Fourth Edition
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`EXHIBIT
`
`
`Page A
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`DIGITAL CHECK CORP. EXHIBIT 1011
`Digital Check Corp. v. e-ImageData Corp.
`IPR2017-00177
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`

`

`FOL RTH EDITION
`
`Fundamentals of
`Machine Component Design
`
`ROBERT C. JUVINALL
`Professor of Mechanical Eng~eering
`University of Michigan
`
`KURT M. MARSHEK
`Professor of Mechanical Engineering
`Univexsity of Texas at Austin
`
`,|OHN WILEY & SONS+ INC.
`
`Page B
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`

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`To Arh~ene a~d Li~da
`
`ACQUISITIONS EDITOR
`MARKETING MANAGER
`SENIOR PRODUCTION EDITOR
`ILLUSTRATIONS EDITOR
`COVt~ DESIGNER
`MEDIA EDITOR
`
`Josepl~ Hay~or~
`
`Elizabeth
`Sigmund Malinowski
`Harry Nolan
`"~oraas Kulesa
`
`This book was ~ in Times i0/12 by Emilcomp and printed a~ bourd by
`R. R. Donnelley & Sons, The c ~,’e~ w~ primed by Lehlgl~.
`Cover illtt~t~tion:
`
`This bt~k is printed on ac.qd.froe paper.
`
`Copyright © 2006 by Jolxa Wiley & Son.z, tnc, AIl fig~ r~served~
`
`No p~ of this pubr~c~on may be rep~uced, steered ia a ~ s~m or ~
`in ~y f~ or ~ any ~m, e~ ~i~l~ ~o~i~, ~g, ~g
`ox ~ ex~ as ~ u~ ~s 1~ ~ 108 of ~ ~976 ~ff~ ~a~s
`Co~ A~. without ei~ the p~r ~t~ ~s~ ~f ~ ~i~er~ ~
`
`~, ~2 R~ew~d ~, ~nv~, MA 019~, (978) 7~-~, f~ 078) ~,
`or ~ t~ wab ~ www,~fi~t,~m~ Roq~sts ~ ~ ~bl~sh~ for ~i~si~ s~uld ~
`add~ to t~ P~ssions Dep~en~ John Wfl~ & Sons, ~e,, I 1 t ~v~ S~et,
`Ho~, NJ 070~5774; (201) 748-~! 1; ~ (~1) 7~@8, or ofl~ at
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`publisher a~d author a~alte no war.my o~ any ki~ ~ ox ~i~ ~ ~ m
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`p~ ~i~ ~m~g ~i~ is su~c~fly c~pl~ ~ its a~ ~
`X~ always ~e a~e of ~ s~iali~ F~ in t~ ~ ~vol~) ~
`b~k~ of ex~fien~ wi~ rel~ ~m~, ~d a~ate ~ to ~mblish
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`da~ges ~mg ~ ~e use or a~licati~ of ~y i~tioa in ~s ~E
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`Print~ i~ d’~ Uni~ S~ of Am~k~
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`109876543
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`Page C
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`CHAPTER
`
`Miscellaneous Machine
`Components
`
`Introduction
`
`Power t~,msmL~sion b~w~n shafts can be ~lished in a
`difion to ge~s (~a~e~ 15 ~ 16),flex~ et~as s~ as
`
`ed by a ~mid~bIe di~, ~us ~vid~ag ~e ~gin~r wi~
`~ ~hfive pl~e~nt of driving and ~.~ ~ine~’.
`Belts ~ re~ti~’dy quiet in ~fion~ Exc~ for 6~ng ~I~ (Fig~ ~9.5),
`~ge ~ i~lt and pulleys can~s s~d ~fi~ to ~
`~st~ i~ ~fimes u~ to ~vanm~ by ~ng ~e pdleys to
`~e~r in order to d~ng~e ~ ~ve. ~ in ~me ~owblowe~
`lawn m~e~. ~is ~y ~ve su~anti~ east, we~ ~d
`~ate clutch. ~e ~]exibHity m~ i~ent damping in ~1~ (~d
`chains) se~es to ~u~ ~e ~smissioa o~ sh~k and vibration.
`~e @sign of ch~ illustrates ~e genemt ~sifion ~t if a ~m~nent of
`~s~ c~acledsti~ is n~a Mmady av~lable, ~ enter shoed consist
`s
`of im’enfng mme~ing new. ~r ex~ e~ (~e ~nvenfional ~ller and inve~-
`ib~
`pl .....
`~-~th ~ains di~us~ in S~fions t 9.5 ~d 19.6 ~ui~ ~ a~ s~ eng~
`a single chin lie in a co~a~on pl~. S~ a ~si~ve
`twin s~ lying in ~ffemnt pl~, ~ li~ ~
`
`ib~ c~ ir~o~s ~1 s~l ~btes ~ a3 ~
`"bu~ons" ~t ~mat~ the ro~ of a ~fi~ mll~ chain. A c~in em~yi~
`
`Album, ~e m~-~we~ a@lane ~at fl~" ~ the ~is~ ~1
`~r ~srr6tti~g snm!l ~o~ts of l~, ~ible ~s ogen ~ ~x~nslve
`solu~oas. ~ ~mmon automotive s~o~r We is a f~li~ ~ample
`~r ~smittlng ~wer ~tween n~in~ty c~fii~r ~, flexible coupling,
`uni~ jo~, ~d ~c~on clutchs have Mr~dy ~n
`~t gen~ c~s~ of ~Iin~ mem~ ~le ~ u~smit ~,~ do ff~ ~ &vd~)~mic ....
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`Page 748
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`|,9~ Flat Belts
`
`19.2 ~ Fl~tBegts
`
`7 ~9
`
`action. These are fluid c~mpt~gs (also called fluid clut~zs) ~ hyd~yn~ic ~ue
`
`~h~ ty~s of ~r ~ssi~m ~vi~s u~ r~ ¢~ cable ~ move ~ lift a
`we~L using ~w~ ~iiv~ ~ a ~fing s~t. ~les L~tude hoist, el~
`
`pm~ts i~o~afion on ~h~icM cable ~d wire
`~, and
`
`A belt drive transmits power between shafts by means of a beat connecting pulleys on
`the shafts, be fiat leather belts were in common u~ a few decades ago when one
`large motor c¢ engine was often used to drive several pieces of machinery. In today’s
`more limited use, thm, light, flat belts usually drive high-speed machines. Olden, the
`vibration-isolating capability of tho belt is an important consideration.
`The basic equations for the limiting torque ~b,.at can be transmitted by a flat belt
`are the sanrte as for band brake u~qac,
`
`T= (P~ - P~- Os2A)
`
`and
`
`PI!P2 =(cid:128)"~
`
`(Ig26)
`
`where P1 and P2 oze the fight and slack side belt tensions..fis the coefficient of file-
`lion, and ~ is the ang~ of contact with the pulpy (see Figure 18.I5). These two equa-
`tions enable P1 and P2 to he determined for any combination of T,f, and 4~. The
`required initial belt tension P~ depends on the elastic characteristics of the belt, but il
`is usually sa~factory to assuum thai
`
`P~ = ~I + Pz~2
`
`(19,1)
`
`Note that the capacity of tl~ belt drive is determined by the angle of wrap ~b on
`the smaller pttlley and that this is parlknAarly critical |br drives in which pulleys of
`greatly differing size are spaced closely together. An important practiced considea’ation
`is that the required initial tension of the belt not he lost when the belt stretches Slight-
`ty over a period of tim~. Of course, one solution aright be to make the initial ~tal-
`lafion with an exce~ssive initial tension, but this v, xuald overload the bearings and shafts,
`as well as shorten belt life. Three methods of maintaining belt tension are ilhLstrated
`in Figure 19.L N~e that al! three show the slack side of the belt on top, so that its ten-
`dency to sag acts to increase the angle of wr~ap,
`The coefficient of friction hetweon bek and pulley *,~u, ies with tim usual 1L,~t of en-
`vironmental factors a~d wi~ the extent of slippage, In addition to on~ary "torque
`transmission slippage," belts experience slip, commonly called "creep," through the
`slight s~,e~ch or comraczion of the hel~ ~ its tens’ion varies between P~ and P2 while
`going th~,’o~gh angles ~b in con~t with the pulleys. For leather bering and cast-iro~
`or steel pulleys,f = 0.3 is often used for design purposes, Rubber-coated belting usu-
`ally giv’es alower value (perhaps f - 0.LS). whereas n~ning on plastic p~lleys usually
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`Page 749
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`gives a slightly higher value. It is always best to obtain friction values from tests or
`from the belt matinfacturer.
`~l~e al|owab]e value (cid:128)ff" fight-slde tension Pt depends on the belt cross ~¢don
`and the strength of the materi~ As the belt makes one revolution, it goes thruugh a
`rather complex cycle of fatigue loading, In addition to the tensile fluctuation between
`P~ and P2, the belt is ~ubjecled to bending stresses when in contact with the pulleys.
`The greater bendi~kg stress occurs with the smaller pulley, and for ~s reason there are
`minimtm~ pttlley diametea’s that should be u,sed with any particular belting. For leather
`belting a fight-side ~en.~ile stress (Pt!A) o1’250 ~o 4(.)0 psi is usually s~ed,
`The above discussion pertains to belts that run slowly enough that centrifugal
`loading can be n cetera,
`egl
`For g
`renter power-trattsmit’dng capaciIy, most belt drives
`operate at relalively high speeds The centrifugal force acting on the belt creates a
`tension Pc of .........
`
`w
`
`’~th mass, pet’ " r~gth f belLV" th belt 1 "ty, d th p Ily .....
`
`al’ld P2 in Eqs, 18.24 and 1826. The result is that Eq. 18.24 is unchanged and
`18.26 becomes .......
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`Page 750
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`19.3 tt ;’:BMt~ 7511
`
`It should also be noted that centrifugal force tends to reduce the angles of wrap ~.
`
`be constant, and the p~wer tra~mitted wooM increase linearly with speed. On the
`other hamL if an unloaded belt drive is driven at suff’rcient slx~..& cen~fugal force
`alone can load the belt to i~s tensile cap~city. |1 follows, then, that d’~ere is some si~d
`at ,*Chich the power wactsmltting c~acity is a m~imm~ With leaiffmr belting this is
`cormnoniy in the vicinity of 30 m/s (6000 fVmin), whh ahom 20 ali s being regarded
`as an ’qdeaF’ operating specd. M1 factors, including nM~ and life. being confidered.
`As was the case in determining appropriate s~e~ of beatings and gears, a vadaty
`of"ex~ fa~tors" should be taken into accotmt when selecting belt sizes. These
`h~cinde torque fluctunfions in the ddving and driven shaft, starting overloads, pulley
`diamete~ mad environmental contamination such as moisture, dirt, and oil.
`
`19.3 V-Belts
`
`V-belts ~ used with elec’Mc motors to drive blowm, compressors, appliance.s, ma-
`chine to~l~ farm and industrial machinery, and so o~ One or more V-belts are used
`to drive the accessories on automotive and most other internal combustion engines~
`They are made to slandard leag~s arm with the s~ cro~-sectiot~ sizes shown
`in Ngt~ 1922, The grooved pulleys that \~betts nm in are called sheaves. They are
`
`0.62
`
`5V
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`Page 751
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`Ch~ 19 ~ Misc~eous Mo~ch~ (cid:128)ompormnts
`
`usually made of cast iron, press~t steel, or die-cz,~t metal. ~(cid:128):belts work well with
`short center distances, Because of the resistance to stretch of the~ interior tension
`cords, V~lts do not r~uire ilequeat adjustment of initial tension.
`When a ~g~e V~b~lt has insofficiem c~p~ity, multipte beats may be ~s~
`shown in Figure 19.3. As n~’~y as 12 or more belts ar~ commor~y used in heavy
`duty applications. It is imporlm~t that these he obtained as matcht~l sets, so t~t the
`load is divided equally~ When ene ~elt tmeds replacemenL a complete r~ew set should
`~e instal|ed~
`Figtwe 19.4a shows how a V-belt rides Jrt the sheav~ groove with contact on the
`sides and d~¢e at the bottom, This "wedging action" increases tbe normal force
`oa a belt element fix:nn dN (as in Figures 18.16 or 19Ab) to dNtsln/~, which is
`proximately equal to 3.25 tiN. Since the friction force a~’ailable for torque transmis-
`sion is assumed prt3portional to normal force, the torque capacity is thus increased
`more tha~ threefold. The flat-belt equations can be modified to take this into account
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`Page 752
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`19.3, = V-Bel~
`
`753
`
`by merely replacing ~ ~fficicot of fficlSco f ~vith the quaatityftsin ~, Bqaation 19.3
`
`Since the capacity of a belt drive is no~ l~ted by the slippage of the sma//er
`patt~< V-belt drives can sometimes be used with a fiat tza’ger pulley (as in Figure
`19.4b) with no sacr~e in capacity. For example, the V-belts driving t~ drum of a do-
`mestic clothes dryer or the flywheel of a large punch press normally rida~x directly on
`the fiat drum or flywbeet surface~
`Some sheaves are made with provision for adjusting the groove width, This
`va6es the effective pkch diameter and permit~ moderate changes in speed ratio. A
`familiar example is the V-bell drive of domestic furnace blowers that I~ave t~ts fan-
`tttre to permit an adjustment in the velocity of the discharged air. An extension of
`this principl~ is used in adjustable slued drives that can be made to vary continu-
`ously. These employ special exUa-wide V-belts with matched pairs of variable-width
`sheaves I~t adjust simultane~msly (wilh the machine rung) to accommodate the
`fixed belt teng~.
`There is a sufficient variation in the strength and friction properties of commer-
`cSal V-belts that the selection for a sp~’~c application is best made after consulting
`test data and details of service experience in the manufacturer’s literamre~ In gener-
`at, it is recommended that belt speeds in the range of 20 mJs (4000 t~dmin) be t~l
`~’he.re feafibleo
`V-bek life is m~y affected by terra,are. V~gaere elevated belt tem~res
`(~y, above 200~F or 93’~C for cons~fional bells) are encoun~:ered, belt life can often
`be substantially improve~l by putting fins on the sheaves to increase air circulation.
`
`SA,~It’t~ I~O~L~t 19,1 Select Belts for V-Belt Drive
`
`A 25-hp, t 750-rpm electric motor drives a ma~e through a muldpte V-belL The size
`5 V-brits used have an angle,/3, of 18~ a~d a unit weight of 0.012 Ibiin. The pulley
`on ~ motor shm~t has a 3 7-in. pitch diameter (a standard size)~ and the geometry is
`such that the angle of wrap is 165°. it is conservatively assumed that the maximum
`belt te~n should be limited to 150 Ib, and that the coefficient of flier.ion will be at
`least 0.20. How many belts are required?
`
`SOLUTION
`
`h~m~u A motor of given ho~epower and speed drives an input pulley of
`known diameter and angle of wrap. The size 5 V-belts have a known unit weight
`and angle fl The maximum belt teosion is 150 lb arid the coefficient of friction
`is 020.
`
`Find: Derermirm the number of belts requh"ed,
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`Page 753
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`Chapte~ 19 ~s Mi~cdl~ M~c~ Compon~r~s
`
`1. The raaximum ~ensioa in ~he b~lt is limited to 150 lb,
`2. 13a~ coe~cient of friction will 1~ m ]~st 0.20,
`3. Power is sb~rcd equally by each belt,
`
`A~*a~y~:
`L TI’~ terms in Eq~ 19.3a are caicul~ first.
`
`1750
`WithFq, 19.2, P,, = mV~w~V = 3.7 (~) ~ = 339indic
`
`0.012
`= (339) =
`
`Substituting in ~. 19,3a ~d solving h~ P~:
`
`150 - 3.57
`
`P2 - 3.57
`
`~nce, P~ = 26.3/b
`
`=6A5 or 1~.4=6,45~-23,0
`
`F~m~. 18.~, T = (P~ - P2)r = (150 - 26.3)~ =
`
`From Eq, t.3, I~’ per bolt Tn 1750(229) 6.36 hpYbelt
`5252 5252(12)
`
`25
`
`~ (m)m~mt~ If a 30-hp motor was used, then 5 ~lts woaM ~ ~. As m~
`~ and m~e ~lts ~ need~ bowever, ~ e~ of misali~w~nt of ~ sh~ (a~
`~ co~nt u~uN s~dag of~e k~) ~ome i~ant.
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`Page 754
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`Toothed oz’ tim~ belt.
`
`Toothed Belts
`
`Fig~ue 19.5 illustrates toothed belts, also known as timing belts. Since the drive is by
`meaos of teeth rather than friction~ there is no slilrpage and the driving and driven
`shafts remain synchronized. This ~ too~ belts to be used for many applica-
`tions like driving an engine canxshafl, from the cmnkshaf~ for which the use of other
`types of belts would be impussibie. The toothed drive, having tension-carrying cords
`with ra’~mum stretch, permits installation with minimal initial tension. This reduces
`bearing loading and shaft-~g loads.
`Toothed bells permit the use of small pulleys and small arcs of contact. Contact
`on only six teeth is sufficient m ~lop fiatl-rat~l cap~ir~; Toothed belts are ~vety
`lightweight, and can give efficient operation at speeds up to at least 80 m/s
`(16,000 ft/mln). Their principal disadvantage is the higher oost of both ~ belt and the
`toothed pulleys. As with other belts, long service life can be obtained, but not as long
`~ts ~ service life of me.lie power transmission members (gears and chains). For ex-
`ample, automotive engines using timing belts for the camsh’dt drive usually require
`belt replacement at around 60,000 miles (100.000 kin), whereas gear and chain
`camshaft drives usually last for the life of the engine.
`
`19.~ Roller Chains
`
`There are several types of power u’an~ssion chains, but the most widely used is the
`roller chain. Of its many applicatior~, the most laminar is the c~ drive on a bicy-
`cle. Figure 19.6 ilta~s the con~on of the chain. Note the alternation of pin
`links and roller links~ For analyzing the lo~ ~hal can be tun’led by a given chain, the
`forc~ flow concept of Section 2.4 is ~ate. The procedure begins w’~ch the por-
`tion of the load (depending on ils dis~bution among the driv’mg sprocket teezh h’~ cor~
`tact) applied to a chain roller by u driving sprocket toolh. From the roIter, the load is
`tear.mitred, in turn, to a hushing, pin, and p~ of tiak plates. Mox~g along lhe chain,
`this load is added to loads from other sprocke~ teeth. F’mally. su~ive pins, hashings,
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`Page 755
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