Jan R. Wright

A Comparison of Blade Tip-Timing Data Analysis Methods

Abstract The experimental determination of the vibration characteristics of rotating engine blades is very important for fatigue failure considerations. One of the most promising techniques for measuring the frequency of blade vibrations is blade tip timing. In this paper, three vibration analysis methods were specifically formulated and applied to the tip timing problem for the first time, using data obtained from a simple mathematical blade tip timing simulation. The results from the methods were compared statistically in order to determine which of the techniques is more suitable. One of the methods, the global autoregressive instrumental variables approach, produced satisfactory results at realistic noise levels. However, all of the techniques produced biased results under certain circumstances.

A Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part I: Theoretical Development

Blade tip timing is a technique for the measurement of vibrations in rotating bladed assemblies. Although the fundamentals of the technique are simple, the analysis of data obtained in the presence of simultaneously occurring synchronous resonances is problematic. A class of autoregressive-based methods for the analysis of blade tip timing data from assemblies undergoing two simultaneous resonances has been developed. It includes approaches that assume both sinusoidal and general blade tip responses. The methods can handle both synchronous and asynchronous resonances. An exhaustive evaluation of the approaches was performed on simulated data in order to determine their accuracy and sensitivity. One of the techniques was found to perform best on asynchronous resonances and one on synchronous resonances. Both methods yielded very accurate vibration frequency estimates under all conditions of interest.

Identification of a Nonlinear Wing Structure Using an Extended Modal Model

The nonlinear resonant decay method identifies a nonlinear dynamic system using a model based in linear modal space comprising the underlying linear system and a small number of additional terms that represent the nonlinear behavior. In this work, the method is applied to an aircraftlike wing/store/pylon experimental structure that consists of a rectangular wing with two stores suspended beneath it by means of nonlinear pylons with a nominally hardening characteristic in the store rotation degree of freedom. The nonlinear resonant decay method is applied to the system using multishaker excitation. The resulting identified mathematical model features five modes, two of which are strongly nonlinear, one is mildly nonlinear, and two are completely linear. The restoring force surfaces obtained from the mathematical model are in close agreement with those measured from the system. This experimental application of the nonlinear resonant decay method indicates that the method could be suitable for the identification of nonlinear models of aircraft in ground vibration testing.

Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method

This paper describes an extension of the force appropriation approach which permits the identification of the modal mass, damping and stiffness matrices of nonproportionally damped systems using multiple exciters. Appropriated excitation bursts are applied to the system at each natural frequency, followed by a regression analysis in modal space. The approach is illustrated on a simulated model of a plate with discrete dampers positioned to introduce significant damping nonproportionality. The influence of out-of-band flexible and rigid body modes, imperfect appropriation, measurement noise and impure mode shapes is considered. The method is shown to provide adequate estimates of the modal damping matrix.

Estimation of mass and modal mass in the identification of non-linear single and multi degree of freedom systems using the force-state mapping approach

Abstract The application of the force-state mapping approach to the identification of single degree of freedom non-linear systems requires the mass of the system to be known. In the case of multi degree of freedom systems both the modal mass and modal matrices need to be available for the necessary transformation into modal space. In this paper a method is presented in which an initial mass or modal mass estimate is refined by examining the sensitivity of identified parameters to the estimated mass using data from two or more excitation frequencies. This sensitivity method effectively compensates for errors in mode shapes by an implicit scaling of the physical equations and the final identified non-linear model has the correct response characteristics.

Multi-Input Multi-Output Modal Testing Techniques for a Gossamer Structure

Inflated space-based structures have become popular over the past three decades due to their minimal launch-mass and launch-volume. Once inflated, these space structures are subject to vibrations induced by guidance systems and space debris as well as from variable amounts of direct sunlight. Understanding the dynamic behavior of space-based structures is critical to ensuring their desired performance. Inflated materials, however, pose special problems when testing and trying to control their vibrations because of their lightweight, flexibility, and high damping. Traditional modal testing techniques, based on single-input, single-output (SISO) methods, are limited for a variety of reasons when compared to their multiple counterparts. More specifically, SISO modal testing techniques are unable to reliably distinguish between pairs of modes that are inherent to axi-symmetric structures (such as an inflated torus, a critical component of a gossamer spacecraft). Furthermore, it is questionable as to whether a single actuator could reliably excite the global modes of a true gossamer craft, such as a 25 m diameter torus. In this study, we demonstrate the feasibility of using a multiple-input multiple-output (MIMO) modal testing technique on an inflated torus. In particular, the refined modal testing methodology focuses on using Macro-Fiber Composite (MFC® ) patches (from NASA Langley Research Center) as both actuators and sensors. MFC® patches can be integrated in an unobtrusive way into the skin of the torus, and can be used to find a gossamer structure’s modal parameters. Furthermore, MFC® excitation produces less interference with suspension modes of the free-free torus than excitations from a conventional shaker. The use of multiple actuators is shown to properly excite the global modes of the structure and distinguish between pairs of modes at nearly identical resonant frequencies. Formulation of the MIMO test as well as the required postprocessing techniques are explained and successfully applied to an inflated Kapton® torus.Copyright

A class of methods for the analysis of blade tip timing data from bladed assemblies undergoing simultaneous resonances - Part II: Experimental validation

Blade tip timing is a technique for the measurement of vibrations in rotating bladed assemblies. In Part I of this work a class of methods for the analysis of blade tip timing data from bladed assemblies undergoing two simultaneous synchronous resonances was developed. The approaches were demonstrated using data from a mathematical simulation of tip timing data. In Part II the methods are validated on an experimental test rig. First, the construction and characteristics of the rig will be discussed. Then, the performance of the analysis techniques when applied to data from the rig will be compared and analysed. It is shown that accurate frequency estimates are obtained by all the methods for both single and double resonances. Furthermore, the recovered frequencies are used to calculate the amplitudes of the blade tip responses. The presence of mistuning in the bladed assembly does not affect the performance of the new techniques.

On the use of control surface excitation in flutter testing

Abstract Flutter testing is aimed at demonstrating that the aircraft flight envelope is flutter free. Response measurements from deliberate excitation of the structure are used to identify and track frequency and damping values against velocity. In this paper, the common approach of using a flight control surface to provide the excitation is examined using a mathematical model of a wing and control surface whose rotation is restrained by a simple actuator. In particular, it is shown that it is essential to use the demand signal to the actuator as a reference signal for data processing. Use of the actuator force (or strain) or control angle (or actuator displacement) as a reference signal is bad practice because these signals contain response information. It may also be dangerous in that the onset of flutter may not be seen in the test results.

Predicting the vibration characteristics of elements incorporating incompressible and compressible viscoelastic materials

In order to predict accurately the vibration characteristics of viscoelastic elements and viscoelastically damped structures, the use of frequency-dependent parameters such as complex modulus and Poissons ratio is important. Several techniques have been developed for measuring the frequency-dependent complex modulus of viscoelastic materials. However, the accurate determination of Poissons ratio of viscoelastic materials is much less developed. This quantity is important as its commonly quoted value of 0.5 can be very different when a viscoelastic material is in its transition or glassy region or if the material is compressible. In this paper, prismatic viscoelastic samples are employed to predict the value of Poissons ratio using the finite element method (FEM). The transmissibility characteristics of these prismatic samples are established experimentally and FEM is used in conjunction with measured complex Youngs modulus and iterated values of Poissons ratio such that the predicted FEM results agree as well as possible with the experimental data. It is shown that the method suggested is able to predict accurately the Poissons ratio of incompressible and compressible viscoelastic materials.

Identification of a Simulated Continuous Structure With Discrete Non-Linear Components Using an Extended Modal Model

In this paper a method capable of the identification of non-linear structures with many degrees of freedom is presented. The Non-Linear Resonant Decay Method achieves this by identifying an underlying linear modal model for the system. Force appropriation is then used to apply sinusoidal bursts to the structure at high levels of force. The system responses to these bursts are used in a regression analysis in modal space to yield a limited number of additional non-linear terms. The method is applied to a simulated continuous system representing a wing/engine structure with discrete non-linear components at the engine attachment points. The resulting identified non-linear modal model is used to generate response data which are compared with responses from the original system.Copyright