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General Design Principles for DuPont Engineering Polymers - Module

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Figures 10.07 and 10.08 show calculated interference<br />

limits at room temperature <strong>for</strong> press-fitted shafts and<br />

hubs of Delrin ® acetal resin and Zytel ® nylon resin.<br />

These represent the maximum allowable interference<br />

based on yield point and elastic modulus data. The<br />

limits shown should be reduced by a safety factor<br />

appropriate to the particular application. Safety factors<br />

of 1.5 to 2 are used <strong>for</strong> most applications.<br />

Where press fits are used, the designer generally seeks<br />

the maximum pullout <strong>for</strong>ce which is obtained by using<br />

the greatest allowable interference between parts,<br />

consistent with the strength of the plastics used.<br />

Allowable interference varies with material properties,<br />

part geometry and environmental conditions.<br />

Interference Limits<br />

The general equation <strong>for</strong> thick-walled cylinders is<br />

used to determine allowable interference between a<br />

shaft and a hub:<br />

I = S dD s ( W + μ h + l – μs) (15)<br />

W E h E s<br />

and<br />

1+( D s) 2<br />

D h<br />

W = (16)<br />

1–( D s) 2<br />

D h<br />

where:<br />

I = Diametral interference, mm (in)<br />

S d = <strong>Design</strong> stress, MPa (psi)<br />

D h = Outside diameter of hub, mm (in)<br />

D s = Diameter of shaft, mm (in)<br />

E h = Modulus of elasticity of hub, MPa (psi)<br />

E s = Elasticity of shaft, MPa (psi)<br />

μ h = Poisson’s ratio of hub material<br />

μ s = Poisson’s ratio of shaft material<br />

W = Geometry factor<br />

Case 1. (SI Units) Shaft and Hub of Same Plastic.<br />

When hub and shaft are both plastic<br />

Eh = Es; μh = μs. Thus equation 15 simplifies to:<br />

I = SdDs W + 1<br />

×<br />

W Eh Case 2. (SI Units) Metal Shaft; Hub of Plastic.<br />

When a shaft is of a high modulus metal or any other<br />

high modulus material, E greater than 50 ×103 MPa,<br />

the last term in equation 15 becomes negligible and<br />

the equation simplifies to:<br />

I = S dD s × W + μ h<br />

W E h<br />

71<br />

Figure 10.07 Maximum interference limits<br />

% of insert θ<br />

6<br />

5<br />

4<br />

3<br />

1.5<br />

2<br />

d<br />

Figure 10.08 Theoretical interference limits <strong>for</strong> press<br />

fitting<br />

Interference limits<br />

cm/cm of shaft diameter<br />

0.10<br />

0.08<br />

0.06<br />

0.04<br />

0.02<br />

0<br />

3<br />

Ratio D/d<br />

2·d<br />

Hub of Delrin ® 500<br />

Max. interference limits<br />

Shaft in Delrin ®<br />

Shaft in Steel<br />

Shaft of Zytel ®<br />

Shaft of steel<br />

4<br />

Hub of<br />

Zytel ® 101<br />

d1<br />

100<br />

80<br />

60<br />

40<br />

0.2 0.4 0.6 0.8<br />

20<br />

1.0<br />

Ratio shaft diameter to<br />

outside diameter of hub, d/D<br />

Based on yield point and elastic modulus at room<br />

temperature and average moisture conditions<br />

D<br />

Interference limits<br />

mils/in of shaft diameter<br />

Theoretical Interference Limits <strong>for</strong> Delrin ® acetal<br />

resin and Zytel ® nylon resin are shown in Figures<br />

10.07 and 10.08.<br />

Press fitting can be facilitated by cooling the internal<br />

part or heating the external part to reduce interference<br />

just be<strong>for</strong>e assembly. The change in diameter due to<br />

temperature can be determined using the coefficient of<br />

thermal expansion of the materials.<br />

Thus: D – Do = a (t – to) Do where:<br />

D = Diameter at temperature t, mm (in)<br />

Do = Diameter at initial temperature to, mm (in)<br />

a = Coefficient of linear thermal expansion

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