Forced response prediction of turbine blades with flexible dampers: the impact of engineering modelling choices

This paper focuses on flexible friction dampers (or “strips”) mounted on the underside of adjacent turbine blade platforms for sealing and damping purposes. A key parameter to ensure a robust and trustworthy design is the correct prediction of the maximum frequency shift induced by the strip damper coupling adjacent blades. While this topic has been extensively addressed on rigid friction dampers, both experimentally and numerically, no such investigation is available as far as flexible dampers are concerned. This paper builds on the authors’ prior experience with rigid dampers to investigate the peculiarities and challenges of a robust dynamic model of blade-strips systems. The starting point is a numerical tool implementing state-of-the-art techniques for the efficient solution of the nonlinear equations, e.g., multi-harmonic balance method with coupled static solution and state-of-the-art contact elements. The full step-by-step modelling process is here retraced and upgraded to take into account the damper flexibility: for each step, key modelling choices (e.g., mesh size, master nodes selection, contact parameters) which may affect the predicted response are addressed. The outcome is a series of guidelines which will help the designer assign numerical predictions the proper level of trust and outline a much-needed experimental campaign

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

Background The presence of parametric excitation in dynamic structures, caused by friction, crack, varying compliance, electromagnetic field, etc. may generate unbounded responses. In the literature there exist several numerical analyses of systems affected by parametric excitation, while experimental studies are less frequent. Objective The goal of the paper is to create a demonstrator of a parametrically excited system, whose stability can be modified through a controlled physical parameter. This work also investigates the applicability of the recently developed stability analysis method named Jacobian Based Approach (JBA). Methods This paper studies a simple experimental set-up comprising of a cantilever beam mounted on a spring with time - varying stiffness, achieved through the use of an electromagnet. The test rig allows measuring directly the magnetic force without any preknowledge of the values of electrical parameters. Results obtained from the test rig are compared with numerical results obtained from the Finite Element model. In this study, Hill's method and JBA are employed to obtain the stability plot highlighting the regions of parametric instabilities. Results Good agreement is found between experimental and numerical data and the presence of unstable behavior is verified through the use of the well - known Hill's method and the JBA. Furthermore, this study demonstrates that the stability plot, highlighting the unstable regions, computed by JBA is in complete agreement with the one obtained by Hill's method. Conclusions It is shown how the parametric instability can be triggered through the regulation of a simple physical parameter, i.e. the gap between the electromagnet and the beam. The numerical model analyzed by the ad - hoc technique proposed by the authors i.e. JBA has been proven to have predictive capabilities in studying a system under parametric excitation and could be a potential substitution for state-of-the-art stability analysis techniques such Hill's method

Tip-timing measurements of transient vibrations in mistuned bladed disks

Bladed disks are usually characterized by a rich dynamic response during service due to the occurrence of several mode shapes that vibrate at resonance within the operative range. In particular, during start-ups and shutdowns, the variable speed causes a temporary crossing of resonance that cannot be neglected to determine stress envelope and safety margins of the system during its whole mission. In fact, fluid flow induces fluctuating loads with variable frequencies (non-stationary regime) on the blades being responsible of a dynamic response which does not follow the so-called steady-state (stationary) response. This paper proposes a novel post-processing method for Blade Tip-Timing (BTT) measurements for the identification of the resonance parameters of mistuned bladed disks working in non-stationary operative conditions. The method is based on a two degrees of freedom model (2DOF) and focuses on transient resonances in which two mistuned modes with close resonance frequencies are involved in the dynamic response. In such circumstances, the identification method based on the single degree of freedom (1DOF) model usually fails.To verify the effectiveness of the method, numerical and experimental investigations have been performed. First, a mathematical simulator based on a lumped parameter model of a bladed disk system is used to generate the BTT simulated data. Experimental signals are measured using a commercial BTT system through a set of optical probes mounted circumferentially around a rotating dummy blisk. It is shown that the method produces accurate predictions for the numerical simulation, even in the presence of considerable noise levels. Moreover, experimental results confirm a successful implementation of the method on the actual BTT measurements

Modeling and Testing Friction Flexible Dampers: Challenges and Peculiarities

This paper deals with the dynamic of blades with strip dampers. The purpose is 1) to present the results of the dynamic numerical calculation, 2) to demonstrate the need for the experimental data on the blade-strip contact to be used as input to the calculation, 3) to propose a new test rig design to obtain them and 4) to test the key components of the new test rig. The forced responses of two blades coupled by a strip damper are calculated at different excitation and centrifugal force values. The dependence of the numerical results on the contact parameter values is confirmed in this significant reference case. The design of a new test rig is then proposed: both the blade frequency response function and the contact hysteresis cycles at the blade-strip contact are measured. It is shown how contact parameters can then be derived from experimental data. The main novelty of the test rig here proposed is the strip loading system, which simulates the uniform pressure distribution provided by the centrifugal force in real operating conditions. This loading system is non-contact and uses compressed air. Classical loading systems which see dead weights directly connected to the strip are assessed and their expected inadequacy is confirmed. The compressed air system is tested by measuring the pressure produced between strip and blades: pressure is uniform across the contact patch, constant in time and its mean value corresponds to realistic pressure values actually experienced by strip dampers during service

Effect of Longâ Term Oral Bisphosphonates on Implant Wound Healing: Literature Review and a Case Report

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141603/1/jper0584.pd