The force equilibrium equation of the unit body is
r r þ
@r r
@r
dr
r þ dr
ð
Þd/ þ qx
2 r
2 drd/ À r r rd/ À r 1 drd/ ¼ 0
The higher order terms are omitted from the above formula, and it is noted that
the variables are only single-valued functions of r, it can be obtained after sorting
out
r r þ r
dr r
dr
À r 1 þ qx
2 r
2
¼ 0
ð9:50Þ
In order to solve r r and r 1 , the relationship between stress and strain is needed.
In the radial direction, the total radial deformation at r is u. The total radial
deformation at r þ dr is u þ du
dr dr, so the radial strain is
e r ¼
u þ du
dr dr À u
dr
¼
du
dr
ð9:51Þ
Fig. 9.48 Force analysis diagram of small gas turbine blade for missile
9.4 Design Principle of Small Gas Turbine for Missile
145