Design and Stress Analysis of Extraterrestrial ... - The Black Vault

a) arB 0 if the disk does not bear a load on the external radius;
b) are = ar .if blades are attached on the disk crown.
Allowing for nonuniform disk heating
(determining thermal stresses)
In turbine operation heat flux is propagated from blades through
the joints to the disk, and in the disk from the crown to the hub.
Thus, disk temperature rises along the radius from the center to the
crown. Due to this, thermal stresses appear in the disk, which
can be of the same order of magnitude as the stresses from centrifugal
forces, and they must be taken into account.
Thermal stresses can be determined separately for nonrotating
disks and then algebraically added with the stresses from centrifugal
forces.
In order to avoid high thermal stresses, the disk material must
have the smallest possible coefficient of linear expansion (thermal
strain will be less) and considerable heat conductivity (temperature
gradient along the disk radius will be less).
The disk material
must have the appropriate mechanical properties with allowance for
their reduction at high temperatures.
In our analysis we shall assume that the temperature in the
disk changes only along the radius (on a given radius we shall assume
the temperature is constant throughout the -hickness).
The modulus of elasticity E and the coefficient of linear
expansion a will be considered constant within each of the sections
in which the disk is divided during analysis.
The equation of equilibrium for a nonrotating disk is obtained
2
from equation (3.55) if we assume C = pw = 0:
S~316
d (,rzh)
dr "(3.69)
31
1*..-i