Forced response of shrouded blades with a coupled static/dynamic approach

A coupled static-dynamic method is proposed and applied to bladed disks with shrouds, in order to calculate the nonlinear forced response in presence of friction damping in the frequency domain. The novel approach allows to improve the already existing methods, which require a preliminary static analysi

Forced response of rotating bladed disks: Blade Tip-Timing measurements

The Blade Tip-Timing is a well-known non-contact measurement technique currently employed for the identification of the dynamic behaviours of rotating bladed disks. Although the measurement system has become a typical industry equipment for bladed disks vibration surveys, the type of sensors, the positioning of the sensors around the bladed disk and the used algorithm for data post-processing are still not standard techniques, and their reliability has to be proved for different operation conditions by the comparison with other well-established measurement techniques used as reference like strain gauges. This paper aims at evaluating the accuracy of a latest generation Tip-Timing system on two dummy blisks characterized by different geometrical, structural and dynamical properties. Both disks are tested into a spin-rig where a fixed number of permanent magnets excite synchronous vibrations with respect to the rotor speed. A new positioning for the Blade Tip-Timing optical sensors is tested in the case of a shrouded bladed disk. Due to the presence of shrouds, the sensors cannot be positioned at the outer radius of the disk pointing radially toward the rotation axis as in the most common applications, since the displacements at the tips are very small and cannot be detected. For this reason a particular placement of optical laser sensors is studied in order to point at the leading and trailing edges' locations where the blades experience the largest vibration amplitudes with the aim of not interfering with the flow path. Besides the typical Blade Tip-Timing application aimed at identifying the dynamical properties of each blade, an original method is here proposed to identify the operative deflection shape of a bladed disk through the experimental determination of the nodal diameters. The method is applicable when a small mistuning pattern perturbs the ideal cyclic symmetry of the bladed disk

Vibration Parameters Estimation by Blade Tip-Timing in Mistuned Bladed Disks in Presence of Close Resonances

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

Smorzatori sotto-pala per turbomacchine: un nuovo metodo basato sul calcolo simultaneo delle forze statiche e dinamiche di contatto

Underplatform dampers are widely used to reduce vibration amplitude of turbine bladed disks by friction. They are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The common procedure used to calculate the static loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed to solve the static and the dynamic balance equations of the system. Numerical case studies are presented in order to show the capabilities of the method and the improvements with respect to the state of the ar

Design and Calibration of a Tri-Directional Contact Force Measurement System

In low pressure turbine stages, adjacent blades are coupled to each other at their tip by covers, called shrouds. Three-dimensional periodic contact forces at shrouds strongly affect the blade vibration level as energy is dissipated by friction. To validate contact models developed for the prediction of nonlinear forced response of shrouded blades, direct contact force measurement during dynamic tests is mandatory. In case of shrouded blades, the existing unidirectional and bi-directional contact force measurement methods need to be improved and extended to a tri-directional measurement of shroud contact forces for a comprehensive and more reliable validation of the shroud contact models. This demands an accurate and robust measurement solution that is compatible with the nature and orientation of the contact forces at blade shrouds. This study presents a cost effective and adaptable tri-directional force measurement system to measure static and dynamic contact forces simultaneously in three directions at blade shrouds during forced response tests. The system is based on three orthogonal force transducers connected to a reference block that will eventually be put in contact with the blade shroud in the test rig. A calibration process is outlined to define a decoupling matrix and its subsequent validation is demonstrated in order to evaluate the effectiveness of the measurement system to measure the actual contact forces acting on the contact

Substructuring for Contact Parameters Identification in Bladed-disks

Single stage bladed-disks are fundamental bricks of the rotating parts of a turbomachine. Although made of nominally identical sectors, the presence of imperfections or misalignment produces a large amplification of the forced response. Furthermore, due to their high modal density, friction dampers must be designed to mitigate resonance stresses, since a perfect detuning of the resonances from the excitation forces is impossible. Blade-root joints in these structures can provide the much-desired damping but the contact between the disk slot platform and blade-root lobes is characterized by uncertainty due to the actual locking position and machining tolerances. The cases of two simple beams and a bladed-disk test rig of an array of blades with dovetail root joints are studied to identify contact parameters. A dynamic Lagrange multiplier frequency based sub-structuring (LM-FBS) method is applied in a hybrid manner (experimental and numerical frequency response functions) to identify a parameter associated to each contact by mounting only one blade at a time. A sensitivity analysis is performed that will provide the basis for future work on non-linear frequency response prediction

Forced response of rotating bladed disks: Blade Tip-Timing measurements

The Blade Tip-Timing is a well-known non-contact measurement technique currently employed for the identification of the dynamic behaviours of rotating bladed disks. Although the measurement system has become a typical industry equipment for bladed disks vibration surveys, the type of sensors, the positioning of the sensors around the bladed disk and the used algorithm for data post-processing are still not standard techniques, and their reliability has to be proved for different operation conditions by the comparison with other well-established measurement techniques used as reference like strain gauges. This paper aims at evaluating the accuracy of a latest generation Tip-Timing system on two dummy blisks characterized by different geometrical, structural and dynamical properties. Both disks are tested into a spin-rig where a fixed number of permanent magnets excite synchronous vibrations with respect to the rotor speed. A new positioning for the Blade Tip-Timing optical sensors is tested in the case of a shrouded bladed disk. Due to the presence of shrouds, the sensors cannot be positioned at the outer radius of the disk pointing radially toward the rotation axis as in the most common applications, since the displacements at the tips are very small and cannot be detected. For this reason a particular placement of optical laser sensors is studied in order to point at the leading and trailing edges' locations where the blades experience the largest vibration amplitudes with the aim of not interfering with the flow path. Besides the typical Blade Tip-Timing application aimed at identifying the dynamical properties of each blade, an original method is here proposed to identify the operative deflection shape of a bladed disk through the experimental determination of the nodal diameters. The method is applicable when a small mistuning pattern perturbs the ideal cyclic symmetry of the bladed disk

Improved identification of a blade-disk coupling through a parametric study of the dynamic hybrid models

Joint identification of blade-root joints in typical bladed-disk assemblies is not possible with the classic decoupling methods due to inaccessibility of interface degrees-of-freedom. In a recent study, an attempt was made to identify such a joint by an expansion based decoupling strategy called System Equivalent Model Mixing (SEMM). The expanded sub-models of the connected substructures and their assembly can be influenced by the measurement errors and the discrepancies between the numerical and experimental sub-models. Therefore, the accuracy of the identified joint is compromised. In this work, we investigate some key factors to improve the expanded sub-models through a new measurement campaign on the unconstrained substructures and the assembly. These factors are i) expansion error, ii) interface type, and iii) singular value filtering. The resulting identified joint properties are validated by recoupling the joint with the respective substructures. It is shown that, by controlling these factors, the joint identification can be highly improved

An electromagnetic system for the non-contact excitation of bladed disks

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 nonlinear 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 damper