D. J. Ewins

Design of High Impedance Test Rig for Composite Structures Vibration Measurements

Experimental vibration measurement of mechanical components are very important for studying the dynamic properties. Electromagnetic (EM) shakers are the most widely used exciters in mechanical testing because of both the broadband dynamic range of excitation and the excitation power. However, there are applications where these exciters can work inefficiently, and so underperform. This can be caused by an impedance mismatch between the shaker armature and test rig, which causes dissipation of the generated power into heating the armature rather than moving the test structure. Clearly, mechanical components presenting a high level of structural damping will require higher level of power to obtain high levels of vibration. Hence, it is important to minimize as much as possible any unwanted power dissipation due to both the test rig design and the connection between the shaker and/or the test rig. This paper demonstrates that a bladed disc type of structure can be used as a high impedance connector for a test rig in order to increase the excitation force level. This is possible thanks to otherwise an undesirably dynamic characteristic of bladed discs, which is represented by mistuning of the blades. When this mistuning characteristic is enhanced, it is possible to produce several resonances each with a high impedance match between the shaker and the test rig and this can increase the force applied to the specimen and thus its displacement amplitude. Also, the test rig proposed here can be used of several resonance frequencies depending on the number of blades. Hence the proposed test rig can improve both the performance of a shaker and increase the amplitude of vibration of the test structure. Further to this the application of the amplification process can be used for fatigue trials of composite material component. This has been an application which has caused some considerable difficulty: few cases have been successful and the results in this paper show evidence of how to proceed for future trials.

Effects of Contact Interface Parameters on Vibration of Turbine Bladed Disks With Underplatform Dampers

The design of high cycle fatigue resistant bladed disks requires the ability to predict the expected damping of the structure in order to evaluate the dynamic behavior and ensure structural integrity. Highly sophisticated software codes are available today for this nonlinear analysis, but their correct use requires a good understanding of the correct model generation and the input parameters involved to ensure a reliable prediction of the blade behavior. The aim of the work described in this paper is to determine the suitability of current modeling approaches and to enhance the quality of the nonlinear modeling of turbine blades with underplatform dampers. This includes an investigation of a choice of the required input parameters, an evaluation of their best use in nonlinear friction analysis, and an assessment of the sensitivity of the response to variations in these parameters. Part of the problem is that the input parameters come with varying degrees of uncertainty because some are experimentally determined, others are derived from analysis, and a final set are often based on estimates from previous experience. In this investigation the model of a commercial turbine bladed disk with an underplatform damper is studied, and its first flap, first torsion, and first edgewise modes are considered for 6 EO and 36 EO excitation. The influence of different contact interface meshes on the results is investigated, together with several distributions of the static normal contact loads, to enhance the model setup and, hence, increase accuracy in the response predictions of the blade with an underplatform damper. A parametric analysis is carried out on the friction contact parameters and the correct setup of the nonlinear contact model to determine their influence on the dynamic response and to define the required accuracy of the input parameters

Modal testing for model validation of structures with discrete nonlinearities.

Model validation using data from modal tests is now widely practiced in many industries for advanced structural dynamic design analysis, especially where structural integrity is a primary requirement. These industries tend to demand highly efficient designs for their critical structures which, as a result, are increasingly operating in regimes where traditional linearity assumptions are no longer adequate. In particular, many modern structures are found to contain localized areas, often around joints or boundaries, where the actual mechanical behaviour is far from linear. Such structures need to have appropriate representation of these nonlinear features incorporated into the otherwise largely linear models that are used for design and operation. This paper proposes an approach to this task which is an extension of existing linear techniques, especially in the testing phase, involving only just as much nonlinear analysis as is necessary to construct a model which is good enough, or ‘valid’: i.e. capable of predicting the nonlinear response behaviour of the structure under all in-service operating and test conditions with a prescribed accuracy. A short-list of methods described in the recent literature categorized using our framework is given, which identifies those areas in which further development is most urgently required.

Robust Strategies for Forced Response Reduction of Bladed Disks Based on Large Mistuning Concept

In this paper, robust maximum forced response reduction strategies based on a large mistuning concept are introduced, including both (i) random and (ii) deterministic approaches. An industrial bladed fan disk serves as an application example for a reliability assessment of the aforementioned strategies using two well-established tools for uncertainty analysis: (i) statistics and (ii) sensitivity and robustness. The feasibility and other practical aspects of implementing large mistuning as a means of preventing excessive forced response levels caused by random mistuning and ensuring the predictability of the response are discussed.

A Systematic Approach to Modal Testing of Nonlinear Structures

The application of experimental modal analysis methods to nonlinear structures (sometimes referred to as “nonlinear modal testing” – NLMT) is not a new field, but only in the past few years has it become mature enough to be approached in a systematic way. Many methods have been developed over the years for dealing with nonlinearities in structural dynamics, but nonlinearity is an extremely complex phenomenon with so many aspects and consequences that is not possible to have a single method capable to deal with all of them. Rather than taking a holistic approach, it is perhaps useful for the engineer to have a set of mathematical tools to analyse separate subsets of the whole problem, i.e. one being within the scope of each individual investigation. The main objective of this paper is to provide a modular framework from which the engineer can choose the most appropriate method to retrieve information about an examined nonlinearity, based on the type of information needed and the available data set. This is achieved by performing a breakdown of the nonlinear modal analysis process into four main stages: detection, localisation, characterisation and quantification – each of these providing a different level of insight into the problem. A review of currently-available algorithms applicable for these four categories is presented, as well as their application to two simple case studies.

Simulation and validation of ODS measurements made using a Continuous SLDV method on a beam excited by a pseudo random signal

Continuous-Scanning LDV (CSLDV) methods are now available as alternative approaches to the conventional Stepping mode for Operational Deflection Shape (ODS) measurements. CSLDV techniques were initially used with sinusoidal excitation where the LDV time history could be also used to extract modal parameters by post-processing the data using modal analysis software. The latest extension of CSLDV is the use of a pseudo random signal to excite the tested structure for this work, a cantilever steel beam was used. Analytical models of the structure, the LDV output signal and excitation waveform were produced to simulate several responses which could be studied to identify the relationship between three fundamental parameters: (i) LDV scan rate, (ii) sampling frequency and (iii) frequency resolution of the pseudo random signal. This paper produces a theoretical background of the study presenting simulations and validations of both LDV output time signals and ODSs, respectively.

Nonlinear Dynamics of a Simplified Model of an Overhung Rotor Subjected to Intermittent Annular Rubs

The dynamic forced response of a two-degrees-of-freedom model of an unbalanced overhung rotor with clearance and symmetric piecewise-linear stiffness is examined in the time domain. The stiffness nonlinearity is representative of the contact between the rotor and a concentric stator ring. This rubbing interaction comes as a result of the rotor transient motion initiated by the sudden application of a static unbalance, such as in a blade loss scenario. The focus of this study is on the range of rotor speeds above resonance, where the contact between rotor and stator is characterised by a “bouncing” or intermittent type of behaviour. Brute-force numerical bifurcation analysis on the long-term forced response revealed ranges of rotation frequency for which there is bi-stability between non-impacting synchronous equilibrium and impacting sub-synchronous motion. It is found that, for sufficiently high levels of transient energy in the rotor, there exists the possibility for the solution to jump into a stable limit cycle characterised by three non-harmonically related frequencies, namely the synchronous response frequency and the forward and backward whirl frequencies. A simple relationship defining the point of synchronisation between these three components is proposed as an explanation to the region of bi-stability detected. The stiffening effect induced by the contact non-linearity enables this synchronisation to be maintained over a range of forcing frequencies rather than just at the single condition determined from the nominal whirl mode frequencies.Copyright

A Comprehensive Procedure to Estimate the Probability of Extreme Vibration Levels due to Mistuning

A new procedure is developed to find the probabilities of extremely high amplification factors in mistuned bladed disk vibration levels, typical of events which occur rarely. While a rough estimate can be made by curve-fitting the distribution function generated in a Monte Carlo simulation, the procedure presented here can determine a much more accurate upper bound and the probabilities of amplification factors near to that bound. The procedure comprises an optimization analysis based on the conjugate gradient method and a stochastic simulation using the importance sampling method. Two examples are provided to illustrate the efficiency of the procedure, which can be 2 or 3 orders of magnitude more efficient than Monte Carlo simulations.

Experimental Non-linear Modal Testing of an Aircraft Engine Casing Assembly

This paper aims to present experimental work on an aircraft engine casing assembly. Nowadays single components of casings can be modeled with such high accuracy that they can be validated by carrying out the model validation process using measured data from a sector of the entire assembly. This smart validation process can be achieved by carrying out the modal analysis with a Scanning LDV (Laser Doppler Vibrometer) system which allows good spatial resolution of the measured mode shapes. The validation process can be assumed valid under linear response conditions obtainable for low vibration amplitudes. Casings are typically connected together by joints which may or may not respond non-linearly under high levels of vibration. Therefore, prior to conducting any non-linear validation, the mode(s) responding non-linearly must be identified beforehand in order to correctly specify the non-linear modal testing required. The work presented here will use a large civil engine casing assembly comprising a Combustion Chamber Outer Casing (CCOC), High Intermediate Pressure Turbine Casing (HIPTC) and Low Pressure Turbine Casing (LPTC.) The Fine Mesh Finite Element Model (FMFEM) was successfully validated using linear modal analysis test data. One of the objectives of this work is to define the key points for conducting non-linear modal testing of such large casing assemblies and sub-assemblies. One outcome of the experimental work was a set of recommendations for performing measurements, which should be carried out within the frequency bandwidth selected during the model validation process. Experimentally derived non-linear response curves are presented in this paper.

Non-contact operational modal analysis of an optical membrane for space application

In recent years, a number of studies have addressed the possibility of replacing the conventional rigid mirrors that are used in space-based telescopes with optical membranes. Weight reduction, reduced cost of transportation and ability to provide a continuous surface for the attenuation of wave front aberrations are some of the benefits given by optical membranes. Given the harsh environmental loading conditions represented by thermal radiation, debris impact and slewing maneuvers, the ability to characterise fully the dynamics of such low-density thin-film membranes is essential. Nevertheless, the testing of membrane-like structures has proven to be a non-trivial process, and requires a considerable amount of work to achieve accurate results, as well as validating experiments against numerical models. Despite typical testing, the inherent low-density feature of membranes requires the use of non-invasive, non-contact sensors and excitation capability. The work presented here, investigates the possibility of using Operational Modal Analysis (OMA) techniques to extract modal parameters from an acoustically-exited membrane, where responses are collected by using a Scanning Laser Doppler Vibrometer (SLDV) as a non-contact velocity transducer. Results from this experiment are validated against an impedance-based numerical model.