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

7WI -
For conical disks equation (3.63) is integrated in hypergeometric
functions (in the form of infinite converging series). Turbine disks
virtually always consist of separate sections with different shapes.
With sufficient accuracy, the separate sections of disks can be
reduced to shapes of the following types.
1. Disks of constant thicknesz (Fig. 3.33a) h = const.
2. Hyperbolic disks; the cross section of the disk is bounded
by hyperbolas of any order (Fig. 3.33b). The thickness of such a
disk changes according to the following law
a
(Dwhere
a is a constant; m is the exponent; D is the current diameter.
The values of coefficient a and exponent m can be determined
for a curvolinear disk shape from the condition that the curve
pass through any two points on the profile with known dimensions.
Thus, If DI, hl, and D 2 , h 2 are given, then
hi a a
hence, taking the logarithm of this expression, we find
M = ( h2 i a==h, (D, )m h
It is obvious that a disk of constant thickness can be considered a
particular case of hyperbolic disk when m = 0.
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