PRECISION
`MACHINE
`
`
`
`Sanofi Exhibit 2214.001
`Sanofi Exhibit 2214.001
`Mylan v. Sanofi
`Mylan v. Sanofi
`IPR2018-01675
`lPR2018-01675
`
`

`

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`ln hw rm i • a trod mark of he Burleigh orp mti n.
`lndu tos •n is a trademark of Farnmd lndustrie ', In
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`ISBN □ - 13 -690918- 3
`9 000 >
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`Print<.'d m th United
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`ISBN □ -13- 6 9 0918-3
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`Premk -Hall lnternati nal (UK) t· · d
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`Sanofi Exhibit 2214.002
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

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`Sanofi Exhibit 2214.003
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

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`The lead angle O is found b I unwr 1pp 11 • 1 , n I(' tu111 c I lhr 1111 1 I , l11d1 n
`the lead ~ at a pitch radiu, R:
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`Sanofi Exhibit 2214.004
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`u, t l f Pon· r Trr11 mi. ion Ele I nr
`
`707
`
`j z
`
`-dFz
`
`R
`
`/
`
`1'hn:ad
`angle o.
`
`haft thre d
`
`co~8 COS([ d.F1
`
`Force crew shaft thread
`appli
`to the nut thread
`
`Fi0 ure 10. . F rce a e tion of leads re\ thread apply to the nut thread whe~ lifti~g
`(\\·orking a~ain t a load. The thread nom1al force ha been decompo ed mto tt
`mponen .
`
`Fieure I 0. . h \\ a e tion of a lead crew thread that i being u ed to lift (work again t)
`a lo d. The relati n between the differential axial force d.Fz and the differential circumferential and
`radial force are ti un
`from a urnmation of the force at a point:
`
`dFe = d.Fz t o o. + _nRµ }
`_xRco a. - µ
`
`_
`dF.
`R-
`
`- dFz ina.
`CO aco 0 - µsin0
`
`For the
`
`e where the
`
`re,
`
`u ed to lower a load
`
`dFa = dFz {-1tRµ - co o.}
`_xRco a.+µ
`
`(10.8.3)
`
`(10.8.4)
`
`(10.8.5)
`
`(10 .
`
`. 6)
`
`The pre ence of the radial force 1 a hint that on mu t look at what el e i happening to the nut in
`additi n to th u ual cal ulation for the required drive torque.
`the d pth of thread i a· urned mall compared to the diameter of the crew, the axial
`in
`an be on idered to be di tributcd around a helical !in through a thread contact angle 'I'.
`fi re
`The differential axial force d.Fz i thu
`
`(10.8.7)
`
`For a right-hand oordinat y tern uperimpo ed at the center of the lea crew haft the Carte ian
`rdinat of an , point on the h lix at an angle 'I' will be
`
`=R o 'II
`
`Y = R sin 'I'
`
`z = \jlt
`2n
`
`(10.8.8)
`
`ted in the a e , here gravity doe not help the lead crew to move the load (i.e.,
`\Ye are inte
`raisin, a load e u lowerin a load). For con enien e, let the following constants be introduced:
`
`CRR =
`
`-
`ino.
`co aco 0 - µ in0
`
`(10.8.9)
`
`Sanofi Exhibit 2214.005
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

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`l 10 .. 11)
`Int ,ratin'-' th diff 'renti,ll mmn nt. ab ut th X. Y. und Z a., s. C'llL 'd by lh diff r ntial force
`\" ~ ~tire helh um.I' 'l'. ) ields lh' m m ·ms imp s don th :e ~,,. :haft" hil r ising a I ad:
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`RR= FzR / , 'rt. + _,rRp \
`\ _,rR · sex - ~Lt /
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`dFz = Fz d'lf dR
`(R0
`- R1) 'If
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`th relation betwe n 0 and R giv n
`in lud
`Equation 10 .. -10 . . l would have to be expanded t
`11 = dF2 { }. Th
`in Equation IO. ·- · The moment quation would then e of the f rm
`t ta!
`f the thread. This i · a
`moment ould then finaJI: be btained by integrating ov r th height
`I nJ t print h "r . and the · ar
`traightforward but t diou pro
`that pr du es quati n t
`rare I needed.
`ote that for th
`a e of a 0111111011 ball crew. th
`nta t i - e · ntiall at a
`on cant radiu .
`A imilar anal
`lower the load i
`
`i • an b performed ~ r the a of l w rin,.. 1 1 ad. Th
`
`t rque requir d to
`
`(10 .. 16)
`
`There are thre int
`
`ting re ult fr m thi analy L that a di u ·ed ind tail b low.
`
`Backdrfreability
`n that if the I nd :atisfie: th f llowi11g: r lationship.
`From Equation 10 .. 16 it an b
`no torque will be required t prevent the crew fr m rurni11g I gardl s,
`f the magnitud of the
`axial load:
`
`t ~ 2nR~L
`co a.
`
`( I 0.8.17)
`
`thi condition i known a, 11011-ba kdril'eob/e or elf-locki11g. For
`~ lead _crew whi h ati fie
`j - oft 11 an importanr feature becau e it
`indu tnal lead ere
`appli atio11 , ba kdriv abilit
`mm1m1ze the holding power and brake ize required. For pre i ion ser
`-contr lied lead. ere
`it
`i ~ot reall an important requir ment alth ugh it d e. help to pr vent for
`p rturbati 11 from
`bemg reflected back through the dri etrain.
`
`Sanofi Exhibit 2214.006
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`Linear Power Transmission Eferne11t.1·
`
`8
`/0,
`
`709
`
`Efficiency
`The cffi iency tis defined as the acwal work divided by the ideal work(µ =
`2R/P1 the worst-ca e efficiency occurs when lifting a load:
`
`O Selling ~ =
`).
`
`_ c sex (rcBcosu. - µ)
`,,-
`1t~cosa. (cosa, + 1tPµ)
`• h d' fr
`t diameter/lead ratio\ and
`,
`.
`_ .
`.
`1 ,eren
`Figure l 0.8.8 shows efhc1enc1es for various types of screws wit
`,
`.
`le
`thread angles a. as defined in Figure J 0.8.8. Note that a s_ta~dar_d ~cme thread ~~\ a~ ~:~e
`between the threads of 29° or ex = l 4.5°.
`he coefficient of friction 1s difficult to pre ic '. _u
`h
`f Jeadscrew and s1zmg t e
`•
`h
`can obtain rea onable estimates for the purposes of choosing t c type o
`·
`drive motor.
`
`(10.8.18)
`
`>. u
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`9
`
`10
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`Figure 10.8.8 Lead crew efficiency: (1) light preload special fini h ball crew ex.= 45°
`andµ= 0.001, (2) light preload ball crew a.= 45° andµ= 0.005 , (3) lubricated lapped
`lightly loaded Acme thread ex= 14.5° andµ= 0.01, (4) heavy preload ball crew ex.= 45°
`andµ= 0.01, (5) lubricated ground Acme thread a= 14.5° andµ= 0.05, (6) lubricated
`tapped Acme thread ex.= l4.5° and µ = 0.1.
`
`Noise Moments
`The analysi above showed that in the proce of creating an axial force with a moment
`about the leadscrcw axis (shaft torque), off-axi moment are also created about axes normal to the
`haft. The e moment are referred to here a noise moments95 not becau e they are cau ed by
`random effects (they are not) but because they are unwanted re ultant moments. The e moment
`are plotted in Figure 10.8.9 for a lapped lead crew with forced light oil lubrication. Similar results
`are obtained for other types of lead crews.
`Figure 10.8.9 how the noise mo_ment functions to be decaying inu oid . The magnitude
`of the inusoid can be large and thus reqmre extreme care on the part of the lead crew manufacturer
`to choose a helix angle to minimize the two moment . The sinusoids are out of phase so there is
`hown in Figure 10.8.10, the rm of the noise
`no point where both moment are zero. A
`moment i minimized at an integer number of turns of the helix angle. Thi also causes the net
`lateral force
`to be zero. A problem ari e when manufacturing errors effectively change the
`amount of contact between the nut and crew and hence the magnitude of the noi e moment. A
`can be een from the graph, a mall variation in number of effective thread turns can ometime
`mean a large increa e in noise moment . Although the
`inusoid are decaying, there i no point
`where the MX and My moments are both zero. The more thread turns that are used, however. the
`
`" oi ·e moment" is not a . tandard term, ·o ometimes you may have to explain that they are moment about axe
`95
`oi e moment is a
`orthogonal to the crew axe .
`imple term that de cribe what they are to the design engineer.
`
`Sanofi Exhibit 2214.007
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`710
`
`10.8 linear Power Transmission Element$
`
`less the chance of a variance in contact area, causing a large disturbance. The noise moments are
`why no leadscrew can be directly bolted to a carriage without causing pitch and yaw errors, even
`though in most cases they are negligible, to be imposed on the carriage's motion. In many cases
`the noise moments will seem to vary randomly as the process of varying contact zones may itself
`be random. In other cases the noise moments may vary sinusoidally as balls enter and leave a
`ballscrew raceway. The noise moments also contribute to the wear of the leadscrew.
`
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`Number of thread turns N'f =7J
`
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`
`Figure 10.8.9 Noise moments on a leadscrew nut with 14.5° thread angle, coefficient
`of friction = 0.1, lead = l O mm, and diameter = 40 mm.
`
`The minimum rms noise moment ratio is independent of the number of thread turns;
`however, the fewer thread turns, the steeper the rms noise moment slope, so if the exact desired
`number of thread turns is not achieved, the consequences will be greater. Figure 10.8.11 shows
`the effect of the coefficient of friction on the minimum rms noise moment ratio. In the limit
`when µ is infinite, a torque applied to the shaft only produces a torque on the nut. This helps to
`explain why sliding contact leadscrews are quieter, in addition to their lack of rolling balls, than
`ballscrews. Figure 10.8.12 shows that a decreasing lead also yields a quieter leadscrew. In the
`limit when p goes to infinity, a rotation applied to the shaft yields no linear motion and hence no
`noise moments. Figure 10.8.13 shows the effect of varying thread flank angle on the minimum
`nns noise moment ratio. The ideal threadform would have square threads (a. = 0). Note that
`ballscrews, which have a large contact angle of 45°, thus typically have large noise moment ratios.
`
`_____...._
`Sanofi Exhibit 2214.008
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`/0.8 linear Power Transmission £/emems
`
`711
`
`....
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`Number of thread 1urns N'{' =1Z
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`Figure 10.8.10 Root mean square of noise moments in Figure 10.8.9
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`Figure 10.8.11 Effect of coefficient of friction on minimum rms noise moments for a
`40 mm diameter, 10 mm lead leadscrew with 14.5° thread angle CL
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`Figure 10.8.12 Effect ?f diam~te~-to-lead ratio ~ on ~inimum rms noise moments for
`a Jeadscrew with coefficient of fricnon of 0.1 and a 14.5 thread angle ex.
`
`100
`
`Sanofi Exhibit 2214.009
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`, - ~~
`
`--
`
`712
`
`~
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`10.8 Linear Power Tran.smi.ssion E/emen.t.s
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`Figure 10.8.13 Effect of thread angle ex on minimum rms noise moments for a
`leadscrew with coefficient of friction of 0.1, 40 mm diameter, and l O mm lead.
`
`The maximum rms noise moment decays asymptotically with the number of thread turns.
`Figure 10.8.14 shows the effect of the diameter-to-lead ratio p on the maximum rms noise
`moment ratio. Changing ~ changes the lead angle, which affects the maximum noise moment
`ratio in a nonlinear manner. Still for a large number of thread turns , the noise moment ratio
`decreases with increasing ~- For a small number of thread turns, one wants ~ to be small to avoid
`the possibility of experiencing large maximum noise moments if the exact desired number of
`thread turns is not achieved. Figure 10.8.15 shows the effect of the coefficient of friction on the
`maximum rms noise moment ratio. Once again, the higher the coefficient of friction, the lower
`the noise moments. This is not to say that one should purposefully increase the coefficient of
`friction, because that could lead to other control problems. Figure 10.8.16 shows that the
`maximum rms noise moments decrease with decreasing thread angle ex and increasing number of
`thread turns.
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`envelope for a leadscrew with coefficient of friction of 0.1 and a 14.5° thread angle a .
`
`6
`
`9
`
`10
`
`Sanofi Exhibit 2214.010
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`{J.<.
`
`ine f P Wl'r Transmission Elements
`
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`Figure 10.8.1S Effect of coefficient of friction on maximum rms noise moment
`envelope for a 40 mm diameter, IO mm lead leadscrew with 14.5° thread angle a.
`
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`Figure 10.8.16 Effect of thread angle a on maximum rms noise moment envelope
`for a Ieadscrew with coefficient of friction of 0.1 , 40 mm diameter, and l O mm lead.
`
`A high-quality leadscrew will have minimal noise moment variations . This is often
`achieved (in general) by increasing the number of thread turns, which also increases load capacity
`and stiffness. Increasing the number of thread turns decreases the slope of the noise moment curve,
`so if the exact number of desired turns is not achieved (and the number may oscillate slightly when
`balls are used), the effects will be minimized. Unfortunately, many manufacturers are not aware of
`the existence of noise moments because noise moments usually only manifest themselves as
`problems when submicron performance is sought. Some manufacturers will provide noise
`moment data if they have ever bothered to make the measurements. In many designs, such as in
`the design of a turning center with I µm r~solution,_ the noise moments create insignificant errors.
`In other cases, such as a diamond tummg machme, the error due to noise moments can be
`significant. Sometimes one just ha_s to ~uy a whole box of leadscrews and test each one until one
`is found that meets the desired spec1ficatwns.
`.
`As discussed in Section I0.8.4, there are vanous types of coupling systems one can use to
`help minimize the magnitudes of loads imposed on the carriage driven by a leadscrew. Ideally. a
`leadscrew would have no mechani~al ~ont~ct between the threads . . This would give it a much lower
`•se moment ratio and no vana11on m contact area; thus 1t would have very consistent
`;~onnance, which could readily be mapped. This type of leadscrew is di scussed in Section
`10.8.3.8.
`
`.
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`Application of the Analysis
`The drive t.orque and efficiency results of th'.s anal_ys1s are w1thm engmeenng tolerance for
`ost types of !eadscrews. The results tor noise moments can be used to provide an
`. h
`use wit m
`·
`.
`.
`f ,·he noise moments that will be generated. These estimates can then be used in the
`.
`estimate o
`
`h,
`
`Sanofi Exhibit 2214.011
`Mylan v. Sanofi
`IPR2018-01675
`
`

`

`714
`
`10.8 Linear Power Transmission Element!I
`
`machine's error budget to help guide the sizing of bearings and carriage structural components. As
`will be seen below, some screws do not have continuous contact around the thread helix. These
`screws would require individual summation of the forces at the contact points. For example, a
`ballscrew manufacturer would use a computer to provide a summation of the differential moments
`caused by all the balls contacting the thread surfaces. This would allow the manufacturer to choose
`just the right number of balls for the recirculating path to carry the desired proper load and to
`minimize noise moments.
`The efficiency (Equation l 0.8.18) can be used to obtain a much simpler equation for the
`relation between drive torque, axial force, and lead. The rotary power into the system is the
`product of the drive motor torque Mz and the rotation ang~e 8 .. This power equals the linear power
`out, which is the product of the force Fz generated, the axial distance moved, and the efficiency of
`the system. The force generated by a leadscrew can therefore be expressed as
`
`Fz= 21tt,,Mz
`e
`
`(10.8.19)
`
`If a leadscrew has a fine lead, a low-torque, high-speed motor can be used to drive the system. In
`addition, if the lead is accurate, a lower-resolution sensor can be used to measure the rotation of the
`screw. Until recently, mechanical systems were more accurate than electronic systems. Today, the
`motivation for using fine leads is to minimize drive-torque requirements and to allow for the use of
`stepper motors.
`With the relations above, it is also not difficult to show that the equivalent linear stiffness
`of a rotary stiffness reflected through a leadscrew is
`
`?
`4n- ~otary
`Klinear equivalent =
`? t
`
`(10.8.20)
`
`As was shown in Section 5.2, the axial stiffness of a leadscrew is almost always (except for screws
`with very large leads) much less than the equivalent linear stiffness of the rotary stiffness. Thus a
`leadscrew can increase the apparent stiffness of an electric motor. This is one reason why linear
`electric motors may never replace leadscrews in machine tool applications. The same magnet
`technology that advances the state of the art in linear motors can always be rolled into a circle and
`used with a leadscrew to achieve a higher performance level.
`
`10.8.3.2 Sliding Contact Thread Leadscrews
`
`Sliding contact thread leadscrews represent the range from least expensive (machine finished)
`to most expensive (hand lapped) leadscrews. Usually, the nut is made of a bearing brass or bronze
`but can also be made from PTFE. The nut can also be formed by casting a polymer of babbit
`. bearing material around the shaft. For low force applications (e.g., for instrument carriages) the
`nut can be bored without threads and then have axial slits cut into it. The nut is then placed over a
`fine pitch leadscrew (e·.g., 100 threads per inch) and O rings used to clamp the nut
`circumferentially. The fine thread screw will then make its own impressions into the nut.
`Molded plastic nuts are often split and preloaded by an O ring, which puts circumferential
`pressure on the nut. A molded plastic nut running on a rolled shaft may have an accuracy of about
`about 1 mm/m. Molded plastic nut leadscrew assemblies can have leads as high as four times the
`pitch diameter of the screw. They are typically used in applications where the loads and shaft
`diameters are low, less than 500 N and 20 mm, respectively. Molded plastic nut leadscrew
`assemblies may only cost on the order of $10-$100.
`·
`Commercially available thread ground and lapped sliding contact thread leadscrew assemblies
`may have nuts preloaded against each other or they may have split nuts that are preloaded with a
`circumferential spring. Some even have built-in flexural couplings. Figure 10.8. l 7 shows size
`and load capacity data for a commercially available ground and lapped leadscrew with an integral
`flexible coupling in the nut. These ground and lapped leadscrews are comparably in cost to
`precision ballscrews. One of the larger units with X accuracy grade may cost about $1800. An
`XXX accuracy grade may cost three times this amount. With a dosed-loop servo-control system
`that uses a linear position sensor, there is generally no need for specifying an accuracy grade higher
`than X.
`
`Sanofi Exhibit 2214.012
`Mylan v. Sanofi
`IPR2018-01675
`
`