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

Some results in analyzing the dynamic behavior of blade rows coupled by shroud contacts

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 sometimes also for the long blades of the low pressure sections.The blades are either inserted with their root into the seat on the shaft in such a way that small clearances remain between adjacent blade shrouds, so that the relative vibration amplitude is restricted by the contact between adjacent shrouds. This mechanism is called “snubbing mechanism”. Another technology for mounting blades on the shaft is to do it in such a way that the blades are slightly forced against each other in correspondence of the shrouds: this should allow the continuity of the contact without clearances also at rated speed and full load. In this case the blades are called “pre-twisted”. Field experience has shown that these kinds of blade rows has a “robust and smooth” behavior. But there is still some lack of theoretical/numerical investigation for defining its dynamical behavior in different operating conditions, both for the blades with clearance and with pre-twist. The aim of this paper is to investigate numerically the non-linear dynamic behavior of a couple of shrouded blades, taking account of contact forces and friction. An equivalent linear model has then been developed for analyzing the behavior of the complete blade row. Also some provisional experimental results on non-rotating blade rows are presented