Closed-Form Formulas for Hyperbolically Tapered Rotating Disks Made of Traditional Materials under Combined Thermal and Mechanical Loads

Abstract

Using the true temperature distribution along the radial coordinate, closed-form formulas are offered for readers to study the thermo-mechanical behavior of variable thickness disks having both convergent and divergent hyperbolic thickness profiles made of conventional materials. Internal and external pressures, centrifugal forces and thermal loads due to the differences in prescribed surface temperatures are all considered with three boundary conditions: free-free (circular annulus), fixed-free (a disk mounted on a rotating shaft at the inner surface), and fixed-fixed (mounted on a rotating shaft at the inner surface and cased at the outer surface) boundary conditions. A parametric study is also conducted in almost real working environment in which the outer surface of the disk has considerably higher temperature rather than the inner surface. The thermomechanical linear elastic response of a hyperbolic mounted rotating disk subjected to the external pressure induced by blades is originally handled by those proposed formulas.