Non-Linear Dynamics of Steam Turbine Blades With Shroud: Numerical Analysis and Experiments

Abstract

The prediction of the aeromechanical behavior of low-pressure blades represents one of the main challenges in the Steam Turbine Industry. The evaluation of forced response and damping is critical for the reliability of new designs and usually requires expensive validation campaigns such as Wheel Box Tests (WBT). A WBT consists of one or more blade rows assembled on a rotor and spun at the desired rotating speed in a vacuum cell, with synchronous excitation provided by various sources. The WBT provides accurate information about the blade modes frequency, the alternating response level, and allows the evaluation of the mechanical damping. Given the large effort in terms of costs and time associated to the experimental activity, the possibility to rely on the output of a numerical code either during the first steps of a new design or to investigate the effect of minor changes to a current design would be extremely beneficial to the development of future products. In order to compute the non-linear forced response of shrouded blades of steam turbines, custom numerical solvers must be developed, since commercial finite element (FE) solvers do not perform this kind of analysis in the frequency domain. In this paper, the forced response of a blade with shrouds of a low pressure steam turbine is computed and numerical results are compared with the experimental Wheel Box Tests performed at GE Oil & Gas. The calculations require a three-step procedure: in the first step, a non-linear static analysis is performed in ANSYS® in order to compute the actual contact area on the shroud surface and the distribution of static normal loads, then a reduced order model of the blade is generated in ANSYS® taking into account the stiffening effect on the blade of the pre-stress due to the centrifugal force, finally the reduced model is imported in a numerical code and the non-linear forced response of the blade is computed. The numerical code solves the balance equations of the system in the frequency domain, by means of the Harmonic Balance Method, imposing cyclic symmetry boundary conditions of the system. An interpolation procedure is implemented in order to manage the non-perfectly matching meshes of the shroud contact surfaces, while the tangential and normal contact stiffness is computed with a numerical model based on the contact mechanics principles. The numerical and the experimental results around some of the critical resonances of the system are compared in order to assess the reliability and accuracy of the numerical tool for its future implementation in the mechanical design practice of the blades.

A novel test rig to study the effect of fretting wear on the forced response dynamics with a friction contact

“…As the wear progresses, more and more area is engaged and can be seen through the evolution of the surface images. Such a localization of the contact area is fully in line with what actually happens in shrouded blades [41], where a small portion of the theoretical contact area ends up being actually in contact.…”

Nonlinear dynamics of mechanical systems with friction contacts: Coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions

“…The reader can refer to Table 1 for the complete list of the system parameters. Despite its simplicity, the proposed test case can be considered as the fundamental brick for the construction of highly detailed FE models of mechanical components with joint interfaces ([3]- [8], [10]- [12]). ; (11) where the vector of contact forces fc( , q q,  t) is defined as ( , , )sin( ) ( , , )cos( ) ( , , ) ( , , )cos( ) ( , , )sin( )…”

“…Different efforts have been made by several authors ([1]- [5]) to take into account the actual stick/slip/lift-off states of the contact in order i) to determine the real amount of change in the resonant frequency (stiffness contribution) and in the resonant amplitude (damping contribution) due to the friction contact and ii) to optimize the contact modelling in order to reduce the calculation time of the forced response, which must be performed iteratively due to the nonlinear nature of the phenomenon. In particular in turbo machinery design, existing joints may be optimized in order to exploit the damping contribution in order to limit the structural vibrations thanks to the dissipated energy at the contact (blade root joints [6], [7], shrouds and snubber [8]- [10]) or dampers can be purposely added to the system (underplatform dampers [11]- [14] and ring dampers [15], [16]).…”

Study on the Damping Mechanism of the Shrouded Blade considering Contact Features

“…Gu et al [22][23][24] proposed a three-dimensional numerical friction contact model to investigate the nonlinear vibration of a damped blade through the FE model. Zucca et al [25] computed the actual contact area on the shroud surface and the distribution of normal static loads through the FE model. Liu et al [26,27] proposed an improved hybrid frequency-time domain method to efficiently study the nonlinear response of blade systems subject to dry friction damping and established a shrouded blade model with frictional contact by the finite element method.…”