DESIGN GUIDES

for
PLASTICS
Clive Maier, Econology Ltd

pdg

Plastics Design Group - Plastics Consultancy Network

plastics design group

British Plastics Federation

November 2004 Edition

This publication is made up of a series of articles published in Plastics and Rubber Weekly as a piece work. The
kind assistance of the author and PRW is acknowledged in the publication of the work.
The publication will be updated in a regular basis as new sections of the guide are published by PRW.

The design hints in this booklet are given in good faith and represent current good practice. The short nature of
the hints means that not all information can be included. No responsibility can be taken for any errors or
consequential damages resulting from using these hints.
This publication may be freely reproduced except for sale or advertising purposes. It may be hosted on web sites
for free downloading providing that it is used in its entirety and that reference is made to the original publication.
Clive Maier 2004

Contents
Preface .............................................................................................. 1
Forward ............................................................................................. 2
Introduction ...................................................................................... 3
Injection moulding ........................................................................... 5
Basics
1.
2.
3.
4.
5.

Wall thickness ..........................................................................................6

Corners ......................................................................................................7
Ribs ...........................................................................................................8
Bosses ....................................................................................................11
Design for recycling ..................................................................... Planned

Special features
6.
7.
8.

Living hinge .................................................................................. Planned

Bearings .................................................................................................14
Gears........................................................................................................17

Assembly
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.

Press fits ..................................................................................................21

Snap-fits .................................................................................................22
Hot air staking .............................................................................. Planned
Ultrasonic welding ........................................................................ Planned
Hot plate welding .......................................................................... Planned
Spin welding .................................................................................. Planned
Friction welding............................................................................. Planned
Induction welding.......................................................................... Planned
Laser welding ................................................................................ Planned
Adhesive and solvent bonding .................................................... Planned

Special techniques
19.
20.

Design for outsert moulding ....................................................... Planned

Design for gas assist injection moulding ................................... Planned

Extrusion.............................................................................................
21.

Design for profile extrusion ......................................................... Planned

Blow moulding ...................................................................................

22.

Design for extrusion blow moulding .......................................... Planned

Thermoforming ..................................................................................
23.

Design for thermoforming ........................................................... Planned

November 2004

Preface
This set of hints and tips for plastics product designers is intended as a source book and an 'aide
mmoire' for good design ideas and practices. It is a source book for plastics product designers at all
levels but it is primarily aimed at:

student designers carrying out design work for all levels of academic studies;

non-plastics specialists involved in the design of plastics products;

plastics specialists who need to explain their design decisions and the design limitations to nonplastics specialists.
The book covers each topic in a single page to provide a basic reference to each topic. This space
constraint means that each topic is only covered to a basic level. Detailed plastic product design will
always require detailed knowledge of the application, the processing method and the selected plastic.
This information can only be provided by raw materials suppliers, specialist plastics product designers
and plastics processors but there is a need to get the basics of the product design right in the first
instance.
Using the hints and tips provided in this guide will enable designers to reduce initial errors and will lead
to better and more economic design with plastics.
I hope this short work will improve the basic design of plastics products and if it can do this then it will
have served its objectives.

Clive Maier
ECONOLOGY Ltd.

November 2004

Forward
For more than 30 years in the plastics business I have been privileged to both participate and observe
quantum changes in the use of polymers in almost every field of consumer and industrial application.
The diversity of material technology and the complexity of form and function continue to contribute
profusely to our daily lives, from packaging and automotive, to medical and aerospace.
Despite this technology powerhouse at our disposal, some knowledge gaps prevail and the consumer is
too often confronted with a failed plastic part or an assembly that is simply just not user-friendly.
Despite the designers ingenuity in fulfilling the most demanding engineering performance, occasionally
the basics of good plastics design are missed.
Clives treatise Design Guides for Plastics is a practical aide mmoire, that has two fold benefit - it
gives the newcomer to plastics design an explicit overview of the broad design criteria in a range of
polymers, and to the experienced engineer a reminder of the criteria for those materials he may not be
utilising on a regular basis. I recommend it thoroughly to any engineer embarking on a new design
project in plastics.

Huw Radley
Chairman
Plastics Design Group
huw@harvestpolymers.com

November 2004

INTRODUCTION
Good design is important for any
manufactured product but for plastics it is
absolutely vital. We have no instinct for
plastics. Most of those we use today have
been around for little more than two
generations. Compare that with the
thousands of years of experience we have
with metals. And plastics are more varied,
more complicated. For most designs in
metals, there is no need to worry about the
effects of time, temperature or environment.
It is a different story for plastics. They creep
and shrink as time passes; their properties
change over the temperature range of
everyday life; they may be affected by
common household and industrial materials.
The philosopher Heidegger defined
technology as a way of arranging the world
so that one does not have to experience it.
We can extend his thought to define design
as a way of arranging technology so that we
do not have to experience it. In other words,
good design delivers function, form and
technology in objects that meet the needs of
users without making demands on them.
The well-designed object gives pleasure or
at least satisfaction in use, and does what it
should do without undue concern.
In these Design Guides we will set out the
basics of good design for plastics. The rules
and recommendations we give will
necessarily be generalisations. They will
apply often but not invariably to
thermoplastics, frequently but not
exclusively to injection moulding. The basic
advice will be good but because plastics are
so complex and varied the golden rule must
always be to consider carefully whether the
advice needs adjusting to suit your particular
application.
Good design combines concept with
embodiment. Unless the two are considered
together, the result will be an article that
cannot be made economically or one that
fails in use. This is particularly important for
plastics. It is vital to choose the right
material for the job. When that is done, it is
equally important to adapt the details of the
design to suit the characteristics of the
material and the limitations of the production
process.
Plastics come in a bewildering variety. There
are a hundred or more distinct generic
types. On top of that, advanced techniques
with catalysts and compounding are creating
new alloys, blends and molecular forms. All
of these materials can have their properties

DESIGN CONSIDERATIONS

modified by control of molecular weight and

by additives such as reinforcements. The
number of different grades of plastics
materials available to the designer now
approaches 50,000. The importance - and
the difficulty - of making the right choice is
obvious.
Plastics can be grouped into categories that
have roughly similar behaviour.
Thermoplastics undergo a physical change
when processed; the process is repeatable.
Thermosets undergo a chemical change; the
process is irreversible. A key distinction
between thermoplastics relates to the
molecular arrangement. Those with random
tangled molecules are called amorphous.
Those with a degree of molecular
arrangement and ordering are called semicrystalline. The difference is significant. For
example, most amorphous materials can be
fully transparent. And the more crystalline a
material is, the less likely it is to have a wide
'rubbery' processing region, so making it
less suitable for stretching processes like
blow moulding and thermoforming
Designers must design for process as well
as purpose and material. In single-surface
processes for example, there is only indirect
control over the form of the second surface.
Design must take this limitation into account.

November 2004

SOME COMMON PLASTICS

COMMON PLASTICS FORMING PROCESSES

4

November 2004

Part 1
Injection moulding

November 2004

1 WALL THICKNESS
Parts that might be made as solid shapes in
traditional materials must be formed quite
differently in plastics. Moulded plastics do not
lend themselves to solid forms. There are two
principal reasons for this. First, plastics are
processed with heat but are poor conductors
of heat. This means that thick sections take a
very long time to cool and so are costly to
make. The problems posed by shrinkage are
equally severe. During cooling, plastics
undergo a volume reduction. In thick
sections, this either causes the surface of the
part to cave in to form an unsightly sink mark,
or produces an internal void. Furthermore,
plastics materials are expensive; it is only
high-speed production methods and netshape forming that make mouldings viable.
Thick sections waste material and are simply
uneconomic.
So solid shapes that would do the job well in
wood or metal must be transformed to a
'shell' form in plastics. This is done by
hollowing out or 'coring' thick parts so you are
left with a component which regardless of
complexity is composed essentially of
relatively thin walls joined by curves, angles,
corners, ribs, steps and offsets. As far as
possible, all these walls should be the same
thickness.
It is not easy to generalise what the wall
thickness should be. The wall plays a part
both in design concept and embodiment. The
wall must be thick enough to do its job; it
must be strong enough or stiff enough or
cheap enough. But it must also be thin
enough to cool quickly and thick enough to
allow efficient mould filling. If the material is
inherently strong or stiff the wall can be
thinner. As a general guide, wall thicknesses
for reinforced materials should be 0.75 mm to
3 mm, and those for unfilled materials should
be 0.5 mm to 5 mm.
Ideally, the entire component should be a
uniform thickness - the nominal wall
thickness. In practice that is often not
possible; there must be some variation in
thickness to accommodate functions or
aesthetics. It is very important to keep this
variation to a minimum. A plastics part with
thickness variations will experience differing
rates of cooling and shrinkage. The result is
likely to be a part that is warped and
distorted, one in which close tolerances
become impossible to hold. Where variations
in thickness are unavoidable, the
transformation between the two should be
gradual not sudden so instead of a step, use
a ramp or a curve to move from thick to thin.

Thick sections and non-uniform walls cause

problems

Solid shapes must be redesigned as shells

Gradual transitions between thick and thin

sections
DESIGNERS NOTEBOOK
n Keep wall thickness as uniform as possible.
n Use gradual transitions between thick and thin sections.
n Wall thickness must suit both function and process.
n Wall thickness guide range is:

0.75 mm to 3 mm for reinforced materials

0.5 mm to 5 mm for unreinforced materials
6

November 2004

2 CORNERS
When the ideas of correct and uniform wall
thickness are put into practice the result is a
plastics part composed of relatively thin
surfaces. The way in which these surfaces
are joined is equally vital to the quality of a
moulded part.
Walls usually meet at right angles, at the
corners of a box for example. Where the box
walls meet the base, the angle will generally
be slightly more than 90 degrees because of
a draft angle on the walls. The easiest way,
and the worst, to join the walls is to bring
them together with sharp corners inside and
out. This causes two problems.
The first difficulty is that the increase in
thickness at the corner breaks the rule of
uniform wall thickness. The maximum
thickness at a sharp corner is about 1.4
times the nominal wall thickness. The result
is a longer cooling time accompanied by a
risk of sink marks and warping due to
differential shrinkage.
The other problem is even more serious.
Sharp corners concentrate stress and
greatly increase the risk of the part failing in
service. This is true for all materials and
especially so for plastics. Plastics are said to
be notch-sensitive because of their marked
tendency to break at sharp corners. This
happens because the stress concentration
at the corner is sufficient to initiate a
microscopic crack which spreads right
through the wall to cause total failure of the
part. Sharp internal corners and notches are
the single most common cause of
mechanical failure in moulded parts.
The answer is to radius the internal corner,
but what size should the radius be? Most
walls approximate to a classical cantilever
structure so it is possible to calculate stress
concentration factors for a range of wall
thicknesses and radii. The resulting graph
shows that the stress concentration
increases very sharply when the ratio of
radius to wall thickness falls below 0.4. So
the internal radius (r) should be at least half
the wall thickness (t) and preferably be in
the range 0.6 to 0.75 times wall thickness.
If the inner corner is radiussed and the outer
corner left sharp, there is still a thick point at
the corner. For an internal radius of 0.6t, the
maximum thickness increases to about 1.7
times the wall thickness. We can put this
right by adding a radius to the outside corner
as well. The outside radius should be equal
to the inside radius plus the wall thickness.
This results in a constant wall thickness

around the corner.

Properly designed corners will make a big
difference to the quality, strength and
dimensional accuracy of a moulding. But
there is another benefit too. Smooth curved
corners help plastic flow in the mould by
reducing pressure drops in the cavity and
minimising flow-front break-up.

Good and bad corner design

Stress concentration factors for cantilever

loading
DESIGNERS NOTEBOOK
n Avoid sharp internal corners.
n Internal radii should be at least 0.5 and preferably 0.6 to 0.75

times the wall thickness.

n Keep corner wall thickness as close as possible to the nominal

wall thickness. Ideally, external radii should be equal to the

internal radii plus the wall thickness.
7

November 2004

3.1 RIBS
So far in this design series we have seen
that plastics parts should be made with
relatively thin and uniform walls linked by
corner radii, not sharp corners. Both ideas
are important in the design of ribs.
When the normal wall thickness is not stiff
enough or strong enough to stand up to
service conditions the part should be
strengthened by adding ribs rather than
making the whole wall thicker. The principle
is the familiar one used in steel girders
where 'I' and 'T' sections are almost as rigid
as solid beams but are only a fraction of the
weight and cost.
A thicker section is inevitable where the rib
joins the main wall. This rib root thickness is
usually defined by the biggest circle (D) that
can be inscribed in the cross-section, and it
depends on the rib thickness (w) and the
size of the fillet radius (r). To avoid sink
marks, this thick region must be kept to a
minimum but there are constraints. If the rib
is too thin it will have to be made deeper to
give adequate rigidity and then it may buckle
under load. There are other problems too;
the mould becomes difficult to machine and
fill. And ribs filled under high injection
pressure tend to stick in the mould.
The fillet radius must not be made too small
either, or it will not succeed in reducing
stress concentrations where the rib joins the
main wall. Ideally, the fillet radius should not
be less than 40 percent of the rib thickness.
The ribs themselves should be between a
half and three-quarters of the wall thickness.
The high end of this range is best confined
to plastics that have a low shrinkage factor
and are less prone to sink marks.
A simple comparison shows the benefit of
good rib design. A rib that is 65 percent of
the wall thickness and has a 40 percent fillet
radius, results in a root thickness that is
about 1.23 times the wall thickness. By
contrast, the root thickness soars to 1.75
times the wall thickness when the rib is as
thick as the wall and has an equal radius.
Ribs of course must be extracted from the
mould, so they must be placed in the
direction of draw or provided with moving
mould parts to free them. Ribs should be
tapered to improve ejection; one degree of
draft per side is ideal. If the rib is very deep
the draft angle must be reduced or the rib
becomes too thin. For this reason ribs are
often limited to a maximum depth of five
times the rib thickness. So far, so good. But
how many ribs are needed to make a part

strong enough and how should they be

arranged? We will examine that in the next
Design Guide.

Ribs create thick sections at the root

How rib root thickness increases

DESIGNERS NOTEBOOK
n Rib thickness should be 50 - 75% of the wall thickness.
n Fillet radius should be 40 - 60% of the rib thickness.
n Rib root thickness should not be more than 25% greater than

the wall thickness.

n Rib depth should not be more than 5 times the rib thickness.
n Taper ribs for mould release.

November 2004

3.2 RIBS
Ribs are used to improve the rigidity of a
plastics part without increasing the wall
thickness so much that it becomes
unsuitable for injection moulding. In the
previous guide we looked at the basics of rib
design. This time we will see how to put ribs
into practice.
Usually we want a part to be equally rigid in
all directions, just like a solid plate. We can
get almost this effect by running ribs along
and across the part, so they cross at right
angles. This creates a thick section where
the ribs cross but if we follow the design
rules for ribs and fillet radii the increase is
within acceptable limits - about 1.3 times the
wall thickness at the worst. This can be
reduced almost to the basic wall thickness
by forming a cored-out boss at the junction,
but a better solution is to use a normal
junction with ribs that are less than 0.75
times the wall thickness.
But how many ribs do we need and how
deep should they be? Rigidity is a function
of the moment of inertia of the rib section.
This tells us that the stiffening effect of a rib
is proportional to its thickness but
proportional to the cube of its depth. So
deep ribs are structurally much more
efficient than thick ribs.
A common task is to develop a relatively thin
ribbed plate that has the same rigidity as a
thick solid plate. Standard engineering text
books provide the basic formulae to make
the calculation but the mathematics can be a
chore to manage manually. To minimise the
work a number of ready reckoners have
been devised, including an elegant cross-rib
solution developed by DuPont. Most of
these reckoners or calculators are based on
a particular set of assumptions so use with
caution if your design varies.
For example, the DuPont ribbed plate
calculator assumes the ribs are the same
thickness as the wall. To see how it works,
lets imagine that we want to design a crossribbed plate with a 2.5 mm wall (tB) that will
be as stiff as a solid plate of 5 mm thick (tA).
Calculate tB/tA the value is 0.5 and find
this value on the left-hand scale. Rule a line
across to the right-hand scale and read off
the value which is 1.75. This value is T/tA
where T is the rib depth including the wall
thickness. So in our example, T = 1.75 times
tA which is 8.75 mm. Now read off the value
on the base scale vertically below the point
of intersection between the 0.5 line and the
curve. The figure is 0.16 and it represents

the product of tA and the number (N) of ribs

per unit of plate width (W). The curve
assumes that W is unity. So N equals 0.16
divided by tA which is 0.032 ribs per mm of
width, or one rib per 31.25 mm.
We can make a pro rata adjustment for ribs
that are correctly designed to be thinner
than the wall. If the ribs are 65 percent of the
wall thickness, the rib spacing becomes 65
percent of 31.25, making it 20 mm for
practical purposes.

Alternative rib junctions

Terms for the calculator

Cross-ribbed plate calculator Source: DuPont

DESIGNERS NOTEBOOK
n Deep ribs are stiffer than thick ribs.
n Follow the basic rules for rib thickness and fillet radii.
n Calculate rib depth and spacing with a reckoner, or by using

math software or finite element analysis.

9

November 2004

3.3 RIBS
Ribs are important in the design of plastics
parts because they allow us to make a
component rigid without making it too thick.
We have already looked at the fundamentals
and seen how to design a cross-ribbed part.
Sometimes though, we only need rigidity in
one direction. This usually happens on a
long thin feature like a handle. In this case,
we can improve stiffness along the length of
the part by adding a number of parallel ribs.
These are called unidirectional ribs.
The first consideration is that these ribs
must not be too close together. This is
because the gap between the ribs is
produced by an upstanding core in the
mould. If this core is too thin it becomes very
difficult to cool and there may also be a
shrinkage effect that will cause ejection
problems. The usual rule is make the gap at
least twice the nominal wall thickness and
preferably three times or more.
As in the case of cross-ribs, design is based
on the principle that rigidity is proportional to
the moment of inertia of the wall section.
This provides a way of working out thin
ribbed sections that have the same stiffness
as thick plain sections. Calculator curves
make the job easier. Curves are available
for calculating deflection (strain) and stress
on various rib thicknesses. Our example
shows a deflection curve for rib thicknesses
equal to 60 per cent of the nominal wall
thickness.
For simplicity, the calculation splits the
unidirectional ribbed part into a number of Tsection strips, each with a single rib. The
width of the strip is known as the equivalent
width or BEQ. To see how the calculator
works, we will design a ribbed part with the
same stiffness as a rectangular section 45
mm wide (B) by 12 mm thick (W d). We
decide on four ribs and a nominal wall
thickness of 3mm (W). There are three
simple calculations to make.
BEQ = B/N = 45/4 = 11.25
BEQ/W = 11.25/3 = 3.75
W d/W = 12/3 = 4
Now find the value 4 on the left-hand axis
and draw a horizontal line to intersect with
the 3.75 curve shown on the right-hand axis.
Drop a vertical from this point and read off
the value, 5.3, on the bottom axis. This
figure is the ratio of rib height (H) to the
nominal wall thickness (W). So the rib height
in this example is:
H = 3(5.3) = 15.9

This is more than 5 times the rib thickness,

so we should be concerned about buckling.
We cant increase the number of ribs without
spacing them too closely so our options are
to make the ribs and/or the wall thicker.
Design often requires a few iterations to get
the best result.
We can also use ribs on side walls. Instead
of making the side wall thicker, we stiffen it
with buttress ribs, often known in the USA
as gussets. The same design rules apply. It
is particularly important to follow the rule for
thickness otherwise sink marks will show on
the outside of the part.

Unidirectional rib calculator

Source: DuPont

Use buttress ribs to stiffen side walls

DESIGNERS NOTEBOOK
n Unidirectional ribs should be spaced apart by at least 2 and

preferably 3 or more times the nominal wall thickness

n Rib depth should not be more than 5 times rib thickness
n Use the calculator curve to work out rib heights
n Use buttress ribs to stiffen side walls

10

November 2004

4.1 BOSSES
The boss is one of the basic design
elements of a plastics moulding. Bosses are
usually cylindrical because that is the
easiest form to machine in the mould and it
is also the strongest shape to have in the
moulded part. The boss is used whenever
we need a mounting point, a location point,
a reinforcement around a hole, or a spacer.
The boss may receive an insert, a screw, or
a plain shaft either as a slide or a press fit.
In other words, the boss is not as simple as
it looks. Depending on its use, it may have
to stand up to a whole combination of
forces tension, compression, torsion,
flexing, shear and bursting - so it must be
designed accordingly.
We can start with some general design
rules, using the principles we have already
developed for ribs and walls. The boss can
be thought of as a special case of a rib; one
that is wrapped round in the form of a tube.
An 'ideal' boss, designed according to rib
rules, would not produce sink marks or stick
in the mould but unfortunately the tubular
form of the boss would not be strong enough
in most cases. In real life, most bosses
break some rib design rules by necessity.
This means that boss design is a
compromise between sink marks and
functionality.
Rigidity is the simplest aspect of boss
design. This can be achieved by supporting
the boss with buttress ribs, and often by
linking the boss to a side wall. The support
ribs can be designed to normal rib rules so
that sink marks and stress points are
avoided.
When the boss is linked to a side wall, either
at an edge or the corner of a component,
there is a right and a wrong way to do it. The
wrong way is simply to extend the boss
outside diameter to meet the wall. This
inevitably produces a thick section that will
result in sink marks, voids, and long cooling
cycles. The right way is to link or tie the boss
to the side wall with a flat rib, preferably
recessed a little below the boss or edge
height so that it cannot interfere with any
assembly conditions. The other ribs that tie
the boss to the base wall remain as buttress
ribs. For economical machining of the
mould, the ribs should be aligned on the X-Y
axes of the component except for the flat
corner rib which is placed at 45 degrees.
The single diagonal rib is better than two XY ribs because it avoids a small mould core
between the ribs. Such small cores are

prone to damage and are difficult to cool;

this may result in slower moulding cycles
and more down time.
So we have established how to connect the
boss to the rest of the component. The more
difficult part of boss design concerns the
hole and the thickness of the boss.

Boss design is a compromise

There is a right and a wrong way to support

bosses

DESIGNERS NOTEBOOK
n Before designing a boss, consider its function and the forces

acting on it during assembly and service

n If the forces are not great, it may be possible to dispense with

support ribs, otherwise:

n Anchor the boss to the base wall with buttress ribs.
n If possible, anchor the boss to the side wall with a

flat rib.
n Avoid rib arrangements that result in small mould

cores or complicated mould machining set-ups.

11

November 2004

4.2 BOSSES
Perhaps the most common function of a
boss is to accept a screw fastener. There
are two types of screw in widespread use.
Thread-cutting screws work by cutting away
part of the boss inner wall as they are driven
in. This produces a female thread, and some
swarf. Thread-forming screws produce the
female thread by a cold flow process; the
plastic is locally deformed rather than cut
and there is no swarf. Generally, threadforming screws are preferred for
thermoplastics whereas thread-cutting
screws are better for hard inelastic materials
such as thermosets. The range of screws on
the market makes it difficult to give a general
design rule, but one approach is to use the
flexural modulus of the material as a guide
to which type to use.
Screw bosses must be dimensioned to
withstand both screw insertion forces and
the load placed on the screw in service. The
size of the hole relative to the screw is
critical for resistance to thread stripping and
screw pull-out, while the boss diameter must
be large enough to withstand hoop stresses
induced by the thread forming process.
Screw bosses have one important additional
feature: the screw hole is provided with a
counterbore. This reduces stress at the
open end of the boss and helps to prevent it
splitting. The counterbore also provides a
means of locating the screw prior to driving.
The dimensions of the boss and hole
depend on two things; the screw thread
diameter and the plastics material type. The
table gives boss, hole and depth factors for
a variety of plastics. To design a screw
boss, look up the material and multiply the
screw thread diameter by the appropriate
factors to dimension the hole, boss and
minimum thread engagement depth. Once
again, the variety of available screw types
and plastics grades means that general
guidelines must be used with caution.
Screw and boss performance can also be
adversely affected by outside influences. If
the boss has been moulded with a weld line,
the burst strength may be reduced. A lot
depends on service conditions too: if the
boss is exposed to a high service
temperature, or to environmental stress
cracking agents, its performance will be
reduced, sometimes drastically.
When designing bosses for screws, use the
manufacturer's recommendations for the
particular screw type but for critical
applications, there is no substitute for testing
before finalising the design.

Flexural Modulus of plastic (Mpa)

Less than 1,400
1,400 to 2,800
2,800 to 6,900
Greater than 6,900

Preferred screw type

Thread-forming
Thread-forming or Thread-cutting
Thread-cutting
Thread-cutting, fine pitch

Screw selection depends on material

Material
ABS
ABS/PC
ASA
PA 46
PA 46 GF 30%
PA 6
PA 6 GF 30%
PA 66
PA 66 GF 30%
PBT
PBT GF 30%
PC
PC GF 30%
PE-HD
PE-LD
PET
PET GF 30%
PMMA
POM
PP
PP TF 20%
PPO
PS
PVC-U
SAN

Hole Factor
0.80
0.80
0.78
0.73
0.78
0.75
0.80
0.75
0.82
0.75
0.80
0.85
0.85
0.75
0.75
0.75
0.80
0.85
0.75
0.70
0.72
0.85
0.80
0.80
0.77

Screw boss design factors

Boss Factor
2.00
2.00
2.00
1.85
1.85
1.85
2.00
1.85
2.00
1.85
1.80
2.50
2.20
1.80
1.80
1.85
1.80
2.00
1.95
2.00
2.00
2.50
2.00
2.00
2.00

Source: DuPont
Depth Factor
2.0
2.0
2.0
1.8
1.8
1.7
1.9
1.7
1.8
1.7
1.7
2.2
2.0
1.8
1.8
1.7
1.7
2.0
2.0
2.0
2.0
2.2
2.0
2.0
1.9

Sources: TR Fastenings and ASP

Boss dimensions are a function of material and screw diameter

DESIGNERS NOTEBOOK
n Select the right screw type - thread-forming or thread-cutting -

to suit the plastics material.

n Use a counterbore to reduce stress at the open end.
n Make the hole deep enough to prevent screw bottoming.
n Use the manufacturer's design recommendation, otherwise

use the factors in this design guide as a starting point.

n Test, if the application is critical.

12

November 2004

4.3 BOSSES
The quality of a screw connection depends
mainly on stripping torque and pull-out force.
Stripping torque is the rotational force on the
screw that will cause the internal threads in
the plastics boss to tear away. Driving
torque, the force needed to insert the screw
and form the thread in the boss, must be
less than stripping torque otherwise the
connection must fail. In practice you will
need a safety margin, preferably not less
than 5:1 for high speed production with
power tools. Stripping torque is a function of
the thread size and the boss material; it
increases rapidly as the screw penetrates
and tends to level off when screw
engagement is about 2 times the screw
pitch diameter. Driving torque depends on
friction and the ratio of hole size to screw
diameter. Modern thread-forming screws for
plastics have been designed to avoid torque
stripping, so there should be no problem if
you follow the hole size recommendations
given in the previous design guide.
The purpose of the screw is to hold
something down. The limiting factor on its
ability to do this is the pull-out force. When
the force needed to hold something down
exceeds the screw pull-out force, the screw
threads in the plastics boss will shear off,
allowing the screw to tear free from the
boss. Pull-out force depends on the boss
material, thread dimensions, and the length
of screw engagement.
Screw pull-out force (F) can be
approximated from the equation:

S
F =
3

DL

where S = design stress, D = screw pitch

diameter, and L = length of thread
engagement. Design stress S is the tensile
stress for the boss material, divided by a
safety factor which is typically given a value
of 2 or 3. Because screws are expected to
be effective over the design life of the
product, the tensile stress value should be
taken from creep data at a suitable time
value such as 5 years (43,800 hours). As
our sample calculation shows, the difference
is significant.
Torque (T) needed to develop the pull-out
force (F) can be calculated from:

T =

FD
P
2f +

2
D

... where f = coefficient of friction, and P =

screw thread pitch.
These simplified calculations assume a
conventional screw form and can only give
an indication of screw performance. In
practice, thread-forming screws will perform
better than indicated because they are
designed to create a stronger plastics
section between screw flights. The variety of
proprietary thread forms on the market also
makes it impossible to provide a simple
universal calculation. If the application is
critical, there is no substitute for testing.

Screw terms

SAMPLE CALCULATION
Using a 2.5 mm nominal diameter screw in an ABS boss.
A typical tensile stress value for ABS is about 35 MPa but the 5year value is only half that at 17.25 MPa. D = 2 mm, L = 6 mm, P
= 1.15 mm. The safety factor is 2, and the dynamic coefficient of
friction for ABS on steel is 0.35.

17.25

2 ( 2 6 ) = 188 Newtons
F=

1.15
188 2
T=
2 0.35 +
= 0.166 Newton metres
2
2

DESIGNERS NOTEBOOK
n Check that pull-out force is adequate for the application,

bearing in mind the design life.

n Remember that performance will be reduced at elevated

temperatures.
n Use only thread-forming screws designed for plastics.
n Test, if the application is critical.

13

November 2004

7.1 BEARINGS
The bearing is a dynamic application of
plastics; one where there is relative motion
between the plastics and another
component. Such bearings offer a number of
advantages over the conventional type. The
plastics bearing is shock and wear resistant,
light in weight, damps down running noise
and vibration, costs little, and requires little
or no lubrication and maintenance.
Plastics bearings can take the form of
plastics-to-plastics assemblies but the most
common design uses a steel shaft running in
a plastics sleeve bearing. The bearing may
be machined or moulded, depending on the
application and material. Some bearing
materials, for example PTFE and UHMWPE,
do not lend themselves to conventional
moulding processes and so are usually
machined. Moulding produces a bearing
with accurate dimensions and a fine surface
finish without imposing any additional
component costs, and so is much to be
preferred. The moulded bearing can take the
form of a bush that is fitted into another
component, or can be formed integrally in
the body of a moulding. This last solution is
only feasible when it is economically and
mechanically practical to make an entire
component in the bearing material. The
technique of outsert moulding is particularly
effective when a number of bearings are
needed in a metal chassis or sub-assembly
(see Part 19).
The performance of the bearing depends on
a number of factors including temperature,
running speed, bearing clearance, and the
shaft characteristics. For steel shafts, the
important characteristics are hardness and
surface finish, in that order. The shaft should
be as hard and smooth as possible; if the
shaft is too soft, a very smooth surface will
not prevent bearing wear.
The bearing capability can be calculated
from the operating pressure and velocity.
The operating pressure (P) is given by:

P=

W = K (PV )
where K is a wear constant known as the Kfactor.
The K-factor is a good guide to wear
performance but the factor does vary with
the PV value, so calculations should be
supplemented by prototype testing. A
limiting value of PV is also used as a design
parameter. The PV limit is the combination
of bearing pressure and velocity beyond
which the bearing is no longer wear
resistant. The table gives representative
values for K-factor and PV limit for common
bearing materials. These values are for
unmodified materials in contact with steel.
Many bearing materials include lubricating
and strengthening additives such as
graphite, PTFE, molybdenum disulphide and
glass. These can make a significant
difference to the values, so obtain specific
grade data before making design
calculations.
Material

V = DN
where N = rotational speed of the shaft.
Bearing wear (W) is proportional to
operating pressure times sliding velocity,
and is given by the expression:

K-factor
10-13(cm 3.min/m.kg.hr)

4.8
4.8
5.8
6.3
6.9

23.7
21.3
3.6
24.9
7.7

Polyamide PA6
Polyamide PA6/10
Polyamide PA6/6
Polybutylene terephthalate
Acetal

Typical figures for PV limit and K-factor

F
LD

where F = load on the bearing, L = bearing

length and D = shaft diameter.
The sliding velocity (V) is derived from:

Limiting PV
(MPa.m/min)

Key bearing features

DESIGNERS NOTEBOOK
n For metal shafts, the harder and smoother the better.
n Keep within the PV limit.
n Use specific grade data for K-factor and PV limit.
n Except for slow-running and lightly loaded bearings, verify the

design by testing prototypes.

14

November 2004

7.2 BEARINGS
In the previous Design Guide we saw that
the performance of a plastics bearing
depends on the PV limit and the K-factor of
the material. We gave typical values for
common bearing materials but do bear in
mind that PV and K values change
significantly when lubricating and reinforcing
additives are included in the plastics
compound. For bearing design, you will
need to get the actual values for the grade
you are using, or for a close equivalent.
The ratio of bearing length to shaft diameter
affects the generation of frictional heat in the
running assembly. When the length is great
compared with the diameter, heat may build
up in the centre portion of the bearing.
However, if the bearing is too short it begins
to fail in its function of guiding the shaft, and
there may also be retention problems if the
bearing is of the press-in type. A good rule
of thumb is to use a ratio of 1:1. In other
words, set the bearing length dimension to
be about the same as the shaft diameter. Of
course, if the shaft runs only slowly or
intermittently, frictional heating is unlikely to
be a problem.
The next issue is to work out the wall
thickness of the bearing. There are two
general considerations. If the bearing is
operating at a high PV value then heating
may be a problem, so use a minimal wall
thickness to help dissipate the heat.
Conversely, if the assembly is likely to be
subject to impact, use a thicker wall to resist
shock. The graph gives a rough guide to a
suitable bearing wall thickness for a range of
shaft sizes. The graph is for general purpose
bearing plastics in average circumstances.
Remember that the strength of reinforced
bearing materials can be much greater than
that of unmodified materials.
Plastics bearings need greater running
clearances than metal bearings, mainly due
to thermal expansion. If we assume that the
outside diameter of the bearing is
constrained then any expansion will result in
a reduction of the bore. Thermal expansion
will occur if the bearing warms up when
running and will also take place if the service
temperature is significantly above normal
room temperature. Other factors that can
affect the running clearance are moulding
tolerances and post-shrinkage, moisture
absorption in polyamide bearings, and the
compression effect when a separate bush is
press-fitted in a rigid bore. As a guide, the
diametral clearance between an assembled

shaft and bearing should be in the range

0.3% to 0.5% of shaft diameter, and should
never be less than 0.3%.
The total clearance needed before assembly
will be this figure plus allowances for any of
the other factors that apply. The temperature
effect on the bearing wall thickness can be
calculated by applying the coefficient of
thermal expansion for the plastic to the
temperature rise expected due to friction or
the environment, whichever is the greater.
The maximum compression effect in a
press-fitted bearing is simply the maximum
bearing outside diameter minus the
minimum diameter of the bore that it is
pressed into.

Bearing wall thickness as a function of shaft

diameter

DESIGNERS NOTEBOOK
n Keep the ratio of bearing length to shaft diameter close to 1:1.
n Bearing wall thickness can normally be in the range 2 mm to 5

mm for small to medium shaft diameters.

n Assembled diametral bearing clearances should not be less

than 0.3% to 0.5% of shaft diameter.

n Consider whether the clearance needs to be increased to

allow for temperature rises, moulding tolerances, postshrinkage, moisture absorption, or press-fitting compression.
15

November 2004

7.3 BEARINGS
So far we have looked at the mechanical
factors affecting the performance of plastics
bearings. These issues include PV limit, Kfactor, length-diameter ratio, and
clearances. Now lets see what effect
physical design can have on performance.
Of course, the wide scope for design
variation means we must generalise. The
effects we discuss will be more severe for
higher running speeds and loads. Where
bearings are slow running and lightly loaded
there is naturally much more design latitude.
The materials of the bearing and shaft can
have a big influence on wear. Soft metals
such as mild steel and non-ferrous metals
do not perform well as shafts in plastics
bearings. This is true even for plastics with
friction-reducing additives. The harder the
shaft, the lower the wear. The shaft should
also have a good surface finish but even a
polished surface will not overcome the
disadvantage of a shaft that is too soft.
Some plastics-to-plastics combinations
result in very low wear. The shaft hardness
graph shows that an acetal/nylon pairing is
much better than any acetal/metal
combination.
The graph also demonstrates that wear
begins gradually then accelerates rapidly.
This happens when wear debris begins to
act as a grinding medium. You can reduce
the problem by providing somewhere for the
debris to go. The simplest way is to design
the bearing with grooves running in the axial
direction. The groove width can be about 10
percent of shaft diameter and should be
deep enough to accommodate wear
particles with room to spare. Use at least
three grooves, and more in a large diameter
bearing. If the bearing wall would be
weakened too much by grooves, you could
use a series of through holes as an
alternative. The holes should be staggered
so that they sweep the full surface of the
shaft. Through holes of course have the
disadvantage that they are much more
difficult to produce in a moulded bearing.
Never forget the difference between theory
and practice. Calculations assume perfectly
cylindrical bearings precisely aligned with
the shaft so that loads are evenly
distributed. This can be difficult to achieve,
particularly when the bearing is an integral
part of a larger moulding. If the bearing is in
the form of an unsupported bush projecting
from a moulding wall, there is a possibility
that cantilever loads on the end of the

bearing or deflection in the supporting wall

will result in a slight misalignment. This
means that the bearing load will be unevenly
distributed and performance will suffer.
Misalignment can be reduced or eliminated
by supporting the bearing bush with ribs.
However, this raises the risk that shrinkage
in the ribs will distort the bearing bore from
the perfectly cylindrical form. In this case, it
may be necessary to mould the bearing bore
undersize and machine out to the final
accurate dimension.

Hard metal shafts are better; plastics shafts

are best

Grooved bearings last longer

Design problems
DESIGNERS NOTEBOOK
n Plastics bearings work best with hard shafts.
n Grooved bearings last longer.
n Use at least three grooves.
n Groove width should be 10 percent of shaft diameter.
n Support bearings adequately.

16

November 2004

8.1 GEARS
Plastics gears have a number of advantages
over the traditional metal gears. They are
lightweight, run quietly, are resistant to
corrosion, and operate with little or no
lubrication. Perhaps the biggest benefit
comes from the injection moulding process
that makes it possible to produce a complex
gear in a single rapid operation. The result is
much cheaper than a machined metal gear.
A moulded gear can also incorporate other
integral features such as springs or cams;
the metal equivalent would almost certainly
be an assembly of separate parts.
Of course, plastics have disadvantages too.
The precision, load-carrying capacity, and
dimensional stability of plastics gears are
generally inferior to those of metals. Both
precision and stability are particularly
affected by injection moulding so best
practice is needed in component and mould
design, in mould manufacture, and in
process optimisation and control.
The most commonly used plastics for gears
by far are polyamides (PA) and acetals
(POM). They are not the only choices
though. Thermoplastic polyurethane (TPU),
polybutylene terephthalate (PBT), polyimide
(PI), polyamideimide (PAI), coether-ester
based thermoplastic elastomer (CEE TPE),
and nylon blends are also used. The table
lists the main pros and cons for gear
applications of each material. Take the table
as a rough guide but remember that
properties vary significantly between the
various types of polyamide, and with
different grade formulations of all the
materials. In particular, reinforcing and
friction reducing additives can have a
marked effect on performance.
Gears are precision elements. Inaccuracies
will affect the smooth running and load
carrying capacity of the gear train, so the
plastics gear must be designed as far as
possible to eliminate sources of inaccuracy.
The general aim should be to attain
symmetry while avoiding excessive
variations in thickness. One approach is to
base the gear proportions on a unit of tooth
thickness. The gear ring bearing the teeth is
connected to the hub by a web. The
symmetry of this web is important to the
accuracy of the moulded gear. An off-centre
or one-sided web is likely to result in a
distorted gear. Similarly, it is better to avoid
reinforcing the web with ribs, or reducing its
weight with perforating holes or spokes. All
are likely to set up differential shrinkages
that will take the gear teeth out of round.

Material

Advantages

PA

Good abrasion and fatigue

resistance.

POM

Good abrasion resistance. Lower

moisture absorption than PA.
Good resistance to solvents.
Good abrasion and tear
resistance. Resistant to oil. Good
energy absorption.

PU TPE

PBT

PI

PAI

CEE
TPE
PA/ABS

Withstands continuous service at

120C. Good combination of
stiffness and toughness.
High wear resistance. Heat
resistant up to 260C. Unaffected
by radiation.
High strength and wear
resistance. Operating temperature
up to 210C.
Good abrasion resistance.
Effective at low service
temperatures down to -60C.
Better impact strength than
unmodified PA.

Disadvantages
Dimensional stability affected by
moisture absorption and post
shrinkage.
Poor resistance to acids and
alkalis. High shrinkage.
High hysteresis leading to
excessive heat generation during
fatigue loading. Continuous use
temperature limited to 70C.
High shrinkage and prone to
warping. Notch sensitive.
Low impact strength. Poor
resistance to acids and hydrolysis.
Expensive.
Attacked by alkalis. Expensive.

Sensitive to hydrolysis at elevated

temperatures.
Lower maximum operating
temperature than unmodified PA.

Gear thermoplastics compared Source: Based on The Plastics

Compendium Volume 1, MC Hough and R Dolbey, Rapra
Technology, 1995.

Suggested proportions for gears

Source: After DuPont

Avoid features that could distort the gear form

DESIGNERS NOTEBOOK
n Consider conditions of service before selecting the material.
n Design for symmetry and avoid excessive variations in

thickness.
n Make the centre web symmetrical and avoid ribs, spokes and

holes.
17

November 2004

8.2 GEARS
A significant cause of distortion in moulded
gears is flow in the cavity and this depends
on the gate position. The shrinkage value of
plastics tends to differ with and across the
direction of flow so the aim must be arrange
for flow to be symmetrical as well. Melt flow
should reach all points of the toothed gear
periphery at the same time and pressure.
This means that the ideal is a single gate in
the centre of a web across the shaft hole.
This is perfect for a gear positioned on the
end of a stub shaft but most gears use
through shafts and this will involve a
secondary finishing operation to remove the
web. This is usually undesirable, so most
gears are produced with compromise gating.
Hot runner or three-plate pin gates can be
positioned either in the hub or gear web, and
the more of them there are, the more nearly
will the flow approximate to central gating.
There should not be less than three equispaced gates; more may be possible on
larger gears. There will be weld lines
between these gates, so gating in or close to
the hub will give stronger weld lines in the
hub. This is important because torque from
the shaft is transmitted to the gear teeth
through the hub. On no account should
gears be gated asymmetrically. The result is
sure to be a component that is out of round.
Gating into the gear teeth also presents a
finishing problem and should be avoided at
all costs.
Once the basic component form and gating
is under control, the next step is to
determine the allowable tooth bending
stress. This is affected by service conditions.
Key factors include service life, operating
environment, tooth size and form, pitch line
velocity, and whether operation is
continuous or intermittent. The pitch line
velocity (PLV) is the linear velocity at the
pitch circle diameter of a running gear and it
can be calculated from the expression:

PLV =

Dn
60000

where D is the pitch circle diameter (mm), n

is the gear rotational speed (RPM) and PLV
is given in metres per second. The
relationship between PLV and gear tooth
bending stress been determined empirically
by DuPont from a study of successful gear
designs. The graph is based on acetal and
nylon gears operating at room temperature.

Avoid edge gates and off-centre gates

Use multiple symmetrical gates when a central

gate is not practical

Suggested proportions for gears

Source: After DuPont

Empirical design range for gear tooth stress

versus PLV
Source: After DuPont

DESIGNERS NOTEBOOK
n Gate the gear at the centre if possible.
n Otherwise use at least three symmetrical gates on the hub or

in the web.
n Keep the tooth bending stress within allowable limits relative to

the pitch line velocity.

18

November 2004

8.3 GEARS
The allowable gear tooth bending stress
depends on the PLV and the tooth size (or
diametral pitch) - see Section 8.2 - but it is
influenced by a number of external factors.
Some of these are environmental and
include dimensional changes due to
temperature or humidity, the operating
environment itself, and the presence or
absence of lubrication. Lubrication may be
external in the form of an oil or grease, or
internal by means of low-friction additives in
the plastics material used to form the gear.
Service conditions, for example the material
of the meshing gear and whether running is
intermittent or continuous, also have a
bearing on allowable gear tooth bending
stress. So too does the design life of the
assembly. Clearly, a higher stress can be
tolerated over a shorter life.
The load (F) normal to the tooth at the pitch
circle diameter (D) is a function of the torque
(T) transmitted through the shaft. For a spur
gear:

F=

Of course, the fatigue strength varies greatly

according to the material grade, particularly
for reinforced types. To carry out working
design calculations, you will need to get the
grade fatigue strength value from the
material supplier. The table gives rough
guide values for typical unfilled grades.
Material Fatigue strength Fatigue strength
(MPa)
(MPa)
at 106 cycles.
at 106 cycles.
Continuously
Initially
lubricated
lubricated
PA
20-35
8-12
POM
35-45
20-25
PBT
15-20
6-8
Sources: DuPont and Plastics Design Library

2T
D

We also need to know the gear module (M).

If (n) is the number of teeth on the gear,
then:

M=

D
n
Gear tooth terms

Then the bending stress (S) on the tooth can

worked out from:

S=

F
MfY

where f is the face width of the tooth and Y

is a tooth form factor.
The tooth form factor depends on the tooth
pressure angle and the number of teeth on
the gear. For a typical plastics spur gear, the
value of Y is in the region of 0.6 and in that
case, the equation for tooth bending stress
becomes:

S=

1.7F
Mf

If F is measured in Newtons, and the values

of M and f are given in millimetres, then S
will be calculated in megaPascals (MPa).
This value of S is the actual tooth bending
stress. We now need to adjust the figure to
take account of fatigue, temperature, and
shock loads.
The adjustment for fatigue is based on the
fatigue strength at one million (106) cycles.

Warning - External lubricants pose a risk

when used with thermoplastics because they
may cause environmental stress cracking
(ESC), particularly with amorphous
thermoplastics. ESC is the most common
cause of failure in plastics products, so avoid
external lubricants unless absolutely
necessary. If you must use them, do so only
after checking the risk with the materials
manufacturer or conducting extensive
testing.
DESIGNERS NOTEBOOK
n The stress on the gear tooth depends on torque, speed and

tooth size.
n The stress is influenced by external environmental factors.
n The allowable stress is determined by adjusting the theoretical

stress for fatigue, temperature and shock.

n Consider environmental stress cracking before lubricating

plastics gears.
19

November 2004

8.4 GEARS
The theoretical tooth bending stress (S) must
lie within the limit for the material. This limit is
not the theoretical strength value but a lower
value representing the practical or allowable
stress limit. This can be calculated by making
adjustments for fatigue, temperature, and
load conditions. Previously, we gave typical
fatigue strength guide values for unfilled gear
materials at 1 million cycles but the design
may be for a different number of cycles. If at
all possible, get fatigue values measured or
interpolated for the number of cycles you
need, and use these in the calculation.
Otherwise you can approximate the value by
applying a correction factor taken from the
fatigue correction graph.
For example, if the fatigue strength of initially
lubricated acetal (POM) at 1 million
(1.0E+06) cycles is 25 MPa, the value at
1.0E+07 cycles would be that figure
multiplied by a correction factor of 0.78 taken
from the graph at the 1.0E+07 intercept. In
other words the figure drops to 19.5 MPa.
The second correction we need to make is
for temperature. The correction factor can be
read from the temperature correction graph
and used in the same way.
The final correction is for shock loads. The
correction factor lies between 0.5 and 1.0
and the table gives values for three broadly
defined service conditions. If you are not sure
about shock loads in service, design for a
more severe condition.

Loading
No shock
Medium shock
Heavy shock

So for our example:

25
4.68 8
30
F=
1.7

So the sustainable load is 18.35 Newtons.

The conditions experienced by loaded
running gears are complex and calculations
alone will not guarantee success. What they
will do is ensure that the design is in the area
of feasibility. If the gear runs in critical
applications, or at high speeds or loads, or at
elevated temperatures, you should test
prototypes to prove the design.

Temperature correction factors

Source: After DuPont

Shock load factor (ks)

1.0
0.75
0.5

We arrive at the allowable stress by

multiplying the theoretical figure by correction
factors for fatigue (kf), temperature (kt) and
shock (ks). Lets illustrate that by working out
the allowable stress for polyamide at 50C
and 10 million cycles, under medium shock
conditions. The theoretical value of S in this
case is 10 MPa. The allowable value of S
becomes:

DESIGNERS NOTEBOOK

S = 10 0.78 0.8 0.75

n The allowable stress is determined by reducing the theoretical

The result is 4.68MPa, a very significant drop

from the theoretical figure. Now we can put
the new value to use in calculating the tooth
load (F) that can be sustained by a gear.
Imagine a spur gear with 30 teeth (n), a width
(f) of 8 mm, and a pitch circle diameter (D) of
25 mm. If we solve our original equation for
F, we get:
S .M .f where
D
F =
M=
1 .7
n

Fatigue correction factor (kf)

Source: After DuPont

stress to allow for fatigue, temperature and shock.

n Remember that correction factors are approximations, so do

not design to the limit of the calculations.

n If possible, use measured or interpolated fatigue values rather

than corrected values.

n If possible, use fatigue values quoted by the manufacturer for

your specific grade of material.

n For critical applications, prove the design by testing.

20

November 2004

9 PRESS FITS
When one object such as a shaft is assembled to another by forcing it into a hole that
is slightly too small, the operation is known
as press fitting. Press fits can be designed
between similar plastics, dissimilar plastics,
or more commonly between a plastic and a
metal. A typical example occurs when a
plastics hub in the form of a control knob or
gear is pressed on a metal shaft. The position is reversed when a plastics sleeve or
bearing is pressed into a metal bore.
Press fits are simple and inexpensive but
there are some problems to look out for. The
degree of interference between the shaft
and the hole is critical. If it is too small, the
joint is insecure. If it is too great, the joint is
difficult to assemble and the material will be
over-stressed. Unlike a snap fit, the press fit
remains permanently stressed and it is the
elastic deformation of the plastics part that
supplies the force to hold the joint together.
When plastics materials are exposed to permanent stress the result is creep. This
means that as time goes by, the force exerted by the press fit becomes less, although not necessarily to a significant extent. There are two other pitfalls for press
fits. Manufacturing tolerances on the shaft
and hole must be taken into account to see
whether the two extreme cases remain viable. And when the joint is made between
dissimilar materials, an increase in temperature will change the degree of interference
between the parts. Remember too, that at
elevated temperatures the effect of creep
will be greater.
One way of countering the effect of creep in
a shaft and hub press fit is to provide a
straight medium knurl on the metal shaft.
The plastics hub material will tend to cold
flow into the grooves of the knurl, giving a
degree of mechanical interference between
the parts. The frictional effect is also greater
because the surface area of the joint has
been increased by the knurl.
When designing a press fit, we need to work
out the correct amount of interference between the parts. Basing the calculation on
classical theory for thick-walled cylinders,
we can derive the following equation for the
allowable diametric interference (Y) for a
metal shaft in a plastics hub:

Sd K + v Hub

Y=
K EHub
where S = design stress, v = Poissons ratio,

E = elastic modulus, K = geometry factor.

The geometry factor K can be calculated
from:

( D)
K =
1 (d )
D
1+ d

The force (W) needed to press the parts together can be worked out from this equation:

Sdl
K
where = coefficient of friction and l =
W=

length of engaged surfaces.

Values for Poissons ratio and coefficient of
friction were given earlier in the Design
Guide series.

Press fit parameters

DESIGNERS NOTEBOOK
n Consider the effect of part tolerances and creep.
n Consider the effect of temperature changes between dissimilar

materials.
n If the press fit will be used at elevated temperatures, verify the

design by testing prototypes.

n If you are still worried about creep, try knurling the metal shaft.

21

November 2004

10.1 SNAP FITS

In Design Guide 4, we looked at bosses
used with thread-forming screws as a
means of joining or assembling plastics
parts. There are many other ways of
achieving the same object, for example by
welding, adhesives, staking and snap-fits.
But of all these methods, the snap-fit is
perhaps the most elegant way of joining
plastics parts together.
Snap-fits involve pushing a projection on
one part past an obstruction on a mating
part. They rely entirely for their effect on the
elasticity of plastics. Generally, one part is
more or less rigid while the other part is
flexible or resilient. Depending on the
design, the joint can be permanent or
releasable. Both parts can be plastics either the same or different types, or one
part can be a foreign material such as a
metal shaft or a laminated circuit board.
There are three principal types of snap-fit:
the cantilever snap-fit, also known as a
snap hook, catch spring, spur, or lug
the cylindrical or ring snap-fit
the spherical snap-fit
A further type, the torsional snap-fit, is not
so common and may be regarded as an
alternative to the snap hook; one in which
the elastic action of the catch is supplied by
placing a plastic member in torsion rather
than flexure.
The cantilever, cylindrical, and spherical
types share common basic principles. In
each case, the joint is assembled by
applying a force (F) to bring the parts
together. When they meet, joining is
opposed by an interference (y) between the
parts. When the force is sufficient, an elastic
deflection that is equal to the interference
allows the parts to come together. The
design of the snap-fit is such that the
deflection is wholly or substantially released
once the interference points have passed
and the parts have come together.
For the cantilever type, the deflection is a
simple bending or flexure of the lug. By
contrast, both the cylindrical and spherical
types require an elastic radial expansion.
Mechanically, the cylinder and sphere are
much stiffer structures than the cantilever,
so the interference dimension is usually
smaller. You may also see these types
provided with a number of radial slots to
make expansion easier. In effect, they have
now become a set of snap hooks arranged
in a circle.

Earlier, we described snap-fits as elegant.

By this we mean that they are efficient,
virtually free of charge, and 'green'. The
snap-fit features can be designed as an
integral part of the moulding without any
increase in cycle time and at the expense of
only a small increase in mould cost and
maintenance. Assembly can be performed
with little or no tooling using almost no
energy, and without the need to purchase
and stock additional parts such as screws,
clips, or adhesives. Additionally when the
time comes to recycle the part, there are no
foreign materials to be removed before
granulating.
For these reasons, snap-fits are likely to
become an even more popular design
feature in plastics assemblies of the future.
Success or failure depends on the detail and
in following guides we will set out the design
principles.

The principal snap-fit types

DESIGNERS NOTEBOOK
n Snap-fits work by using the elasticity of plastics.
n The three main types are cantilever, cylindrical, and spherical.
n Joints can be permanent or releasable.
n Snap-fits are cheap, efficient and green.

22

November 2004

10.2 SNAP FITS

In the previous design guide, we looked at
the general principles of snap-fits. Now let's
examine the most popular type - the
cantilever or hook - in more detail. The
cantilever type clicks or snaps into
engagement when it is pushed past a catch
on a mating part. The hook has a tapered
face with a shallow engagement angle to
help it past the obstruction. A releasable
snap hook has a second tapered face set at
a release angle to allow it to be removed
again. The release angle is greater than the
engagement angle, to make release
relatively difficult. If release is too easy, the
snap-fit will not act as a reliable fastener.
When the release angle approaches 90
degrees, removal by pulling is virtually
impossible and the snap-fit becomes a
permanent joint.
When the cantilever hook is pushed past the
catch, it is forced to flex. The amount of
deflection is equal to the interference
between hook and catch, and this must be
kept to a dimension that does not exceed
the allowable strain for the cantilever
material. The table shows approximate
design data for a range of unfilled materials.
The allowable strain figures are for a snap-fit
that is used just a few times. If it is to be
used once only, the strain figures can be
doubled. The figures in the table should be
taken as a guide only. For accurate design,
you will need to get grade-specific figures
from your materials supplier.
For a snap hook with a constant cross
section, the maximum deflection Y can be
worked out from this equation:

y=

el2
1.5t

The equation assumes that only the snap

hook flexes. In many cases, the moulding
face that it is attached to will also flex a little.
This can be regarded as a safety factor. If
the hook mounting is rigid, then you should
reduce the calculated maximum deflection
by a safety factor.
The normal force P needed to move the
snap hook through deflection y comes from
this equation:

P=

wt 2Ee
6l

This result can be used to work out the force

W needed to engage the snap fit with the
catch.

+ tan a
1 tan a
In the case of a releasable snap hook, the
same formula can be used to work out the
release force by substituting the release
angle b for the engagement angle a. If the
release force approaches the tensile
strength of the snap hook, then it is likely to
break as you try to release it. Similarly, the
catch will shear off if its cross-section is too
weak compared with either the engagement
force or release force. Of course, if the snap
hook is properly designed, the release force
will always be the greater, even in a
releasable design.
W =P

Snap-fit dimensions and forces

Material

Allowable strain Flexural modulus

(e) (%)
(E) (Gpa)

PS
ABS
SAN
PMMA
LDPE
HDPE
PP
PA
POM
PC

2
2
2
2
5
4
4
3
4
2

Coefficient of
friction ( )

3.0
2.1
3.6
2.9
0.2
1.2
1.3
1.2
2.6
2.8

0.3
0.2
0.3
0.4
0.3
0.3
0.3
0.1
0.4
0.4

DESIGNERS NOTEBOOK
n Keep within the allowable strain figure.
n If the calculated allowable deflection is too small, try

increasing the snap hook length.

n Design so that the snap hook is no longer flexed after it has

clicked into the catch

n Snap-fits are meant to be used either once or just a few times,

so fatigue and wear can be neglected.

n Radius the root of the snap hook to reduce stress

concentration.
23

November 2004

10.3 SNAP FITS

The cylindrical or ring snap-fit has a
continuous internal undercut that is engaged
by a groove on a shaft. It is often used to
retain a plastics part such as a knob on a
metal shaft but it can also be used to secure
two plastics parts together. Like other snap
fits the joint can be designed to be
releasable or permanent depending on the
slope of the release angle. When the joint is
inserted or released, the hub is forced to
expand elastically. This makes for a spring
that is inherently stiffer and stronger than the
cantilever hook type of snap fit. Strength is
usually an advantage but there are some
drawbacks too. The insertion force can be
quite high and it is often necessary to make
the undercut relatively small. The hub works
best when it is moulded in a comparatively
elastic material, not least because it must be
ejected off an undercut core in the mould.
This means that stiff glass-filled and other
reinforced grades may not be suitable for
the ring snap fit.
The stiffness of the hub spring depends not
only on its thickness but also on its free
length and crucially on how close the
undercut is to the free end. Ring snap fits
should always be designed with the
undercut reasonably near the hub free end,
otherwise the stiffness of the spring will
significantly greater and the joint may fail.
Assembly of the joint is made easier by
providing a draft or engagement angle on
the end of the shaft . An angle of 20 to 30
works well. The release angle determines
how easily the snap fit can be disengaged.
The greater the angle, the harder it is to
release. An angle of 40 to 50 is usual. Use
a greater angle if you want the joint to be
permanent.
The diagram shows the key features for a
cylindrical snap-fit. The maximum allowable
undercut can be worked out from this
equation:

y=

P=

[tan a + ]S y dl
K

where = coefficient of friction and Sy =

stress due to interference. Values for the
coefficient of friction were listed in the
previous Design Guide.
Material

Poissons ratio
v

PS
PMMA
LDPE
HDPE
PP
PA
PC
PVC
PPO
PPS
Steel

0.38
0.40
0.49
0.47
0.43
0.45
0.42
0.42
0.41
0.42
0.28

Main features of cylindrical snap-fits

Sd K + vhub 1 v shaft
+

K Ehub
Eshaft

where S = design stress, v = Poissons ratio,

E = Modulus of elasticity and K = geometry
factor.
The geometry factor K can be calculated by:

K=

The table gives approximate values for

Poissons ratio for a range of unfilled
materials. For accurate design, you will need
to get grade figures from your materials
supplier.
The expansion force exerted on the hub is
given by the equation:

d
1+
D

d
1
D

DESIGNERS NOTEBOOK
n Dont use cylindrical snap-fits with very stiff materials.
n Use an engagement angle of 20 to 30 and a release angle

of 40 to 50.

n Place the undercut near the open end of the hub.

n Size the undercut so that the design stress figure is not

exceeded.
24

November 2004

10.4 SNAP FITS

As its name implies, the torsion snap-fit
relies for its spring effect on twisting rather
than flexing like the other types. It is less
common than cantilever or ring snap-fits but
it is particularly useful when you want to be
able to release the catch easily and often.
For example, a torsion snap fit can be a
good way of fastening a hinged lid on a box
or container.
The torsion snap-fit catch is moulded with
integral supporting shafts on which it twists
when an opening force is applied. The
design often includes a dimple or some
other feature to indicate the right place to
press. The principle of levers applies, so
depending on the dimensions of the catch it
is possible to arrange for a small opening
force to overcome quite a strong snap-fit.
The catch portion is relatively stiff compared
to the integral shafts so that when the
opening force is applied to the catch the
shafts are twisted in torsion and it is this that
supplies the spring effect. The stiffness of
the spring depends on the thickness and
length of the shafts. Ideally the shafts will be
cylindrical as this is the most efficient form
for torsion but other shapes can be used.
The torsion snap fit can lead to some
mouldmaking complications and in these
circumstances it may be easier to use
square or cruciform section shafts.
The degree of twist or torsion on the shafts
should be kept to the minimum necessary to
clear the snap fit undercut. It is usually
possible to arrange the design so that the
catch meets an obstruction just after the
undercut has been released. This prevents
the catch being broken by an overenthusiastic user. The minimum angle in
radians that the catch must be moved
through is:

x=

2 r 4 Ey
180a 2 l

And now, by applying the principle of levers,

we can work out the opening force W thus:

W=

Pa
b

where b = length of opening lever.

So by making b relatively large compared to
a, we can arrange for the opening force to
be quite small. Be careful how you do this
though. If a is made too small, the angle of
twist x becomes too great.

Main features of torsion snap-fits

y
180a

where y = catch undercut and a = length of

catch lever.
The general formula for torsion in cylindrical
shafts is:

x =

P=

2Pal

E r
where P = force to free undercut, l = shaft
length, E = modulus of rigidity and r = shaft
radius.
From these two equations we can deduce
that:
4

DESIGNERS NOTEBOOK
n Use torsion snap-fits when you want to be able to release the

catch easily.
n Include a design feature to show where to press.
n Design a stop feature to prevent excessive torsion.
n Do not make the catch lever length too short otherwise the

twist angle and torsion becomes too great.

n Reduce the opening force by making the length of the opening

lever longer than the catch lever.

25

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