Design calculations for press fit joints made from engineering plastics

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Contents

1. Introduction 4

2. Requirements for press-fit joints 4

3. Critical parameters for a press-fit joint 5

3.1 Coefficient of friction fj,0 5

3.2 Interference U 5

3.3 Relaxation modulus Er 6

4. Design calculations for press-fit joints 7

4.1 Determination of the maximumtransmissible axial force Fmax.

4.2 Determination of the maximumtransmissible torque Mt max.

4.3 Determination of the joint pressure p 7

4.3.1 Metal shaft/plastic hub4.3.2 Plastic bushing/metal housing 8

4.3.3 Plastic shaft/plastic hub 8

4.4 Determination of dimensional changedue to deformation 8

5. Calculation examples 9

6. Applications 11

7. Key to symbols in the equations 13

8. Literature 13

Hostaformacetal copolymer (POM)

Hostacomreinforced polypropylene (PP)

Celanexpolybutylene terephthalate (PBT)

= registered trademark

1. Introduction

Press fitting is a simple, low-cost method of obtainingformfitting joints between plastic parts.

This technology is frequently used in precision engineering for shaft/hub connections to secure gear wheels,positioning elements, drivers and couplers, fan rotors,

pump impellers etc.

Another important application is fastening plastic bearingbushes. In this case, one of the mating elements is nor

mally made of metal.

Press-fit joints have the following advantages over other

joints:

- simple design- simple assembly- nondestructive detachment of joint.

The low production and assembly costs of plastic press-fits have to be weighed against their lower ability to withstand loads as compared to metals.

2. Requirementsfor press-fitjoints

Press-fit joints should transmit external forces and/or

torque between the contacting surfaces by friction with

out slippage up to the maximum load-bearing limit.

For this purpose it is necessary to pretension the joint("joint pressure"). This is accomplished by pressing the

parts together with an interference fit (for "Press-fitting"see also DIN 7190) and is made possible by the elastic

properties of the material.

The maximum transmissible force is directly dependent on the joint pressure and the coefficient of friction

between the contacting surfaces.

Using the following calculations, the designer can check

whether a press-fit joint is suitable for the intended application.

3. Critical parameters fora press-fitjoint

In design calculations for press-fit joints, the coefficient offriction fj.Q, interference U and relaxation modulus Er(t)are particularly critical parameters.

3.1 Coefficient offriction [to

Table 1 gives coefficient of friction ranges for various combinations of mating element materials. The appropriatevalues should be used in design calculations. A highdegree of surface roughness means a high coefficient offriction and vice versa.

3.2 Interferences U

Experience has shown that the interferences U is dependent on the joint diameter Db see table 2. InterferenceU is defined as the difference in diameter between thecylindrical joint elements.

In hub/shaft press-fit joints, the shaft diameter is used as

the basis for design calculations, and in bushing/housingjoints, the outside diameter of the bushing.

Table 1 : Coefficient of friction values for various

press-fit joints

Press fit joint Coefficient offriction [to*

Plastic/metal:

plastic hub/metal shaftor 0.25 - 0.40

plastic bushing/metal housing

Plastic/plastic:

plastic hub/plastic shaftor 0.30 - 0.40

plastic shaft/plastic housing

:;"Note: Press-fit surfaces technically dry

Table 2 shows the relative interference

defined as rpr- 100 (%) for various groups of plastics,Uj

broken down according to joint diameter ranges.

The load-bearing capacity of the joint (joint strength)is mainly determined by the interference value.

Table 2: Recommended relative interference for press-fit joints in various Hoechst engineering plastics

Material Relative interference ^s~' 100 (%)

L*i

Joint diameter DIup to 5 mm 5-30 mm over 30 mm

Hostaform T 1020 ]Hostaform C 2521

Hostaform C 9021

Hostaform C 13021 and C 13031

Hostaform C 27021

Hostaform C 9021 TFHostaform C 9021 K

Hostaform C 9021 M

Hostalen PPN 1060

Hostacom G2 N01

Hostacom M2 N01Hostacom M4 N01

25 23 > 0.5 to 1.0

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 to 1.0

Celanex 2300 GV 1/30 and 2360 GV 1/30 FL 21.0 21.0 20.5

3.3 Relaxation modulus Er

Owing to the viscoelastic behaviour of plastic, the jointpressure p (see 4.3) decreases with increasing loadingtime (stress relaxation). This characteristic is particularlynoticeable at high temperature. The reduction in jointpressure p with time is characterized by the relaxation

modulus Er determined in a stress relaxation test

(DIN 53441), figs. 1 to 5. With a high elongation

e = y=r, i-e- when a large relative interference is chosen,

only a fairly low modulus of elasticity can be expected,although the actual value will ultimately depend on

loading time (subscript "t" in Er(t)).

Fig. 3: Relaxation modulus Er of Hostacom M2 N01

in accordance with DIN 53441

10-' 10 102 103

Loading rime

10 h 105

Fig. 1 : Relaxation modulus Er of non-reinforcedHostaform in accordance with DIN 53441

!§- IQÖ 10' 102 103 104 h 105

Loading time

Fig. 4: Relaxation modulus Er of Hostacom G3 N01

in accordance with DIN 53441

10-'

Loading time

10 102 103 10" h 105Id 1 mo 3 mos

Kg, 2: Relaxation modulus Er of non-reinforced and

glass fibre reinforced Hostaform, Hostacomand Hostalen PP in accordance withDIN 53441

tf

7000N/mm2

500

"9I

pi

. Hostaform C 9021 GV 1/30

4(6=1

Fig. 5: Relaxation modulus Er of unreinforced,glass-fibre-reinforced and flame-retardantCelanex in accordance with DIN 53441

10000

N/mm2

8000W

J3"3-oo

I

6000

4000

2000

Celanex 2360 GV1/30 FL(6 = 1%)

n | (,=.!%) j>=2%)10-' 10 10 104 h 105

Loading time Loading time

4. Design calculations

for press-fitjoints4.1 Determination of the maximum transmissible

axial force Fmax.

Fig. 6

4_Î

*L

ii i

i

v\ X^

v>S>

} 11

L shaft

hub

When a press-fit joint is stressed in the axial direction,the maximum transmissible axial force is:

Fmax. = JT Di L p |UO [N]where

DI = outside diameter of metal shaft, or jointdiameter (mm)

L = length of press-fit surfaces (mm)p = joint pressure (see 4.3) (N/mm2)jUo = coefficient of friction (see table 1)

4.2 Determination of the maximum transmissible

torque Mt ma*.

(1)

Fig. 7

*L-H

\\

^i\Vs

v>

When a press-fit joint is under torsional stress, the maxi

mum transmissible torque is:

D,2 TMtmax. = ^r- -L-p-po- [N-mm] (2)

Equation symbols as in 4.1.

4.3 Determination ofjoint pressure p

4.3.1 Metal shaft/plastic hub

Fig. 8

Pi=DTEr(t)-A^[N/mm2] (3)

whereU = interference (mm)

A =

MiDkJ + 1

uY-iD,1(see fig. 9)

v = Poisson's ratio for plastics * 0.4

Er(t) = time-dependent relaxation modulus whichvaries according to the relative interferenceselected and the loading time (see figs. 1 to 5)

DI = outside diameter of shaft (mm)D2 = outside diameter of hub (mm)

Fig. 9: Geometry factor. as a function of

diameter ratio

For plastic bushings press-fitted onto metal shafts,

§* should be ä 1.6J^i

4.3.2 Plastic bushing/metal housing

Fig. 10

w.here:

P2 = D,' E' '

B^7 [N/mm2] (4)

B =

ï+<LJ0

te.Y_w

(see fig. 11)

DO = inside diameter of bushing (mm)Other symbols as in 4.3.1

For plastic bushings press-fitted into metal components,

-^ should be > 1.2L>o

Fig 1 1 : Geometry factor 03: as a function of

diameter ratio

z.u

-Z

Tpq

01

1.67

./

z.0 1

z5 2

D,/I

^

0 2

D,

>o =

^

5 3

'D0

^

0 3 5 4.

4.3.3 Plastic shaft/plastic hub

Fig. 12

p3=^f-^[N/mm2] (5)where:

nA + v B v r 2/xriC =-g; h T= [mmvN 1tr(t), tr(t)2

A = see 4.3.1

B = see 4.3.2

Er(t)i = time-dependent relaxation modulus of thehub material which varies according to therelative interference selected and the loadingtime [N/mm2] (see figs. 1 to 5)

Er(t)2 = time-dependent relaxation modulus of the

plastic shaft which varies according to therelative interference selected and the loadingtime [N/mm2] (see figs. 1 to 5)Other symbols as in 4.3.1

4.4 Determination ofdimensional changedue to deformation

In the case of metal/plastic combinations, which are fre

quently used, the whole deformation corresponding to

interference U is taken up by the plastic part. This re

duces, for example, the bearing play of a plastic bearingbush press-fitted into a metal housing (see fig. 13).

Fig. 13

To

O

J_

8S ^

dT31ual

The reduction of the inside diameter of the bearing bush j Calculation CXaMplcScan be calculated as follows: -t

(6)ZlDo = U

2Dl

2'D^D,

- [mm]

g -(I-,) + (1 + .)where:

DO = inside diameter of bearing bush (mm)DI = inside diameter of metal housing (mm) or

joint diameter

Equation (6) is plotted in fig. 14 as a function of the

diameter ratio j^- for various interferences U.JL>o

Fig. 14: Change in the inside diameter of a plasticbearing bush press-fitted into a metal housingas a function of the diameter ratio for variousinterferences U

5.1 A pump impeller (see fig. 15) made from Hostaformis to be press-fitted onto the drive shaft of a motor.

Fig. 15

EL

SS\\\

G5Ê

T*dû

z-M

D./DO

Care should be taken to ensure that no material is shearedoff at the plastics part during the joining operation. In

order to achieve this

- a 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

140C),- in the case of the plastic bushing/metal housing arrange

ment, the plastics part is cooled.

Given:

D) = 10 mm; Lmax. = 15 mm

Mt = 3 Nm; service life about 10 years

Problem:

Can a press-fit joint be used and what is the maximumtransmissible torque?

The length of the interference surface is assumed to beL = 12 mm and the wall thickness of the plastic hub

^ - = s = 3.5 mm

The outside diameter of the hub is thus

D2 = D, + 2 s

= 10 mm + 2 3.5 mm

D2 = 17 mm.

The diameter ratio is

^= ^=17

D, 10

Table 2 shows that for the joint diameter range 5 to

30 mm, a relative interference of maximum

^- 100 = 3 % should be used.JL>1

Fig. 9 shows that for ~^ = l-7> the geometry factor

T-^ = 0.4.A + v

The relaxation modulus for

pT- 100 = e = 3 % in accordance with fig. 1

Er(t) = 800 N/mm2.

Thus according to equation (3), the joint pressure

U 1P1 = Di" ^

= 0.03-800

Given:

A + v

Nmm2

PI = 9.6 N/mm2

0.4

Table 1 shows that for a plastic/metal combination,a friction coefficient of ^0 = 0.3 is assumed.

Thus according to equation (2), the maximum trans

missible torque is

D,2 TMtmax. = JT- ^--L-pi-fj.0102

= jt- 12 9.6 0.3

Mt max.= 5428 N mm

Mtmax. = 5.4N-m>3N-m

Result:

The maximum torque which can be transmitted bythe press-fit joint over a long period is greater than the

required value. A press-fit joint is therefore suitable for

securing the impeller.

5.2 A bearing bush is to be press-fitted into a metal

housing (see fig. 16)

Fig. 16

UDo = 16 mm; ^- A 1.5%

JJiDI = 20 mm

Problem:

By how much is the inside diameter D0 reduced whenthe bushing is press-fitted into a metal housing?

The diameter ratio is

^1=20= 125

Do 16

1.5%

The interference U can be determined from

JJD,u =0.015 -DI

= 0.015 20= 0.3 mm

Fig. 14 shows that the change in diameter

AD0 = 0.32 mm.

Result:

After press-fitting, the inside diameter of the bearingbush is reduced to

DO acmai = 16 mm 0.32 mm

DO acmai = 15.68 mm

y//////////,

Q Q

10

6. Applications6.1 Guide bush for swivel chair

The Hostaform C 9021 guide bushes consist of an inner

pipe of 2 mm wall thickness with 10 outer radial ribs

(photo 1). The diameter of the ribs over the interference

length of 80 mm is 48.35 0.05 mm. The bush is press-fitted into a drawn steel pipe with an inside diameterof 48.00 0.05 mm. The largest interference is thus0.45 mm ^ 0.94%, the smallest 0.25 = 0.52%.

Because of differential cooling in injection moulding, thebush is not exactly cylindrical. The inside surface is therefore machined after press-fitting.

6.2 Transport chain for bottle filling machines

The individual chain links (photo 2) made from Hosta

form T 1020 (fig. 17) are joined by steel pins 12 mm in

diameter which are press-fitted into a 11.8 mm hole in

the chain link. The interference is 0.2 mm = 1.6%, theinterference length 2 x 14 mm.

Fig. 17: Press fit of the steel pin in the chain link

6.3 Fan rotor for car ventilation

The Hostaform C 9021 fan rotor (photo 3) is press-fittedonto a smooth drive shaft. The shaft diameter d = 6 mm,hole diameter = 5.8 mm, interference = 0.2 mm = 3%,inter-ference length 17 mm. The hub is enclosed by a

slotted steel ring spring which increased the joint pressureand hence the transmissible torque.

6.4 Recordplayer body

A steel pin 5 mm in diameter has to be permanentlysecured on the outsert moulded steel plate of a record

player. The joint chosen for this purpose is made by press-

fitting the steel pin into a Hostaform C 13021 hub outsert

moulded into the plate (photo 4) .The interference is

0.2 mm = 4% and the interference length 13 mm.

The steel pin is recessed to 11 mm diameter at two pointsfor a length of 5 mm so elastic recovery of the chain linkin these small diameter regions provides an additional

key fit.

11

Photo 1 Photo 3

Photo 2 Photo 4

12

7. Key to symbols usedin the equations

Symbol

1

A + v

C

Unit

mm2/N

Explanation

geometry factor

plastic hub)

geometry factor

(metal shaft/

(plastic shaft/

l

B- v

Do

ADQ

D!

D2

Er(t)

e

|0

v

mm

mm

mm

mm

N/mm2

N

L

Mtmax.

P

S

U

mm

Nm

N/mm2

mm

mm

plastic hub)

geometry factor (plastic bushing/metal housing)inside diameter of bushing

change in diameter

joint diameter (outside diameterof the shaft or inside diameterof the metal housing)outside diameter of hub

time-dependent relaxationmodulus

maximum transmissible axialforce

length of interference surface

maximum transmissible torque

joint pressure

wall thickness of hub or bushinginterference

relative interference ^s~ ' 100 (/)>~>\

elongationcoefficient of friction

Poisson's ratio

( 0.4 for plastics)

8. Literature

Schmidt, H. Pressverbindungen bei Kunststoff-Teilen,Kunststoffe 66 (1976) No. 2, pp. 90 - 97, No. 3,pp. 170 - 173

Wiemer, A. Die Schrumpfverbindung zur Übertragungvon Drehmomenten VDI-Z, Vol. 86 (1942) Nos. 17/18

DIN 7190 Berechnung einfacher Presspassungen

13

Engineering plasticsDesign Calculations Applications

Publications so far in this series:

A. Engineering plasticsA. 1.1 Grades and properties - HostaformA. 1.2 Grades and properties - HostacomA. 1.4 Grades and properties - Hostalen GUR

A. 1.5 Grades and properties - Celanex,Vandar, Impet

A.2.1 Calculation principlesA.2.2 Hostaform - Characteristic values and

calculation examplesA.2.3 Hostacom - Characteristic values and

calculation examples

B. Design of technical mouldingsB. 1.1 Spur gears with gearwheels made from

Hostaform, Celanex and Hostalen GUR

B.2.2 Worm gears with worm wheels made from

HostaformB.3.1 Design calculations for snap-fit joints in

plastic partsB.3.2 Fastening with metal screws

B.3.3 Plastic parts with integrally moulded threads

B.3.4 Design calculations for press-fit jointsB.3.5 Integral hinges in engineering plasticsB.3.7 Ultrasonic welding and assembly of

engineering plastics

C. Production of technical mouldingsC.2.1 Hot runner system - Indirectly heated,

thermally conductive torpedoC.2.2 Hot runner system - Indirectly heated,

thermally conductive torpedoDesign principles and examples of moulds

for processing HostaformC.3.1 Machining HostaformC.3.3 Design of mouldings made from

engineering plasticsC.3.4 Guidelines for the design of mouldings

in engineering plasticsC.3.5 Outsert moulding with Hostaform

In this technical information brochure, Hoechst aim to

provide useful information for designers who want to

exploit the properties of technical plastics such as Hosta-form. In addition, our staff will be glad to advise youon materials, design and processing.

This information is based on our present state of knowl

edge and is intended to provide general notes on our

products and their uses. It should not therefore be con

strued as guaranteeing specific properties of the productsdescribed or their suitability for a particular application.Any existing industrial property rights must be observed.The quality of our products is guaranteed under our

General Conditions of Sale.

Applications involving the use of Hostaform, Hosta-com and Celanex are developments or products of the

plastics processing industry. Hoechst as suppliers of the

starting material will be pleased to give the names of processors of plastics for technical applications.

© Copyright by Hoechst Aktiengesellschaft

Issued in August 199673rd edition

14

Hostaform®, Celcon®

polyoxymethylene copolymer (POM)

Celanex®

thermoplastic polyester (PBT)

Impet®

thermoplastic polyester (PET)

Vandar® thermoplastic polyester alloys

Riteflex®

thermoplastic polyester elastomer (TPE-E)

Vectra®

liquid crystal polymer (LCP)

Fortron®

polyphenylene sulfide (PPS)

Celstran®, Compel® long fiber reinforced thermoplastics (LFRT)

GUR®

ultra-high molecular weight polyethylene (PE-UHMW)

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