Page 26 - Mechanical Engineer's Data Handbook

STRENGTHS OF MATERIALS 15
(6) Z=(bd+d2/3)t; J=t(b+d)j/6 (9) Z = zD2t/4; J = xD3t/4

yi

.-x

1.2.7 Stresses due to rotation

Flywheels are used to store large amounts of energy
and are therefore usually very highly stressed. It is
necessary to be able to calculate the stresses accu-
rately. Formulae are given for the thin ring, solid disk,
annular wheel and spoked wheel, and also the rotating
thick cylinder.
(4bd2 +d3)t dZ Thin ring
Z= (at bottom); x=-
(6b + 3d) 2(b+d)
Symbols used:
p =density
r = mean radius
T Tangential stress u, =po2 = pr2w2
u = tangential velocity = rw
E

(8) Z= (2bd+d2/3)t; J= (2b3 + 6bd2 +d3)t/6
Yb3 P (density)

b 1 ‘
Solid disk
d
X- Maximum tangential and radial stress (a,)
ut = u, = pu2(3 + v)/8 at r = 0
where: v = Poisson’s ratio, u =rw.