Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Then, set σ θ equal to the allowable normal stress and solve for a:
a = b
σ
σ
θ
θ
−
+
pi
p
i
= (136.5 mm)
The wall thickness must have a minimum value of
140 MPa − 45MPa
140 MPa + 45MPa
= 97.8 mm
t ≥ b − a = 136.5 mm − 97.8 mm = 38.7 mm
Ans.
14.7 Interference Fits
In some practical applications, two or more concentric cylinders are arranged to fit one
inside of the other. There are two main reasons for doing this. Firstly, it may be desirable to
construct a thick-walled cylinder with a lining of a specific material that has particular
physical or chemical properties, such as improved wear or corrosion resistance. In this
case, the cylinders may be made to fit each other as closely as possible or an interference
fit may be specified. An interference fit is a type of connection in which a critical radial
dimension of the first part is slightly larger (or smaller) than the corresponding dimension
of the second part. Force or temperature change is used to temporarily make the radial dimensions
match so that the parts can be fit together, one inside of the other. The forces
between the components joined in this manner are substantial, creating large friction forces
that keep the pieces attached to each other so that the completed assembly acts as a single
unit.
Secondly, two (or more) cylinders (often of the same material) may be assembled with
interference fits between them. The compound cylinder is formed by “shrinking” an outer
thick-walled cylinder (herein designated the jacket) over an inner cylinder (frequently
termed the tube). This process creates a compound cylinder that can withstand higher internal
pressures than a single cylinder with the same overall dimensions can. The process can
be efficient when very high pressures, perhaps on the same order of magnitude as the
allowable stress of the material, must be contained in the vessel.
A similar process, using either force or temperature, is frequently used to attach gears
and pulleys to shafts in mechanical devices. When force is used, the connection is called a
press-fit or force-fit connection. When temperature change is used, the process is termed
shrink fit. In either case, the basic concept is the same. Parts that don’t exactly match in one
critical dimension (such as a radial dimension) are forced to fit together (with the use of
either large external forces or temperature change). After the parts are combined, very large
friction forces are created on the mating surfaces between the two components. These friction
forces keep the components attached to each other, whether they consist of a jacket
surrounding a tube or a gear attached to a shaft. For this discussion, we will refer to shrinkfit
connections but understand that exactly the same concepts apply to press-fit or force-fit
connections as well.
When a cylinder is shrink fitted onto another cylinder, the internal diameter of the
larger cylinder (i.e., the jacket) is made slightly smaller than the external diameter of the
smaller cylinder (i.e., the tube). Let the difference in preassembly dimensions between the
inside radius of outer cylinder (i.e., the jacket) and the outside radius of the inner cylinder
(i.e., the tube) be denoted as the radial interference δ. The geometry of the shrink-fit components,
both before and after fabrication, is shown in Figure 14.13.
In the process of “shrinking” a jacket onto a tube, the internal diameter of the jacket is
increased by heating the jacket enough so that it fits over the tube. (Alternatively, the tube
δ
Tube
Jacket
Compound
cylinder
a
b
Tube
Jacket
c
δ T
δ J
FIGURE 14.13 Interference
between tube and jacket.
609