Ermittlung von Ersatzbiegesteifigkeiten zur Bestimmung biegekritischer Drehzahlen
When operating gas or steam turbines, a safe margin from critical bending speeds must be ensured. This requires that these speeds can be reliably determined during the design phase. If no FEM models are available, turbine developers often resort to simple beam models that can be easily solved numerically.
Since, neglecting gyroscopic effects, the critical bending speed is equal to the first bending eigenfrequency of the rotor, the accuracy of the simple calculation depends on the accuracy of the assumed equivalent bending stiffnesses of the turbine disks joined via Hirth gearing. Due to the geometry of the turbine disks, additional inversion effects occur during bending deformation, which influence the bending stiffness.
For this purpose, FEM models of the turbine disks were statically loaded, and the equivalent bending stiffnesses were determined from the deformation. By automatically varying the disk geometry, equivalent stiffnesses for a large number of turbine disks could be determined largely automatically. By solving overdetermined systems of equations, approximate formulas were derived that allow the calculation of the bending stiffness of a turbine disk by specifying key geometric dimensions.
