The Optimum Design of Stepped Shafts: A Study in Computational Optimization FREE

[+] Author Affiliations
C. J. Maday

North Carolina State University, Raleigh, NC

Paper No. 82-GT-173, pp. V005T13A005; 8 pages
  • ASME 1982 International Gas Turbine Conference and Exhibit
  • Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; Process Industries; Technology Resources; General
  • London, England, April 18–22, 1982
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-7960-3
  • Copyright © 1982 by ASME


Optimum stepped shaft designs are obtained through an application of Pontryagin’s Minimum Principle. Optimum designs are obtained for a given critical speed of specified order. Indexes of Performance to be minimized include mass and rotating inertia. A general problem formulation illustrates how constraints on stress, deflections, and geometric design are taken in account. Numerical solutions are obtained to nonlinear multi-point-boundary-value-problems. A Newton-Raphson algorithm was developed to determine step locations precisely in order to facilitate the convergence of the shooting method used to solve the boundary value problem. Numerical solutions are determined with an assumed critical speed; a Rayleigh quotient calculation is used to verify that the optimum design possesses the assumed value.

Copyright © 1982 by ASME
Topics: Design , Optimization
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