4 . 3 . B S N O I T A C I L P P A · N G I S E D · S N O I T A L U C L A C
Design calculations for press t joints made from engineering plastics
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NOTICE TO USERS:
To the best of our knowledge, the information contained in this publication is accurate, however we do not assume any liability whatsoever for the accuracy and completeness of such information. The information contained in this publication should not be construed as a promise or guarantee of specific properties of our products. Further, the analysis techniques included in this publication are often simplifications and, therefore, approximate in nature. More vigorous analysis techniques and prototype testing are strongly recommended to verify satisfactory part performance. Anyone intending to rely on any recommendation or to use any equipment, processing technique or material mentioned in this publication should satisfy themselves that they can meet all applicable safety and health standards. It is the sole responsibility of the users to investigate whether any existing patents are infringed by the use of the materials mentioned in this publication. Properties of molded parts can be influenced by a wide variety of factors including, but not limited to, material selection, additives, part design, processing conditions and environmental exposure. Any determination of the suitability of a particular material and part design for any use contemplated by the user is the sole responsibility of the user. The user must verify that the material, as subsequently processed, meets the requirements of the particular product or use. The user is encouraged to test prototypes or samples of the product under the harshest conditions to be encountered to determine the suitability of the materials. Material data and values included in this publication are either based on testing of laboratory test specimens and represent data that fall within the normal range of properties for natural material or were extracted from various published sources. All are believed to be representative. These values alone do not represent a sufficient basis for any part design and are not intended for use in establishing maximum, minimum, or ranges of values for specification purposes. Colorants or other additives may cause significant variations in data values.
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Contents 1.
Introduction
4
2.
Requirements for press-fit joints
4
3.
Critical parameters
5 5
3.2
Coefficient of friction fj,0 Interference U
3.3
Relaxation modulus Er
6
3.1
4.
for a press-fit joint
5
Design calculations for press-fit joints
7
Determination of the maximum
4.1
transmissible axial force Fmax. 4.2
Determination of the maximum
4.3
transmissible torque Mt Determination of the joint pressure p
4.3.1
Metal
4.3.2
Plastic
bushing/metal housing
4.3.3
Plastic
shaft/plastic
4.4
Determination of dimensional
max.
due
shaft/plastic
to
Calculation examples
6.
Applications
7.
Key
8.
Literature
to
symbols
hub
in the
equations
polypropylene (PP)
Celanex
polybutylene terephthalate (PBT)
registered
8
13
13
Hostacom
=
change
11
copolymer (POM)
reinforced
8
9
Hostaform acetal
8
hub
deformation
5.
7
trademark
Introduction
1.
2.
Requirements
for press-fit joints fitting is a simple, low-cost formfitting joints between plastic
Press
method of
obtaining
Press-fit
torque between the
parts.
technology is frequently used
for shaft/hub connections
ing positioning elements, pump impellers etc.
in
precision engineer
to secure
drivers and
gear
couplers,
wheels,
fan
rotors,
slippage
see
important application
bushes. In this
mally
case,
one
is
of the mating elements is
joints have the following
nor
-
-
friction with
up
to
the maximum
also DIN 7190) and is made
possible by
the elastic
of the material.
The maximum transmissible force is
directly depend
the joint pressure and the coefficient of friction between the contacting surfaces. ent on
advantages
over
other
Using the following calculations, the designer can check whether a press-fit joint is suitable for the intended appli
joints: -
by
fastening plastic bearing
made of metal.
Press-fit
surfaces
an
properties Another
contacting
and/or
load-bearing limit. For this purpose it is necessary to pretension the joint ("joint pressure"). This is accomplished by pressing the interference fit (for "Press-fitting" parts together with out
This
joints should transmit external forces
simple design simple assembly
cation.
nondestructive detachment of joint.
The low
production and assembly
fits have
to
stand loads
be as
costs
weighed against their compared to metals.
of plastic press-
lower
ability
to
with
a
In
Table 1 : Coefficient of friction values for various
Critical parameters for
3.
design
press-fit joint calculations for
friction fj.Q, interference are
press-fit joints
particularly critical
Press fit
Coefficient of
joint
friction [to*
press-fit joints, the coefficient of
U and relaxation modulus
Er(t)
Plastic/metal:
parameters.
plastic
hub/metal shaft
or
3.1
plastic hub/plastic
values should be used in
design calculations. A high roughness means a high coefficient
-
0.40
plastic shaft/plastic housing
versa.
Interferences
Experience
0.30
shaft
or
of
:;"Note:
3.2
0.40
Plastic/plastic:
Table 1 gives coefficient of friction ranges for various com binations of mating element materials. The appropriate
friction and vice
-
plastic bushing/metal housing
Coefficient offriction [to
degree of surface
0.25
Press-fit surfaces technically dry
U
has shown that the interferences
U is
depen
Table 2 shows the relative interference
dent
on the joint diameter Db see table 2. Interference U is defined as the difference in diameter between the
defined
cylindrical joint elements.
broken down
In hub/shaft press-fit joints, the shaft diameter is used as the basis for design calculations, and in bushing/housing
The
joints, the outside diameter of the
as
rpr-
100
Uj
is
(%) for various
according to joint
groups of
plastics,
diameter ranges.
load-bearing capacity
mainly
determined
by
of the joint (joint strength) the interference value.
bushing.
Table 2: Recommended relative interference for
Material
press-fit joints
in various Hoechst
Relative interference
'
^s~
100
L*i
engineering plastics (%)
Joint diameter DI up
Hostaform T 1020
to
5
mm
5-30
mm
over
30
mm
]
Hostaform C 2521 Hostaform C 9021 Hostaform C 13021 and C
13031
Hostaform C 27021 Hostaform C 9021 TF Hostaform C 9021 K Hostaform C 9021
25
23
>
0.5
to
M
Hostalen PPN 1060 Hostacom G2 N01 Hostacom M2 N01 Hostacom M4 N01
Hostaform C 9021 GV 1/30
2 1.0
a 1.0
2 0.5
Hostacom G3 NO 1
22.0
22.0
21.0
Celanex2500
a 3.0
22.0
0.5
Celanex 2300 GV 1/30 and 2360 GV 1/30 FL
21.0
21.0
20.5
to
1.0
1.0
Relaxation modulus Er
3.3
Fig.
3:
Relaxation modulus Er of Hostacom M2 N01 in accordance with DIN 53441
Owing
the viscoelastic behaviour of
to
plastic, the joint
(see 4.3) decreases with increasing loading time (stress relaxation). This characteristic is particularly noticeable at high temperature. The reduction in joint pressure p
pressure p
with
time
is characterized
modulus Er determined in
5. With
(DIN 53441), figs.
1
to
i-e- when
a
large
e
=
y=r,
a stress
a
by the
relaxation
relaxation
test
high elongation
relative interference is chosen,
only fairly low modulus of elasticity can be expected, although the actual value will ultimately depend loading time (subscript "t" in Er(t)). a
on
10
103
102
10
10-'
h
105
Loading rime
Fig.
1 : Relaxation modulus Er of non-reinforced
Hostaform in accordance with DIN
!§-
IQÖ
10'
103
102
Fig.
Er of Hostacom G3
h
105
10
10-'
Loading time
Er of non-reinforced and glass fibre reinforced Hostaform, Hostacom
2: Relaxation modulus
10"
103
102
Id
Kg,
N01
in accordance with DIN 53441
53441
104
4: Relaxation modulus
1
mo
3
h
105
h
105
mos
Loading time
Fig.
5: Relaxation modulus
Er of unreinforced,
glass-fibre-reinforced and flame-retardant Celanex in accordance with DIN 53441
and Hostalen PP in accordance with DIN 53441
10000
N/mm2 7000
N/mm2
tf
500
.
Hostaform C 9021 GV 1/30
W
8000
4(6=1
Celanex 2360 GV1/30 FL
J3 "3 -o o
(6
6000
=
1%)
"9
I
I
4000
2000
pi n |
10-'
Loading
time
(,=.!%) 10
j>=2%) 104
10
Loading time
ofjoint pressure p
Design calculations
4.3
Determination
for press-fit joints
4.3.1
Metal shaft/plastic hub
4.
Fig. 4.1
of the maximum
Determination
8
transmissible
axial force Fmax.
Fig.
6 *L
i 4_
Î
}
i
i
1
1
i
L shaft v\ X^
hub
v>S> When
is stressed in the axial
press-fit joint
a
Pi=DTEr(t)-A^[N/mm2] where
direction,
U
the maximum transmissible axial force is:
Fmax.
JT
=
L
Di
p
|UO
[N]
A
outside diameter of metal shaft,
=
diameter L p
jUo
length
=
joint
=
=
uY-i D,1
(mm) (see 4.3) (N/mm2)
pressure
v
Er(t)
(see table 1)
of the maximum
transmissible
=
=
7
^
i
v>
\Vs
mum
press-fit joint
is under torsional stress, the maxi
transmissible torque is:
Mtmax.
D,2 =
^r-
Equation symbols
as
-L-p-po- [N-mm] T
in 4.1.
(2)
plastics
*
0.4
time-dependent relaxation modulus which varies according to the relative interference selected and the loading time (see figs. 1 to 5) outside diameter of shaft (mm)
D2
=
outside diameter of hub (mm)
9:
Geometry
factor
diameter ratio
\\
a
Poisson's ratio for
=
Fig. *L-H
When
(see fig. 9)
DI
torque Mt ma*.
Fig.
1
(mm)
Determination
4.2
iDkJ
joint
of press-fit surfaces
coefficient of friction
=
or
interference (mm)
M+
(1)
where
DI
=
.
as a
function of
(3)
For
plastic bushings press-fitted onto metal shafts,
§*
should be
Plastic
Fig.
shaft/plastic hub
ä 1.6
Fig.
J^i
4.3.2
Plastic
4.3 .3
12
bushing/metal housing
10
p3=^f-^[N/mm2]
(5)
where: A
n
C
P2
=
'
D,
E'
'
B^7 [N/mm2]
A
ï+<
B
LJ0
Er(t)i
(see fig. 11)
=
te.Y_
4.3.1
=
see
4.3.2
Other
2/xri
r
[mmvN
tr(t)2
see
=
v
T=
symbols as
1
time-dependent relaxation modulus of the
according to the selected and the loading
hub material which varies relative interference
inside diameter of
=
h
=
w
DO
B
+ v
-g;
tr(t),
(4)
w.here:
B
=
[N/mm2] (see figs.
time
bushing (mm) Er(t)2
in 4.3.1
=
1
to
5)
time-dependent relaxation modulus of the plastic shaft which varies according to the relative interference selected and the
For
plastic bushings press-fitted
-^ L>o
should be
Fig
11
:
>
into metal components,
Other
1.2
Geometry
[N/mm2] (see figs.
time
factor
as a
03:
Determination
4.4
function of
symbols
due
to
as
1
to
loading
5)
in 4.3.1
of dimensional change
deformation
diameter ratio In the
case
of
quently used,
z.u
D,/I >o
1.67
the whole deformation
are
fre
corresponding to
interference U is taken up by the plastic part. This re duces, for example, the bearing play of a plastic bearing
=
bush
^
-Z
Fig.
^
T
metal/plastic combinations, which
press-fitted
into
a
metal
housing (see fig. 13).
13
^
pq
./
0
z
31
o
O
z.
1 0
dT
T
u
al
J_ 1 5
2 0
2 5
D, 'D0
3 0
3 5
4.
8S
^
The reduction of the inside diameter of the
bearing bush
Calculation CXaMplcS
j
be calculated as follows:
can
2
-t
(6)
2'D^
ZlDo = U
-
D,
g
-(I-,)
+
(1
+
is
be
to
press-fitted
[mm]
.)
impeller (see fig. 15) made
A pump
5.1
Dl
Fig.
onto
from Hostaform
the drive shaft of
a motor.
15
where:
DO
=
DI
=
inside diameter of
bearing bush (mm)
inside diameter of metal
housing (mm)
or
joint diameter EL
Equation (6)
is
diameter ratio
plotted
in
fig.
14
function of the
as a
T*
dû
j^-
for various interferences U.
z-M
JL>o
SS
Fig.
14:
Change
in the inside diameter of
bearing
bush
as a
press-fitted
into
a
\
plastic metal housing a
\ \
G5Ê
function of the diameter ratio for various
interferences U
Given:
Lmax.
D) =
10
Mt
3 Nm; service life about 10 years
=
mm;
=
15
mm
Problem: Can
a
press-fit joint
transmissible
L = 12
mm
^
=
-
torque?
of the interference surface is assumed
length
The
be used and what is the maximum
and the wall thickness of the
=
s
3.5
to
plastic hub
mm
The outside diameter of the hub is thus
D2 = D, = 10
D2 =
D./DO
17
+
2
s
mm
+
2
3.5
mm
mm.
The diameter ratio is Care should be taken
to ensure
that
no
material is sheared
^ =
off
at
order
plastics part during the joining operation.
the to
In
D,
10
achieve this
Table -
-
^=17
sufficiently large chamfer should be provided, in the case of the plastic hub/metal shaft arrangement, the plastics part is heated (approx. 100 to maximum a
30
mm, a
^JL>1
the joint diameter range 5 relative interference of maximum
2 shows that for
100 = 3 %
to
should be used.
140C), -
of the
plastic bushing/metal housing
in the
case
ment,
the plastics part is cooled.
arrange
Fig.
9 shows that for
T-^ A
+ v
=
0.4.
~^
=
l-7> the geometry factor
be
The relaxation modulus for 100
pT-
Er(t)
=
e
=
3 % in
according to equation
P1
(3), the joint
Di"
^
A +
U
Do
=
DI
=
16
mm;
20
^-
1.5%
A
JJi
mm
Problem: pressure
By how much
1
U
=
accordance with fig. 1
800 N/mm2.
=
Thus
Given:
the
v
is the inside diameter D0 reduced when
bushing is press-fitted into
a
metal
housing?
N =
0.03-800
PI
0.4
mm2
The diameter ratio is
9.6 N/mm2
=
^1=20 Do
Table 1 shows that for a
a
=
0.3 is assumed.
according to equation (2),
The interference U
the maximum
trans
missible torque is
JJ D, u
D,2
JT-
102 =
T
=0.015
-DI
0.015
20
=
^--L-pi-fj.0
jt-
12
9.6
Fig.
0.3
0.3
Mt
max.
Mtmax.
=
N
14 shows that
The maximum torque which
can
be transmitted
by
the press-fit joint over a long period is greater than the required value. A press-fit joint is therefore suitable for
impeller.
bearing bush is to housing (see fig. 16) A
Fig.
press-fitting,
bush is reduced
Result:
5.2
mm.
Result:
5.4N-m>3N-m
the
the change in diameter
mm
After
securing
be determined from
mm
AD0 = 0.32 = 5428
can
1.5%
=
Mtmax. =
= 125
plastic/metal combination,
friction coefficient of ^0
Thus
16
be
press-fitted into
16
y//////////,
Q
Q
a
metal
DO acmai =
16
DO acmai
15.68
=
the inside diameter of the
to
mm
mm
0.32
mm
bearing
Applications
6.
6.3
Fan
rotor
for car ventilation
The Hostaform C 9021 fan
Guide bush for swivel chair
6.1
bushes consist of
guide
an
inner
slotted steel
of 48.00
6.4
over
0.45
^ mm
mm.
The
largest interference
0.94%, the smallest 0.25
Because of differential
fore
length 17 ring spring
interference = 0.2
mm.
mm
cooling
in
=
is thus
joint
by
not
Record player
the
inside surface is there
steel
pin
secured
pressure
body
on
5
mm
the
in diameter has
outsert
be permanently moulded steel plate of a record to
player. The joint chosen for this purpose is made by pressfitting the steel pin into a Hostaform C 13021 hub outsert moulded into the plate (photo 4) The interference is .
0.2
Transport chain for bottle filling machines
(photo 2) made from joined by steel pins 12
The individual chain links
form T 1020
(fig. 17) are diameter which are press-fitted
into
a
the chain link. The interference is 0.2 interference
Fig.
length
2
x
14
mm
mm
mm
in
hole in
= 1.6%, the
mm.
17: Press fit of the steel
steel
11.8
Hosta
pin in
the chain link
diameter at two points pin is recessed to 11 for a length of 5 so elastic recovery of the chain link in these small diameter regions provides additional
The
mm
mm
an
key
fit.
a
0.52%.
injection moulding,
exactly cylindrical. The machined after press-fitting.
6.2
6 mm,
= 3%,
The hub is enclosed
which increased the
=
and hence the transmissible torque.
A
bush is
press-fitted
mm.
mm
0.05
mm,
inter-ference
wall thickness with 10 outer radial ribs pipe of 2 the interference (photo 1). The diameter of the ribs The bush is pressis 48.35 0.05 length of 80 fitted into a drawn steel pipe with an inside diameter mm
is
smooth drive shaft. The shaft diameter d
onto a
hole diameter = 5.8 The Hostaform C 9021
(photo 3)
rotor
mm
=
4%
and the interference
length
13
mm.
Photo 1
Photo 3
Photo 2
Photo 4
Key
7.
to
used
symbols
8.
Literature
in the equations Symbol
Unit
Schmidt,
Explanation
Kunststoffe pp. 170
geometry factor
1 A +
C
(metal
mm2/N
geometry
factor (plastic shaft/
B-
metal
v
Do
mm
(plastic bushing/
housing)
inside diameter of
bushing
ADQ
mm
change
D!
mm
joint diameter (outside diameter
in diameter
of the shaft of the metal
D2
Er(t)
mm
N/mm2
inside diameter
or
housing)
outside diameter of hub
time-dependent
relaxation
modulus N
maximum transmissible axial
force L
mm
length
of interference surface
Mtmax.
Nm
maximum transmissible torque
P
N/mm2
joint
pressure
S
mm
wall thickness of hub
U
mm
interference
relative interference
^s~
'
100
e
elongation
|0
coefficient of friction
v
Poisson's ratio
(
0.4 for
plastics)
or
(/)
>~>\
(1976)
von
A. Die
No.
2,
pp. 90
-
97, No. 3,
bushing
Schrumpfverbindung zur Übertragung VDI-Z, Vol. 86 (1942) Nos. 17/18
Drehmomenten
DIN 7190
geometry factor
66
173
-
Wiemer,
plastic hub) l
Pressverbindungen bei Kunststoff-Teilen,
shaft/
plastic hub)
v
H.
Berechnung einfacher Presspassungen
In this technical
provide
Engineering plastics Design
Calculations
Publications
A.
A. 1.2 Grades and A. 1.4 Grades and A. 1.5 Grades and
This information is based
properties properties properties properties
A. 2.1 Calculation
calculation
-
our
present
provide general
edge
-
Hostacom
products
and their
-
Hostalen
strued
guaranteeing specific properties
-
GUR
as
described
Celanex,
or
their
to
uses.
It should
suitability
for
a
not
state
notes
Characteristic values and
-
Characteristic values and
examples
Spur gears with gearwheels made from Hostaform, Celanex and Hostalen GUR
B.2.2
Worm gears with
therefore be
of the
worm
Applications involving and
Celanex
are
the
use
of Hostaform,
developments
Design calculations for snap-fit joints plastic parts
B.3.2
Fastening
with metal
as
suppliers of the
starting material will be pleased to give the cessors of plastics for technical applications.
in
screws
Integral hinges in engineering plastics Ultrasonic welding and assembly of engineering plastics
of technical mouldings
Indirectly heated, thermally conductive torpedo Hot runner system - Indirectly heated, runner
thermally
system
Design principles for
-
conductive
processing
and
torpedo examples of moulds
Hostaform
C.3.3
Machining Hostaform Design of mouldings made engineering plastics
C.3.4
Guidelines for the
C.3.1
in
from
design of mouldings
engineering plastics
C.3.5 Outsert
Hosta-
products of the
B.3.3 Plastic parts with integrally moulded threads B.3.4 Design calculations for press-fit joints
C.2.2
products
or
wheels made from
B.3.1
C.2.1 Hot
con
particular application.
Hostaform
C. Production
our
names
B. 1.1
B.3.7
on
General Conditions of Sale.
com
Design of technical mouldings
B.3.5
of knowl
Any existing industrial property rights must be observed. The quality of our products is guaranteed under our
plastics processing industry. Hoechst B.
want to
examples
A.2.3 Hostacom
calculation
and is intended
on
Hostaform
principles
A.2.2 Hostaform
who
-
Impet
Vandar,
designers
on
Engineering plastics A. 1.1 Grades and
useful information for
to
exploit the properties of technical plastics such as Hostaform. In addition, our staff will be glad to advise you materials, design and processing.
Applications
far in this series:
so
information brochure, Hoechst aim
moulding with Hostaform
©
Copyright by
Hoechst
Aktiengesellschaft
Issued in August 199673rd edition
of pro
Hostaform ® , Celcon ® polyoxymethylene copolymer (POM)
Celanex ® thermoplastic polyester (PBT)
Impet ® thermoplastic polyester (PET)
Vandar® thermoplastic polyester alloys
Riteex® thermoplastic polyester elastomer (TPE-E)
Vectra ® liquid crystal polymer (LCP)
Fortron ® polyphenylene sulde (PPS)
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GUR ® ultra-high molecular weight polyethylene (PE-UHMW)
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