rJUCTION AND WEAR
`oF MATERIALS
`-----
`
`second Edition
`
`ERNEST RABINOWICZ
`
`A Wiley~Interscience Publication
`JOHN WILEY & SONS, INC.
`• Brisbane
`New y k or
`• Chichester
`
`• Toronto
`
`• Singapore
`
`Sanofi Exhibit 2212.001
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`'l'hls tt~t Is t r,nttxl on it ·ltl•l't'-~ 1-mt 1\
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`owner Is unlawl\1l. R~uc.sls ibr pcrmls~lon t)f t\uth~1'
`lnfurm;1tlon shunl I ~ 1duressed tu th~ I m1hisim,s Oupmtm~nt,
`John Wik. & Soll!i, ln~,
`
`irnadu,
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`
`Sanofi Exhibit 2212.002
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`68
`
`FRICTION
`
`0.3
`
`E 0.2
`E
`.5
`
`0.1
`
`L= 300g
`P= 200g
`
`20
`Time
`Fig. 4.3 Displacement-time cuive for steel on indium, unlubricated.
`
`10
`
`30
`
`40 days
`
`variables: the applied load, the size of the region of contact, and the sliding
`velocity. The three quantitative relations are as follows:
`
`1. The friction force F is proportional to the nonnal force L:
`
`F =fl.
`
`(4.1)
`
`178°
`
`1so0
`
`1a2•
`
`steel
`so
`o
`•
`200 mm
`.
`100
`150
`. . direcuon,
`.
`Fig. 4.4 Di r
`on steel l
`r:ec mn of the fnction force as measured from the shdmg
`' ubncated by a machine oil. Load 1000 g velocity 50 mm/sec.
`
`Sanofi Exhibit 2212.003
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`4.2 QUANTITATIVE LAWS OF SLIDING FRICTION
`
`69
`
`""-is relationship enables us to define a coefficient f f . .
`'u
`. .
`ft
`o nct1on f (o
`)
`.
`Allematively, 1t 1s o en convenient to express this 1
`r µ. •
`aw m tenns of
`.
`f
`l
`fri
`cuonal angle 8 defined by
`constant ang e o repose, or
`a
`
`tan 8 = f.
`
`(4.2)
`It may readily be shown that 8 is the angle of an inclined pl
`h
`·
`h
`·
`·
`ane sue
`that
`any obJect, w atever its weight, placed on the plane will re
`.
`•
`· f th
`mam station-
`l
`· ·
`ary, but that 1
`e ang e 1s mcreased by any amount whatever th b'
`, e o ~ect
`(F' 4 S)
`• d
`will slide own
`.
`.
`1g.
`2. The friction force is independent of the apparent area of contact A Th
`h
`all b.
`us
`a·
`large and sm
`o ~ects ave the same coefficients of friction.
`3. The friction force is independent of the sliding velocity v. This implies
`that the force required to initiate sliding will be the same as the force to
`maintain sliding at any specified velocity.
`
`Taken together, these three laws provide the quantitative framework within
`which friction is generally considered by engineers. It is therefore important
`to discover how closely these laws apply in actual practice.
`The first two quantitative laws are generally well obeyed, to within a few
`percent in most cases (Figs. 4.6, 4.7). Exceptions to the first of them occur
`mostly with very hard materials like diamond or very soft materials like Teflon
`(Fig. 4.8) or at loads down to the milligram range (Rabinowicz 1992). In many
`cases sliding combinations involving materials such as these obey a law of the
`kind
`
`(4.3)
`
`where c is a constant and x a fraction varying somewhere in the range from i
`to 1. Naturally, in cases where the first law is obeye~, x is exactly l ..
`Another case where the friction force is not proportional to the load mvolv~s
`a surface with a thin hard surface layer and a softer substrate. At 1?w loads 1 _e
`f · t' on properties predom1-
`d ·
`.
`h rd
`thin surface layer remains unbroken, an
`a
`its nc i
`
`\
`
`\
`
`w
`
`\L
`.
`Fi
`g. 4·5 Equilibrium diagram for an obJect on
`Plane·
`·
`16 imminent.
`
`F= W sin6
`L= Wcos6
`E.= t= tan6
`L
`
`e down the
`l.
`an inclined plane. S ippag
`
`Sanofi Exhibit 2212.004
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`. -. ' .
`
`•
`
`•
`
`•
`
`h
`(l SO)
`11\H\,lllU"'
`UI \1 ·~ ·t:e(t
`
`l
`
`10~
`
`10•
`
`,
`
`"'
`
`• ~ c \-
`
`, ~
`
`.. surfa ,. \~ er is hro~--en through, tmd the properties l)f
`i 1portant Fig. 4. ).
`·
`t
`~ nd qn~mtimtive la'. , which st<.ites that friction i~
`, re t re~ f · nttl~t, are s metirnes n ted in very sm()Qth
`.
`. nditions very trong interaction betw~n
`s ,,. ~-
`nde.r the
`..
`.\!,.; . . . ,~ .... ·,~ u, ~~ pl ~. nd th~ fri ti n furce becomes independent of th"" lood
`lere-1~ m the 3P~1rent area of conta t "hich has become the
`· "nsl
`~~---~"'" • Sucll cases are dis ussed Inter.
`ph sired that th first and s
`nd qunntitati e laws are gen-
`yro and th t pron , unced e."Xception
`to them are rarities.
`·oi _re si m1ti n where if w chanooe the load or the area by a
`fficient hanges by a fuctor of 10 or less. Rather
`fricti n
`,
`'"' J)(r · · n f the thiro law which suites that friction is independent
`
`·
`
`~ ·
`
`.....
`
`t i~
`
`·--__,,;-----------
`•
`•
`
`Wood on steel
`unlubricated, L • 30 g
`
`0 --.a. __ ---1. __ --1, __ ___,J~---'
`/64
`1/ 16
`1/4
`1
`4
`Area, sq in.
`. 1 l1
`Tbe_ e~ of changes in contact area on the friction of wood 00 st
`ee ·
`·-=..uu ,-an-s.n n is found.
`
`Sanofi Exhibit 2212.005
`Mylan v. Sanofi
`IPR2018-01675
`
`