Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment — Part I

For industrial condensing steam turbines operating at variable speed, Siemens has developed a last stage SK-blade family in the early 80s. The principle goal was to design a robust blade profile for the highest reliability and a good performance, which allow the operation in resonances under high steam mass flow and excessive condensing pressures. To suppress resonance stresses through friction dissipation, loosely fitted conical bolts are applied to the upper part of adjacent airfoils. In the early 80s, these capabilities were experimentally investigated and validated for the smallest SK-blade at a set-up of the real turbine unit. The tapered and twisted geometry of the smallest SK-blade has been scaled under consideration of the similar mechanical and aerodynamic characteristics. The entire scaled-up SK-blade family has proved its reliability in more than 500 industrial turbine units arranged for different power and speeds. In the last years there could be seen a trend to very large compression units, like GTL (Gas to Liquids), PTA (Acid Terephtalic) or Methanol plants. Therefore, the SK-blade family has been extended to larger airfoils using the well established scale concept based on the smallest SK-unit. In this paper, the mechanical capabilities of the smallest and large SK-blades coupled by the bolts are verified by using the Finite Element (FE) Method. The static analyses with friction sliding on the bolts and the linear dynamic behaviour of tuned disc assemblies are considered. The FE mesh quality and the proper restraint conditions at the radial root are accomplished by getting good agreements between the computed and measured resonance frequencies of the large freestanding blade at standstill. The validated mesh refinement and root boundary conditions are used further in all numerical FE analyses. For the large SK-disc assembly under spin pit conditions, the obtained FE results are in very good agreement with the experimental Campbell diagram. The determined positions of the gauges allow for identifying either stick-slip or sticking contact conditions at the bolts. The experimental spin pit results show mainly sticking contact conditions at the bolts because of too weak air jet excitation. Only in very narrow frequency ranges around resonance peaks, micro-slips on the friction bolts occur due to the resonance amplification of blade vibrations. This is proved indirectly by the evaluated damping values for spin pit conditions, which are bigger than the damping magnitudes of the disc assembly at standstill, which was measured with hammer tests. This empirical statement is approved by the FE steady-state dynamic results for the analytically determined amplitudes of the air jet excitation. The obtained results show that the proposed linear dynamic concept can be successfully applied to the design process of the scaled turbine discs of different dimensions with loosely assembled friction bolts for assessment of maximum static stresses and free vibration behaviour. The scaling design criteria of the blades with friction bolts are confirmed fully for natural frequencies and excitation conditions, but their real responses depending on the excitation amplitudes need to be obtained from the non-linear dynamic simulation which is considered in paper GT2007-27506 (Szwedowicz et al., 2007).