Page 239 - Improving Machinery Reliability
P. 239
210 Improving Machinery Reliability
A suitable contoured diaphragm coupling has a diaphragm diameter of 16.5 in and
an angular spring rate kB = 18,800 Ib-iddegree. Thus, for the misalignment angle
used earlier,
M, = (18,800) (0.057) = 1,080 Ib - in
M, = (193,000) (sin 0.057) = 193 Ib - in
M,,, = d(l,080)2 + (193)' = 1,095 lb - in
Alternating Stresses Compared
Comparing the bending moments caused by gear couplings with those resulting
from contoured diaphragm couplings shows the former to be significant and the lat-
ter virtually negligible in comparison.
The cyclic bending stress imposed on a gear-coupling-equipped shaft can be com-
puted from
where C and I are the shaft radius and shaft area moments of inertia, respectively.
Thus
(64,435) (2.25)
0, =
nd4/64
- (64,435) (2.25) (64)
- = 7,206 psi
n (4.34
In addition, there is a mean tensile stress acting on the shaft cross-sectional area.
This mean stress equates to
0, = TP
(D~ 2) (d)
e
/
COS
- (193,000) (0.3) = 860 psi
-
(4.5) n (2.25)' (0.94)
where 8 = 20°, the pressure angle assumed for the gear teeth.
The cyclic bending stress seen by the diaphragm-coupling-equipped shaft can be
obtained by a rapid ratio calculation:
