Contents
A

Snap Joints/General• Common features• Types of snap joints• Comments on dimensioning

B

Cantilever Snap Joints• Hints for design Calculations• Permissible undercut• Deflection force, mating force• Calculation examples

C

Torsion Snap Joints• Deflection• Deflection force

D

Annular Snap Joints

The illustration above shows a photograph of two snap-fit models taken in polarized• Permissible undercut

light; both have the same displacement (y) and deflective force (P).

• Mating force• Calculation example

E

Both Mating Parts
Elastic

F

Symbols

Top: The cantilever arm of unsatisfactory
design has a constant cross section. The
non-uniform distribution of lines (fringes)
indicates a very uneven strain in the outerfibers. This design uses 17% more material
and exhibits 46% higher strain than the optimal design.

Bottom: The thickness of the optimal snapfit arm decreases linearly to 30% of the original cross-sectional area. The strain in theouter fibers is uniform throughout the lengthof the cantilever.

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Snap-Fit Joints for Plastics - A Design Guide
3

Snap Joints GeneralA

Common features
Snap joints are a very simple, economical
and rapid way of join-ing two different components. All types of snap joints have incommon the principle that a protruding partof one component, e.g., a hook, stud or beadis deflected briefly during the joining operation and catches in a depres-sion (undercut)in the mating component.
After the joining operation, the snap-fit features should return to a stress-free condition.
The joint may be separable or inseparable
depending on the shape of the undercut; theforce required to separate the compo-nents
varies greatly according to the design. It isparticularly im-portant to bear the following
factors in mind when designing snap joints:• Mechanical load during the assembly
operation.
• Force required for assembly.

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Snap-Fit Joints for Plastics - A Design Guide

A

Types of snap joints
A wide range of design possi-bilities exists
for snap joints.
In view of their high level of flexibility,
plastics are usually very suitable materials
for this joining technique.
In the following, the many design possibilities have been reduced to a few basic shapes.
Calculation principles have been derived forthese basic designs.
The most important are:
• Cantilever snap joints
The load here is mainly flexural.
• U-shaped snap joints
A variation of the cantilever type.
• Torsion snap joints
Shear stresses carry the load.
• Annular snap joints
These are rotationally sym-metricaland involve multiaxial stresses.

Page 4 of 26

Snap-Fit Joints for Plastics - A Design Guide
5

Snap Joints/GeneralA

Cantilever snap joints
The four cantilevers on the control panel module shown in Fig. 1 hold the module firmly inplace in the grid with their hooks, and yet it canstill be removed when required. An economical
and reliable snap joint can also be achieved byrigid lugs on one side in combination withsnap-fitting hooks on the other (Fig. 2). This
design is particularly effective for joining two
similar halves of a housing which need to beeasily separated. The positive snap joint illustrated in Fig. 3 can transmit considerable
forces. The cover can still be removed easily
from the chassis, however, since the snap-fitting 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 similarities with an annular snap joint. The presence of slits, however, means that the load ispredominantly flexural; this type of joint istherefore classified as a "cantilever arm" fordimen-sioning purposes.

Fig 4: Discontinuous annularsnap jointPage
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Snap-Fit Joints for Plastics - A Design Guide

A
Torsion snap joints
The tor-sion snap joint of the design shown for
an instrument housing in Fig. 5 is still uncommon in thermoplastics, despite the fact that it, too,amounts to a sophisticated and economical joining method. The design of a rocker arm whose
deflection force is given largely by torsion of its
shaft permits easy opening of the cover under aforce P; the torsion bar and snap-fitting rocker
arm are integrally molded with the lower part of
the housing in a single shot.

Annular snap joints
A typical application for annular snap joints isin lamp housings (Fig. 6). Here, quite small
undercuts give joints of considerable strength.

Fig 5: Torsion snap joint on a housing made of Makrolon polycarbonate

Fig 6: A continuous annular snap joint
offers a semi-hermetic seal and is betterfor single assembly applications

Page 6 of 26

Snap-Fit Joints for Plastics - A Design Guide

Snap Joints/GeneralA

Combination of different snap
joint systems – The traffic light illus-• The reflector catches at three points on the

trated in Fig. 7 is an example of an effective

pressure point 3b may be chosen here, so

The calculation procedures applicable todesign for a functional unit. All the compo-that there is polygonal deformation of thevarious types of joints are briefly described

nents of the housing are joined together by

inner ring of the housing.

on the following pages, but in such a way as
to be as general as possible. The user cansnap joint.
• The lens in the front door is either pro

Details:

duced in the second of two moldings 4a• Housing and front access door engage ator, if a glass lens is desired, this can be

the fulcrum 1a. The lugs 1b (pressure

held by several cantilever snaps 4b .

point) hold the door open, which is usefulfor changing bulbs.
• The cantilever hook 2 locks the door. The
door can be opened again by pressing theAssumptions

periphery. Either a snap-fittin hook 3a or atherefore apply this information to types ofjoints not dealt with directly.
In all the snap-fit designs that follow, it isassumed initially that one of the mating parts• The sun visor engages at 5 like a bayonet

remains rigid. This assumption represents ancatch. Good service-ability and low-cost

additional precaution against material fail-production can be achieved with carefully

ure. If the two com-ponents are of approxi-

thought-out designs such as this.

mately equal stiffness, half the deflection

hook through the slit in the housing at 2.

can be assigned to each part. If one component is more rigid than the other and the total
strength available is to be utilized to thefullest, the more complex proceduredescribed in Section E must be adopted.
What is said in the remainder of thebrochure takes into account the fact that theplastics parts concerned are, for brief periods, subjected to very high mechanicalloads. This means that the stress-strain
behavior of the material is already outside
the linear range and the ordinary modulus ofelasticity must therefore be replaced by thestrain dependent secant modulus.

Fig. 7: Cross-sectional sketch (above) and photo (below) of a traffic light made of
Makrolon®polycarbonate. All the components are held together entirely be means ofsnap joints

Page
8 7 of 26

Snap-Fit Joints for Plastics - A Design Guide

Cantilever Snap Joints

B

Design Hints
A large proportion of snap joints are basicallysimple cantilever snaps (Fig. 8), which may beof rectangular or of a geometrically more
complex cross section (see Table 1).
It is suggested to design the finger so thateither its thickness (h) or width (b) tapers fromthe root to the hook; in this way the load-bearing cross section at any point bears a more
appropriate relation to the local load. The
maximum strain on the material can therefore
be reduced, and less material is needed.

Fig. 8: Simple snap-fitting hook
Good results have been obtained by reducing
the thickness (h) of the cantilever linearly sothat its value at the end of the hook is equal to
one-half the value at the root; alternatively, thefinger width may be reduced to one-quarter ofthe base value (see Table 1, designs 2 and 3).
With the designs illustrated in Table 1, the vulnerable cross section is always at the root (seealso Fig. 8, Detail A). Special attention must
therefore be given to this area to avoid stressconcentration.
Fig. 9 graphically represents the effect the root
radius has on stress concentration. At first

Fig. 9: Effects of a fillet radius on stress concentration

glance, it seems that an optimum reduction instress concentration is obtained using the ratio
R/h as 0.6 since only a marginal reduction
occurs after this point. However, using R/h of
0.6 would result in a thick area at the intersection of the snap-fit arm and its base. Thick sections will usually result in sinks and/or voids
which are signs of high residual stress. For thisreason, the designer should reach a compromise between a large radius to reduce stressconcentration and a small radius to reduce thepotential for residual stresses due to the creation of a thick sec-tion adjacent to a thin section. Internal testing shows that the radius
should not be less than 0.015 in. in any
instance.

Page 8 of 26

Snap-Fit Joints for Plastics - A Design Guide
9Cantilever Snap Joints

B

Calculations

Table 1: Equations for dimensioning cantilevers

SymbolsNotesy= (permissible) deflection (=undercut)

1)

E= (permissible) strain in the outer fiberatthe root; in formulae: E as absolute

These formulae apply when the tensilestress is in the small surface area b. If it
occurs in the larger surface area a, however, a and b must be interchanged.

The section modulus should bedetermined for the surface subject totensile stress. Section moduli for crosssection shape type C are given in Fig. 11.
Section moduli for other basic geometricalshapes are to be found in mechanical2)

If the tensile stress occurs in the convex
surface, use K2, in Fig. 10; if it occurs
in the concave surface, use K1,
accordingly.

Permissible stresses are usually more affectedvalue = percentage/100 (see Table 2)
1= length of armh= thickness at rootb

= width at rootc

= distance between outer fiber andneutral fiber (center of gravity)Z= section modulus Z = I c,
where I = axial moment of inertia

Es= secant modulus (see Fig. 16)

P= (permissible) deflection forceK= geometric factor (see Fig. 10)

3)

c is the distance between the outer fiber
and the center of gravity (neutral axis) in
the surface subject to tensile stress.

4)by temperatures than the associated strains. One
pref-erably determines the strain associated withthe permissible stress at room temperature. As afirst approximation, the compu-tation may bebased on this value regardless of the temperature. Although the equations in Table 1 may
appear unfamiliar, they are simple manipulations of the conventional engineering equa-tions
to put the analysis in terms of permissible strainlevels.

Page
10 9 of 26

Snap-Fit Joints for Plastics - A Design Guide

Geometric factors K and Z for ring segment

Fig 10: Diagrams for determining K1 and K2 for cross-sectional shape type C in Table 1.
K1: Concave side under tensile load, K2: Convex side under tensile load

Fig 11: Graphs for determining the dimensionless quantity (Z/r23) used to derive the section modulus (Z) for crosssectional shape C in Table 1.
Z1: concave side under tensile stress, Z2: convex side under tensile stress

Page 10 of 26

Snap-Fit Joints for Plastics - A Design Guide
11

Cantilever Snap Joints

B

Fig 12: Undercut for snap joints

Fig 13: Determination of the permissible strain for the joining operation (left: material with distinct yield point;right: glass-fiber-reinforced material without yield point)

Permissible undercut

In general, during a single, brief snap-fitting
operation, partially crystalline materials may

The deflection y occurring during the joining

be stressed almost to the yield point, amor-

operation is equal to the undercut (Fig. 12).

phous ones up to about 70% of the yield strain.

Glass-fiber-reinforced molding compounds do
not normally have a distinct yield point. The
permis-sible strain for these materials in thecase of snap joints is about half the elongation
at break (see Fig. 13)

The permissible deflection y (permissible
undercut) depends not only on the shape but
also on the permissible strain E for the material used.

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Snap-Fit Joints for Plastics - A Design Guide

B
Deflection force
Using the equations given in Table 1, the permissible deflection y can be determined easily
even for cross sections of complex shapes.
The procedure is explained with the aid of an
example which follows.
A particularly favorable form of snap-fitting
arm is design 2 in Table 1, with the thicknessof the arm decreasing linearly to half its initialvalue. This version increases the permissible
deflection by more than 60% compared to a

Fig. 14: Determination of the secant modulus

snap-fitting arm of constant cross section(design 1).
Complex designs such as that shown in Fig. 15
may be used in applications to increase thePermissible short term
strain limits at 23˚C
(73˚F)

effec-tive length. Polymers Division Design
Engineering Services would be pleased to

Unreinforced

assist you in a curved beam analysis if you

Apec®

choose this type of design.

®

Bayblend

Makroblend®

The deflection force P required to bend thefinger can be calculated by use of the equa-

Makrolon®

High Heat PC

4%

PC/ABS

2.5%

Polycarbonate
BlendsPC

3.5%
4%

tions in the bottom row of Table 1 for crosssections of various shapes.

Glass-Fiber-Reinforced (%Glass)Es is the strain dependent modulus of elastici-

Makrolon®(10%) PC

2.2%

ty or "secant modulus" (see Fig. 14).

Makrolon®(20%) PC

2.0%

Values for the secant modulus for various

Table 2: General guide data for the allowable

Bayer engineering plastics can be determinedshort-term strain for snap joints (single join -from Fig. 16. The strain value used should

ing operation); for frequent separation andalways be the one on which the dimensioning

rejoining, use about 60% of these valuesof the undercut was based.

Fig. 15: U-shaped snap-fitting arm for alid fastening

Polyurethane Snap-Fits
Snap-fits are possible using certain
polyurethane systems. For more
information call Polymers Design
Engineering at 412-777-4952.

Page 12 of 26

Snap-Fit Joints for Plastics - A Design Guide
13

Cantilever Snap Joints

B

Fig. 16: Secant Modulus for Bayer engineering plastics at 23°C (73°F)

Page
14 13 of 26

Snap-Fit Joints for Plastics - A Design Guide

B

Fig. 17: Relationship between deflection force and mating force

Mating Force
During the assembly operation, the deflection
force P and friction force F have to be overcome(see Fig. 17).
The mating force is given by:
W = P • tan (␣ + p) = Pµ + tan ␣
1 – µ tan ␣µ + tan ␣
The value for 1 — µ tan ␣ can be taken directlyfrom Fig. 18. Friction coefficients for various
materials are given in Table 3.
In case of separable joints, the separation force
can be determined in the same way as the mating
force by using the above equation. The angle ofinclination to be used here is the angle ␣'

Page 14 of 26

Snap-Fit Joints for Plastics - A Design Guide
15

Cantilever Snap Joints

The figures depend on the relative speed of themating parts, the pressure applied and on thesurface quality. Friction between two different
plastic materials gives values equal to orslightly below those shown in Table 3. With
two components of the same plastic material,
the friction coefficient is generally higher.
Where the factor is known, it has been indicated in parentheses.

B

PTFE
PE rigid
PP
POM
PA
PBT
PS
SAN
PC
PMMA
ABS
PE flexible
PVC

0.12-0.22
0.20-0.25
0.25-0.30
0.20-0.35
0.30-0.40
0.35-0.40
0.40-0.50
0.45-0.55
0.45-0.55
0.50-0.60
0.50-0.65
0.55-0.60
0.55-0.60(x 2.0)(x 1.5)(x 1.5)(x 1.5)(x 1.2)(x 1.2)(x 1.2)(x 1.2)(x 1.2)(x 1.0)

Table 3: Friction coefficient, µ.
(Guide data from literature for the coefficientsof friction of plastics on steel.)Page
16 15 of 26

Snap-Fit Joints for Plastics - A Design Guide

B
Calculation example I
snap-fitting hook
This calculation is for a snap-fitting hook ofrectangular cross section with a constantdecrease in thickness from h at the root to h/2
at the end of the hook (see Fig. 19). This is an
example of de-sign type 2 in Table 1 andshould be used whenever possible to per-mit
greater deformation and to save material.

Given:
a. Material = Makrolon® polycarbonateb. Length (1) = 19 mm (0.75 in)c. Width (b) = 9.5 mm (0.37 in)d. Undercut (y) = 2.4 mm (0.094 in)e. Angle of inclination (a) = 30°

Find:a. Thickness h at which full deflection y willcause a strain of one-half the permissible
strain.
b. Deflection force P
c. Mating force W

Fig. 19: Snap-fitting hook, design type 2, shape A

Solution:a. Determination of wall thickness h
Permissible strain from Table 2: ⑀pm = 4%
Strain required here ⑀ = 1/2 ⑀pm = 2%
Deflection equation from Table 1, type 2, shape A:
Transposing in terms of thickness

y = 1.09 ⑀1
h2

h = 1.09 ⑀ 12y
= 1.09 x 0.02 x 192
2.4= 3.28 mm (0.13 in)b. Determination of deflection force P
Deflection force equation from Table 1, cross section A: P = bh2 Es ⑀•
6
1
From Fig. 16 at ⑀ = 2.0%
Es = 1,815 N/mm2 (264,000 psi)
P = 9.5 mm x (3.28 mm)2 1,815 N/mm2 x 0.02
•
6
19 mm
= 32.5 N (7.3 lb)

c. Determination of mating force W
W = P•µ + tang ␣
1 – µ tan ␣

Friction coefficient from Table 3 (PC against PC) µ = 0.50 x 1.2 = 0.6
From Fig. 18:µ + tan ␣= 1.8 For µ = 0.6 and a = 30°
1—µ tan ␣
W = 32.5 N x 1.8 = 58.5 N (13.2 lb)

Page 16 of 26

Snap-Fit Joints for Plastics - A Design Guide
1Cantilever Snap Joints

B

Calculation example IIsnap-fitting 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). Thisis design type 2, shape C in Table 1.
This taper ratio should be used when possible toevenly distribute stresses during arm deflection.
It also reduces material usage.

Given:
a. Material = Bayblend® PC/ABS
b. Length (1) = 25.4 mm (1.0 in)

Fig. 20: Snap-fitting hook, design type 2, shape C

c. Angle of arc (␪) = 75°
d. Outer radius (r2) = 20 mm(0.787 in)e. Inner radius (r1) = 17.5 mm(0.689 in)f. Thickness (h) = 2.5 mm (0.1 in)

Solution:g. ␾/ =␪/2=37.5°

Find:
a. The maximum allowable deflection for asnap-fit design which will be assembled
and unassembled frequently.

The permissible strain for a one-time snap-fit assembly in Bayblend® resin is 2.5%. Since thedesign is for frequent separation and rejoining, 60% of this value should be used or ⑀ pm = (0.6)(2.5%) = 1.5%.
Deflection equation from Table 1, type 2, shape C: y = 1.64 K(2) ⑀ 12

r2

The variable for K(2) can be obtained from the curves in Fig. 10. Note that if the member isdeflected so that the tensile stress occurs in the convex surface, the curve for K1 should be used;
if it occurs in the concave surface, K2 should be used. In this case, the tensile stress will occur inthe convex surface, therefore the curve for K2 should be used.
r1/r2 = 0.875 and 0 = 75°
from Fig. 10, K(2) = K2 = 2.67
y – 1.64(2.67) (0.015) (25.4 mm)2
= 2.11 mm (0.083 in)
20 mm

Alternate Solution:
This method may be used as a check or in place of using the curves in Fig. 10.

⑀ 12Deflection equation from Table 1, type 2, shape D: y = 0.55

The value for c(3) which is the distance from the neutral axis to the outermost fiber, can becalculated from the equations shown below:
1)]c2 = r2[1– 2 sin ␾ (1 – h/r2 +
2–h/r
2
3␾
c1 = r2[

2 sin ␾ + (1 – —)h
2 sin ␾ – 3␾ cos ␾ ]3␾(2 _ h/r2)
3␾
r2

Use c2 for c(3), if the tensile stress occurs in the convex side of the beam. Use c1 for c(3) if thetensile stress occurs in the concave side. For this particular problem, it is necessary to calculate c2.
c(3) = c2 = 20 mm [12 sin 37.5

3 (0.654)
Solving for y using c2 yields;(1 –2.5 mm
20 mm+] = 2.52 mm

1
2 – 2.5 mm/20mm

y = 0.55 (0.015) (25.4 mm) = 2.11 mm (0.083 in)(2.52 mmBoth methods result in a similar value for allowable deflection.
2

Page 17 of 26

Snap-Fit Joints for Plastics - A Design Guide
18

Torsion Snap Joints
Deflection
In the case of torsion snap joints, the deflection is not the result of a flexural load as with
cantilever snaps but is due to a torsional
deformation of the fulcrum. The torsion bar(Fig. 21) is subject to shear.

C

The following relationship exists between the total angle of twist --and the deflections y1 or y2 (Fig. 21):where
sin ␸ =

y1 = y211 12␸= angle of twist

Y1 , Y2
11 , 12= deflections= lengths of lever arm

The maximum permissible angle ␸pm is limited by the persmissible shear strain ␥pm:
where

␸pm =

180 ␥pm • 1
 • r(valid for circular cross section)

␸pm= permissible total angleof twist in degrees

␥pm
1
r

= permissible shear strain= length of torsion bar= radius of torsion bar

The maximum permissible shear strain ␥pm for plastics is approximately equal to:where␥pm  (1 + ␯) ⑀pm
␥pm  1.35 ⑀pm

␥pm
⑀pm
␯

= permissible shear strain= permissible strain= Poisson's ratio(forplastics approx. 0.35)

Fig. 21: Snap-fitting arm with torsion bar

Page 18 of 26

Snap-Fit Joints for Plastics - A Design Guide
19

Torsion Snap Joints

C

Deflection force
A force P is required to deflect the lever arm
by the amount y(1,2). The deflection force canact at points 1 or 2. For example see Fig. 21.
In this case,P1l1 = P212 = ␥GIp (x2)*rwhere
G = shearing modulus of elasticity
␥ = shear strain
IP = polar moment of inertia
 r4=; for a solid circular cross section
2*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:G=

Example of snap-fitting rocker arm (flexure and torsion about the Y axis)Es
2(1+␯ )

where
ES = secant modulus
␷ = Poisson's ratioPage
20 19 of 26

Snap-Fit Joints for Plastics - A Design Guide

Annular Snap Joints

D

Permissible undercut
The annular snap joint is a con-venient formof joint between two rotationally symmetricparts. Here, too, a largely stress-free, positive
joint is normally ob-tained. The joint can beeither detachable (Figs. 22a, 23), difficult todisassemble or inseparable (Fig. 22b)
depending on the di-mension of the bead andthe re-turn angle. Inseparable designs should
be avoided in view of the complex toolingrequired (split cavity mold).
The allowable deformation should not be
exceeded either during the ejection of thepart from the mold or during the joining
operation.

Fig. 23: Annular snap joint on a lamp housing

The permissible undercut as shown in Fig. 24
is limited by the maxi-mum permissible
strainYpm = ⑀pm .dNote: ⑀pm is absolute value.
This 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 correspondingly smaller. (With components of equal flexibility, the strain is halved,i.e., the undercut can be twice as large.)
W = mating force
y = undercut
␣ = lead angle
␣' = return angle
t = wall thickness
d = diameter at the joint

Fig. 24: Annular snap joint—symbols used

Fig. 22: Annular snap joint

Page 20 of 26

Snap-Fit Joints for Plastics - A Design Guide
21

Annular Snap Joints

D

Deflection force, mating force
The determination of the mating force W issomewhat 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. 25). Accordingly, the stress isalso distributed over a large area of thematerial surrounding the bead.
Experimentally proven answers to thisproblem are based on the "theory of a beamof infinite length resting on a resilient
foundation." Two extreme cases are depicted
in Fig. 26.

Fig. 25: Stress distribution during joining operation

Fig. 26: Beam resting on a resilient foundation
1

The force P is applied at the end of the beam. (This corresponds
to a snap joint with the groove at 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 = y • d • Es • X

W=P

2

The force P is applied a long distance (co) from the end of thebeam. (This is equivalent to an annular snap joint with the groove
remote from the end of the tube)µ + tan ␣
1 — µ tan ␣

where

where

µ = friction coefficient␣ = lead angle

P = transverse force
y = undercut
d = diameter at the joint ES = secant modulus
Es = secant modulus
X = geometric factor

The geometric factor, assuming that the shaft
is rigid and the outer tube (hub) is elastic, is asfollows:
XN = 0.62

The geometric factor X takes into account thegeometric rigidity.
As far as the mating force is concerned, friction
conditions and joint angles must also be taken into
consideration.

Page
22 21 of 26

 (d0/d — 1) / (d0/d + 1)[( d0/d)2 + 1]/[(d0/d)2 – 1] +␯

where
d0 = external diameter of the tube
d = diameter at the joint␯ = Poisson's ratio

Snap-Fit Joints for Plastics - A Design GuideD
If the tube is rigid and the hollow shaft
elastic, thenXw = 0.62

 (d/di – 1)/(d/di + 1)[(d/di)2 + 1]/[(d/di)2 – 1] – ␯

whered = diameter at the joint
di = internal diameter of the hollow shaft
The geometric factors XN and Xw can befound in Fig. 27.
The snap joint is considered "remote" if the
distance from the end of the tube is at least␦  1.8 d • t
where
d = joint diametert = wall thickness
In this case, the transverse force P and mating
force W are theoretically four times as great
as when the joint is near the end of the tube.
However, tests have shown that the actual
mating forces rarely exceed the factor 3
Premote  3Pnear
Wremote  3Wnear
This means that if the joint lies be-tween O
and ␦ minimum, then the factor is between 1
and 3.
The secant modulus Es must be determined asa function of the strain e from Fig. 16. For thesake of simplicity, it may be assumed here thatthe strain

Fig. 27: Diagrams for determining the geometric factor X for annularsnap jointsy⑀ = d . 100%where
y = undercut
d = diameter,over the entire wall thickness. (In fact,
it varies at different points and in different
directions on the wall cross section).

Page 22 of 26

Snap-Fit Joints for Plastics - A Design Guide
23

Annular Snap Joints

D

Solution
Secant modulus ES from Fig. 16
Strain:
y
⑀= d

1 mm*
⑀ = 200 mm • 100%

⑀ = 0.5%

Fig. 28: Lamp housing with coverCalculation example annularsnap joint*Since both mating parts have approximately
equal stiffness, the deflection for each partis approximately half the undercut.
This strain is permissible for polycarbonate
according to Table 2.

Ex = 2,200 MPa (320,000 psi)
P = 1 mm x 200 mm x 2,200 MPa x
1.7 x 10-3 = 748 N
P = 748 N (168 lb)
Mating force, µ = 0.6 from Table 3:
W=Pµ + tang ␣= 748 N x 1.8 =1 — µ tan ␣= 1,346 N

Transverse force P:

Value 1.8 (from Fig. 18)

P = y • d Es • X

W = 1,346 N (302.5 lb)

As the mating parts are of approximately
equal stiffness, the calculation may be
performed for either component. In this casethe lamp cover (hub) has been chosen.

The mating and opening force W in this caseis a considerable force. It should be remembered, however, that such a force would only
occur if mating parts in true axial align-ment
were joined by machine. In manual assembly,
the greater part of the bead is first introduced
into the groove at an angle and only theremaining portion is pressed or knocked into
position. The mating forces occurring underthese circumstances are much smaller, as only
part of the bead is deformed.

Given:
Lamp cover and housing made of Makrolon®
polycarbonate.
Snap-fitting groove near the end.
Dimensions:d = 200 mm (7.87 in)
t = 2.5 mm (0.098 in) for both mating parts
y = 2 x 1 mm (0.039 in)
␣ = 45°

XN from Fig. 27 withd0 = 200 + 2 x 2.5 = 1.025d200
XN = 0.0017 = 1.7 x 10-3

The lead and return angle is 45°. The edge isrounded, however, and the effective angle
may be assumed to be ␣ = 30°.
Required:Occurring strain ⑀
Deflection force P
Mating force W

Page
24 23 of 26

Snap-Fit Joints for Plastics - A Design GuideBoth Mating Parts Elastic
With all the examples of snap joints mentioned so far, the stiffer of the two mating parts
was assumed to be absolutely rigid.
Consequently, the more flexible of the two
com-ponents was theoretically deformed by
the full amount of the undercut.
Where both parts are deformable, however,the sum of these deformations is equal to theundercut, i.e., each deformation is smaller.

The mating force and the deformations occurring in two flexible mating parts can be determined most simply by using a graph.
For this purpose, the transverse force for eachcomponent is determined as a function ofdeflection on the assumption that the othercomponent is absolutely rigid; a "deflective
curve" is then plotted for each mating part asshown in Fig. 29a and b.

E
These "deflection curves" are then superimposed (Fig. 29c). The point of intersection of
the two curves gives the actual deflection
force P and the deflections y1 and y2.
With the aid of these quantities P, y1 and y2,
the individual strains and the mating force canthen be determined without diff i c u l t y, as
described earlier.

Fig. 29: Determination of deformation and transverse force when both mating parts are flexible

Page 24 of 26

Snap-Fit Joints for Plastics - A Design Guide
25

SymbolsFadimensions

␣

angle of inclinationb

dimensions␣'

return anglecdistance between outer fibreand neutral fibre␦ddiameter at the joint

distance of snap-fitting groovefrom the end

diinternal diameter⑀straindo

external diameter⑀Pmmaximum allowable strain

Eomodulus of elasticity (intrinsic
tangential modulus)⑀ultstrain at break⑀yyield strain

ES

secant modulus␸angle of twistFfriction force␥

shear strain

G

shear modulusµ

friction coefficientHheight thickness at the root␷Poisson's ratioIP

polar moment of inertia

P

angle of repose

K

geometric factor for ring
segments␴stress1

length, length of lever arm␪

arc angle of segment

Nnormal force due to insertionP

deflection forceR

resultant insertion forcerradiustwall thickness

Wmating forceX

geometric factor for annularsnap jointindex W=shaft
index N=hubyundercut, deflection

Z

axial section modulus

Health and Safety Information
Appropriate literature has been assembled which provides information pertaining to
the health and safety concerns that must be observed when handling Bayer products, appropriate industrial hygiene and other safety precautions recommended bytheir manufacturer should be followed. Before working with any product mentioned inthis publication, you must read and become familiar with available information concerning its hazards, proper use and handling. This cannot be overemphasized.
Information is available in several forms, such as Material Safety Data Sheets andProduct Labels. Consult your Bayer Representative or contact the Product Safety
Manager for the Bayer MaterialScience within Bayer’s Corporate Occupational and
Product Safety Department, Bayer MaterialScience L L C, 100 Bayer Road,
Pittsburgh, PA 15205 -9741, (412) 777-2000.

Page
26 25 of 26

Snap-Fit Joints for Plastics - A Design Guide

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