Numerical and Experimental Study of Shrouded Blade Dynamics Considering Variable Operating Points

The optimization of the mechanical design process of turbomachinery has been a subject of research for decades. In this context, many researchers developed efficient numerical methods to calculate the vibration response of bladed disks. In most cases, the studies are restricted to one single operating point of the system, which is sufficient for many applications. For turbomachinery with variable operating points, the conventional computation methods must be extended. Changing the turbine’s rotational speed Ω leads to entirely new load conditions. On the one hand, structural mechanical properties (e.g. stiffening effects) depend on the rotational speed. On the other hand, in case of coupled blades, the pressure distributions in the joints are sensitive to the rotational speed. In this paper, a model of a steam turbine blade is investigated numerically and experimentally. Beside the tip shroud contact, multiple contacts at the root of the blade are considered. The steady-state vibration response is calculated by the well-known harmonic balance method (HBM) and an alternating frequency-time scheme (AFT). In case of variable operating conditions, the stiffness matrix can be described as a matrix polynomial of second order in Ω². The preload at the joints is based on nonlinear quasistatic finite element analysis and also depends on the rotational speed. For the first time, a computational methodology is presented for the calculation of the forced response of a fully bladed disk with multiple contacts considering rotational speed dependent structural mechanical properties and, in particular, contact pressures. The experimental study is conducted in two steps. Firstly, a single blade model is investigated at non-rotating test conditions. Here, the blade is clamped with two dummies at the shroud. The vibration response is measured for various pressure distributions at the shroud contact. The comparison with simulation results shows a very good agreement. The second step of the experimental study will be the future investigation of a bladed disk assembly on a rotating test rig. An overview of the test rig including operation conditions, excitation methods and measurement techniques is given at the end of the paper.