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 p resented in this paper. The governing equilibrium equations and the co nstitutive relations for the rotating disk element are written in term s of the radial stress. A numerical simulation is performed based on r epeated applications of a truncated Taylor's expansion to advance alon g 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 di sk geometries, including disks of constant thickness, linearly tapered thickness, and hyperbolic variation of thickness, respectively, are p rovided. Both radial as well as circumferential stresses are obtained and compared with existing analytical solutions to validate the presen t formulations. Particular consideration is given to the industrial ex ample of turbine rotors carrying buckets. The simple procedure develop ed in this study may serve as an effective tool for performing prelimi nary design calculations for complex rotating components.