Damping Performance of Axial Turbine Stages With Loosely Assembled Friction Bolts: The Nonlinear Dynamic Assessment

An entire family of twisted and tapered low pressure steam turbine fast rotating condensation blading (SK) blades with pinned radial root and loosely assembled conical bolts is designed by scaling the aerodynamic and mechanical properties of the smallest airfoil. For SK blades operating with variable speed, the friction bolts, mounted in the upper airfoil part, provide either damping or coupling capabilities for the blades with respect to resonance conditions. The damping and coupling performance have been proven experimentally in the test rig of the real turbine. The measurements of the smallest SK-disk assembly under different operating conditions have allowed us to understand the dynamic and damping behavior of the bolts that are either friction dampers or coupling devices for the vibrating blades depending on the excitation level. In this paper, nonlinear dynamic analyses of the smallest and large SK-turbine stage are performed and compared with the experimental data. The modal blade dynamics is defined by 30 complex finite element (FE) mode shapes of the freestanding blades coupled by the disk whereby the bolt’s motion is described by six rigid body modes. The sticking contact condition between the blades and bolts is represented by the normal and tangential contact stiffnesses. These values are firstly estimated analytically with Hertz’s formulas for the FE reaction forces and contact areas. More realistic contact stiffness values are obtained from the iterative process, in which the resonance frequencies are calculated with the steady-state simulations and compared to the FE nodal diameter curves for sticking contact conditions that meet the experimental frequencies very well (Szwedowicz, J. et al., 2007, “Scaling Concept for Axial Turbine Stages With Loosely Assembled Friction Bolts: The Linear Dynamic Assessment Part 1,” Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17, ASME Paper No. GT2007-27502). In nonlinear simulations, in case of exceeding the sticking contact condition, the induced friction forces are linearized by the harmonic balance method. In this manner, the microslipping and sticking contact behavior at all contact points are calculated iteratively for the specified excitation amplitudes, friction coefficient, contact roughness, and aerodamping values that are known from the experiment. The computed results of the tuned smallest SK blades agree with the experimental resonance stresses of 12 measured blades. Differences between the computed and measured stresses are caused by mistuning, which was not quantified in the experiment. The nonlinear dynamic analyses provide evidence of good damping performance for the smallest and large SK blades with respect to a wide range of excitation forces, different friction coefficients, and various aerodynamic damping values. For the analyzed resonances of the eighth engine order, the scalability of damping performance is found for the SK blades of different sizes.