Thermo Mechanical Analysis and Design of Rotating Disks

Abstract

This study proposes a numerical method for evaluation of thermo-elastic stresses and deformation states of rotating varying thickness disks, either solid or annular. The solutions are obtained under plane stress assumption and up to the elastic limit of the material by using minimization of total potential energy principle. The solution algorithm is implemented with the help of MATLAB computational simulation software. The results are validated with those of other researchers for appropriate values of system parameters and very good agreement is observed. Some new results are furnished in the form of limit angular speed of rotating disks under thermo-mechanical loading. The results considering density variation with temperature are also presented but they have not much effect on limit angular speed for different disk geometries and temperature distribution profiles.

Appendix

a, b:

Inner and outer radii of disk

$c_{i}$ :

The vector of unknown coefficients

$h_{0}$ :

Thickness at the root of the disk

h :

Thickness at any radius r

n, k:

Parameters controlling the thickness variation of the disk

r, θ, z:

Radial, tangential and axial directions

u :

Displacement field of the disk

U :

Strain energy of the disk

V :

Work potential of the disk

δ :

Variational operator

$\rho ,\upsilon ,\alpha ,E$ :

Density, Poisson’s ratio, coefficient of thermal expansion and elasticity modulus of the disk material

ω :

Dimensional angular speed of the disk

ω _y :

Dimensional value of limit angular speed

T :

Temperature at any radius r

$T_{a} ,T_{b}$ :

Inner and outer surface temperature of the disk

$\in_{r} , \in_{\theta }$ :

Strains in radial and tangential direction

$\sigma_{r} ,\sigma_{\theta }$ :

Radial and tangential stresses

$\sigma_{VM}$ :

Von-Mises stress

$\sigma_{0}$ :

Yield stress of the disk material

$\emptyset_{i}$ :

Set of orthogonal functions used to approximate displacement field

$\emptyset_{0}$ :

Start function of orthogonal set of functions

ξ :

Normalized co-ordinate in radial direction