A Method for Theoretical Prediction of Frequency Scatter Ranges for Freestanding Forged Steam Turbine Blades

Large steam turbine end stage rotating blades are commonly manufactured by forging and machining to the final geometry. As in every manufacturing process certain geometric tolerances have to be granted. In particular, the allowed tolerances on the airfoil geometry do have a significant influence on the natural frequencies of the final blades. The resulting frequency scatter is appreciated in terms of mistuning the whole ring of blades, as an adequate mistuning has shown advantages under unstalled flutter conditions. An excessively large band is not acceptable, due to the fact that the blade frequencies are tuned to not-coincide with harmonic multiples of the rotor speed under stationary operation. This paper describes a theoretical method for prediction of a manufactured blade design frequency scatter, based only on nominal geometric information about the blade. Therefore, it is suited to be used during the development of a blade without having a prototype produced. The method is divided into three different steps. First, a numerical experiment is performed creating a number of geometrically modulated FE models. These models are used in a calculation of natural frequencies. Second, these frequencies serve as input for an identification of a simple algebraic representation of the frequencies. This allows a fast calculation by interpolation without the need to process the FE models. Third, the identified simplified equation is used in conjunction with different optimization algorithms for analysis of the specific design characteristics. The validity of the chosen matrix equation is shown by comparison to the FE calculations, before different blade types are investigated. Characteristics and options of the implemented optimization routines are discussed. Finally, the comparison of differently tuned blade types are used to demonstrate the capabilities of the described algorithm.