Anthony B. Stanbridge

Underplatform Dampers for Turbine Blades: Theoretical Modeling, Analysis, and Comparison With Experimental Data

This paper describes a theoretical model for analyzing the dynamic characteristics of wedge-shaped underplatform dampers for turbine blades, with the objective that this model can be used to minimize the need for conducting expensive experiments for optimizing such dampers. The theoretical model presented in the paper has several distinct features to achieve this objective including: (i) it makes use of experimentally measured contact characteristics (hysteresis loops) for description of the basic contact behavior of a given material combination with representative surface finish, (ii) the damper motion between the blade platform locations is determined according to the motion of the platforms, (iii) three-dimensional damper motion is included in the model, and (iv) normal load variation across the contact surfaces during vibration is included, thereby accommodating contact opening and closing during vibration. A dedicated nonlinear vibration analysis program has been developed for this study and predictions have been verified against experimental data obtained from two test rigs. Two cantilever beams were used to simulate turbine blades with real underplatform dampers in the first experiment. The second experiment comprised real turbine blades with real underplatform damper. Correlation of the predictions and the experimental results revealed that the analysis can predict (i) the optimum damping condition, (ii) the amount of response reduction, and (iii) the natural frequency shift caused by friction dampers, all with acceptable accuracy. It has also been shown that the most commonly used underplatform dampers in practice are prone to rolling motion, an effect which reduces the damping in certain modes of vibration usually described as the lower nodal diameter bladed-disk modes.

Detecting damage in vibrating structures with a scanning LDV

It has been demonstrated, through experiments on laboratory-scale structures, that structural defects such as cracks can be detected and located using a continuously scanning laser Doppler vibrometer (LDV) if vibration sufficient to flex the defect can be induced and if the defects are such as to produce localised mode shape discontinuities. This paper describes such a method of defect detection using a short linear scan at the crack location. Through-cracks are easily detected in thin metal plates whereas narrow slots in a solid cantilever beam have no easily identifiable effect unless they extend more than half-way through the thickness. Cracks in a reinforced-concrete beam introduced marked and identifiable discontinuities in mode shapes. Speckle noise affects the measurements, sometimes seriously. A simple low-pass filter may improve the signal quality.

Measurement of Translational and Angular Vibration Using a Scanning Laser Doppler Vibrometer

An experimental procedure for obtaining angular and translational vibration in one measurement, using a continuously scanning laser Doppler vibrometer, is described. Sinusoidal scanning, in a straight line, enables one angular vibration component to be measured, but by circular scanning, two principal angular vibrations and their directions can be derived directly from the frequency response sidebands. Examples of measurements on a rigid cube are given. Processes of narrow-band random excitation and modal analysis are illustrated with reference to measurements on a freely suspended beam. Sideband frequency response references are obtained by using multiplied excitation force and mirror-drive signals.

Measurement of total vibration at a point using a conical-scanning LDV

Previous studies have demonstrated convenient techniques using a continuously-scanning Laser Doppler Vibrometer for measuring and quantifying vibration mode shapes defined along straight or circular scan lines, and for measuring angular vibration. This paper concentrates on a new conical- scanning technique which gives an easily-quantifiable measure of the magnitude and direction of the vibration of a point, even if the vibration is in-plane. Where the vibration is complex (i.e. it follows an elliptical path), derivation of the component vectors is more difficult. However, easy solutions exist for some practical special cases.

Measurement of translational and angular vibration using a scanning laser Doppler vibrometer

An experimental procedure for measuring angular rotation vibration as well as translation, using a continuously-scanning Laser Doppler Vibrometer, is described. Sinusoidal scanning enables one angular vibration component to be measured but, by circular scanning, two principal angular vibrations and their direction can be derived directly from the frequency response sidebands. Examples of sine excitation measurements on a rigid cube are given. Processes of narrow-band random excitation and modal analysis are illustrated with reference to measurements on a freely-suspended beam. The laser beam was scanned by using x-y axis deflection mirrors; if this facility was not available, circular scanning could probably be achieved by using a rotating tilted mirror. Sideband frequency response references were obtained by using multiplied excitation force and mirror-drive signals.

Vibration measurements in a rotating blisk test rig using an LDV

Three methods of using an LDV to measure the vibration of a bladed disc in a rotating rig are described. I.e. (i) the response of one blade is monitored continuously by diverting the laser beam via a small mirror on the rotating disc, and a fixed, annular, conical mirror. Any of the blades may be targeted, by indexing the rotating mirror. (ii) circular scans give circumferential response mode shapes directly, or (iii) via spectra, as nodal diameter coefficients. Some natural modes of blisks (integral bladed discs) occur in isolated pairs, with amplitude distributions which are sinusoidal around a circular scan line. The natural frequencies increase with the number of sinusoids around the circumference, asymptotically to the cantilever blade frequency. Forced vibration of these modes, in a rotating situation, produces various combinations of standing and rotating waves. With a mistuned blisk, the close modes couple to create natural mode shapes which are very irregular. Excitation frequencies are at multiples of rotation speed, exciting modes with equivalent numbers of nodal diameters, sometimes aliased with the number of blisk blades. The LDV techniques described can cover all these effects, and some example measurements are included to illustrate their potential.

Turbomachinery blade vibration measurements with tracking LDV under rotation

A method of measuring vibration response on rotating components using an LDV and its application on bladed disks are presented. Understanding and controlling of vibration amplitudes of bladed disks has been a primary concern for aero-engine manufacturers for many years. The vibration amplitudes of these components are known to be significantly affected by break down of symmetry due to variations in dimensional or material properties. A bladed disk exhibiting these variations is said to be mistuned and considerable research effort is put into acquisition of prediction tools to calculate the effects of these variations. However, the validation of these tools against real measurements is often ignored because of the difficulties involved in application of appropriate excitation and measurement techniques in rotating conditions. In this paper we present successful use of non-intrusive measurement and excitation techniques towards achievement of this goal. These techniques are independent of rotational speed. The so-called self-tracking LDV measurement method used in this paper was introduced in a previous paper by the authors. Here the use of method for acquisition of high quality reference response data for validation of mistuned bladed disks and those fitted with under-platform friction dampers are given.

Underplatform Dampers for Turbine Blades: Theoretical Modelling, Analysis and Comparison With Experimental Data

This paper describes a theoretical model for analysing the dynamic characteristics of wedge-shaped underplatform dampers for turbine blades, with the objective that this model can be used to minimise the need for conducting expensive experiments for optimising such dampers. The theoretical model presented in the paper has several distinct features to achieve this objective including: (i) it makes use of experimentally-measured contact characteristics (hysteresis loops) for description of the basic contact behaviour of a given material combination with representative surface finish, (ii) the damper motion between the blade platform locations is determined according to the motion of the platforms, (iii) three-dimensional damper motion is included in the model, and (iv) normal load variation across the contact surfaces during vibration is included, thereby accommodating contact opening and closing during vibration.A dedicated non-linear vibration analysis program has been developed for this study and predictions have been verified against experimental data obtained from two test rigs. Two cantilever beams were used to simulate turbine blades with real underplatform dampers in the first experiment. The second experiment comprised real turbine blades with real underplatform damper. Correlation of the predictions and the experimental results revealed that the analysis can predict (i) the optimum damping condition, (ii) the amount of response reduction and (iii) the natural frequency shift caused by friction dampers, all with acceptable accuracy. It has also been shown that the most commonly-used underplatform dampers in practice are prone to rolling motion, an effect which reduces the damping in certain modes of vibration usually described as the lower nodal diameter bladed-disc modes.© 1999 ASME

Measuring strain response mode shapes with a continuous-scan LDV

A continuous-scan LDV can be used to give the response mode shape (of a vibrating surface as a spatial polynomial series. Second spatial derivative(s) of the deflection equation are then easily derived, and these should, in principle, give a curvature equation from which, for a beam or plate of known cross-section, stresses and strains can be obtained. Unfortunately, the stress and strain distributions depend critically on higher terms in the series, which are not accurately measured. This problem is avoided by a method described in this paper, which enables accurate stress and strain distributions to be derived for uniform beams, from a straight-line LDV scan, using only five terms in the mode- shape polynomial series. An application to uniform plates is being developed; the analysis in this latter case is rather more complicated.