Page 45 - Shigley's Mechanical Engineering Design

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20 Mechanical Engineering Design
• Interference. The opposite of clearance, for mating cylindrical parts in which the
internal member is larger than the external member (e.g., press-fits).
• Allowance. The minimum stated clearance or the maximum stated interference for
mating parts.

When several parts are assembled, the gap (or interference) depends on the dimen-
sions and tolerances of the individual parts.

EXAMPLE 1–3 A shouldered screw contains three hollow right circular cylindrical parts on the screw
before a nut is tightened against the shoulder. To sustain the function, the gap w must
equal or exceed 0.003 in. The parts in the assembly depicted in Fig. 1–4 have dimen-
sions and tolerances as follows:
a = 1.750 ± 0.003 in b = 0.750 ± 0.001 in

c = 0.120 ± 0.005 in d = 0.875 ± 0.001 in

Figure 1–4 a
An assembly of three
cylindrical sleeves of lengths a,
b, and c on a shoulder bolt
shank of length a. The gap w is
of interest.
b c d w

All parts except the part with the dimension d are supplied by vendors. The part con-
taining the dimension d is made in-house.
(a) Estimate the mean and tolerance on the gap w.
(b) What basic value of d will assure that w 0.003 in?

Solution (a) The mean value of w is given by

Answer ¯ w =¯a − b −¯ − d = 1.750 − 0.750 − 0.120 − 0.875 = 0.005 in
¯
c
¯
For equal bilateral tolerances, the tolerance of the gap is
Answer t w = t = 0.003 + 0.001 + 0.005 + 0.001 = 0.010 in
all
Then, w = 0.005 ± 0.010 in, and
w max =¯w + t w = 0.005 + 0.010 = 0.015 in
w min =¯w − t w = 0.005 − 0.010 =−0.005 in

Thus, both clearance and interference are possible.
(b) If w min is to be 0.003 in, then, ¯w = w min + t w = 0.003 + 0.010 = 0.013 in. Thus,

Answer d =¯a − b −¯ −¯w = 1.750 − 0.750 − 0.120 − 0.013 = 0.867 in
¯
¯
c