A unified numerical approach for the analysis of rotating disks including turbine rotors

A numerical procedure for the analysis of the stresses due to rotation that are produced in disks of a general, arbitrary configuration is presented in this paper. The governing equilibrium equations and the constitutive relations for the rotating disk element are written in terms of the radial stress. A numerical simulation is performed based on repeated applications of a truncated Taylor's expansion to advance along the radius of the deformed disk. The treatment of both initial value problems and two point boundary value problems is presented based on a corresponding iterative root finding method. Examples for various disk geometries, including disks of constant thickness, linearly tapered thickness, and hyperbolic variation of thickness, respectively, are provided. Both radial as well as circumferential stresses are obtained and compared with existing analytical solutions to validate the present formulations. Particular consideration is given to the industrial example of turbine rotors carrying buckets. The simple procedure developed in this study may serve as an effective tool for performing preliminary design calculations for complex rotating components.