• Energy Research
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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.

In this paper a non-contact excitation system based on electromagnets is described. The system aims at exciting cyclically symmetric structures like bladed disks by generating typical engine order-like travelling wave excitations that bladed disks encounter during service. Detailed description of the analytical formulation for the electromagnets sizing, quality assessment and practical implications of the final assembly for the bladed disk excitation are addressed. In particular, the paper proposes an original method to setup the excitation system in order to perform step-sine controlled force measurements. This feature is necessary when non-linear forced response must be measured on bladed disks in order to characterize the dynamic behaviour at different level of excitation. Typical applications of the designed excitation system are two: the first is the study of the effect of a force pattern characterized by a particular engine order on the forced response of mistuned bladed disks, the second is the characterization of intentional non-linear damping source occurring, for instance, for friction phenomena in presence of shrouds or underplatform dampers.

The paper presents a calculation procedure for the design of turbine blades with underplatform dampers. The procedure involves damper “pre-optimization” before the coupled calculation with the blades. The pre-optimization procedure excludes, since the early design stage, all those damper configurations leading to low damping performance. Pre-optimization involves plotting a design “damper map” with forbidden areas, corresponding to poorly performing damper geometries and admissible design areas, where effective solutions for the damper shape can be explored. Once the candidate damper configurations have been selected, the damper equilibrium equations are solved by using both the multi-harmonic balance (MHB) method, and the direct time integration method (DTI). Direct time integration of the damper dynamic equations is implemented in order to compute the trend of the contact forces in time and the shape of the hysteresis cycles at the different contact points. Based on these trends, the correct number of Fourier terms to represent the contact forces on the damper is chosen. It is shown that one harmonic term together with the static term, are enough in the MHB calculation of a pre-optimized damper. The proposed method is applied to a test case of a damper coupled with two blades. Experimental forced response functions of the test case with a nominal damper are available for comparison. The purpose of this paper is to show the effectiveness of the “damper maps” in excluding all those damper configurations, leading to undesirable damper behavior and to highlight the strong influence of the blades mode of vibration on the damper effectiveness. From the comparison of dampers with different geometrical parameters, the pre-optimized damper proved to be not only the most effective, in terms of damping capability, but also the one that leads to a faster and more flexible calculation of the damper, coupled with the blades.

Abstract Underplatform dampers are used to limit the resonant vibration of turbine blades. In recent years, various strategies have been implemented to maximize their damping capability. Curved-flat dampers are preferred to ensure a predictable bilateral contact, while a pre-optimization procedure was developed to exclude all those cross-sectional shapes that will bring the damper to roll and thus limit the amount of dissipated energy. The pre-optimization bases its predictions on the assumption that the effective width of the flat contact interface corresponds to the nominal one. It is shown here that this hypothesis cannot be relied upon: the energy dissipated by two nominally identical dampers, machined according to the usual industrial standards, may differ by a factor up to three due to the morphology of the flat-to-flat contact interface. Five dampers have been tested on two dedicated test rigs, available in the AERMEC laboratory, specially designed to reveal the details of the damper behavior during operation. Their contact interfaces are scanned by means of a profilometer. In each case, the mechanics, the kinematics, and the effectiveness of the dampers in terms of cycle shape and dissipated energy are correlated to the morphology of the specific contact surface. To complete the picture, a state-of-the-art numerical simulation tool is used to show how this tribo-mechanic phenomenon, in turn, influences the damper effect on the dynamic response of the turbine.

The paper presents an original multiple excitation system based on electromagnets with force control. The system is specifically designed in order to investigate the dynamics of bladed disks, since it mimics the excitation existing in a real engine. Moreover, the system is suitable for forced response tests of bladed disks with nonlinear dynamic response, like in the case of presence of friction contacts, since the amplitude of the exciting force is known with good precision. For this purpose, a device called force-measuring electromagnet (FMEM) was designed and employed during the system calibration. The excitation system is applied to the test rig Octopus, which includes underplatform dampers (UPDs). Tests were carried out under different excitation force amplitude values. The tests put in evidence the presence of mistuning and the UPDs' capability of attenuating the mistuning phenomena.

Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multistage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper, a novel reduced order model (ROM) is proposed for studying nonlinear vibration due to contacts in multistage bladed disks. The methodology exploits the shape of the single-stage normal modes at the interstage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the interstage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the interstage boundary only depends on the specific engine order (EO) excitation acting on the multistage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the single harmonic balance method (SHBM), the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multistage bladed disk and its performance is tested using as a benchmark the Craig–Bampton ROMs of each single stage.