Design calculations for
`snap fit joints in plastic parts
`
`CALCULATIONS · DESIGN · APPLICATIONS B.3.1
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 1 of 26
`
`

`

`Contents
`
`1.
`
`Introduction
`
`2. Requirements for snap-fit joints
`
`3.2
`
`Basic types ofsnap-fit joint
`Barbed leg snap-fit
`3.1
`Barbed leg snap-fit supported
`on both sides
`Cylindrical snap-fit
`Ball and socket snap-fit
`
`3.3
`
`3.4
`
`3.
`
`4.
`
`Critical dimensions for a snap-fit joint
`Maximum permissible undercut depth Hmax.
`4.1
`and maximum permissible
`elongation s,^
`Elastic modulus E
`Coefficient of friction M
`Assembly angle a\ and retaining angle 2
`
`4.2
`
`4.3
`
`4.4
`
`5. Design calculations for snap-fit joints
`Barbed leg snap-fit
`5.1
`Cylindrical snap-fit
`Ball and socket snap-fit
`
`5.2
`
`5.3
`
`6.
`
`Calculation examples
`Barbed leg snap-fit
`6.1
`Cylindrical snap-fit
`Ball and socket snap-fit
`Barbed leg snap-fit supported
`on both sides
`
`6.2
`
`6.3
`
`6.4
`
`7. Demoulding ofsnap-fitjoints
`
`8.
`
`Applications
`Barbed leg snap-fit
`8.1
`Cylindrical snap-fit
`Ball and socket snap-fit
`
`8.2
`
`8.3
`
`9.
`
`Explanation of symbols
`
`10. Literature
`
`3
`
`3
`
`4
`
`4
`
`4
`
`4
`
`5
`
`6
`
`6
`
`10
`
`10
`
`1 1
`
`12
`
`12
`
`13
`
`14
`
`16
`
`16
`
`16
`
`18
`
`1 8
`
`20
`
`21
`
`21
`
`23
`
`24
`
`24
`
`25
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 2 of 26
`
`

`

`2. Requirements
`for snap-fit joints
`
`Snap-fits are used to fix two parts together in a certain
`position. In some cases, it is important to exclude play
`between the assembled parts (e. g. rattle-free joints
`for automotive applications). The axial forces to be
`transmitted are relatively small. In the majority of appli
`cations, the joints are not subject to permanent loads
`(e. g. from internal pressure).
`
`Special fasteners such as rivets and clips also work on the
`snap-fit principle. They should be easy to insert, suitable
`for blind fastening, require low assembly force and be
`able to bridge the tolerances of the mounting hole.
`
`1. Introduction
`
`Snap-fits are formfitting joints which permit great design
`flexibility. All these joints basically involve a projecting
`lip, thicker section, lugs or barbed legs moulded on one
`part which engage in a corresponding hole, recess or
`undercut in the other. During assembly, the parts are
`elastically deformed. Joints may be non-detachable or
`detachable, depending on design (figs. 4 and 5). Non-
`detachable joints can withstand permanent loading even
`at high temperatures. With detachable joints, it is neces
`sary to test in each individual case the permanent load
`deformation which can be permitted in the joint. In the
`unloaded state, snap-fit joints are under little or no stress
`and are therefore not usually leaktight. By incorporating
`sealing elements, e.g. O-rings, or by using an adhesive,
`leaktight joints can also be obtained.
`
`Snap-fits are one of the cheapest methods of joining
`plastic parts because they are easy to assemble and no
`additional fastening elements are required.
`
`Hostaform
`Acetal copolymer (POM)
`
`Hostacom
`Reinforced polypropylene (PP)
`
`Celanex
`Polybutylene terephthalate (PBT)
`
`@Vandar
`Impact-modified
`polybutylene terephthalate (PBT-HI)
`
`lmpet
`Polyethylene terephthalate (PET)
`
`= registered trademark
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 3 of 26
`
`

`

`3. Basic types ofsnap-fit joint
`
`The parts with an undercut can be cylindrical, spherical
`or barbed. There are three corresponding types of snap-
`fit joint:
`
`1 . Barbed leg snap-fit
`2. Cylindrical snap-fit
`3. Ball and socket snap-fit
`
`3.1
`
`Barbed leg snap-fit
`
`Hg.l
`
`The undercut depth H is the difference between the
`outside edge of the barb and the inside edge of the hole
`(% 1):
`
`undercut depth H = LI
`
`L2
`
`(1)
`
`The leg is deflected by this amount during assembly.
`
`In designing a barbed leg, care should be taken to pre
`vent overstressing at the vulnerable point of support
`because of the notch effect. The radius r (fig. 1) should
`therefore be as large as possible.
`
`3.2
`
`Barbed leg snap-fit supported on both sides
`
`Fig. 3
`
`i
`
`(/}
`
`t
`
`S 1
`
`PjT
`
`HJ1
`
`t
`
`>~
`
`1,
`_vu
`
`-\
`
`T -
`
`1
`
`/R
`
`l
`
`Barbed legs are spring elements supported on one or
`both sides and usually pressed through holes in the
`mating part (fig. 1). The hole can be rectangular, circular
`or a slot. The cross-section of the barbed leg is usually
`rectangular, but shapes based on round cross-sections are
`also used. Here, the originally cylindrical snap-fit is
`divided by one or several slots to reduce dimensional
`rigidity and hence assembly force (fig. 2).
`
`Fig.2
`
`This joint employs a barbed spring element supported
`on both sides. The undercut depth H is the difference
`between the outside edge of the barb and the width of
`the receiving hole (fig. 3). Hence as in formula (1) we
`obtain:
`
`undercut depth H Lt
`
`L2
`
`(la)
`
`This snap-joint may be detachable or non-detachable
`depending on the design of the retaining angle.
`
`3.3
`
`Cylindrical snap-fit
`
`Cylindrical snap-fits consist of cylindrical parts with a
`moulded lip or thick section which engage in a corre
`sponding groove, or sometimes just a simple hole in the
`mating part.
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 4 of 26
`
`

`

`Fig. 4: Non-detachable joint
`
`compression ( ) of the shaft
`
`^1DG
`^ _==*. 100%
`UG
`
`elongation (+) of the hub
`
`, AV*
`e2 = + ~^-WO%
`i-TC
`
`(4)
`
`(5)
`
`As it is not known how the undercut depth H is appor
`tioned between the mating parts, it is assumed for sim
`plicity that only one part undergoes a deformation e
`corresponding to the whole undercut depth H.
`
`s
`
`H
`Dr,
`
`-100%
`
`or e=^^-100%
`DK
`
`Fig. 5: Detachable joint
`
`3.4
`
`Ball and socket snap-fit
`
`Fig. 6
`
`The difference between the largest diameter of the
`shaft DG and the smallest diameter of the hub DK is the
`undercut depth H.
`
`undercut depth H = DG
`
`DK
`
`(2)
`
`DG largest diameter of the shaft [mm]
`DK smallest diameter of the hub [mm]
`
`The parts are deformed by the amount of this undercut
`depth during assembly. The diameter of the shaft is
`reduced by ADC, and the diameter of the hub increased
`by +ZlDK.
`
`So the undercut depth can also be described as
`
`H = ADC + JDK
`
`(3)
`
`Ball and socket snap-fits (fig. 6) are mainly used as motion
`transmitting joints. A ball or ball section engages in a
`corresponding socket; the undercut depth H is the differ
`ence between the ball diameter DG and the socket open
`ing diameter DK.
`
`undercut depth H = DG
`
`DK
`
`(7)
`
`DG ball diameter
`[mm]
`DK socket opening diameter [mm]
`
`Because the shaft is solid and therefore very rigid, the
`hole undercut depth H must be overcome by expanding
`the hub. As a result of this diameter change, the hub is
`deformed as follows:
`
`100%
`
`(8)
`
`H D
`
`K
`
`100% =
`
`DG-DK
`,
`elongation e = ^
`jL>K
`
`-
`
`As a result of these diameter changes, the shaft and hub
`are deformed as follows:
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 5 of 26
`
`

`

`4.
`
`Critical dimensions
`for a snap-fit joint
`
`the deformation is lower. So barbed legs are stressed
`much less than cylindrical snap-fits. As a result of this,
`higher elongation is permissible and in many cases is
`necessary for design reasons.
`
`Irrespective of the type of snap-fit there is a linear relation
`between the undercut depth H and elongation e. The
`maximum permissible undercut depth Hmax. is limited by
`the specified maximum permissible elongation e^^ .
`
`For non-rectangular barbed leg cross-sections, the follow
`ing relationships apply between undercut depth H and
`deformation e in the outer fibre region (outer fibre elon
`gation):
`
`The load-carrying capacity of snap-fits depends on the
`elastic modulus E and coefficient of friction //. It can be
`matched to the requirements of the joint by adjusting
`undercut depth H and assembly angle i or retaining
`angle K2 (see section 4.4).
`
`4.1
`
`Maximum permissible undercut depth Hm
`maximum permissible elongation &max.
`
`and
`
`In barbed legs (fig. 7), the following relation applies
`between undercut depth H (= deflection) as a result of
`deflection force FB and elongation or compression in the
`outer fibre region of the barbed leg cross-section
`(rectangular section):
`
`undercut depth Hmax. = -|-- - ^
`
`(9)
`
`barbed leg length
`[mm]
`barbed leg height
`[mm]
`x. permissible elongation [/o]
`
`Fig. 7
`
`semicircular
`
`cross-section
`
`Hmax.= 0.578
`
`third of a circle
`
`cross-section
`
`Hmax. = 0.580
`
`I2
`
`r
`
`I2
`
`r
`
`en
`100
`
`(10)
`
`en
`100
`
`(H)
`
`quarter of a circle
`cross-section
`
`Hmax.= 0.555-^-^-
`
`(12)
`
`These relationships also apply approximately to leg
`cross-sections in the form of sectors of an annulus.
`
`A comparison between formula 9 and formulae 10 to
`12 shows that the maximum permissible undercut
`depth Hmax. for barbed legs with cross-sections in the
`form of segments of a circle is 15% lower than that of
`a rectangular barbed leg cross-section (assumption:
`h -I).
`
`The maximum permissible undercut depth Hmax. for
`barbed legs of different length and height with a
`rectangular cross-section can be read off figs. 10 to 13.
`
`Kg- 9
`
`\
`
`a
`n t
`
`\ '
`
`fi s
`'T
`
`1
`
`Fig. 8: Elongation in cross-section A- A (fig. 7)
`
`The maximum deformation (fig. 8) only applies in the
`critical region A - A, fig. 7, while in other cross-sections
`
`The maximum permissible undercut depth Hmax. for
`barbed leg snap-fits supported on both sides can be
`calculated with the aid of fig. 14, irrespective of the
`material. Fig. 14 applies for emax = 6% (see calculation
`example 6.4).
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 6 of 26
`
`

`

`Fig. 10: Maximum permissible undercut depth Hn
`for Hostaform and Hostalen PP
`
`Fig. 12: Maximum permissible undercut de
`for Hostacom M 4 N01 and G 3 N01
`
`1=50 mm
`s_
`iH
`|5
`
`mrr
`
`[
`
`s
`
`V
`
`Sk
`s
`
`1
`
`\
`
`x=
`
`^s
`
`SJ = 15
`m\
`
`S.
`
`\
`s
`
`s
`
`Vl = 30
`s
`X
`
`20 mn
`
`mm\
`
`\
`
`\
`
`s
`
`N
`
`v
`X
`
`max. = 2%
`^|
`
`: \
`
`V
`
`> s
`
`~13^
`LU u=L
`f
`1 E
`i"
`X
`
`~
`
`s,
`
`N
`
`s
`
`3a
`
`o^
`<^i
`
`4^
`
`oj
`
`KJ
`
`mm
`
`Xj = 10 rn
`
`\.
`x
`\
`
`v
`\
`
`X
`
`1= 5 mm
`
`oö
`pppf
`
`^b
`
`4*
`
`\
`
`s
`
`V
`
`\Is
`
`A = 20 mm
`\.
`mmN.
`
`v
`
`S
`
`s \
`
`\
`
`\
`
`max. = 8%
`^
`
`N S sS
`
`l=15
`\
`
`sl = 10 mm
`X
`
`s
`
`mm
`30
`
`20
`
`ny*iln*L
`&
`
`\
`
`s
`
`s
`
`s
`
`10
`
`8 6
`
`4
`
`3
`
`M^ t-
`
`%
`
`5 V
`\
`
`\
`
`po
`
`Ui
`
`fo
`
`Hmax.
`depth
`undercut
`permissible
`Maximum
`
`N \
`
`\
`
`\
`
`\
`
`s
`
`2
`
`Si =
`\
`
`5 mi
`
`n
`
`S
`
`\
`
`0.8
`
`1.0
`
`345 6mm 8
`Height of barbed leg h
`
`o
`
`l^
`0.5
`
`0.8
`
`1.0
`
`2345 6mm8
`
`Height of barbed leg h
`
`5
`
`I 0
`
`Fig. 11: Maximum permissible undercut depth Hn
`for Hostaform C 9021 CV 1/30
`
`Fig. 13: Maximum permissible undercut depth Hmax.
`for Hostacom G 2 N01 and M 2 N01
`
`Py rr
`
`"" X
`
`s
`X
`
`X X
`
`mm
`
`t
`
`10
`
`8 6 5 4 3
`
`2
`
`II
`
`0.1
`0.5
`
`0.8
`
`1.0
`
`345 6mm8
`
`Height of barbed leg h
`
`1
`
`1.5
`
`0.8
`
`1.0
`
`345 6mm8
`
`Height of barbed leg h
`
`L max. = 6%
`
`^\
`
`s
`
`x\r
`
`s
`
`30r
`
`on
`
`\
`
`S
`
`\
`
`\
`
`V X
`
`s
`
`X S
`
`\ \ s
`\ X
`
`S
`s.
`JV
`X
`^V 1 = 20 mm
`Sj=15mmS
`s
`
`\
`N
`
`N
`
`X
`
`Si = 10 mm
`
`N^
`
`5 mr
`
`n
`
`X
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 7 of 26
`
`

`

`The undercut depth H is calculated as follows:
`
`maximum permissible undercut depth
`
`(14)
`
`J~lmax.
`
`en
`100
`
`DC
`
`Dt outside diameter of the shaft [mm] in cylindrical
`snap-fits or ball diameter [mm] in ball and socket
`snap-fits
`
`The maximum permissible elongation of materials with
`a definite yield point (e. g. Hostaform) should be about
`a third of the elongation at yield stress es (fig. 15a).
`For materials without a definite yield point (e. g. glass
`fibre reinforced Hostacom, fig. 15b), the maximum per
`missible elongation (see table 1) should be about a third
`of the elongation at break SR.
`
`Fig. 15a: For materials with a definite yield point os
`(e. g. Hostaform)
`
`es
`3
`
`Fig. 15b: For materials without a definite yield
`point os (e. g. Hostacom)
`
`IE.
`3
`
`SR
`
`Fig. 16
`
`r (-!)' (>+4)
`(-1)
`barb width [mm]
`length of hole [mm]
`thickness of leg [mm]
`Smax. maximum permissible elongation (table 1) [%]
`
`b
`1
`
`s
`
`Fig. 14: Barbed leg snap-fit supported on both
`
`TT
`
`sides; relative undercut depth
`
`j as a function of barb
`width and spring leg thickness for emax. = 6%
`
`relative spring leg thickness y = 0.01
`
`1.0
`
`0.8
`
`0.6
`
`0.4
`
`0.2
`
`0.1
`
`0.08
`
`0.06
`
`0.04
`
`0.02
`
`0.01
`
`0.008
`
`0.006
`
`0.004
`
`0.002
`
`El-
`
`|T
`
`B
`eü
`
`,
`
`12
`
`m ^ ()
`
`0.001
`0.3
`
`0.4
`
`0.5
`
`0.6
`
`F
`^o
`
`Relative barb width -r
`
`With cylindrical snap-fits and ball and socket snap-fits,
`the maximum permissible undercut depth can be
`calculated from the maximum permissible elongation
`emax. (%) using the formula:
`
`ES
`
`'
`
`/
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 8 of 26
`
`

`

`Table 1 :
`Maximum permissible elongation emax. for determination of the maximum permissible undercut depth Hn
`
`Material
`
`Maximum permissible elongation emax. (%)
`
`Barbed leg
`
`Cylindrical snap-fits,
`ball and socket snap-fits
`
`Hostaform C 52021
`Hostaform C 27021
`Hostaform C 13021
`
`Hostaform C 13031
`
`Hostaform C 9021
`
`Hostaform C 2521
`Hostaform C 9021 K
`Hostaform C 9021 M
`Hostaform C 9021 TF
`Hostaform T 1020
`Hostaform S 9063/S 27063
`
`Hostaform C 9021 GV 1/30
`
`Hostaform S 9064/S 27064
`
`Hostacom M2 N02
`
`Hostacom M2 N01
`
`Hostacom G2 N01
`
`Hostacom M4 N01
`
`Hostacom G2 N02
`
`Hostacom Ml U01
`
`Hostacom G3 N01
`
`Hostacom M4 U01
`
`Impet 2600 GV 1/30
`
`Vandar 4602 2
`
`Celanex 2500
`
`Celanex 2300 GV 1/30
`
`1.5
`
`10
`
`1.5
`
`S 1.0
`
`^ 3.0
`
`S 2.0
`
`S 1.0
`
`0.8
`
`1.0
`
`S 0.5
`
`^2.0
`
`1.0
`
`S 0.5
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 9 of 26
`
`

`

`4.2
`
`Elastic modulus E
`
`The elastic modulus E0 is defined in DIN 53 457 as the
`slope of the tangent to the stress-strain curve at the
`origin (fig. 16, page 8).
`
`E0 =
`
`at the point e = 0
`
`(15)
`
`With greater elongation, e. g. Si (fig. 16), the elastic modu
`lus is smaller because of the deviation from linearity
`between a and e. The elastic modulus then corresponds
`to the slope of a secant which is drawn from the origin
`through the e\ point of the stress strain curve. This is
`known as secant modulus Es and is dependent on the
`magnitude of elongation e .
`
`Fig. 17: Secant modulus Es as a function of outer fibre
`elongation (based on 3-point flexural test)
`(el%/min)
`
`a Celanex 2300 GV 1/30
`b Hostaform C 9021 GV 1/30
`
`c Hostacom G 3 N01
`d Hostacom M 4 N01
`e Hostaform C 9021
`f Celanex 2500
`g Hostacom M 2 N01
`h Hostacom G 2 N01
`i Vandar4602Z
`
`The following applies:
`
`N/mm2
`
`,a
`
`Es = f(8)
`
`(16)
`
`7500
`
`S,
`
`7000
`
`6500
`
`6000
`450(f
`
`4000
`
`3500
`
`3000
`
`2500
`
`2000
`
`1500
`
`1000
`
`500
`
`0
`
`w |
`
`This secant modulus ES is used in design calculations for
`snap-fits. Fig. 17 plots the secant modulus against elonga
`tion e up to the maximum permissible elongation for
`barbed legs.
`
`4.3
`
`Coefficient offriction fj.
`
`In assembling snap-fits, friction has to be overcome. The
`degree of friction depends on the materials used for the
`mating elements, surface roughness and surface loading.
`Table 2 gives coefficient of friction ranges for various
`combinations of mating element materials. The friction
`values quoted are guide values only.
`
`Table 2
`
`Mating element materials
`
`Coefficient of friction //
`
`Hostaform/Hostaform
`Hostaform/other plastics
`Hostaform/steel
`
`Hostacom/Hostacom
`Hostacom/other plastics
`Hostacom/steel
`Impet/Impet
`Impet/other plastics
`Impet/steel
`Vandar/Vandar
`Vandar/other plastics
`Vandar/steel
`
`Celanex/Celanex
`Celanex/other plastics
`Celanex/steel
`
`10
`
`0.2 to 0.3
`
`0.2 to 0.3
`
`0.1 to 0.2
`
`0.4
`
`0.3 to 0.4
`
`0.2 to 0.3
`
`0.2 to 0.3
`
`0.2 to 0.3
`
`0.1 to 0.2
`
`0.3 to 0.4
`
`0.2 to 0.3
`
`0.2 to 0.3
`
`0.2 to 0.3
`
`0.2 to 0.3
`
`0.1 to 0.2
`
`\\
`
`V
`
`\N
`
`sf__
`sjX
`\
`^1 ^S
`
`.ü!^
`
`1
`
`[*-_
`' ^^^
`
`---^
`
`- =
`
`25*^.
`
`^s
`
`l"**
`T
`
`*-
`
`-
`
`calculation example 6.2
`
`1
`
`1 1
`
`3456
`
`Elongation E
`
`r v\
`
`\\
`
`\V
`
`\v
`
`V
`S3
`"V
`Vs
`_\
`^
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 10 of 26
`
`

`

`4.4
`
`Assembly angle at and retaining angle a2
`
`Fig. 18: Detachable joint
`
`The assembly angle a\ (figs. 18 and 19), along with the
`barb dimensions and coefficient of friction fj, between
`the mating elements (table 2), determines the required
`assembly force F, (fig. 20). The greater a\ the higher the
`assembly force required. With a large assembly angle
`(! ä 45) and high coefficient of friction //, it may no
`longer be possible for parts to be assembled. The barb
`then shears off rather than being deflected. The recom
`mended assembly angle for barbed legs and cylindrical
`snap-fits is i = 15 to 30.
`
`With ball and socket snap-fits, the assembly angle cannot
`be freely chosen. It depends on the maximum permissible
`socket opening diameter DK (fig. 27).
`
`The retaining angle 2 (figs. 18 and 19) decides how much
`loading the joint can stand. The maximum load-bearing
`capacity is reached when the retaining angle is a2 = 90
`(fig. 19). During long-term loading and/or in the event
`of elevated ambient temperatures, the retaining angle 2
`should always be 90. The joint is then permanent. For
`detachable joints, a retaining angle 2 = 45 should be
`provided, preferably a2 = 30 to 45.
`
`Fig. 19: Non-detachable joint for 2 = 90
`
`Fig. 20
`
`F] = assembly force required
`
`11
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 11 of 26
`
`

`

`5. Design calculations
`for snap-fit joints
`
`5.1
`
`Barbed leg snap-fit
`
`Fig. 22
`
`The assembly force FI and pull-out force F2 (fig. 22) for
`barbed legs can be calculated from the formula:
`
`Fl,2 =
`
`3H ES -J
`1
`
`// + tan Ii2
`
`1
`
`jM-tan!^
`
`[N]
`
`(17)
`
`undercut depth
`[mm]
`secant modulus
`[N/mm2] (Fig. 17)
`moment of inertia [mm4] (table 3)
`barbed leg length [mm]
`coefficient of friction (table 2)
`assembly angle
`[]
`retaining angle
`[]
`
`H E
`
`s
`
`J 1 f
`
`t i 2
`
`The factor -^
`^
`l-w-tanai.2
`fig. 23.
`
`can be taken directly from
`
`'
`
`tr
`
`i-i c
`
`V- + tan gl,2
`Fig. 23: Factor -r^
`1
`tan 1,2
`\JL
`(from formulae 17, 22 and 25) as a function of
`assembly/retaining angle i, 2
`
`15
`
`30
`
`45
`
`60
`
`90
`
`Assembly/retaining angle
`
`t , 2
`
`The load-bearing capacity of snap-fits under steady
`(short-term) stress depends primarily on:
`
`1 . the mechanical properties of the plastics concerned,
`particularly stiffness as expressed by the elastic
`modulus ES,
`
`2. the design of the snap-fit, i. e. wall thickness,
`undercut depth H, retaining angle 2-
`
`Load-bearing capacity is defined as the pull-out force F2
`which the joint can stand in the opposite direction to
`assembly without the parts separating.
`
`In many cases, it is possible to design the direction of
`snap-fit assembly at right angles to the actual loading
`direction F during service (fig. 21). Then the load-bearing
`capacity of the joint is not determined by pull-out
`force F2 but by the break resistance or shear strength of
`the vulnerable cross-section. This design technique is
`most often used with ball and socket snap-fits.
`
`Fig. 21
`
`r
`
`j
`
`Table 3
`
`Barbed leg cross-
`section
`
`Moment of inertia [mm4]
`
`rectangle
`
`^\1
`xNSN
`
`b'h3
`
`|2
`
`i,p.
`wnere
`
`b leg width [mm]
`h leg height [mm]
`
`semicircle
`
`_j
`
`^ 0.110 r4
`
`r radius [mm]
`
`|>_
`
`0.0522 r4
`
`^_ 0.0508 r4
`
`third
`
`of a circle
`
`quarter
`of a circle
`
`12
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 12 of 26
`
`

`

`With the retaining angle a2 = 90, the pull-out force F2
`is determined by the shear-stressed area and the
`shear strength TB of the plastic used.
`
`Fig. 24
`
`Ultimate tensile
`strength OR and
`tensile strength OB
`[N/mm2]*
`
`The shear stress TS is
`
`Ts = A [N/mm2]
`
`(18)
`
`Taking into account ultimate tensile strength OR or
`tensile strength 0B (table 4), the following holds true for
`shear strength
`
`TB = 0.6
`
`CTR
`
`or TB = 0.6 OB
`
`F2max. = A TB = b c
`
`rB [N]
`
`(19)
`
`(20)
`
`(21)
`
`5.2
`
`Cylindrical snap-fit
`
`Fig. 25
`
`Table 4
`
`Material
`
`Hostaform C 52021
`
`Hostaform C 27021
`
`Hostaform C 13021
`
`Hostaform C 13031
`Hostaform C 9021
`Hostaform C 2521
`
`Hostaform C 9021 K
`Hostaform C 9021 M
`Hostaform C 9021 TF
`
`Hostaform T 1020
`
`65
`
`64
`
`65
`
`71
`
`64
`
`62
`
`62
`
`64
`
`49
`
`64
`
`Hostaform C 9021 GV 1/30
`
`110
`
`Hostaform S 27063
`
`Hostaform S 9063
`Hostaform S 27064
`Hostaform S 9064
`
`Hostacom M2 N02
`
`Hostacom M2 N01
`
`Hostacom M4 N01
`
`Hostacom G2 N01
`
`Hostacom G2 N02
`
`Hostacom G3 N01
`
`Hostacom Ml U01
`
`Hostacom M4 U01
`
`Celanex 2500
`
`Celanex 2300 GV 1/30
`
`Celanex 2300 GV 3/30
`
`Vandar 4602 Z
`
`Impet 2600 GV 1/30
`
`50
`
`53
`
`42
`
`42
`
`19
`
`33
`
`33
`
`32
`
`70
`
`80
`
`36
`
`33
`
`65
`
`150
`
`50
`
`40
`
`165
`
`I Test specimen injection moulded according to DIN 16770 part 2.
`
`The assembly force FI and pull-out force F2 for cylin
`drical snap-fits - unlike for barbed legs - can only be
`roughly estimated. This is because the length a (fig. 25)
`which is deformed during assembly of the parts with
`consequent increase in assembly force FI is unknown.
`The length a depends on both the wall thickness of the
`hub and the undercut depth H. A useful guide to a has
`proved to be twice the width b of the moulded lip.
`
`13
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 13 of 26
`
`

`

`The assembly force FI and pull-out force F2 can be calcu
`lated from the formula:
`
`c
`
`r r>
`
`->u M + tan 1,2
`Fu-p.rt.IV2b f_
`
`'
`
`rxn
`
`[N]
`
`(22)
`
`Fig. 26: Geometry factor K as a function of diameter
`Ji
`DG
`DG
`DK
`
`ratio
`
`or
`
`y J
`
`so
`
`(23)
`
`joint pressure [N/mm2]
`p
`DG outside diameter of the hub [mm]
`b
`width of the moulded lip [mm]
`coefficient of friction (table 2)
`assembly angle []
`retaining angle []
`
`fj.
`
`a i
`
`2
`
`Between undercut depth H and joint pressure p, the
`following relationship applies:
`
`H
`
`1
`
`p = ^-Es-^ [N/mm2]
`
`DK smallest diameter of the hub [mm]
`
`The geometry factor K depends on the dimensions of the
`snap-fit:
`
`1.2
`
`1.5
`
`Diameter ratio _
`L>G
`
`a
`
`or -pj
`UK
`
`K=
`
`mv
`VDGj + 1
`fuy-i
`loj
`
`+1
`
`(24)
`
`Fig. 27
`
`outside diameter of the hub [mm]
`Da
`DG outside diameter of the shaft [mm]
`
`Here it is assumed that the whole undercut depth H is
`accommodated by expansion of the hub. With thin-
`walled shafts, the shaft deforms as well but this can be
`ignored in the case described here. Fig. 26 shows the geo
`metry factor K as a function of the diameter ratio Da/Dc.
`
`5.3
`
`Ball and socket snap-fit
`
`In this design (fig. 27), the assembly angle j and retain
`ing angle 2 and hence assembly force FI and pull-out
`force F2 are the same.
`
`Table 5
`
`a
`DG
`
`0.07
`
`0.10
`
`0.12
`
`0.14
`
`The assembly/retaining angle is between 8 (e = 1%)
`and 16 (e = 4%), depending on elongation.
`
`=
`
`-^100%
`
`UK
`
`Assembly angle a\
`Retaining angle 2
`
`8
`
`11.4
`
`13.9
`
`15.9
`
`1 2 3 4
`
`14
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 14 of 26
`
`

`

`To estimate assembly or pull-out force, the formulae for
`cylindrical snap-fits are used:
`
`The relationship between undercut depth H and joint
`pressure p can be described by the following formula (23):
`
`T-.
`
`T^2
`
`a
`
`ß + tan
`T [N]
`Fi = F2 = p n Dé fs~ '
`DG l jM-tana
`
`i
`
`r-Nn
`
`a
`
`joint pressure [N/mm2]
`p
`DG ball diameter [mm]
`f deformation length divided by the
`DG l ball diameter (table 5)
`coefficient of friction (table 2)
`assembly or retaining angle [] (table 5)
`
`H
`
`a.
`
`(25)
`
`P = rJ'Es'T tN/mm2]
`
`H undercut depth [mm]
`DK socket opening diameter [mm]
`secant modulus [N/mm2] (fig. 17)
`ES
`geometry factor
`K
`
`K=
`
`mybJ + i
`fAi- 1
`iDj
`
`+1
`
`(26)
`
`15
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 15 of 26
`
`

`

`6.
`
`Calculation examples
`
`b) Assembly force FI
`
`6.1
`
`Barbed leg snap-fit
`
`The top and bottom plates of a time switch are to be
`detachably joined by two diagonally opposite spacers
`and two barbed legs. The hole diameter in the top plate
`is DK = 8 mm. The pull-out force F2 required per barbed
`leg is 50 N. The barbed legs are to be injection moulded
`from Hostaform C 9021 and will have a slotted circular
`cross-section (fig. 28).
`
`Fig. 28
`
`a) What should the dimensions of the barbed leg be?
`b) What assembly force FI is required ?
`c) What pull-out force F2 is obtained?
`
`For the assembly force FI formula (17) applies:
`
`P _
`
`3H ES J
`I3
`
`// + tani
`\-fjL- tan 0.1
`
`H = 0.3 mm
`ES = 2800 N/mm2 (fig. 17).
`
`For the Hostaform/steel mating elements, it is assumed
`that the friction coefficient fi = 0.2 (table 2).
`
`Using table 3 we obtain for the semicircular cross
`section:
`
`J = 0.110 r4 = 0.11
`
`44 = 28.2 mm4
`
`So assembly force FI works out as
`
`F,=
`
`3-0.3-2800-28.2
`
`0.2 + 0.577
`
`153
`
`1 - 0.2 0.577
`
`FI = 18.5 N
`
`Each securing element comprises two barbed legs which
`each have to be deflected by H. The assembly force per
`element is therefore 2 FI = 37 N.
`
`c) Pull-out force F2
`
`The pull-out force F2 is calculated in the same way as
`assembly force except that 2 = 45 is substituted for a\.
`The pull-out force is thus
`
`F2 = 31.6N
`
`a) The maximum permissible outer fibre elongation is
`chosen to be emax. = 1 % For the semicircular cross-
`section, the following applies using formula (10):
`
`Each element withstands a pull-out force of
`2 31.6 N 63 N, which is greater than the required
`pull-out force of 50 N.
`
`H = 0.578-^-smax.
`r--^-
`
`1 is chosen to be 15 mm
`
`H = 0.578
`
`-0.01
`
`4
`
`H= 0.3mm
`
`6.2
`
`Cylindrical snap-fit
`
`The body of a rubber-tyred roller is to be made in two
`parts which are permanently joined together (fig. 29).
`Because of the relatively high stress involved and the fact
`that the roller bears directly onto a steel axle, Hostaform
`is used as the construction material.
`
`The diameter of the undercut is calculated from
`DK + 2H = 8.6 mm. The slot width is chosen to be
`1 mm, the assembly angle a\ 30 and the retaining
`angle a2 45.
`
`a) What should the dimensions of the snap-fit be
`(undercut depth H) ?
`
`b) What assembly force FI is required?
`
`c) What is the pull-out force F2?
`
`16
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 16 of 26
`
`

`

`a) Maximum permissible undercut depth Hmax.
`
`To determine the maximum permissible undercut depth
`Hmax., it is assumed that only the hub is deformed.
`The greatest elongation takes place at the diameter DK
`which is expanded during assembly to DG = 16 mm.
`The maximum permissible elongation for Hostaform
`is 6max. = 4%, according to table 1.
`
`Fig. 29
`
`b =
`
`H
`
`2 tan i
`
`H
`
`2 -tan 30
`
`0.64
`
`2-0.577
`
`b = 0.55 mm
`
`The joint pressure p is calculated from formula (23).
`
`1
`
`\
`
`?
`
`H
`
`P"W E*-i
`
`1
`
`With ^- = ^r = 1.5 fig. 26 shows a value for K of 3.6.
`L>G
`
`I"
`
`The secant modulus for emax. = 4% for Hostaform
`(fig. 17) is Es = 1800 N/mm2.
`
`So the joint pressure works out as
`
`p-0.04.Jff
`
`p = 20 N/mm2
`
`The assembly force FI is
`
`Fi = 20-yt-16-2 -0.55
`
`0.2 + 0.577
`
`1-0.2-0.577
`
`FI = 970.8 N
`
`c) Pull-out force F2
`
`Because the retaining angle 2 = 90, the joint is perma
`nent. The force required to separate the mating elements
`can be calculated from the shear strength rB and the
`shear-stressed area A (shear surface).
`
`According to formula (20) the shear strength is
`
`So the maximum permissible undercut depth can be
`calculated according to Formula (14):
`
`TT
`
`_
`
`max.
`100
`
`~
`
`100
`
`p\
`
`16
`
`Hmax. = 0.64 mm
`
`DK = DG-H
`= 16 - 0.64
`
`DK = 15.36 mm
`
`The diameter DK is chosen to be 15.4 mm.
`
`TB = 0.6
`
`OB
`
`b) Required assembly force FI
`
`OB = 62 N/mm2 e.g. for Hostaform C 2521 (table 4)
`
`For the assembly force FI, formula (22) applies:
`
`F! = p JT DG 2b
`
`fj, + tan !
`
`1
`
`fj. tan !
`
`The assembly angle a\ is 30. The coefficient of friction
`for Hostaform/Hostaform mating elements is asumed to
`be /A = 0.2 (table 2). The width b of the undercut can be
`determined from the assembly angle a\ and the undercut
`depth H.
`
`TB = 0.6 62
`
`TB = 37.2 N/mm2
`
`The shear surface in this case is
`
`A = it DG b
`
`= n 16
`
`0.55
`
`A = 27.6 mm2
`
`17
`
`F
`<f^
`
`7r*
`
`3S
`
`B
`
`1Q
`^ r ^~
`K0
`
`Qil^: c
`
`a
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 17 of 26
`
`

`

`So using formula (21), the pull-put force ist:
`
`b) Assembly force FI = pull-out force F2
`
`For e = 1 %, table 5 gives a retaining angle of 2 = 8.
`The deformation length divided by the ball diameter is
`
`~- = 0.07 according to table 5.
`
`For Hostacom/Hostacom the coefficient of friction is
`(JL = 0.4 (table 2).
`
`D
`14
`For Y^r" = ~5~~ = 1-75 for K using formula (26).
`JLG
`
`0
`
`K=
`
`myVDj + 1
`AY.
`loj
`
`+ 1
`
`+ 1
`
`( 14 V
`\7.92J
`P1_Y_
`\7.92j
`
`-+1
`
`K=2.94
`
`According to fig. 17 the secant modulus of Hostacom
`G3N01fore = l%is
`
`Es = 4400 N/mm2.
`
`The joint pressure can be calculated with H = DG
`from formula (23):
`
`DK
`
`P=D~'Es'"K [N/mm2]
`
`0.1
`
`7.92
`
`1
`4400-
`' 2.94
`
`p = 18.89 N/mm2
`
`The assembly or pull-out force is then (formula 25):
`
`F2 max.
`
`= A TB
`
`= 27.6-37.2
`
`F2max. = 1027N
`
`6.3
`
`Ball and socket snap-fit
`
`In a car, the movement of the accelerator pedal is trans
`mitted via a linkage to the carburettor. A ball and socket
`joint connecting the pedal to the linkage (fig. 30) and
`made from Hostacom G 3 N 01 is required to have a
`pull-out force F2 of at least 100 N. The ball diameter
`DG = 8 mm, the outside diameter Da = 14 mm.
`
`Fig. 30
`
`a) How large should the socket opening diameter DK be?
`
`b) What assembly force F] or pull-out force F2 is
`obtained?
`
`a) Socket opening diameter DK
`
`According to table 1 the maximum permissible elon
`gation for Hostacom G3 N01 is emax. = 1%.
`
`Thus using formula (8)
`
`fJ. + tan
`a_
`^p-^Dë-g:-^-
`A.
`fc' 1
`
`T^-f
`
`U T L
`
`//tan a
`
`e = -
`
`_
`
`DG ~ DK
`DK
`
`100%
`
`DK =
`
`DG
`
`r>
`
`+ 1
`
`100
`
`DK =
`
`0.01 + 1
`
`DK = 7.92 mm
`
`= 18.89 -;r-82- 0.07-
`
`0.4 + 0.14
`
`1-0.4-0.14
`
`Fi.2 = 152 N
`
`6.4
`
`Barbed leg snap-fit supported on both sides
`
`The two housing halves of a box-shaped moulding made
`from Hostacom M2 N01 are to be non-detachably joined
`by 2 barbed leg snap-fits supported on both sides (fig. 31).
`
`18
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 18 of 26
`
`

`

`For an assumed spring element thickness of s = 3 mm,
`a spring element thickness ratio of
`
`s
`
`3
`"T" = "örf 0-15 is obtained.
`
`With the aid of fig. 14, an undercut ratio of
`is determined.
`
`p_r
`-p = 0.019
`
`The undercut H of the barb is then calculated from
`
`H = 0.019 1
`
`= 0.019 20
`
`H 0.4 mm
`
`Note:
`A possible flow line in the region of the spring element
`could provide a weak point. By increasing wall thickness
`at this point, design strength can be improved (see also
`C.3.4 Guidelines for the design of mouldings in engineer
`ing plastics, p. 25, no. 18).
`
`El
`1
`\ ,
`\, l
`J
`
`1
`
`\\
`\ \
`
`11
`
`1 V
`
`)
`
`k
`
`ir
`
`1
`
`/
`
`f
`KP
`
`*-b-
`
`1
`
`u
`
`Fig. 31
`
`f
`
`1
`
`What should the dimensions of the snap-fit joints be?
`
`The receiving holes in the moulding are 1 = 20 mm.
`
`The maximum permissible elongation emax. according
`to table 1 is
`
`6max. = 6%
`
`The width of the barb is assumed to be b = 8 mm.
`This gives a barb width ratio of
`
`--04
`~ '4
`1 ~
`20
`
`19
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 19 of 26
`
`

`

`7. Demoulding of
`snap-fit joints
`
`The undercut on which the effect of the snap-fit depends
`has to be demoulded after injection moulding. The im
`portant question here is whether the parts can be directly
`demoulded or whether it is necessary to bed the under
`cut in slides, followers or collapsible cores.
`
`There is no general answer to this. The maximum per
`missible deformation values quoted in table 1 can of
`course be applied equally well to parts during demould-
`ing. Problems usually arise from the introduction of
`deformation forces into the component. These can result
`in local stretching of the part or cause the ejector to press
`into the part, among other undesirable consequences.
`A disadvantage here is that the demoulding temperature
`is considerably above room temperature and hence mate
`rial stiffness is correspondingly low.
`
`With cylindrical snap-fits, it should be remembered that
`the dimensional stiffness of a tubular part under com
`pression is greater than under tension. The hub of a
`snap-fit (fig. 32a) is generally easier to demould than the
`shaft. In some cases, the parting line of the mould can
`run through an undercut edge, for example with a
`through hole and inwardly projecting lip (fig. 32a) or
`with an outwardly projecting lip (fig. 32b).
`
`In the more frequent case of a blind hole (fig. 33), the
`inner and outer faces of the undercut must be demoulded
`in succession. When the mould has opened (A), the
`cylinder 1 is pressed out of the mould cavity by ejector 3.
`It takes core 2 along with it until stop 4 is reached (B).
`Through further movement of the ejector, the cylinder
`is stripped from the core. Expansion of the hub by an
`amount corresponding to undercut depth is not pre
`vented (C).
`
`Fig. 32
`
`Fig. 33
`
`A
`
`_ plastic part
`
`< \
`
`split core
`
`\\\\\\\\\\^*
`
`plastic part
`
`20
`
`AMT Exhibit 2001
`CORPAK v. AMT IPR2017-01990
`Page 20 of 26
`
`

`

`Photo 2 shows Hostaform fasteners which considerably
`facilitate assembly, particularly in mass production.
`Nos. 1, 2 and 3 are used to fix interior trim in cars.
`No. 4 is a cable holder as used in washing machines and
`dishwashers. No. 5 is a clip with a similar function. Here
`the snap-fit is secured by driving a pin into the hollow
`shank (expanding rivet). The clips for fixing car exterior
`trim (no. 6) work on the same principle. No. 7 shows
`the hinge fixing for a detergent dispenser tray flap on a
`washing machine.
`
`8. Applications
`
`8.1
`
`Barbed leg snap-fit
`
`Photo 1 shows examples of snap-fits in which the defor-
`mability of the cylindrical snap-fit has been increased by
`means of slots. In the top half of the picture there are
`two rollers with Hostaform bearings for dishwashers.
`In the left roller, each barbed leg is deflected by
`f = 0.75 mm during assembly. With a barbed leg length
`of 1 = 7 mm and a barbed leg height of h = 2.5 mm, the
`maximum elongation at the vulnerable cross-section of
`the leg support point is:
`
`f-h
`
`=1
`
`= 0.058 = 5.f
`
`The lower half of the picture shows how a Hostaform
`bearing bush is fixed. The bush is secured axially at one
`end by a barbed leg and at the other by a flange.
`Rotation of the bush is prevented by flattening off the
`flange.
`
`In all the examples shown, the assemb