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2024年3月11日发(作者：continue语句详解)
M
ECHANICAL
E
NGINEERING
D
ESIGN
T
UTORIAL
4-17: P
RESS AND
S
HRINK
F
ITS
A
PPLICATION OF
T
HICK
-W
ALL
C
YLINDRICAL
P
RESSURE
V
ESSEL
T
HEORY
R
ELATING TO
S
TRESSES
D
EVELOPED FROM
I
NTERFERENCE
F
ITS
:
1. Design application which uses the cylindrical pressure vessel Thick-Wall Theory.
2. Stresses develop between cylinders due to the contact pressure generated by an
interference fit. The interference fit is achieved by pressing a larger inside member
into the smaller opening of an outside member. In the specific case of a shaft press fit
into the hub of a gear, the outside diameter (OD) of the shaft is slightly larger than the
inside hole diameter (ID) of the hub. The diametral difference between the shaft OD
and the ID of the hub hole is referred to as the interference fit.
• The radial deformation required by the interference fit causes an interfacial
pressure, p, to develop at the nominal radius, at r = R. Consequently, radial
and tangential stresses,
σ
r
and
σ
t
, are produced.
• Assuming uncapped ends (
σ
l
=0), a biaxial state of stress exists for which
two non-zero principal stresses must be considered.
• From the cylindrical pressure vessel theory, the radial and tangential stresses
represent principal stresses.
• The length of the outer member is assumed to be equal to the length of the
inner member.
r
o
Outer
Member
R
r
i
R
r
o
δ
Inner
Member
r
i
(a) End view of inner and outer
members, press fit together.
(b) Cross-section of cylinders
showing internal outside radius
larger than externalinside radius
by a small amount of δ.
FIGURE T4-17-1 Interference fit of two
cylinders of finite length and equal lengths.
Text Eq. refers to Mechanical Engineering Design, 7
th
edition text by Joseph Edward Shigley, Charles
R. Mischke and Richard G. Budynas; equations with the prefix T refer to the present tutorial.
†
3. Referring to Fig. T4-17-1, the geometric features of the cylindrical parts are defined
as:
r
i
=
the inside radius of the inner cylinder
R
=
nominal radius of internal outside radius and external inside radius after assembly
r
o
=
outside radius of the outer cylinder
δ
=
radial interference
I
NSIDE
C
YLINDER
• Inner member experiences an external pressure, p
o
= p, resulting in compressive
tangential and radial stresses.
• Thick-Wall Theory may be applied with r
o
= R:
§
R
2
+
r
i
2
·
Eq.4-57)(
σ
t
)
ir
=
R
=−
p
o
¨
22
¸
=−
pC
it
(Text
©
R
−
r
i
¹
(
σ
r
)
ir
=
R
=−
p
o
=−
p
O
UTSIDE
C
YLINDER
• Outer member only experiences internal pressure, p
i
= p, resulting in tensile
tangential stress and compressive radial stress.
• Thick-Wall Theory is, as always, applicable with r
i
= R:
§
r
o
2
+
R
2
·
(
σ
t
)
or
=
R
=
p
i
¨
2
=
pC
ot
(Text Eq. 4-58)
2
¸
©
r
o
−
R
¹
(
σ
r
)
ir
=
R
=−
p
i
=−
p
D
EFINITION OF
I
NTERFACIAL
P
RESSURE
We presently have two equations and three unknowns for both the inside and outside
cylinder analyses. A third equation which relates the contact pressure and the interference
can be derived by examining the deformation of the members.
Deflection Equation
The total radial interference may be defined as:
δ
total
=
δ
i
+
δ
o
where,
Shigley, Mischke & Budynas
Machine Design Tutorial 4-17: Press and Shrink Fits 2/11
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