Some Remarks on the Dynamic Behaviour of Integrally Shrouded Blade Rows

Actual trend in steam turbine design is to use blades with integral shrouds, for high pressure and intermediate pressure steam turbine sections, as well as also for the long blades of the low pressure sections. The blades are inserted with their root into the seat on the shaft in such a way that the blades are slightly forced against each other in correspondence of the shrouds. In long blades of low pressure stages the forcing can be obtained by the untwisting of twisted blades due to the effect of the huge centrifugal forces. The dynamic behavior of these blade rows is difficult to predict due to the nonlinear effect of the contact forces and due to friction. Different models for the contact are proposed and compared. The resulting natural frequencies of the blade row as a function of the different nodal diameter mode shapes are highly depending on the assumed models. For avoiding resonant conditions with engine order excitations, the natural frequencies must be calculated with good accuracy. Some of the modes of the blade row, typically for the last stage of the low pressure steam turbine, can couple with some vibration modes of the rotor: flexural vibrations of the shaft couple with 1 nodal diameter mode shape of the row in axial direction and torsional vibrations of the shaft couple with the 0 nodal diameter mode in tangential direction. Therefore analyses of lateral and torsional vibrations of low pressure steam turbine shafts require also an accurate analysis of the blade row vibration modes.