• Energy Research

Abstract This paper presents experimental and numerical investigation of mistuned forced responses of an integrally bladed disk with full set of underplatform dampers (UPDs). This research aims at providing: 1. An experimental benchmark for nonlinear dynamics of a mistuned bladed disks with UPDs. 2. A numerical model that can account for features of a mistuned forced response level. Accordingly, a detailed experimental campaign is conducted on a static test rig called Octopus. This rig is specifically designed to investigate the dynamics of a full-scale integrally bladed disk (blisk) with UPDs in a noncontact manner so that the dynamic response of the system is not modified. The effect of mistuning on experimental forced response levels is assessed and a linearized model is proposed to predict the modulation of frequency response functions (FRFs) due to the frequency splitting. In the development of the model, the mistuning pattern identified from the linear blisk without UPDs is used and it is assumed that adding the dampers does not change the structural mistuning of the blisk. In this study, the fundamental mistuning model identification (FMM ID) was employed to identify the mistuning pattern of the blisk. It is shown that the proposed model successfully predicts the modulation of linear mistuned FRFs. The linearized model is also able to predict the modulation of nonlinear mistuned FRFs in stick condition (when nonlinear friction damping is negligible) with a good accuracy validating this assumption that adding the dampers does not change the mistuning pattern.

Abstract This paper explores two different blisk dynamic models for resonant vibration prediction of a rotating blisk test piece, i.e. the Model-BDTID and GMM. The former represents a mistuned blisk model with blade mistuning pattern experimentally retrieved by a recently proposed blade mistuning identification method based on blade detuning tests (BDTID). It falls into the scope of the frequency-mistuning modeling approach. The latter refers to a geometrically mistuned model constructed upon high-precision blisk geometry data by leveraging the advanced optical geometry measurement technology. A specifically developed ‘Sector Mode Assembling Reduction Technique’ is exploited for efficient dynamic analyses of the large-sized GMM. Forced response tests are performed in a spinning rig under well-controlled laboratory condition. The Blade Tip-Timing technique is employed to give all-blade vibration measurements of the rotating blisk. Correlation results between the forced response predictions to BTT measurements demonstrate that both the Model-BDTID constructed upon the identified blade mistuning of the blisk at rest and the GMM, can predict the resonant vibration of the rotating blisk with satisfactory accuracy.

This paper presents a novel blade mistuning identification method based on blade detuning tests. Blade detuning tests consist of blade-by-blade impact testing in a blisk with detuning masses purposefully attached on all the blades except the one currently under test. Due to the quite simple test setup and implementation, the detuning tests enable to estimate the blade frequency mistuning pattern of the blisk with low experimental effort. However, it was proved that non-negligible residual inter-blade coupling is responsible for an inaccurate identification of the truly ‘blade-alone’ mistuning pattern from the blade detuning test results. Therefore, a novel mistuning identification method is herein proposed in order to improve the accuracy of the estimated mistuning pattern. This method fully exploits the blade detuning test results and includes the residual inter-blade coupling due to the mass detuning mechanism. The quantification and the introduction of the residual inter-blade coupling into the identification procedure leads to the determination of a more accurate ‘blade-alone’ frequency mistuning pattern. This novel mistuning identification method is firstly validated in a numerical test case and then applied to a real blisk test piece.

Abstract The paper focuses on the cylindrical underplatform damper, a friction damping device widely used in power generation turbines. The first goal of the paper is to estimate the stiffness and damping contribution of cylindrical dampers interposed between adjacent blades vibrating along a typical in-phase mode. For the first time, the damper characterization is performed through the direct measurement of contact forces and platform displacements. Measurements show that the damper does not introduce damping or stiffness if the two platforms, with which the damper is in contact, share the same angles (i.e. blade with symmetrical platform) and are vibrating in-phase. This is an adequate design choice if only the damper sealing function is required, while changes to the disk dynamics are not desired. The damper produces a small stiffening effect only if the two adjacent platforms have different angles. These findings are confirmed by an analytical derivation performed on the basis of a simple yet effective damper model. The damper numerical model requires parameters which may be calibrated, i.e. the cylinder-on-flat tangential contact stiffness. The second goal of the paper is to use the experimental evidence on contact forces and platform displacements to estimate these parameters for different centrifugal loads using a purposely developed technique. These values are compared with those obtained at an identically designed contact interface on a curved flat damper (i.e. cylindrical damper with a flattened side). The differences found in the calibration parameters show that the local stiffnesses depends not only on the local geometry of the contact but also on the damper kinematics.

Blade mistuning in blisks arises primarily from the scatters of blade geometry profiles caused by manufacturing tolerance, in-service wear, blade repairs, etc. There is a recent trend to capture the blade-to-blade geometry variances through precise geometry measurements by a 3D optical scanning system in order to obtain an improved blade geometric mistuning evaluation capability. However, this usually leads to prohibitive computational costs due to the large-scale, high-fidelity industrial blisk finite element models. This paper develops an original model reduction approach, Sector Mode Assembling Reduction Technique (SMART), specifically for the high-fidelity blisk model fully mistuned by blade geometric variances, with either topologically compatible or incompatible blade meshes. The basic idea of SMART is to construct the sector-level reduction mode basis by strategically assembling the truncated cyclic modes independently computed for each “isolated” sector with assumed cyclic symmetry at the sector interfaces. Benefiting from the block structure of the SMART mode basis, the reduced-order models are derived by a series of sector-level projections with a relatively low memory requirement and computational cost. Another hidden benefit is that the SMART approach enables efficient structural modification predictions of the global blisk modes because only the modes of the sectors undergoing blade modification need to be re-evaluated and replaced in the SMART mode basis. The SMART approach is applied into a high-fidelity “as-measured model” of a blended blisk, constructed upon the geometry measurement by the state-of-the-art 3D optical scanning technology. It is fully demonstrated that the reduced-order model derived by SMART, featured by a minimal size, is able to reproduce the dynamics of the full-order as-measured blisk model with high accuracy.

The present paper is focused on the post processing of the data coming from the Blade Tip-Timing (BTT) sensors in the case where two very close peaks are present in the frequency response of the vibrating system. This type of dynamic response with two very close peaks can occur quite often in bladed disks. It is related to the fact that the bladed disk is not perfectly cyclic symmetric and the so called “mistuning” is present. A method based on the fitting of the BTT sensors data by means of a 2 degrees of freedom (2DOF) dynamic model is proposed. Nonlinear least square optimization technique is employed for identification of the vibration characteristics. A numerical test case based on a lump parameter model of a bladed disk assembly is used to simulate different response curves and the corresponding sensors signals. The Frequency Response Function (FRF) constructed at the resonance region is compared with the traditional Sine fitting results, the resonance frequencies and damping values estimated by the fitting procedure are also reported. Accurate predictions are achieved and the results demonstrate the considerable capacity of the 2DOF method to be used as a standalone or as a complement to the standard Sine fitting method.

Abstract Increasing demand on turbine power and efficiency requires larger and higher loaded turbine blades, which in turn requires the consideration of aeromechanical interactions. Whilst CFD tools can reliably predict stability using aerodynamic damping as an indicator, the component of mechanical damping also needs consideration. An understanding of the mechanical damping in the system becomes key to a robust blade design. Mechanical damping for such a part comes predominantly from friction occurring at the coupling contact faces. It is well established and published that such contact forces are nonlinear in relation to the relative movement at the contact interface. Moreover, contact area, the rigidity in the contact, friction coefficient, and normal contact force must also be considered and included as parameters that influence the result. Consequently, the level of system damping is not a constant, and depends highly on the system response itself, as well as the other forementioned parameters. In the case of self-excited vibration such as flutter, the evaluation of the damped limit response is a part of the blade design process. A tool has been developed to numerically simulate contact friction forces with the intention of parametrically evaluating the limit response and relating this to the mechanical integrity of the part. This paper presents the modelling of a coupled blade system with friction contact forces, results coming from this evaluation, and a comparison with test data.

The purpose of this paper is to offer a practical demonstration of how essential preoptimization is in the design of underplatform dampers for turbine blades. Preoptimization can be thought of as a “prescreening” which allows excluding, since the early design stages, a high number of poorly performing damper–platform configurations. This concept, previously presented by the authors, is here extended and its generality for all blade bending modes is rigorously demonstrated. The paper addresses a test case where the introduction of curved-flat underplatform dampers is necessary to avoid a dangerous resonance crossing in the operating rotational speed range of a real turbine disk. It is shown how preoptimized dampers are the only ones that manage to satisfy all functional requirements, including those in the nonlinear operating regime. The same set of dampers may have been identified by exploring, through hundreds of computationally intensive nonlinear calculations, the performance of all possible damper configurations. The latter approach, i.e. iterative design, is unpractical and has to be repeated for each new set of blades since it is based on a test case-specific trial-and-error procedure. Preoptimization substitutes iterations with knowledge of the damper behavior and can therefore be considered as “informed design”: viable damper configurations are instantly singled out through simple but insightful considerations on the damper equilibrium of forces and moments.

Abstract The paper presents the planning, structure and preliminary results of a new test rig for the validation of numerical models that calculate the dynamic response of bladed disks with underplatform dampers (UPDs).