarding 11~4 and r/b as stress concentration factors due to asperities and wear particles, respectively. A pair of asperities in contact can be regarded as a local Hertz contact stress problem (Fig. rra). The ratio of the asperity maximum shear stress (-cmsx**p)to the maximum shear stress (tmax) in the gross contact region is defined as the stress concentration factor k (k > r) tmsx=P
=
hmax
(7)
To prevent local plowing from occurring trnax’~
=
ktmar <
ty
(*I Wear> 7 (1964) 354-367
366
w. c. cLImos,
et al.
Therefore, I
(0)
tmax < - ty k
Hence, I
(10)
k=-5232 a
Similarly, (I//I) = k' can be thought of as a stress concentration factor. For materials not sensitive to fretting corrosion k’ w 2, indicating that the stress concentration may be again associated with the asperities. For materials sensitive to fretting k’ M 5, which can be thought of as a stress concentration factor between wear particles and asperities. The contact between wear particles and asperities can be again regarded as a local Hertz contact stress problem (Fig. orb).
Fig. II. Stress concentration
factors due to asperities and to fretting particles.
It is generally known that to a first order of approximation, the stress concentration factor is practically a constant for different materials if the geometry remains the same. This may offer an explanation of the fact that LXand B have discrete values for all the materials investigated. Palmgren’s equation3 for a rolling-contact bearing is
where PI and PZ are the loads and LI and LZ are bearing life times in revolutions. P is proportional to r,,& and therefore in terms of stress, eqn. (II)becomes (t, 8X1 )QLl = (tmax2)QLz
(12)
The present wear model postulates that, for wear corresponding to the surface roughness, wear is the same for two sets of conditions of stress and of number of passes and the conditions are related by the following modified form of Palmgren’s equation (Tm P.X1 )9Nl =
(7max2)9N2
(13) Wear, 7 (1964) 354-367
ENGINEERING
367
MODEL FOR WEAR
where rmaxl and tmaxZ are the values of the maximum shear stresses and N1 and Nz are the number of passes. Line A in Fig. 8 is drawn according to the relationship indicated by eqn. (13). Points 2 and g fall on this line. The wear on the slider corresponding to these two points is approximately equal to the surface roughness. Points 3, 5,6, 7, and 8 are to the right of this line and there is measurable wear on the slider associated with these five points. The number of passes (N’) in Fig. 8 is indicated with reference to the slider and is determined by eqn. (2). Figure 8 clearly indicates that for a zero wear condition the modified Palmgren’s equation (eqn. (13)) is a sensible criterion for predicting the maximum allowable shear stresses for a given number of passes. It should be pointed out that to maintain the zero wear condition according to eqn. (13), a decrease in rmax by a factor of 2 allows an increase in the number of passes by a factor of 500. It is also worthwhile to mention that the exponent of tmax in eqn. (13) is probably of the order of 8 or 9; the experimental accuracy is not sufficient to pinpoint the exact value. Other experiments4 show that p can have a value of 1.0 under a quasi-hydrodynamic condition. This condition is in contrast to the boundary lubricated condition reported in the present paper. Experimental results show that, for certain sliding combinations of materials, p M 0.5 for 2000 passes (N). At the same time OLM 0.5 foI the same materials for I pass (N). The possible variation in the values of j3 for these materials in the range between I pass (N) and 2000 passes (N) should be investigated further. REFERENCES R. G. BAYER, W. C. CLINTON, C. W. NELSON AND R. A. SCHUMACHER, Engineering model for wear, Wear, 5 (1962) 378-391. B. W. MOTT, Micro-indentation Hardness Testing, Butterworths Sci. Publ., London, 1956. M. C. SHAW AND E. F. MACKS, Analysis and Lubrication of Bearings, McGraw-Hill BookCompany Inc., New York, 1949, 411. A. R. WAYSON, A study of fretting on steel, Wear, 7 (1964) no. 5.
Wear,
7 (1964) 354-367