Computational technique of plotting campbell diagrams for turbine blades

Abstract

The technique of plotting the Campbell diagrams for turbine blades is developed by means of mathematical modeling. Equations of blade oscillations in the field of centrifugal forces are derived. The turbine blade is supposed to be a naturally twisted rod. The numerical solution of the eigenvalue problem gives the required dependencies of oscillation frequency on angular velocity. Calculations are performed using the shooting method in Mathcad. The computational results for a particular turbine blade are presented.