Keywords: rotational periodicity, subsystem, natural vibration characteristics, bladed disk, continuous binding, steam turbine.

When designing turbines the producer must take into account many, sometimes opposite points of view. From the point of view of dynamics, the knowledge of the natural vibration characteristics of the turbines individual structural parts is important for the assessment of the design suitability. On the basis of those characteristics it is possible to assess, according to various criteria and experience, the danger of resonant vibration excitation due to acting forces.

In the computational model for the determination of the natural vibration characteristics based on rotational periodicity of the bladed disk [1] it is considered that the bladed disk can be divided into the certain number of identical parts or subsystems. The subsystem discretization will be performed in such a way that the subsystem may be coupled at an equal number of points to the same degrees of freedom to the left-side and right-side adjacent subsystems. Compared with the solution of the system as a whole the main advantage of the method using the rotational periodicity consists in the fact that the order of stiffness and mass matrices does not increase but it is at most double than in the case of considering a single subsystem.

The motivation for introducing this paper is the topical application of the method using the rotational periodicity of the structure for calculating the natural vibration characteristics of the steam turbine bladed disk with the blades connected with the continuous binding in the form of the integral shrouding and in the middle of the blade with the tie-boss connection [2]. Blades are continuously coupled at contact interfaces by the blades untwisting due to the centrifugal forces acting. The originality consists in applying the method utilizing the system periodicity in the case, in which the contact stiffness in the places of mutual "bottoming" of adjoining blades is modelled as a continuum. Natural frequencies of the model of the disk with free blades and the model of the disk with the "rigid" connection between the blades and the binding define the intervals of the possible values of the natural frequencies of the real bladed disk because its natural frequencies must be between these limiting cases.

The next step in the investigation of this bladed disk will consist of a comparison of the calculated natural vibration characteristics with the results of the experimental measurement and the probable changes in the model of the binding or the probable modification of the chosen stiffness in the connection between the blades and the binding on the basis of the experimentally assessed values. The comparison is necessary from the point of view of the verification of the applicability of the approach to the calculation models creation and from the point of view of acquiring knowledge for the further development of the computer modelling in the field of steam turbines' bladed disks with the continuous binding.

1

P. Polach, "Calculation of Natural Vibration of Linear Undamped Rotationally Periodic Structures", Engineering Mechanics, 15(2), 81-97, 2008.

2

P. Polach, J. Jankovec, P. Kindelmann, "Calculation of Dynamic Characteristics of the Steam Turbine Bladed Disk with the Blades with the Continuous Binding in the Form of Shrouding and Tie-boss", Research Report VYZ 0904/06, Škoda Research Ltd., Pilsen, Czech Republic, 2006. (in Czech)

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