Page 403 - Shigley's Mechanical Engineering Design

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378 Mechanical Engineering Design

This is low. We will look up data for a specific retaining ring to obtain K f more
accurately. With a quick online search of a retaining ring specification using the
website www.globalspec.com, appropriate groove specifications for a retaining ring
for a shaft diameter of 1.625 in are obtained as follows: width, a = 0.068 in;
depth, t = 0.048 in; and corner radius at bottom of groove, r = 0.01 in. From
Fig. A–15–16, with r/t = 0.01/0.048 = 0.208, and a/t = 0.068/0.048 = 1.42
K t = 4.3, q = 0.65 (Fig. 6–20)
K f = 1 + 0.65(4.3 − 1) = 3.15
32K f M a 32(3.15)(2398)
σ a = = = 17 930 psi
πd 3 π(1.625) 3
S e 33 300
n f = = = 1.86
σ a 17 930
Quickly check if point M might be critical. Only bending is present, and the moment
is small, but the diameter is small and the stress concentration is high for a sharp
fillet required for a bearing. From the moment diagram,
M a = 959 lbf · in, and M m = T m = T a = 0.
Estimate K t = 2.7 from Table 7–1, d = 1.0 in, and fillet radius r to fit a typical
bearing.
r/d = 0.02, r = 0.02(1) = 0.02
q = 0.7 (Fig. 6–20)
K f = 1 + (0.7)(2.7 − 1) = 2.19
32K f M a 32(2.19)(959)
σ a = = = 21 390 psi
πd 3 π(1) 3
S e 33 300
n f = = = 1.56
σ a 21 390
Should be OK. Close enough to recheck after bearing is selected.
With the diameters specified for the critical locations, fill in trial values for
the rest of the diameters, taking into account typical shoulder heights for
bearing and gear support.
D 1 = D 7 = 1.0in
D 2 = D 6 = 1.4in
D 3 = D 5 = 1.625 in
D 4 = 2.0in

The bending moments are much less on the left end of shaft, so D 1 , D 2 , and D 3
could be smaller. However, unless weight is an issue, there is little advantage to
requiring more material removal. Also, the extra rigidity may be needed to keep
deflections small.