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`Designing with Plastics
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` 
`Gunter Erhard
` 
`
`ISBN 3-446-22590-0
`
` 
`
`Leseprobe 2
` 
`
`Weitere Informationen oder Bestellungen unter
`http://www.hanser.de/3-446-22590-0 sowie im Buchhandel
`
`http://www.hanser.de/deckblatt/deckblatt1.asp?isbn=3-446-22590-0&style=Leseprobe
`
`05.01.2006
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 1 of 15
`
`

`

`8
`
`Flexing Elements
`
`Structural elements that are required to have high deformability should be designed so that
`they are capable of withstanding the flexural or torsional loads associated with the application
`(see also Section 6.1). Two examples of such designs common in parts made from polymeric
`materials are snap-fit or interlocking joint elements and elastic elements. Another common
`feature in parts designed for high deformability is their relatively thin wall thickness. For
`example, integral hinges are structural elements having extremely low wall thicknesses.
`
`8.1
`
`Snap-Fit Joints
`
`Definition
`
`Joint types are defined according to the mechanisms acting at the points of attachment holding
`the assembled parts together (see Figure 8.1) [8.1]. On this basis, a snap-fit joint is a frictional,
`form-fitting joint.
`The structural features of a snap-fit joint are hooks, knobs, protrusions, or bulges on one of
`the parts to be joined, which after assembly engage in corresponding depressions (undercuts),
`detents, or openings in the other part to be joined.
`Accordingly, the design of a snap-fit joint is highly dependent on the polymeric material(s).
`Snap-fit joints are also relatively easy to assemble and disassemble. A key feature of snap-fit
`joints is that the snap-fit elements are integral constituents of the parts to be joined.
`
`Figure 8.1 Types of joints (schematic) [8.1]
`a) Form-fitting joint
`b) Frictional joint
`c) Adhesive joint
`d) Frictional form-fitting joint
`←→ Direction of action of forces
`
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`CORPAK v. AMT IPR2017-01990
`Page 2 of 15
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`312
`
`8 Flexing Elements
`
`[References on Page 362]
`
`Differentiated and Integrated Construction
`
`Design solutions using “differentiated” construction assign certain functions separately to the
`individual structural elements with the goal of fulfilling all of the functional requirements in
`an optimum manner. This inevitably means that there are a number of parts in a subassembly.
`“Integrated” construction, on the other hand, uses fewer parts and consequently results in
`lower assembly costs but may require the acceptance of restrictions or compromises in
`functionality. Figure 8.2 shows this trade-off with reference to the example of a bayonet
`coupling.
`
`Figure 8.2 Design variants for a coupling as described in [8.12] and [8.16]
`
`The systematic reduction in the numbers of parts finally leads to variant d), a snap-fit joint
`made from polymeric material. Injection molding technology is so versatile, that it allows for
`the integration of functions directly into the parts to be joined.
`
`Classification
`
`Snap-fit joints are classified according to the most varied attributes [8.2, 8.3, 8.4, 8.13]. However,
`a classification based on geometrical considerations appears to be most appropriate here (see
`Figure 8.3).
`
`Figure 8.3 Classification scheme for snap-fit elements based on geometrical considerations
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 3 of 15
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`

`

`8.1 Snap-Fit Joints
`
`313
`
`Dimensions and Forces
`
`The dimensions and forces associated with assembly/disassembly are discussed in the following
`figures.
`
`Figure 8.4 Dimensions and their
`designations for snap-fit hooks
`α1 = Joining angle
`α2 = Retaining angle
`b = Breadth of cross section
` (hook breadth)
`h = Height of cross section
`l
`= Snap-fit length
`H = Snap-fit height (undercut)
`
`of the snap-fit joint
`
`} } }
`
`Figure 8.5 Dimensions and their designations in cylindrical annular
`snap-fit joints
`dmax = Greatest diameter
`dmin = Smallest diameter
`do = Outer diameter
`= Wall thickness
`so
`di
`= Inner diameter
`si
`= Wall thickness
`
`of the outer part
`
`of the inner part
`
`Figure 8.7 Dimensions and their designations
`in torsional snap-fit joints
`}
`lT = Length
`rT = Radius
`β = Torsion angle
`γ
`= Twisting angle
`l1,2 = Lever arm lengths
`f1,2 = Elastic excursions
`Q1,2 = Deflection forces
`
`of torsion rod
`
`Figure 8.6 Dimensions and their designations
`in spherical annular snap-fit joints
`
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`CORPAK v. AMT IPR2017-01990
`Page 4 of 15
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`

`314
`
`8 Flexing Elements
`
`[References on Page 362]
`
`Figure 8.8 Angles and forces at the active surface
`Q = Deflection force
`F
`= Assembly force
`FN = Normal force
`FF = Friction force
`Fres = Resultant force
`α1 = Joining angle (lead-in angle)
`ρ = Friction angle
`
`U
`
`FF
`
`The forces and angles at the assembly contact surfaces of the joints (see Figure 8.8) apply in an
`analogous manner for all snap-fit joint design variations.
`
`Assembly Operation
`
`A review of the snap-fit assembly operation is helpful to gain a better understanding of the
`factors at work and of the calculations discussed below. The assembly force F, generally acting
`in the axial direction, is resolved at the mating surface in accordance with the mathematical
`relationships associated with a wedge (see Figure 8.8). The transverse force Q causes the
`deflection needed for assembling the joint. At the same time, friction and the joining angle
`determine the conversion factor η.
`
`(8.1)
`
`α
`
`tan
`tan
`
`⋅
`
`α1
`
`1
`
`f
`
`1
`
`−
`
`+
`
`f
`
`)
`
`α + ρ =
`
`η =
`
`tan(
`
`1
`
`The relationship in Eq. 8.1 is plotted in Figure 8.9 against α1,2 for common values of η.
`The retaining or release force of the joint can be altered using the retaining angle α2. The use
`of a value of α2 ≥ 90° creates a self-locking geometric form-fitting joint. Figure 8.10 illustrates
`that a joint constructed in this way can be released again without forced failure of the joint
`when the moment of the force couple represented by the retaining and reaction forces is able
`to overcome the friction force in the active surface.
`A design countermeasure to prevent release in this way is to attach a retaining guard or locking
`ring (see also Sections 8.1.1.3 and 8.1.3.3).
`As snap-fit features are being assembled, the assembly force follows the characteristic pattern
`shown in Figure 8.11. This is also described in [8.11] and [8.23]. After a steep rise, the assembly
`force reaches a peak, falls to a lower level where it remains fairly constant as the lead angle
`causes the part to deform, and then falls back to zero, once the joint area of the part snaps into
`place.
`Deformation during the assembly of snap-fit joints can be significant. As a result of these
`deformations during the assembly operation, the geometric relationships change (e.g., the
`relative angular positions) [8.21, 8.10]. This, however, is not taken into account in the
`calculation of the assembly forces in the sections below. The local variation of the plane of
`action and its effect on transverse force during the assembly operation is likewise not taken
`into account (see Section 5.4).
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 5 of 15
`
`

`

`8.1 Snap-Fit Joints
`
`315
`
`Figure 8.9 Conversion factor η for various coefficients of friction f as a function of the joining (lead-in)
`angle or the retaining (snap-out) angle [8.11]
`
`Figure 8.10 Forces and moments acting on a snap-fit hook
`having a retaining angle of 90° at the time of release
`
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`CORPAK v. AMT IPR2017-01990
`Page 6 of 15
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`

`316
`
`8 Flexing Elements
`
`[References on Page 362]
`
`Figure 8.11 Assembly force over the assembly path for cylindrical snap-fit joints having different size
`undercuts. Outside part is made of POM (H 2200) with dmin = 40 mm; inside part is made of
`steel [8.18].
`
`Loss of Retaining Force
`
`In the case of snap-fit elements that are repeatedly joined and separated, or those that remain
`under a residual stress, the time-dependence of the material properties should be taken into
`account. In line with viscoelastic behavior, the strain (deformation) imposed during the
`assembly operation diminishes only gradually. Test results on separated [8.21] and on assembled
`snap-fit joints made from POM and PP [8.11] have shown that recovery after release of stress
`can take as long as 4 to 5 hours. The residual strain found in these cases was in the range of 1
`to 3% for disassembly strain values of 8 to 10%.
`These residual strain values are reached asymptotically after 5 to 10 assembly or release cycles.
`Lower assembly related strains lead to lower residual strains. In addition, after a large number
`of assembly cycles, no further loss of retaining force is observed.
`If the snap-fit joint element is deformed enough during assembly resulting in a residual stress,
`this stress relaxes over time after assembly in line with the relaxation behavior of the material.
`The residual stress or residual elastic force remaining can be estimated theoretically by
`linearizing the isochronous stress-strain diagram (see the example calculation in Section 5.3.2).
`
`Figure 8.12 Relationship between residual strain and number of release cycles for an annular snap-fit
`joint made of POM having a rigid inner part for different undercut sizes [8.11]
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 7 of 15
`
`

`

`8.1 Snap-Fit Joints
`
`317
`
`8.1.1
`
`Snap-Fit Beams
`
`8.1.1.1
`
`Types of Snap-Fit Beams
`
`The most common structural element in snap-fit joints is a beam, subject to a bending load,
`in the form of a cantilever snap-fit beam with a hook. Its useful snap-fit height (momentary
`interference) can be altered by changing the cross-sectional shape of the beam and, of course,
`by its effective snap-fit length.
`Good utilization of material is reflected in high values for the geometry factor C (see
`Figure 8.13).
`
`Figure 8.13 Material utilization as reflected by the geometry factor C in snap-fit hooks having different
`cross-sectional shapes according to [8.5]. The values of C for the trapezoidal cross section
`apply to the case in which the tensile stress acts in the wide face of the trapezium.
`
`Uniform loading of the material and hence optimum utilization of the material for a
`cantilever snap beam is achieved by a linear decrease in width or a parabolic decrease
`in thickness along the length of the beam.
`
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`CORPAK v. AMT IPR2017-01990
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`

`318
`
`8 Flexing Elements
`
`[References on Page 362]
`
`Figures 8.14 to 8.17 indicate some aspects of importance for production in the design of snap-
`fit hooks. For example, two opposing hooks are more easily produced if they have a cross
`section in the form of a cylinder segment rather than a rectangular cross section. The simpler
`production due to the cylindrical shape of the geometric envelope affords substantially lower
`mold production costs. The production costs for drilling, reaming, and polishing the circular
`cross section may have a cost ratio of 1 : 4 compared to those for producing a rectangular
`cross section by spark erosion and milling [8.7].
`By skillful partitioning of the snap features within the mold and the use of shut-offs or piercing
`cores (see Figure 8.15), snap-fit hooks can be produced without complicated mold actions.
`When shut-offs are used to produce snap-fit beams and hooks, the designer must allow for
`the shut-off angle (0.5 to 1°).
`In clamshell housing parts, such as those illustrated in Figure 8.16, the undercuts of built-in
`hooks are most easily molded if the hook faces outward (top) rather than inward (bottom).
`The maximum stress that occurs when a beam bends is usually at the transition from the
`snap-fit beam to the molding. Radii of curvature have to be provided here, even if this increases
`mold-making costs. Even a radius of 0.5 mm reduces the peak stress at the transition
`considerably (see Figures 8.17 and 10.4). Generous radius values are also recommended for
`segmented annular snap-fit joints (Figure 8.17).
`Adequate snap-fit hook height can be achieved by extending the length of the elastic section of
`a hook (see Figures 8.18 and 8.19).
`Interlocking joints with a series of joining positions arranged one behind the other allow for
`assembly at various positions. Figures 8.19 to 8.21 show examples of this concept applied to
`molded parts.
`The concept of an elastic snap-fit beam with a hook and a rigid undercut may also be “reversed”
`to form the variant of a rigid hook and an elastic beam with an undercut. An example of this is
`shown in Figure 8.22. Figure 8.23 shows an example of an automobile headlight housing
`incorporating this concept (see also Figures 8.27 and 7.60).
`
`Figure 8.14 Snap-fit hook with circular (a) and rectangular (b) envelope shape and associated details
`of the injection molds [8.7]
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 9 of 15
`
`

`

`8.1 Snap-Fit Joints
`
`319
`
`Figure 8.15 Principle of demolding a snap-fit beam and hook without special mold action [8.20]
`
`Figure 8.16 Beam hooks (undercuts) on the core
`side (bottom) cause higher mold costs
`than those facing outward (top) [8.13]
`
`Figure 8.17 Rounding-off the segment
`gap for slotted annular
`snap-fit joints to reduce
`peak stress values
`
`Figure 8.18 Principle of extending the
`length of the elastic (bending)
`section of a snap-fit hook [8.9]
`
`Figure 8.19 Interlocking joint with saw
`tooth profile and retaining
`guard on a clamping ring
`
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`CORPAK v. AMT IPR2017-01990
`Page 10 of 15
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`

`320
`
`8 Flexing Elements
`
`[References on Page 362]
`
`Figure 8.20 Interlocking joint capable of adjustment [8.2]
`
`Figure 8.21 Plug housing capable of being fixed
`sideways in two locking positions
`
`Figure 8.22 Housing cover joint assembled
`using cantilever beams with
`undercuts rather than hooks
`[8.5]
`
`Figure 8.23 Joint composed of a rigid hook and an elastic bracket
`
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`CORPAK v. AMT IPR2017-01990
`Page 11 of 15
`
`

`

`8.1 Snap-Fit Joints
`
`321
`
`8.1.1.2
`
`Snap-Fit Beam Calculations
`
`Permissible Size of Undercut
`
`A snap-fit hook (snap-fit bracket) may be simplified as a bending beam fixed at one end (i.e.,
`a cantilever beam). Calculations can be performed on the basis of classical bending theory*.
`In the assembly calculations, the beam is theoretically deflected by at least the depth of the
`undercut. In this rough calculation, the effect of shear stress due to the transverse force is usually
`neglected because l ✱ h. Any deflection of the mating surface is usually estimated or neglected
`in the classical calculations, although it may be considered in Finite Element Simulations.
`The permissible size of the undercut (snap-fit height) for a cantilever snap-fit beam can be
`determined based on the permissible outer fiber strain εperm for the material from which the
`beam will be made.
`
`H
`
`perm
`
`=
`
`C
`
`2
`
`l
`h
`
`⋅ ε
`
`perm
`
`where
`
`(8.2)
`
`= Geometry factor (see Figure 8.13)
`C
`εperm = Permissible outer fiber strain as an absolute value (m/m)
`Guide values for one-shot assembly:
`Semi-crystalline thermoplastics ≈ 0.9 εY
`Amorphous thermoplastics ≈ 0.7 εY
`Reinforced thermoplastics ≈ 0.5 εY
`Guide values for frequent assembly:
`Strain at σ0.5% (see Figure 5.2c).
`
`Snap beams having shapes and cross sections other than those shown in Figure 8.13 cannot
`usually be analyzed in this way. A method for analysis of beams with more complex cross
`sections is given in Section 5.4.
`
`Assembly Force and Retaining Force
`The assembly force, F, is calculated from the deflection force Q and the conversion factor η.
`
`F Q
`
`=
`
`⋅ η
`
`(8.3)
`
`where η is obtained from Figure 8.9.
`The retaining force is calculated by analogy with the retaining (or return) angle α2 (for α2 ≥ 90°
`see Figure 8.10). During assembly, plastic deformation may occur so that as a result of changed
`geometry, the actual retaining force may be smaller than the one calculated [8.11]. Even when
`the retaining and joining angles are the same, the separating force is a little smaller than the
`assembly force. This can be attributed to the fact that the bending moment between the planes
`of action of the actuating forces and the plane of action of the reaction force in the material
`tends to open the snap-fit connection during assembly.
`
`* Using classical handbook equations or commercially available computer programs such as the SNAPS PC program
`from BASF or Fittcalc from Ticona.
`
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`CORPAK v. AMT IPR2017-01990
`Page 12 of 15
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`

`322
`
`8 Flexing Elements
`
`[References on Page 362]
`
`The deflection force is given by
`
`Q W
`
`=
`
`⋅ ε
`
`SE
`
`l
`
`where
`
`W = section modulus for a rectangular cross section (I/c) where c = h/z.
`
`W
`
`=
`
`2
`
`⋅
`
`b h
`6
`
`for a trapezoidal cross section (with tensile stress in the wider face)
`
`(8.4)
`
`W
`
`=
`
`2
`
`a
`
`⋅
`
`2
`
`h
`12
`
`+
`
`4
`2
`b
`
`+
`
`a b
`a
`
`+
`
`2
`
`b
`
`for other cross sections see Hütte, Dubbel and other reference works.
`ES = secant modulus in MPa for the strain arising associated with the deflection
`ε = strain arising as an absolute value (m/m)
`
`8.1.1.3 Additional Functions
`
`Overstrain Safeguards
`
`Snap-fit hooks, especially thin fragile ones or those made using brittle materials, must be
`adequately protected against excessive stress or deflection (see Figures 8.24 and 8.25).
`
`Figure 8.24 Overstrain safeguards for snap-fit hooks [8.19]
`
`Figure 8.25 Snap-fit hooks can be safeguarded against excessive strain or fracture by means of a
`deflection limit or stop
`(Photograph: Siemens AG, Munich)
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 13 of 15
`
`

`

`8.1 Snap-Fit Joints
`
`323
`
`Figure 8.26 Tabs act as retaining guards, guide surfaces, and provide tolerance compensation
`a) Undercut
`b) Tab
`c) Snap-fit beam and hook
`
`Retaining Guards
`
`In order to prevent inadvertent or unwanted release of a snap-fit joint (see also Figure 8.10)
`with certainty, the snap-fit hook can be secured after assembly by another element in the
`structural unit. Figure 8.26 shows one of many possibilities by the example of the base of a
`coffee machine. The hot plate is inserted into the two parts of the housing where it presses the
`tab against the snap-fit hook and in this way secures it against release. Additionally, these tabs
`provide guidance for the assembly of the hot plate and compensate for any tolerance variations.
`
`Opening Aids
`
`An extension of the snap beam (beyond the hook) in the form of a recessed grip is a simple
`way to facilitate release of a snap-fit joint by hand (see Figure 8.24). Designs, such as the one
`shown in Figure 8.27, have also proved to be effective. In this case, however, the bending stress
`has to be absorbed by the very short fillet between the housing and the actual connecting
`element.
`In the locking mechanism shown in Figure 8.28, a spring provides the force required to keep
`the fulcrum snap-fit in place.
`In the case of snap-fit opening aids involving tools, appropriate means of access and gripping
`must be designed into the parts to be assembled (see, e.g., Figure 8.29).
`
`Energy Storage Devices
`
`Permanent pretensioning is not easily obtained with molded snap-fit connections made of
`polymeric material due primarily to the limitations of polymeric materials. Therefore, stresses
`in the joint should be released as much as possible after assembly. When, however, only relatively
`small amounts of energy are to be stored, e.g., for compensating tolerances or obtaining small
`prestress, this can be accomplished using pretensioned snap-fit elements made of polymeric
`materials. Glass-fiber reinforced materials are best for these applications, but unreinforced
`materials such as POM can also be used (see Figure 8.28). The residual pretensioning can be
`estimated from the creep modulus Ec (see example calculation in Section 5.3.2).
`
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`324
`
`8 Flexing Elements
`
`[References on Page 362]
`
`Figure 8.27 During assembly, mainly the snap-fit bracket is deformed, while during separation,
`only the short fillet is deformed
`
`Figure 8.28
`Locking mechanism
`for a housing cover
`(Photograph: Siemens AG,
`Munich)
`
`Figure 8.29 Opening a pipe clamp by means of a
`screwdriver
`
`Seals
`
`Reliable sealing of two components joined by snap-fit beams can be achieved only if a sufficient
`number of snap-fit beams is provided and if the pressure of the elastic seal is accomplished by
`tensile stress (not bending stress) in the beam (see Figure 8.30).
`
`Figure 8.30 Principle for designing an elastic seal
`
`AMT Exhibit 2004
`CORPAK v. AMT IPR2017-01990
`Page 15 of 15
`
`