r t;n þ 1 À r t;n
À
Á ðnÞ ¼ l r r;n þ 1 À r r;n
À
Á ðnÞ
r t
ð Þ
ðnÞ ¼ u Dr r
ð
Þ
ðnÞ
ð9:59Þ
The labeling ðnÞ in the above equations indicates the calculation in the outer ring
junction surface of n-segment.
It is now possible to plot the solution in this way, using known boundary
conditions, such as the radial stress of the outer ring of n þ 1 in Fig. 9.51, the
r
n þ 1
ð
Þ
r;n þ 1 has been obtained, so point O can be obtained in Fig. 9.52. Making line MN
crosses point O at any slope, then MM 00 ¼ r
ðnÞ
r;n þ 1 and NN 00 ¼ r
ðnÞ
t;n þ 1 . From
Eqs. (9.58) and (9.59), there are
r
ðnÞ
r;n ¼ MM 00 b n þ 1
b n
¼ M 0 M 00
r
ðnÞ
t ¼ MM 0 l ¼ NN 0
In this way, the M 0 N 0 connection specifies the solution of stress in n-segment.
Fig. 9.51 Stress of
cross-section wheel disc
9.4 Design Principle of Small Gas Turbine for Missile
149