ML20236Q882
| ML20236Q882 | |
| Person / Time | |
|---|---|
| Site: | Pilgrim |
| Issue date: | 11/05/1976 |
| From: | Rabinowicz E RABINOWITZ, E. |
| To: | |
| References | |
| NUDOCS 8711200341 | |
| Download: ML20236Q882 (25) | |
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7 j I' . EnNEST H AGINOW1CZ
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. Boston Edison Q 23.1.3
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l j FRICTION COEFFICIENTS OF WATER-LUBRICATED STAINLESS STEELS
- ' FOR A SPENT FUEL RACK FACILITY l
i fl November 5, 1976 I Su: . mary A series of experiments have been carried out on a pin-on-disk friction
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l rtester"to determine the frictional characteristics of a 304 sto!.nless steel .i on 304 stainless steci sliding combination in distilled water. Tests were carried out at two normal pressures,' two sliding speeds, and two tempera- ; tures, and the ef f ects of introducing iron oxide contaminant particles ' and varying the surface roughness were determined. It was concluded that, provided that the initial surfaces are reason-ably cican, a design based on friction coefficient value.s between 0.80 and l 0.20 should cover all eventualities. l I
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fh Ernest Rabinowicz j DESIGNATED ORIGINAL -
, certifded By__ [g;t,1. -
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hy - - - - . IA EIMDolcKA9 . Ngw TgN,22 ACE. 51f59 November 5, 1076 Soston Edison Q 23.1.3 Report to Boston Edison Co. Attn:- Dr. Mukti L. Das Friction coefficients of water-lubricated stainless steels, Introduction It is my understanding that Boston Edison is in the process of designing a new spent fuel rack. In order to consider the feasibility of this design, I it is necessary to know the friction coefficient to be anticipated between two of the conponents of the system, namely the bearing plates attached to
. the ra'ck module and the spent fuel floor. j In order to determine the friction coefficient, it was decided to carry i
out testing using a standard method for measuring friction, that involving a pin-on-disk friction apparatus which has been in use for'many years in the l Surface Laboratory at M.I.T. With this apparatus, it is possibic to reproduce l the significant variables of the application, namely the contacting mater- l tals, the lubricant, the interf acisi pressure , the temperature, surf ace roughness and the anticipated sliding velocity. A f ew significant variabics could not be well matched, in particular the amount of surf ace contamination (introduced during the various machining
, processes ,or during assembly) likely to be on the sliding surfaces at the beginning of the operation of the system. But experience with other similar sliding systems, and indeed experience gained in these tests, suggests that this initial contamination is worn off relatively quickly and thercafter 9 sh ee e .. .. -m amme. - **m=* ** * * * * * *
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reistively clean sliding conditions prevail. Apparatus and experimgf al procedure A rehematic illustration of the pin-on-disk apparatus used in these tests is shown in figure 1. In this apparatus the top specimen, the pin, is held essentially stationary in a dynamometer while it is pressed against the rotating disk by a dead weight load. The angular speed of the disk is con-t trolled by an infinitely-variable motor drive and pulley system, and the pos- ! ition of the pin is adjusted so as to produce the desired sliding speed. The friction force is measured using a strain gage ring, and recorded continu-ously with a Sanborn recorder. For these tests, the bottom disk was replaced by a cup, so that the flat sliding specimen mounted in the cup could be immersed to a depth of 2 em by distilled water. In some of the tests, this water was. heated, by~an immersion heater, to a temperature in the range 72 C - 78 C (162F - 172F). In other of the tests, fine iron oxide particles (F 023) were introduced into the water to simulate the effect of corrosion products in the spent fuel ( l tank. A more complete discussion of the experimental procedure is to be found 3 l in Appendix 1, which outlines the various experimental conditions used in the tests, and which was approved by Dr. Das. Two sliding speeds were used in the tests. One of them, nancly 4"/sec- , ond, corresponds to the maximum sliding speed derived from Figure 6, entitled "Filgrim - relative displaecment of floor and mass,", of the report "A feas-ibility studi report on the spent fuel rack nodules for Yankee Atomic Elcetric Company Pilgrim Station 1," dated September 29, 1976, hv A. J., Sturm and K. E. Neumeier of Programmed Remote System Corporation. The other speed. 0.04"/ l 1 -
L . 4 sa'cond, was chosen to be two orders of magnitude slovar than tha tcp spasd..
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so as to bracket all speeds likely to be encountered. During the slow speed j.. - ss tests, five determinations of the static' friction coefficients, after the 4'd/'s* / ".
'Y sliding specimens were kept at rest for one minute under the normal load of 2 kg, were also made.
A normal load of 2 kg was used in all the tests. In some of the tests a pin was used on whose end a circular flat of diameter 0.09" had been machined. This gave a mean contact pressure of 690 psi, closely similar to that of the application (770 psi when a force of 22,000 lb acts on a circular bearing plate of diameter 6 inches). In other cases the end of the pin was rounded of f, and this produced much higher pressures, similar to those which arise in the application when the bearing plate and the spent fuel floor only contact l over~a'few patches. a All the tests were of one hour duration, except for some of the high temperature tests which were shortened to 0.5 hours when it was discovered that prolonged exposure to high temperatures had an adverse effect on the dynamometer ring. In addition, a more systematic series of static friction tests were car-ried out on surfaces which had been stationary for times of. 1, 10, 100,'1000, i l 10,000 and 50,000 seconds. For these tests, the relative speed applied to induce sliding was 6 x 10" in/sec. Host of the testing was donc using flat specimens of surface roughness
- 22p" CLA (27 p" RMS) as measured with the Talysurf Profilometer. A few tests ,
]
were carried out with much coarser surfaces, with surface roughness values of 260 p" CLA (320 p" RMS). In both cases the surf aces were obtained by abrasion against abrasive papers. The surfaccc were introduced in:o the sli- 1
, i Wing system without further cleaning or surfcca tractmant citer the abrasion 4 and surface roughness determination procedures. j . \ Results
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The results of the various tests are described in turn. During each sliding test ten friction coefficient values obtained at roughly' uniform intervals of time were determined, and these are given, as is their mean, and in some cases comments about extreme friction values are also provided. For the slow speed tests, the five static friction coefficient values and
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l their mean are also given. 9 In the case of the static friction tests, the various friction values, as well as the mean of the last batch of values, af ter enough sliding had been produced to wear off some small amount of surface contamination, are
. also given.
Test 1. 304 steel on 304 steel. Room temperature. Hemispherically ended slider. Roughness 29 microinches rms. Distilled water lubricant. Sliding speed = 4 in/sec. J ' f values:- 0.38, 0.45, 0.41, 0.35, 0.35, 0.37, 0.37, 0.34, 0.33, 0.33 Hean friction coef ficient = 0.36 ' i 4 Test 2. 304 steel on 304 steel. Room temperature. Ihmispherica11y j ended slider. Roughness 29 microinches rms. Distilled water lubricant. Sliding speed = 0.04 in/sec.
. s J f values:2 0.37, 0.46, 0.62, 0.65, 0.64, 0.64, 0.64, 0.61, 0.66, 0.62 Hean friction coefficient = 0.59. Peak friction vclue = 0.8 I r~s n >
Static f:- 0.62, 0.58, 0.57, 0.63, 0.74, mean = 0.62 4 Sy - e .
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. Test 3. '304 steal cn 304 stes1. 73C - 74C.- Hemispherically endsd - ~
.. l slider. Roughness 29 microinches rms. -Distilled water lubricated. Sliding :- I
! speed 4 in/sec.
l f values:- 0.35, 0.42, 0.44, 0.39, 0.46,'O.50,_0.49, 0.49, 0.41, 0.39 I i Hean f riction coefficient = 0.43 j 1 Test 4. 304 steel on 304 steel. 72-76C. Hemispherically ended slider. Roughness 29 microinches ras. Distilled water lubricated. Sliding speed = 0.04 in/sec. f values:- 0.46, 0.52, 0.'51, 0.64, 0.65, 0.71, 0.76, 0.60,.0.67, 0.82 j Mean frictiun coefficient = 0.63 Peak friction value = 0.91 l
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Static f:- 0.64, 0.46, 0.57, 0.56, 0.74 mean =_0.59. -
, 2. - .
Test 5. 304 steel on 304 steel. Room temperature. Slider end diameter ! i i 0.09". Roughness 27 microinches rms. Distilled water lubricant. Sliding' { speed 3.9"/sec. f values:- 0.36, 0.27, 0.32, 0.21, 0.25, 0.21, 0.31, 0.27, 0.33, 0.38 Mean friction coef ficient = 0.29, minimum friction = 0.20. ;
. 4 Test 6. 304 steel on 304 steel. Room temperature. Sliding speed =
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4.3 x 10 "/sec. S11' der end diameter 0.09", distilled water, roughness 27 u" rns. f values:- 0.41, 0.43, 0.49, 0.50, 0.45, 0.47, 0.50, 0.53, 0.53, 0.49 j Hean friction coefficient = 0.48, maximum friction = 0.61 Static f:- 0.51, 0.49, 0.52, 0.47, 0.49, mean ~= 0.50 Test 7. 304 steel on 304 steel. 71-79C. Slider end diameter 0.09". i Roughness 27 microinches rns. Distilled water lubricant.- Slidinn speed - 3.8/sec. ; f va. lues:- 0.51, 0.51, 0.39, 0.40, 0.40, 0.41, 0.36, 0.27, 0.30, 0.38 .l
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Hean friction coefficient = 0.31 I w 0e .w -n r s, w ,,
r-- c. 4
, Test 8. 304 steci en 304 sesel. 72-76 C. Slider and dicmmter 0.09".
Roughness 27 microinches rms. Distilled water lubricant. Sliding speed l 4.1 x 10~ "/see f values:- 0.42, 0.38, 0.53, 0.44, 0.46, 0.44, 0.60, 0.47, 0.68, 0.43 ! l Hean friction coefficient = 0.48
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Static f:- 0.36, 0.36, 0.45, 0.70, 0.55, mean = 0.48 ! Test 9. 304 steel on 304 steel. . Room temperature. Slider end diameter l l 0.09". Roughness 27 microinches ras. Distilled water lubricant with fine j J iron exide particles to a depth of .005". -2 Sliding speed 4.2 x 10 in/sec. f values:- 0.46, 0.53, 0.51, 0.52, 0.53, 0.49, 0.56, 0.57, 0.61, 0.54 j Haan friction coefficient = 0.53_ l 1
=
- 4,.
Test 1q. Same as test 9 but iron oxide particles to a depth of 0.25". !
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f values:- 0.61, 0.58, 0.57, 0.63, 0.54, 0.53, 0.54, 0.57, 0.56, 0.58 l 1 l Hean friction coefficient = 0.57. Maximum friction = 0.72 j l Static friction test I. 304 steel on 304 steel. Room temperature, j Slider end diameter 0.09". Rous,hness 27 microinches rms. Distilled water lubricant. Initiating sliding speed = 6 x 10 ' in/sec.
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Mean of i Time Friction coefficient values last vale 1 sce .23, .33, .44, .23, .70 .62, .56, .61, .68, .68, .64 .63 10 .39, .39, .42, .32, .50 .61, .54, .61, .68, .66, .67
.63 100 .36, .51, .37, .47, .50 .59, .54, .62, .67, .69, .68 .63 1,000 .33 .46, .35, .48, .60 .61, .63, .69, .60 .63 10,000 .29 .58, .72 .65 50,000 .59 O
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Sam 2 as. tatic friction tast I, but surfaco Static friction test II. I rouchness is 310 microinches rms. Time Friction coefficient valv g ifean friction 1 see . 44, .46, .48, .45, .49, .49, .54, .49 48 10 . 52 46 49 .48 .51 .53 . 52 .60' .51 100 . 45 .45 43 .49 .50 .51 . 45 .60 49 43 49 .52 .51 49 1,000 . 10,000 . 50 .49 .46 .54. .50-50,000 . 43 .43 Discussion Looking at the frictional data themselves, we note that they seem pretty consistent. The typical batch of ten friction coefficient values shows just about the trend and amount of scatter I would have expected, with initial friction values somcwhat low, but with overall scatter (as ' defined by the i i standard deviation) about 20% of the mean value. , The effect of the variables seems typical, also. Temperature had very .j little effect, because the stainless steel-stainless steel system is not affected by moderate changes of temperature, and the water is such a poor ubricant that temperature has little effect on its performance. Interfacial pressure also has little effect. in linc with general experience with fric-tion coefficient determinations. Sliding speed has a major effect, in that the friction is distinctly higher at lower sliding speeds; however the time of ; stick seems to have relatively little effect. As anticipated, iron oxide particles introduced into the sliding system produced no noticeable change in friction, because they are too easily pushed aside during sliding. Surface roughness has some influence, in that the very rough surfaces gave somcwhat lower friction. I would anticipate that very smooth surfaces (for example 1 or 2 4" rms) woald give distinctly i hisNerfrictionvaluesstill. ' 4
" " " .+.,.-.v..ws. - 4
- 1
, What kind of friction coefficient values should noston Edison expect?
Before starting the project it was my feeling based on previous experience that f riction coef ficient values between 0.4 and 0,65 would be typical 'of this sliding system, and indeed the results obtained are in good agreenent l with this'~ expectation. Ibwever, previous ~ cxperience provided little guidance on the extrene values to be expected. These experiments described above suggest that f = 0.80 and f = 0.20, the extrene values reliab1v observed in these tests, might be regarded as the upper and lower limits respective 1v._ At first sight it scens that, by using the largest and smallest' values observed in our tests as the extreme values. to be anticipated in practice we.
. are providing no margin of safety, but in practice a substantial margin of safety is inherent in our experiment, in which the friction is measured over a small area of about .006 in , whereas in the application the friction is 1
2 averaged over the much larger area of 100 in . This tends to average the 4
. friction coefficient and to suppress extreme values. ,
What guidance do the results provide for those designing the Boston " Edison spent fuel rack module system. .The only helpful fact that emerges is 1 that the rough surfaces (250 4" rms) seen preferable. Both theory and prac- ) tice suggest that the extremely high friction values are avoided, because the geometry discourages the formation of large, atrong junctions. At the same ! J time it is probably easier to scrape contaminants from the peaks of large sharp asperities, so that low friction coefficients are less likely to per-sist for any length of time.
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4 1 j COUNTER W EIG H T i n
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LOAD $ / - STRAIN GAGES l IN T E RC H A NG E ABLf STR AIN RING @ @, QSTICK - SLI P CI R CULT l RID E R - e ; y TIME
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SPECIME N s MOTOR / /
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i Figure 1. Schematic illustration of the pin-on-disk tester. For these tests, the flat specimen was in a cup-fixture which was immersed in distilled
, water, and for the high temperature tests an immersion tester was used.
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Appendix 1. Operatine' procedure - Th'c win-on-dink_ tenter
- In the pin on disk tester, one of the ' sliding esterials is in the fo:-.
I of a pin or cylinder, typically 1" long and 0.25". dis =eter, with an end vhich The other surfsee, the may be either fist, hemispherical or a trunksted cone. fist, is typically a piste of dimensions 2" x 2" x 1/4" nounted either en a fist ourface, or in a cup if a liquid lubricant is to be used. The flat sur- ! face is rotsted vis a varisbic speed motor and a pulley systen, thus pro-ducing sliding speeds anywhere in the range 3 x 10' to 3 x 10 ce/sec. The i norns1 load is typically a dead weight in the range 10 gn to 5 kg, while the f riction force is mensured by the strain nages counted on the strain rinr,, and recorded continuously by a Sanborn recorder. Calibration is by dead-- veight, vis string-and-pulicy system, and is applied directly to the rider. . Pin on disk machines represent one of the most fler.ible vays of studyinr, friction. Various machines of this type are described on pp 150 to 222 of a the comp 11stion " Friction and ticar Devices," ind Edition, American Society l of Lubrication Engineers, Park Ridge, Ill.1976. The operation of the pin-on-disk tester has been discussed in a nu.ber of my published papers. The earliest and the most recent are the following:- E. Rabinovic:, "The frictional properties of titaniun and its alloys," itetsi Progress 6_5,, 5 No. 2, 107-110, 1957. E. Rsbinovic:, "The boundary friction of very well lubricated surfaces," . Lubriestion Engineering, M , 205-208, 1954 E.'Rabinovie: and P. A. Itsrch, " Friction and vcar of rare carth ectals in sir," J. Less Com. mon ?tetals, 10,,145-151,1973. E. Rabinovica, " Friction and wear of scif-lubricating metallic nater-isis," J. Lubrication Technology. Trans. AS"E T. E , 217-220, 1975. e t
. WID e6 9
., : The pin cn' disk tester'es. wall as othar friction nessuring apparatus,. j are discussed in section 4.17 of my book " Friction and Wear of Materials,"
John Wiley and Sons, NY,1965. In the tests- to b'e carried out for Boston- Edison, the basic' variables to be used are the following. Haterials.. 304 stainless steel. . The flat specimen is to be a plate of dimensions 2" x 2" x 1/4",'with a surface finish of '2'microinches + a factor of two as determined'in a Talysurf model 4 Profilometer. The sur-face finish is to be generated by hand lapping against ey,ery paper. In addition, tests may be carried out at a surface' finish of'250 microinches
+ a factor of two, generated and measured in the same way. The Talysurf has been recalibrates this week against a standard surface.
,,The pin is 304 stainicss steel of 1/4" diameter. and approximately 1" in length. Two configurations are used. In one of-then, the. pin is term- ,
inated by a hemisphere of diameter 1/4", and this produces point contact. ! In the other case, the pin is terminated by a flat of' diameter 0.09". 1 1 When loaded by a dead weight load of 2 kg, this configuration produces the same surface stress as the actual [hd of 6" diameter when _ loaded by 22,000 I lb. Lubricant. Distilled water, applied to a depth of about 1". Two i lubricant temperatures are used, namely room temperature (70-80*F) and an i elevated temperature (160-180*F). i Sliding speed. Two sliding speeds are used, namely 4"/sec, corresp-onding.co the maximum speed anticipated in the application and 0.04"/sec, ) or17ofthemaximumspeed. Sliding tests are to be of one hour duration. In the slow speed tests, the static friction after static load ~ application for 1 minute are niso to be measured. !
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. Farce measurement The normal force is to be applied by dead weight loading, while the friction force is to be measured and continuously recorded, by a Sanborn model'150 recorder. Calibration of the whole apparatus, namely the friction dynamometer and the Sanborn recorder as a' unit, are to be madeLbefore each day's runs by a dead-veight-and-pulley method.
Personnci All the tests will be carried out by Professor Ernest Rabinovicz of H.I.T. Prof. Rabinovicz has used the pin-on-disk tester for over twenty years, and has carried.out friction testing using this and other methods continuously for the past twenty-nine years. His technical biography is appended. Oct24
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'N.f fechnical Bioaraphy_ of truest Rabinov'.as Education '
Cambridge University, England 1944-1947 3.A. is Ph/ stas cambridge University, England 1947-1950 Ph.D. in Physissi Chemistry l Thesis title "Autoradiographie study of frictieaal damage." Positions. 1950-1954 assearch staff member, L I.T. i 1954-1961 Assistaut Profsseer of Mechanical Engineertag, Lt.T. P- ~ 1961-1967~ 1967-Assoaiste Professor of Machanical Engine sring,'EI.T. ' Professor of Machanical Engineer 1ag, M.I.T. [~ [. 1961 Summer. consultant 15N '. - 1969 5pring Visittaa Professor, Raifa Techsten . 1970
. . ., . . ... . 3, . Summer consultant, IBM ,
, . . . . , ., 1 Prefasstenal Ormanisations.. -
Hember, Amerioca physical sostaty l Member, Ameriaan Boeisty of Lubrication Engineers Member, Astrissa Society of Nashanical Enginaara I Feliev, Physisal Society of Londen 4 Group ' Subscriber, lastitution of Meehaniaal Engineers, London -
. Registered Profeestaan Engineer, Commonwealth of Massachusetts e . *l Awards -
f Rodeon Award of the Ameriaan Boeisty of Lubrication Er sineers for 1957. ! Basearch Exoarience ' l His research has been in the fielde of friction and wisr, matarisis, mach- . anisal reliability, the mechaniens of polishing and at mainution, and,the see of radioisotopes. '
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feeshina Enserience -- Courses taught have been in the tialde of Frietten and,'Jear, Applied Mech-saios, Materials, Esperiasatation, and Naterials Ptocat sing . Pubitcations ' ht.9.ht. .
'Pristian and Wear of Haterials,' Wiley, New York,196. . .
'An Introduction to Experimentation,' Addietn-Wesley, i ending, Mass.,19'10. . '
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(with R M. Seek) ' Physical Measurement and Analysisi' Addison-Wes'ie'y , Reading, Mass., 1963. ' ' (edited) ' Friction - Selected Reprints,' Amer. Inst. F1ys., New York, 1964.. (with six other authors) ' Mechanical Behavior of Mater:als,' ed. F. A. HaClintock ud A. B. Argon, Addison 4tesley, Reading, E.ss.,1966.
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-(An st[daher authers) 'An . Introduction to the Manhat.ies of Solids,'
l od. 3. M. Crandall and N. C. (Whi, McGrav till, N.Y., ' 959..: . . . . . . . . - i
. - 4 yideotano 14stura Series *
"An Introduction to Experindatation, A Belf.Itudy Subject," Centar for.
Advanced Engineering Study, N.I.T.. Cambridge, Mass., :.978.
"Engineering Friction, Lubrientionk and Wear, a self-5tudy Subjoetj Center for Advance Study, M. ,T4, Cambridge, Mass. 1974. ,
other teahn' ital writint _ One patent and eighty articles, including Waar, Rusyslopaedia Brittanica 1 Friction Encyclopedia Americana Tribology, Encyclopedia Brittanina Reference Work Listinas . f" Who's Who in Ameries - , p Anertaan Han and Women in Sciones b . ). . .
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. Appendix 2. Discussion of experimental errors The design and mode'of operation of the pin-on-disk friction apparatus are such that errors in the determination of the friction coef ficient tend to be kept to reasonably small values. For example, measurements have shown that the dead weights totalling 2 kg, used for applying the normal load,
{ actually had a weight of 2.006 kg, but this introduced no error because the same weight is used in calibrating the friction force measurement with the dynamometer, i Whtr errors there are arise mainly from some zero drif t in the exper-iment, arising partly from slight instability of the Sanborn recorder in its maximum gain position, and partly from slight drif t in the performance of i the strain Fage ring, resulting from creep of the adhesive bonding the ! I strain gages to the aluminum ring. To counteract this zero drift, we fre-
, quently unloaded the dynamometer, during a friction test, to determine the instantaneous zero position. All in all, I would anticipate that the error #
in the friction coefficient due to this zero drift would be less than 0.02 in all cases, and generally only 0.01 or less. For the typical friction coefficient of 0.5, these would amount to errors of 4% and 2% respectively. A more serious error arises from the fact that the dynamic character-istic of our dynamometer tends to introduce vibration into the friction trace which are probably more extreme than the fluctuations in the' friction coefficient, and we compensate for this by introducing a little damping into the electronic circuitry . The consequence is that there is no error in determining the average va'lue of the friction coefficient, which consti-tutes almost all the friction values tabulated above, but there may be an error, which I estimate to be about 0.03, in the ' maximum friction' values M
. em . .
cs d2termined in the slow speed tests. An additional source of error may exist in the high temperature tests, in which, towards the ends of the tests, the strain gage ring became sub- . i stantially warm, and in consequence, took on a few of the characteristics of { s' resistance thermometer. Perhaps a random error of as much as 0.10 could , i have afflicted some of the friction values. This has serious consequences q i ' only,in regard to test 4, in which the highest average friction value of O.82 was measured, as well as the highest peak friction value of 0.91. If we cuppose that these data points were afflicted with an error of up to 0.11,
-1 then we can state that there were many occasions in which friction coefficient values ',
i above 0.70 were measured, but it is not dertain that the friction coefficient ever ! rose above 0.80. ( 1 L I l 1 i i 1 O W 99 4
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Appendix 3. Effect of timefof stick on static friction- ' In most. sliding systems, the friction coefficient is increased if the surfaces are kept at rest for long periods of time before sliding is com-menced. According to some workers, this effect continues as_long as the time at rest is increased, while according to others, the friction coef-ficient ceases to increase after the time of stick reaches some time in the-interval 100-10,000 seconds. (A good summary of the various points of view of this problem are to be found in the paper, "Some considerations on char-acteristics of static friction of machine tool slideway," S. Kato, N. Sato and T. Matsubayashi, J. Lubrication TechnoloSy, Trans ASME F, 94, 234-247,. 1972).- ' In our situation, we hardly measured any increase of friction with increased time of stick. But let us make an extreme-case assumption that ; the static friction coefficient is 0.65 after 10,000 sees at rest, and I
.I increases by 5% for every factor of 10 increase of time from that point on.
Then in 20 years (6 x 10 years), the time will have increased by nearly five factors of ten _and the friction will have increased by about 24% to 0.80. Thus, an upper design licit of 0.80 seems adequate, even if we assume that the friction coef ficient continues to increase. (Incidentally, I per-sonally believe that the friction does continue to increase with time of stick and have published papers to that effect. According to the'Kato paper referred to above, this is by now a minority position). i e W 9 e
._..__m _ _ _ _ _ _ -------- ----- - _ - - - -
Appendix 4 Statistical analysis of friction eacfficient values A short statistical analysis of the friction data has been carried out in order to determine, by standard statistical techniques, the highest and lowest friction values which night reasonably be anticipated. As vill be seen by examining the actual friction' coefficient values, the f riction cnef-ficicnt values observed in this series of tests cover a wide range, since there is systematic variation of the friction with the degree of surface contamination and with the sliding speed (as well as considerabic random . variation caused by local variations in bond strengths between the various junctions found between the top and the bottom sliding surfaces). According-ly, it seems sensibic to perform separate analyses to determine the highest expected friction coefficient value and the lowest expected f'riction coef-ficient values. . A. 111ghest friction coefficient values
! I Herc we consider all the friction runs which gave high friction values, namely tests 2, 4, 6, 8 and 10 (eliminating in cach case the first two values, which might have been af fected by contamination), as well as the second half of the results obtained in static friction test 1 and all the results of static friction test'2.
In this way we obtain 134 friction coefficient values, and their his-togram is shown in figure 1. The normal distribution which best fits these data (i.e. by having the some number of data points, the same uean, and the same standard deviation) is superposed. The mean f riction coef ficient value for these data in .563, and the standard deviation is .096. The procedure for carrying out-these computations is discussed on pps
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we a _m_.______m_____ _ . _ _ _ _ . _ _ _m---__ - _ _ _ - - - --
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- 47 to 51 cf the b sk "An Introduction to Experimentation," E. Rabinewicz, Addison-Wesley, Reading, MA, 1970.
B. Lov friction coefficient value, . All the friction data given in the body of the report but not shown in ! l figurc 1 is plotted in figure 2. Again the corrcsoonding normal distribu- l 1
- 1 tion is superposed.
The mean friction coefficient value in this case is .380, and the standard deviation is .080. Discussion At this point we must decide how many standard deviations to go above and below the mean, in order to conpute the highest and lovest anticipated friction value. Under normal circumstances, a value of three or four times
- the standard deviation vould seem to be appropriate. In this case, I think l a value of twice the normal distribution is more sensible, in that there is alrea'dy a considerabic degree of averaging in going fron the tests with an j area of .006 in to the application with an area of 100 in . Mominally, a standard deviation of 67 + 29) or (x - 29) is execeded about once in every 40 occasions, but because of this arca ef f cet, in this case the likelihood i of exceeding the extreme value is very small.
As regards the high friction value,5i + 29 is .755 l As regards the leu friction value, 3i - 2G'is .224. i Note, in deriving these values, we have allowed only for randon fluct-untions, not systematic effects. As regards the high friction value, there is the likelihood that the f riction value may continue to risc with time of i
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,. stick, cnd bcnes socic small allowance for this, raising the friction coef--
ficient to .80, may be appropriate. . As rer,ards the' lou f riction value, an allowance for 3rcater contamination appears to be prudent, thus louering the-
. friction coefficient to .20 or even a little further. N g ,4 The method used in this analysis,-of separating the experimental data 'l
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.into high friction and low friction values nay strike the reader as being D $r '$,~ .
I very artificial. If we simply lunp all the 199 friction values together, . kw.w 2 w . Th -
. the overall population has a mean of .303 ,and a standard deviation of .125. L u d ]; -
Thus the upper. limit (E +' 26') would be .753, and the louer limit (E - 26%) hMjt'
.a w amounts to .253. . It'v111 be seen that these values are alnost the same as Su y (
% F5 those yicided by the other analysis. msv Incidentally, we have also analysed the data'shown in fic.ures 1 and 2 .:$' ' .(.
2 by ', carrying out a K analysis (as outlined on pps 52 to 55 of the "An Intro- . duction to Experimentation" text cited above). The data shown in figure 1 s i are quite unlikely to be a nornal distribution,. since~X~ is 16.29 with 6 degrees of frcedom, giving a P value of .014 only. The data of figure 2 gives a)( value of 3.40 for four degrees of- freedon and a. P value of .49, and may well bg part of a normal distribution. In. this particular case, I don't believe the above analysis is invalidated by the finding that the exper- ! imental data shown in figure 1 are not norna11y distributed, l ! I i i 1 i
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;.. .' Enutry tLG 3)W Appandix 5. Outstions-subnitted to me throup.h Besten Edisen
, (Based on the main body of the report and the first three appendices).
Question 1. We should be concerned only with static coefficients. Long term sliding. which produces high coefficients are not germain to our probicm. Test 6 Test 8, and Static Friction Tests I & II are the only ones which appear.to be useable. , My comment This may possibly be correct, though I should make cicar that modern friction workers regard the distinction between static and kinetic friction. coefficients as being rather artificial, since all friction coefficients are functions of other variables, such as speed, time, rate cf increase of the shear force, and stif fness of the sliding system. ! Question 2. . The use of a small rounded pin with high contact stresses and deforma- !
' tion are not valid. Data taken using this equipnent should be disregarded. i This includes Tests 1 through 4 k My comment For an opposite opinion, I quote from p 98 of the classic book " Friction !
l and Lubrication of Solids ," F. P. Bowden and p. Tabor, Clarendon Press, I Oxford, 1954. "It follows that the real area of contact A' depends only on the loud U and the hardnecs p and is almost independent of the apparent area 3 of the surfaces. Consequently, the friction force F should be independent of the apparent area of the surfaces. This is Amonton's first law,"
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e. e 9 e & Sum sube Wasm fom m tem e W #4 IB
, - 4
,d Qusstion 3. i Using the data presented from the four tests which appear to be valid
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for our situation the maximum values for static friction are .52 in Test 6, i
.68 in Test 8, .72 in Static Friction Test I and .60 in Static Friction Test II. It appears to us that based on these tests and using a standard bell .i curve for data distribution we should have an effective coefficient no higher than .70.
- My comment ,
I don't agree that only four tests are valid. 1 l 1 Final statenent submitted to me i Since the required analysis is not sensitive to changes in friction between .7 and .8 Yankee agrees that the .8 value should be specified. j.
. 1
- My comment Fortunately the required analysis applies equally to frict'on coeffi-cients of 0.7 and of 0.8, so that all is well.
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b;,a-1 - Ernest Rabinowicz e 4 e e p m _._______.__m.__.___._______.__m.-}}