EB Bayer MaterialScience
`
`a design guide
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 1 of 26
`
`

`

`Contents
`
`Snap Joints/General
`• Common featuns
`• 'l)pes of map johafll
`•Comments OD dhnemlonlng
`
`Cantilever Snap Joints
`•Hints for design Calculations
`• Permissible unclen:ut
`• Defledion fon:e, mating force
`• Calc:ulation aamples
`
`Torsion Snap Joints
`• Deflection
`• Deflection fon:e
`
`Annular Snap Joints
`• Permissible undercut
`• Mating force
`• CaJcglatlon enmple
`
`Both Mating Parts
`Elastic
`
`A
`
`B
`
`C
`
`D
`
`E
`
`F
`
`Symbols
`
`The illustration above shows a photograph of two snap-fit models taken in polarized
`light; both have the same displacement (y) and deflective force (P).
`
`Top: The cantilever arm of unsat:isfactmy
`design has a constant cro&s section. The
`non-unifmm distribution of lines (fringes)
`indicates a very uneven strain in the outer
`fiben. Thia design uses 17% more material.
`and exluDits 46'li higher strain than the opti(cid:173)
`mal design.
`
`Bottom: The thickness of the optimal snap(cid:173)
`fit arm decreases linearly to 30% of the orig(cid:173)
`inal cross-sectional area. The strain in the
`outer fibers is uniform dlroughout the length
`of the cantilever.
`
`Page2of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 2 of 26
`
`

`

`Snap Joints General
`Common features
`
`A
`
`Snap joints are a very simple, economical
`and rapid way of join-ing two differaat com(cid:173)
`ponents. All types of snap joints have in
`common the principle that a protmding part
`of one component, e.g., a hook. stud or bead
`is deflected briefly during the joining opera(cid:173)
`tion and catches in a depres-sion (Ulldercut)
`in the mating component.
`
`After the joining openti.on. the snap-fit fea(cid:173)
`tures should retum to a stress-free condition.
`The joint may be separable or inseparable
`depending on the shape of the undercut; the
`force required to separate the compo-nents
`varies greatly according to the design. It is
`particularly im-partant to bear the following
`factors in mind when designing snap joints:
`
`• Mechanical load during the assembly
`operation.
`
`• Fotee required for assembly.
`
`Page3of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 3 of 26
`
`

`

`A
`
`l'fYpes of snap joints
`
`I
`A wide range of design possi-bilities exists
`for snap joints.
`
`In view of their high level of flexibility,
`1plastics are usually very suitable materials
`·for this joining technique.
`
`I
`,In the following, the many design possibili-
`ties have been reduced to a few basic shapes.
`Calculation principles have been derived for
`these ba&ic designs.
`
`The mollt important are:
`
`• Cantilever map joints
`The load here is mainly flexural.
`
`• U-sbaped SDllP joints
`A variation of the cantikver type.
`
`• 'lbrsion map joints
`Shear stresses carry the load.
`
`• Ammlllr snap joints
`These are rotationally sym-metrical
`and involve multiaxial stresses.
`
`Pag94of26
`
`Snap-Fit Joints for Plastics -A Design Guide
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 4 of 26
`
`

`

`Snap Joints/General
`
`A
`
`Cantilever snap joints
`
`The four cantilevers on the control panel mod-
`ule shown in Fig. 1 hold the module firmly in
`place in the grid with their boob, and yet it can
`still be removed whml required. An economical
`and reliable snap joint can also be achieved by
`rigid lugs on one side in combination with
`snap-fitting hooks on the other (Fig. 2). This
`design is particularly effective for joining two
`similar halves of a housing which need to be
`easily separated. The positive snap joint illus-
`mited in Fig. 3 can transmit cxmsiderable
`forces. The cover can still be removed easily
`from the chassis, however, since the map-:fit(cid:173)
`ting arms can be re-leased by pressing on the
`two tongues in the direction of the arrow.
`
`The example shown in Fig. 4 has certain simi(cid:173)
`larities with an 1111Dular snap joint. The pres(cid:173)
`ence of slits, however, means that the load is
`predominantly flexural; this type of joint is
`therefore classified as a "cantilever arm" for
`dimen-sioning purposes.
`
`h
`2
`
`h --;..J----
`!;::;::::::::::::~::::::::-~
`
`Fig. 1: Module for control panels
`with four cantilever lugs
`
`Fig. 2: Cap with two cantilever
`and two rigid lugs
`
`Fig. 3: Separable snap joints for a chassis cover
`
`Fig 4: Discontinuous annular
`snap joint
`
`Page5of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 5 of 26
`
`

`

`Torsion snap joints
`
`The tor-sion snap joint of the design shown for
`an instrument housing in Fig. 5 is still uncom(cid:173)
`mon in damcplastics, despite tbe fact that it, too,
`IUIIOUDbi to a sophisticated mi ecoonmical join(cid:173)
`ing method The design of. a rocker arm whose
`deflection force is givm largely by torsion of its
`shaft pamits easy ~ of 1he cover under a
`fa'ce P; the tmsion bar and map-fitting rocker
`arm are integrally molded wilh the lowfl" part of
`1he housing in a single shot.
`
`Annular snap joints
`
`A typical application for annular snap joints is
`in lamp housings (Fig. 6). Here, quite small
`
`A
`
`Torsion bar
`
`p
`~
`
`undercuts give joints of considerable stlength.
`
`Fig 5: Torsion snap joint on a howing made of Makrolon polycarbonate
`
`Fig 6: A continuous annular map joint
`offers a semi-he~tic seal and is better
`for single assembly applications
`
`Page 6of26
`
`Snap-Fit Joints for Plastics - A Design Guide
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 6 of 26
`
`

`

`Snap Joints/General
`
`Combination of different snap
`joint systems - The traffic light illus(cid:173)
`trated in Fig. 7 is an example of an effective
`design for a functional unit. All tbe compo(cid:173)
`nents of the housing are joined together by
`snap joint.
`
`Details:
`• Housing and front access door engage at
`the fulcrum la. The lugs lb (plesaure
`point) hold the door open, which i11 useful
`for changing bulbs.
`
`• The cantilever hook 2 locks tbe door. The
`door can be opened again by pressing the
`hook through the slit in tbe housing at 2.
`
`• The reflector catches at three points on the
`periphery. Either a snap-fittin hook 3a or a
`pressure point 3b may be chosen here, so
`that there is polygonal deformation of the
`inner ring of the housing.
`
`• The lens in the front door is either pro
`duced in the second of two moldings 4a
`or, if a glass lena is desired. this can be
`held by several cantileva maps 4b .
`
`• The sun visor engages at 5 like a bayonet
`catch. Good ~ability and low-cost
`production can be achieved with carefully
`thought-out designs such as this.
`
`A
`
`Assumptions
`
`The c:alculation procedures applicable to
`various types of joints are briefly described
`on the following pages, but in such a way as
`to be as general as possible. The user can
`therefore apply this information to types of
`joints not dealt with directly.
`
`In all the anap-fit designs that follow, it is
`assumed initially dult one of the mating parts
`1'elDIUns rigid. This assumption represents an
`additional precaution against material fail(cid:173)
`ure. If the two com-ponenta are of approxi(cid:173)
`mately equal stiffness, half the deflection
`can be assigned to each part. If one compo(cid:173)
`nmt ism.me rigid dwl the odler and the total
`strength avail.able is to be utilized to the
`fullest.
`the more complex proc:edure
`described in Section B must be adopted.
`
`What is said in the remainder of the
`brochure takes into account the fact that the
`plastics parts concerned are, for brief peri(cid:173)
`ods, subjected to very high mechanical
`loads. This means tbat the stress-strain
`behavior of the material is already outside
`the linear range and the ordinary modu1us of
`elasticity must therefore be replaced by die
`strain dependent secant modulus.
`
`Signal lens
`Housing Reflector Front
`access door
`
`Sun visor
`
`Fig. 7: CTOSs-sectionol sketch (above) and photo (below) of a troj/ic light made of
`Makrolon®polycOl'bonate. All the components an held together enti~ly be means of
`snap joints
`
`Page 7of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 7 of 26
`
`

`

`Cantilever Snap Joints
`Design Hints
`
`B
`
`Tensile stress
`
`(.)
`
`....
`.9
`.E
`c
`0
`
`~ .... c Q)
`(.) c
`8
`
`(/)
`(/)
`~
`Ci5
`
`0.2
`
`0.4
`
`0.6
`
`0.8
`
`1.0
`
`1.2
`
`1.4
`
`Fig. 9: Effects of a fillet 7rldiru on stress concentralion
`
`A large proportion of snap joints are buically
`simple cantilever snaps (Fig. 8), which may be
`of rectangular or of a geometrically more
`comp'lex cross section (see Table l).
`
`It is suggested to design the finger so that
`either its thickness (h) or widlh (b) tapers from
`the root to the hook; in this way the load-bear(cid:173)
`ing cross section at any point bears a more
`appropriate relation to the local load. The
`muimum strain on the material can therefore
`be reduced, and less material is needed.
`
`Good results have been obtained by reducing
`the thickness (h) of the cantilever linearly so
`tbat its value at the end of the hook is equal to
`one-half the value at the root; alternatively, the
`finger widdl .may be reduced to one-quarter of
`the base value (see Table 1, designs 2 and 3).
`With the designs illustrated in Table 1, the vul(cid:173)
`nerable cross section is always at the root (see
`also Fig. 8, Detail A). Special attention must
`therefore be given to this area to avoid stress
`concentration.
`
`Fig. 9 graphically~ the effect the root
`radius has on stress concentration. At first
`glanoe, it seems that an optimum reduction in
`stress concentration is obtained using the ratio
`Rib as 0.6 since only a marginal reduction
`occurs after this point However, using Rib of
`0.6 would reault in a thick area at the intersec(cid:173)
`tion of the snap-fit arm and its base. Thick sec(cid:173)
`tions will usually result in sinks and/or voids
`which are signs of high residual stress. For this
`reason, the designer should reach a compro(cid:173)
`mise between a large radius to reduce stress
`concentration and a small radius to reduce the
`potential for reai.dual stresses due to the cre(cid:173)
`ation of a thick sec-tion adjacent to a thin sec(cid:173)
`tion. Internal testing shows that the radius
`should not be less than 0.015 in. in any
`instance.
`
`Page8of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 8 of 26
`
`

`

`Cantilever Snap Joints
`
`Calculations
`
`B
`
`lllo.
`Shape of the
`cross section ,..
`
`Type of design
`T
`
`~
`J5
`·~ All dimensions in direction y.
`·E
`e.g., h or 6r, decrease to One-half
`:;;
`~
`
`All dimensions in direction z,
`e.g., band a, decrease to one-quarter
`
`~Q) 1,2,3 ~
`
`oo
`Q) ~
`~.g
`Cl
`
`A
`
`B
`
`c
`
`D
`
`Trapezoid
`
`Ring segment
`
`E · 12
`y = 0.67. -
`h
`
`2
`a+ b CIJ E • J
`y= - - · - -
`2a+b
`h
`
`E • 12
`y =1.09·(cid:173)
`h
`
`a+ b (IJ E • (2
`y = J.64·- -·-
`2a + b h
`
`y =0.86· (cid:173)
`
`E · [2
`h
`
`Y = 1.28 a+ bo, . .:..i_
`2a+b
`b
`
`z
`0
`p =~·E,e
`6
`I
`
`z
`~
`h2 a2 + 4ab,,1 + b2
`p =Z
`.E,E
`p = -
`. - - - " - ' ' - - -
`I
`<4>
`12
`2a+ b
`. E,e
`I
`
`I E. I2
`y= - ·-
`3 c (l)
`
`E • )2
`y = 0.55 ·-
`
`C 2
`
`y = 0.43· (cid:173)
`
`E • 12
`
`c(l)
`
`p =Z .E.,e
`I
`C4l
`
`Subscript numbers in parenthesis designate the note to refer to.
`
`1bble 1: Equations for dimensioning cantikveTS
`Symbols
`y
`=(permissible) deflection (=undercut)
`E
`= (permissible) strain in the outa fiber
`the root; in formulae: E as ab6olute
`at
`value= percentage/100 (see Table 2)
`=length of arm
`.. thickness at root
`.. width at root
`.. distance between outer fiber and
`neutral :fiber (c:cnter of gravity)
`= section modulus Z =I c,
`where I = axial moment of inertia
`= secant modulus (see Fig. 16)
`=(permissible) defl.ecti.on force
`=geometric factor (see Fig. 10)
`
`1
`h
`b
`c
`
`z
`
`Es
`p
`K
`
`Notes
`1) These formulae apply when the tensile
`stress is in the small surface area b. If it
`occurs in the larger surface area a, how-
`ever, a and b must be interchanged.
`
`2)
`
`If the tensile stress occurs in the convex
`surface. use K2. in Fig. 10; if it occurs
`in the concave surface, use Kl,
`accordingly.
`
`3)
`
`c is the distance between the outa :fiber
`and the centa of gravity (neu1nl axis) in
`the sur.f8':e subject to tensile stress.
`
`4) The section modulus should be
`determined for the surface subject to
`tensile stress. Section moduli for cross(cid:173)
`section shape type C are given in Fig. 11.
`Section moduli for other basic geometrical
`shapes are to be found in mechanical.
`
`Permissible stresses are usually more affected
`by temperatures than the associated strains. One
`pref-aably determines the strain associated with
`the pamisaible stress at room temperatwe. As a
`first approximatiOD, the compu-tation may be
`based on this value regardless of the tempera·
`ture. Although the equations in Table 1 may
`appear UDfamiliar, they are simple manipula(cid:173)
`tions of the conventiODal. engineering equa-tiom
`to put the analysis in terms of permissible strain
`levels.
`
`Page9of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 9 of 26
`
`

`

`Geometric factors K and Z for ring segment
`
`K,
`
`(J 1n
`10-r--r---ir-----.---.---....--.-~....,---.----.....-----.
`15
`8-t--t--__,f----!~-+---+---+---+-~+-~+-----1
`30
`6 -t--t--__,f----!~-+---+---+---+---.,.4--~+-----I
`
`45
`
`60
`
`75
`
`90
`
`105
`120
`135
`150
`165
`180
`
`05
`
`06
`
`0.7
`
`08
`
`r1/r2
`
`0.9
`
`10
`
`0.5
`
`0.6
`
`0 .7
`
`08
`
`0.875 0.9
`
`1 0
`
`r1/ r2
`
`Fig 10: Diagrams for detennining Kl and K2 for cross-sectional shape type C in Table I.
`Kl: Concave side under tensile load, K2: Convex sUk under tensile load
`
`Zlri'
`2
`
`10-•
`
`6
`
`2
`
`6
`4
`
`2
`
`10 3
`
`6
`4
`
`2
`
`10· •
`050
`
`060
`
`0 70
`
`0 80
`
`090
`
`IJ 1rf
`
`1'>0
`
`......
`
`,_ ----- -r-.
`... _ ....
`-- -....
`....
`s I'---... r-
`~ ~ ~
`s: ~ ~ r--..:
`I"'--- ~ ~ 165
`r--..
`r--..
`~ ........ 0 135
`r----. I"""--
`~ tS ~ I"'---
`..
`r---..
`........
`120
`"""
`"-.
`.... ·--
`..... , .......
`--
`-
`..... ........
`.....
`.....
`'"
`' .........
`' ........
`............
`.... 90
`~ ~ ' 75
`..
`"I " "'"'
`'
`'
`.....
`" '
`\' 30
`'\ \
`
`e on
`
`Zlrz3
`2
`
`10-•
`6
`
`4
`
`2
`
`10-2
`
`6
`
`4
`
`2
`
`10- 3
`
`6
`4
`
`10· 4 -t--'---+--'--+--'---1-L..f-+-.JL...!~
`0 .60
`0.50
`0 70
`0 80
`0.90
`1.00
`0.875
`
`Example:
`r1 = 8.75 mm (0.344 in)
`r2 = 10 mm (0.394 in)
`e = 75°
`
`3 = 0.0038
`From Graph: Z/r2
`Z2 = (10 mm)3 x 0.0038
`= 3.8 mm3 (2.3 x 1 o-4 in3)
`
`60
`
`~"
`
`\
`
`15
`1 00
`
`Fig 11: Graphs for determining the dimensionless quantity (Z/723) used to derive the section modulus (Z) for cross(cid:173)
`sectional shape C in Table 1.
`Zl: concave side under tensile stress, Z2: convex side under tensile stress
`
`Page 10of26
`
`S~lt Joints for P/ssttcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 10 of 26
`
`

`

`Cantilever Snap Joints
`
`B
`
`Fig 12: Underr:utfor snap joints
`
`Strain c
`
`0.5 E uk
`I
`I
`I
`
`Strain c
`
`Fig 13: Detennination of the permissible stminfor the joining operation (left: material with distinct yield point;
`right: glass-fiber-reinforced material without yield point)
`
`Permismble undercut
`
`The deflection y occurring during the joining
`operation is equal to die undm:ut (Fig. 12).
`
`The permissible deflection y (permissible
`undercut) depend& not only on the shape but
`also on the permissible strain B for the mate(cid:173)
`rial used.
`
`In general, during a single, brief snap-fitting
`operation. partially crystalline materials may
`be stressed almost to the yield point, amor(cid:173)
`phous ones up to about 709& of the yield slrain.
`
`Gla&s-fiber-reinfon:ed molding compounds do
`not nmmally have a distinct yield point The
`permis-sible strain for these materials in the
`case of snap joints is about half the elongation
`at break (see Fig. 13)
`
`Page 11 of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 11 of 26
`
`

`

`Deflection force
`
`Using the equations given in Table l, the per(cid:173)
`missible deflection y can be determined easily
`even for cross sectiODS of complex shapes.
`The procedure is explained with the aid of an
`example which follows.
`
`A particularly favorable form of soap-fitting
`arm is design 2 in Table l, with the thickness
`of the arm decreaaing lioeatly to half its initial
`value. This version increases the permissible
`deflection by more than 60% compared to a
`snap-fitting um of constant Cl'OllS section
`(design l).
`
`Complex designs such as 1hat shown in Fig. lS
`may be used in applications to increase the
`~tive length. Polymers Division Design
`Engineering Services would be pleased to
`assist you in a curved beam analysis if you
`choose this type of design.
`
`The deflection force P iequired to bend the
`finger can be calculated by use of the equa(cid:173)
`tions in the bottom row of Table 1 for cross
`sections of various shapes.
`
`Ea is the strain dependent modulus of elastici(cid:173)
`ty or "secant modulus" (see Fig. 14).
`
`Values for the secant modulus for various
`Bayer engiDeeriDg plastics can be determined
`from Fig. 16. The strain value used should
`always be the one on which the dimensioning
`of the UDdmmt was based.
`
`B
`
`' I
`I
`
`Eo /
`
`Secant modulus
`E = £L
`E 1
`s
`
`' ' I
`I
`a,--------7--------
`' I
`I ' I ' I
`I ' ' ' I
`
`I
`
`I
`
`(/)
`(/)
`~
`U5
`
`Fig. 14: Determination of the secant modldus
`
`Strain e
`
`Permissible short term
`strain limits at 23°C
`(73°F)
`
`Unreinforced
`HighHeetFC 4%
`Apetta
`2.5%
`~ FC/ABS
`~ ~ 35%
`4%
`
`~ FC
`
`Table 2: Gt!Mm/ guide data for IM allowahle
`slwrt-tenn strain for .map joinb (sillgle join -
`illg operation): for fiw/111!111 separation mu/
`rejoining, 11.te '11»11160% ef tllese Wlllll!s
`
`Fig.15: U-1haped snap-fitting armfora
`lid /Oltening
`
`Polyurethane Snap-Fits
`
`Snap-fits are possible using certain
`polyurethane systems. For more
`information call Polymers Design
`Engineering at 412-777-4952.
`
`Page 12of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 12 of 26
`
`

`

`B
`
`- 14
`
`- 12
`
`- 10
`
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`2?.
`x
`- 8 ~
`
`- 6
`
`- 4
`- 2
`
`5
`
`12,000
`
`11,000
`
`10,000
`
`-
`
`-
`
`Bayblend®
`PC/ABS
`
`9,00
`0
`8.000
`
`7,000
`
`- - -.
`
`6,000
`
`5,000
`
`4,000
`
`3,000
`
`2,000
`
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`
`'° Q.
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`"' " :;
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`"' " .. Cl)
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`T~ical Ba)oblend '!!!
`I Resin
`
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`
`4
`
`2
`Strain£, o/o
`
`3
`
`Cantilever Snap Joints
`
`12,000
`
`11 ,000
`
`I-
`
`Makrolon®
`Polycarbonate
`
`10,000
`
`-9,00
`
`0
`~ 8.000
`'E
`7,000 I-
`.€
`~ 6,000
`::> :;
`
`5,000 I-
`"O
`0
`E
`c: 4,000
`g
`
`C/)
`
`3,000 -
`1,000 -
`
`2,000
`
`0
`0
`
`2
`Strain£, o/o
`
`- 1 4
`
`-1 2
`
`- 10
`- 8
`- 6
`
`-g
`x
`~
`
`30%GR PC - 4
`
`I
`
`I
`
`T)l)ical Makr~lon®Resin
`3
`
`4
`
`- 2
`
`5
`
`~"" "
`' Twcial
`
`12,000
`
`11,000
`
`10,000
`
`9.00
`0
`8,000
`
`7,000
`
`6.000
`
`- - - -
`
`5.000
`
`4,000
`
`3.000
`
`2,000
`
`1,000
`
`;f
`5
`'E
`.E z
`"' ::> :;
`E c:
`B .. en
`
`"O
`0
`
`Apec illi
`High Heat
`Polycarbonate
`
`~
`x
`0 ..
`
`-1 4
`
`-1 2
`
`-
`
`10
`
`- 8
`
`- 6
`- 4
`- 2
`
`T)l)ical .Apece!!Resin
`
`4
`
`5
`
`Strainr, %
`
`0
`0
`
`Makroblend®
`PC Blend
`
`- -
`
`~.
`
`- 1 4
`
`- 12
`
`- 10
`
`- 8
`
`- 6
`
`- 4
`
`- 2
`
`5
`
`---
`
`-
`
`Makroblend®ur 1018
`I
`I
`3
`4
`
`Strain£,%
`
`12,000
`
`11,000
`
`10,000
`
`9.00
`
`0 I a.ooo
`
`NE 7,000
`.€
`~ 6,000
`::> :;
`'8
`E
`~ 4,000
`Jl 3.000
`
`5.000
`
`2,000
`
`1,000
`
`0
`
`
`
`- - - - - - 0
`
`Fig. 16: Secant Modulus for Bayer engineering plastics at 23°C (73°F)
`
`Page 13of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 13 of 26
`
`

`

`B
`
`~~-------....
`a'
`T
`
`Fig. 17: Relationship between deflection force and mating force
`
`Friction Coefficient µ =tan p
`
`Mating Force
`
`During the usembly operation, the deflection
`fmce P and friction fon:e F have to be oven:ome
`(see Fig. 17).
`
`The mating force is given by:
`W• P•tan(a+p) • P
`
`µ+tancx
`1-µtana
`
`µ+tana
`The value for 1 - µ tan a can be taken directly
`from Fig. 18. P.ri.ction coefficients for various
`materials are given in Table 3.
`
`In cue of separable joints, the separation force
`can be determined in the same way as the mating
`fmce by using the above equation. The angle of
`inclination to be used here is the angle <s'
`
`Page 14 of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 14 of 26
`
`

`

`Cantilever Snap Joints
`
`B
`
`I
`
`J
`
`'
`
`µ=1
`
`µ = 0.8
`
`'
`J µ = 0.4 ,
`I
`I
`I
`I
`•
`/
`/~ µ=O
`/
`,.V ~
`~ ---
`
`J
`
`j µ = 0.2
`
`J
`I
`
`10
`
`8
`
`6
`
`t$
`c
`.....,
`lU
`+
`::t
`
`t$
`c
`.....,
`lU
`::t
`I 4
`..--
`
`2
`
`0
`
`0
`
`J
`
`j
`
`--
`--
`
`~
`
`~
`
`/
`
`~
`
`J I
`' I
`J
`, , /
`I J
`/
`/
`v l/ ~ /
`,,,,,
`,,__,,,, ::::.-.............- ~ .......
`-
`~ ~ ----
`-
`----
`
`'µ = 0.6
`
`.4
`
`~
`
`I
`I
`I
`/
`/
`,,,_. ......
`---
`----
`
`10
`
`20
`
`30
`
`40
`
`50
`
`60
`
`70
`
`Angle of inclination a
`
`Figure 18: Diagram for determining µ+ tan a
`1 - µ tan a
`
`The figures dqJend on the rehW.ve speed of the
`mating parts, the pressure applied and OD the
`surface quality. Friction between two diffenmt
`plastic materials gives values equal to or
`slightly below those shown in Table 3. With
`two components of the same plastic material,
`the friction coefficient is generally higher.
`Where the factor i11 known. it bas been indicat(cid:173)
`ed in parentheses.
`
`PTFB
`PE rigid
`pp
`POM
`PA
`PBT
`PS
`SAN
`PC
`PMMA
`ABS
`PE flexible
`PVC
`
`0.12-D.22
`0.20-0.25 (x2.0)
`0.25-0.30 (x l.S)
`0.20-0.3S (x l.S)
`0.30-0.40 (x l.S)
`0.3S-0.40
`0.40-0.50 (x 1.2)
`0.45-0.55
`0.45-0.5S (x 1.2)
`0.50-0.60 (x 1.2)
`0.50-0.65 (x 1.2)
`0.55-0.60 (x 1.2)
`0.55-0.60 (x 1.0)
`
`Tlll>le .J: Fl'icfi'1.11 coejjic~p.
`(Gllide data from liteMllH'efor IM coejficielll.t
`of friclio11ofplo.rtics011 steel)
`
`Page 15of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 15 of 26
`
`

`

`Calculation example I
`snap-fitting hook
`
`This ca1culation is for a snap-fitting hook of
`rectangular cross section with a constant
`decrease in thickness from h at the root to hl2
`at the end of the hook (see Fig. 19). This is an
`example of de-sign type 2 in Table 1 and
`should be uaed whenever possible to per-mit
`greater deformation and to save material
`
`Given:
`a. Material = Makrolon@ polycarbonate
`b. Length (1) = 19 mm (0.75 in)
`c. Width (b) = 9.5 mm (0.37 in)
`d. Uodercu.t (y) = 2.4 mm (0.094 in)
`e. Angle of inclination (a) .. 30°
`
`Find:
`
`a. Thickness h at which full detlection y will
`cause a main of one-half the pennis&ible
`strain.
`b. Deflection force P
`c. Mating force W
`
`B
`
`'-:1, ............ ------..-t-
`
`~~-E~-~a
`
`. b
`
`A-A
`
`Fig. 19: Snap-fitting hook. design type 2, shape A
`
`Solution:
`a. Determination of wall thickness h
`Permissible strain from Table 2: £,. = 4%
`Strain n:quiml here E = 1J2 E,.. = 2%
`Deflection equation from Table 1, type 2, shape A:
`Transposing in terms of tbickoess
`
`y=l.09~
`
`h=l.09E P
`y
`.. 1.09 x 0.02 x llP
`2.4
`.. 3.28 mm (0.13 in)
`
`b. Determination of deflection force P
`Deflection force equation from Table l, cross section A:. P = bh2 Es E
`6"_1_
`
`From Fig. 16 at E = 2.0'Ji
`E9 = 1,815 N/mm.1 (264,000 psi)
`P = 9.5 mm x (3.28 mm)2 1,815 Nlmllr x 0.02
`6
`•
`19mm
`= 32.5 N (7.3 lb)
`c. Determination of mating force W
`W = P• 11+tanga
`1-ptancx
`
`Friction coefficient from Table 3 (PC against PC) I' .. 0.50 x 1.2 .. 0.6
`
`From Fig. 18: I' + tan a
`1--ptana
`W .. 32.S N x 1.8 = 58.5 N (13.2 lb)
`
`.. 1.8 For p .. 0.6 and a .. 30°
`
`Page 16of26
`
`S~lt Joints for P/sstlcs ·A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 16 of 26
`
`

`

`Cantilever Snap Joints
`
`B
`
`Calculation example D
`snap-titting hook
`
`This calculation example is for a snap-fitting
`hook with a segmented ring cross section
`decreasing in thickness from h at the root to h/2
`at the end of the hook (see Fig. 20). This
`is design type 2, shape C in 'Dible 1.
`
`This taper ratio should be used when possible to
`evenly distribute stresses during arm deflection.
`It also reduces material usage.
`
`Given:
`
`a. Malerial = Bayblend® PC/ABS
`b. l.ellgth (1) .. 2S.4 mm (1.0 .in)
`c. Angle of arc (9) .. 75a
`d. Outer radius (r2) .. 20 mm
`(0.787 in)
`e. Innerradiu& (r1) .. 11.s mm
`(0.689in)
`f. 'Ibickm:ss (h) = 25 mm (0.1 in)
`g. c/J! =6n=31.5°
`
`Find:
`
`a. The maximum allowable deflec:tion for a
`snap-fit design which will be assembled
`and unassembled frequently.
`
`A '-:1,
`
`t
`~a
`
`A
`
`t\12
`
`C1 •
`
`A·A
`
`Fig. 20: Snap-fitting hook. design type 2, shape C
`Soludon:
`The permissible strain for a onc-tmw snap-fit assembly in Bayblend® resin is 2.S'h. Since the
`design is for frequent separation and rejoining, 60% of this value should be used or E "" .. (0.6)
`(2.S%) - l.S%.
`Deflection equation from 'Dible 1, type 2, shape C: y .. 1.64 Ka> E 12
`The variable for Ka> can be obtained from the curves in Fig. 10. No~2that if the member is
`deflected so that the tensile stress occurs in the convex surface, the curve for Ki should be nsecl;
`if it occurs in the concave surface, K2 should be used. In this case, the tensile stress will occur in
`the convex smface, therefore the curve for K2 should be used.
`rilr2 = 0.875 and 0 = 75°
`from Fig. 10, ~2) = K2 .. 2.67
`y- 1.64 <2·67) (0.=~25·4 mm.)2
`
`.. 2.11 mm (0.083 in)
`
`Alternate Solution:
`
`This method may be u9ed as a check or in place of using dte curves in Fig. 10.
`
`Deflection equation from 'Dible l, type 2. shape D: y .. O.SS
`
`E 12
`
`The value for c(3) which is the di9tance from the neutral axis to the outermost fiber, can be
`calculated from the equation& shown below:
`
`~ .. r2[1- 2 sin tk (1 - hlr2 + _1_)]
`3 tf>
`2-hlr2
`2 sin </> + (1 - -b-) 2 sin tf> - 3c#> COS If> ]
`r2
`3ef>
`34>(2 _ hlr2)
`
`Ct '"r2[
`
`Use~ for c(3), if dte tensile stress occurs in dte convex side of the beam. Use c1 for c(3) if the
`tmsile slless oa:uIS in die oom:ave side. For dlis particuJar problem, it is necessary to calculate ~·
`c(3) = ~ .. 20 mm [1
`
`] =2.52mm.
`
`1
`2 - 2.5 mm/20mm
`
`2 sin 37.S (l - 2.S mm +
`
`3 (0.654)
`Solving for y using C2, yields;
`
`20mm
`
`y = O.SS (0.015) (25.4 mm)'= 2.11 mm (0.083 in)
`(2.52mm.
`Bodi methods result in a similar value for allowable deflection.
`
`Page 17of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 17 of 26
`
`

`

`Torsion Snap Joints
`
`c
`
`Deflection
`In the cue of torsion snap joints, the~
`tion is not the result of a flexural load as with
`cantilever snaps but is due to a toniional
`defarmation of the fulcrum. The torsion bar
`(Fig. 21) is subject to shear.
`
`The following relationship exists betweentbetnlalangle mtwist-and thedeftectians YI oryz(Fig. 21):
`
`where
`.. angle of twist
`cp
`y I • y 2 = deflectiODS
`1 to 12 = J.engtbs of lever arm
`
`y,
`
`The maximum permissible angle IPpm is limited by the persmissible shear strain 'Ypm.:
`
`180 'Ypm• 1
`r
`3t •
`
`IPpm=
`
`(valid for circular cross section)
`
`where
`
`'Ppm
`
`'Ypm
`1
`r
`
`= pmnissible total angle
`of twist in degrees
`.. permisu'"ble shear strain
`= length of torsion bar
`=radius of torsion bar
`
`The maximum permissible shear strain 'Ypm for plastics is approximately equal to:
`
`Fig. 21: Snap-fitting arm with tomon bar
`
`'Ypm .. (1 + 11) £pm
`'Ypm,. 1.3S £pm
`
`where
`
`'Ypm
`Epm
`..,
`
`.. permisu'ble shear strain
`.. permisu'ble strain
`=Poisson's ratio(for
`plastics approx. 0.35)
`
`Page 18 of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 18 of 26
`
`

`

`Torsion Snap Joints
`
`c
`
`y
`I
`i
`
`Example of snap-fining rocker arm (flaure and torsion about the Yam)
`
`Deflection force
`
`A force P is required to deflect the lever arm
`by the amount Yu.2)· The deflection force can
`act at points 1 or 2. For example see Fig. 21.
`In this case,
`
`where
`G = shearing modulus of elasti.clly
`'Y = shear strain
`Ip = polar moment of inertia
`.,...,WAI cross section
`x r4
`ti
`~; or a
`solid -'-··--
`.
`
`*Note: The factor 2 only applies where there
`are two torsion bars, as in Fig. 21.
`
`The shear modulus G can be determined
`fairly accurately from the secant modulus
`as follows:
`Es
`G= - -
`2(1+v)
`
`where
`
`Es = secant modulus
`u = Poisson's ratio
`
`Page 19 of26
`
`Snap-Fit Joints for Plastics -A Design Guide
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 19 of 26
`
`

`

`Annular Snap Joints
`
`D
`
`DetailX
`
`Fig. 23: Annular snap joint on a lamp homing
`
`Permissible undercut
`
`The annular snap joint is a con-venient fmm
`of joint between two rotatioually symmetric
`parts. Here, too, a largely slress-:fiee, positive
`joint is normally ob-tainecl. The joint can be
`either detachable (Figs. 22a, 23), difficult to
`disassemble or inseparable (Fig. 22b)
`depending on the di-mensi.on of the bead and
`the re-turn angle. Inseparable designs should
`be avoided in view of the complex tooling
`requiJed (split cavity mold).
`
`The allowable deformation should not be
`exceeded either during the ejection of the
`part from the mold or during the joining
`opendon.
`
`The pmnissible undercut as shown in Fig. 24
`is limited by the maxi-mum permiS&ible
`strain
`
`Ypm= Epm .d
`Note: Epn is absolute value.
`
`ThiB is based on the assumption that one of
`the mating parts re-mains rigid. If this is not
`the case. then the actual load on the material
`is cmrespondingly smaller. (With compo(cid:173)
`nents of equal fleD'bility, the strain is halved,
`i.e., the undercut can be twice as large.)
`
`W =mating force
`y=undercut
`DI = lead angle
`DI' ""return angle
`t = wall thickness
`d = diameter at the joint
`
`Fig.22:Annularsnapjoint
`
`Page20of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 20 of 26
`
`

`

`Annular Snap Joints
`
`D
`
`Deftection force, mating force
`
`The determination of the mating force W is
`somewhat more com-plicated for annular snap
`joints. This is because the snap-fitting bead on
`the shaft expands a relatively large portion of
`the tube (Fig. 2S). Accordingly, the stress is
`also distributed over a large area of the
`material sunounding the bead.
`
`Experimentally proven answers
`to
`this
`problem are based on the "theory of a beam
`of illfillite length reatiog on a resilient
`foundation." Two extreme cases are depicted
`inflig. 26.
`
`xi>
`
`ie-I~ --5---~f ---· .. +-
`
`I
`
`w
`
`Fig. 25: Stress distribution during joining operation
`
`CD •
`
`Beam
`
`Resilient foundation
`
`Fig. 26: Beam resting on a resilient foundation
`
`L------___ J
`
`Beam
`
`Resilient foundation
`
`0) The force Pis applied at the end of the beam. (This corresponds
`to a snap joint with the groove at the end of the tube.)
`
`@ The force P is applied a long distance (co) from the end of the
`beam. (This is equivalent to an annular map joint with the groove
`remote from the end of the tube)
`
`A somewhat simplified version of the theory may
`be expressed as follows for joints near the end of
`the tube:
`
`P .. transverse force
`y=undereut
`d = diameter at the joint ES = secant modulus
`Eg =secant modulus
`x .. geometric factor
`
`The geometric factor X takes into account the
`geometric rigidity.
`
`As far as the mating force is concerned, friction
`conditions and joint angles must also be taken into
`consideration.
`
`where
`
`Jl .. friction coefficient
`ex .. lead angle
`
`The geometric factor, assuming that the shaft
`is rigid and the outer tube (hub) is elastic, is as
`follows:
`
`~=0.62
`
`"(dt/d-1)/(d()ld+ 1)
`[( dJd)" + 1)/((dJd)1-1] +11
`
`where
`do = external diameter of the tube
`d = diameter at the joint
`v = Poisson's ratio
`
`Page21 of26
`
`S~lt Joints for P/sstlcs -A Design Gulde
`
`AMT Exhibit 2006
`CORPAK v. AMT IPR2017-01990
`Page 21 of 26
`
`

`

`D
`
`0.04 r;::---;-:---;--;:-,....,..-:-:--:-----.------.-----,.------.
`Elastic shaft. rigid hub
`
`1.08
`1.12
`1.20
`1.16
`0.48 r----------..------.-----.-------.
`____ !L-~
`
`Elastic shaft. rigid hub
`
`0.40
`
`did; (Shaft) dJd (Hub)
`
`0.32 r------.-----+---7'1!f-----I----~
`
`o.oa 1--------=A---=,,,-.~--+-------I
`
`Rigid shaft, elastic hub
`
`. m~lt __ .=k......J
`0.00 ~--1---,..L----..L.--=:::.:m:.:.:.::::-1
`_ _tt
`
`1.0
`
`1.4
`
`2.2
`1.8
`d/d1 (Shaft) d.,/d (Hub)
`
`.:.-.:1:!.!,
`2.6
`
`3.0
`
`Fig. 27: Diagrams for determining the geometric factor Xfor annular
`snap joints
`
`If the tube is rigid and the hollow shaft
`elastic, then
`
`X.,-0.62
`
`" (Cl/di -1)/(dldl + 1)
`[(d/dj)' + l]/[(d/dj)' - 1] -11
`
`d = diameter at the joint
`~ = intemal. diameter of the hollow shaft
`
`'lbe geometric factors XN and X.. can be
`found in Fig. 27.
`
`'lbe snap joint is considered "remote" if the
`distance from the end of the tube is at least
`a ... uva: t
`
`where
`
`d =joint diameter
`t ... wall dlickness
`
`Jn this case, the trausvene force P and mating
`force Ware thcoretic.ally four times as great
`as when the joint is near the end of the tube.
`However, tests have sho