Ibrahim A. Sever

Modeling and Validation of the Nonlinear Dynamic Behavior of Bolted Flange Joints

Linear dynamic finite element analysis can be considered very reliable today for the design of aircraft engine components. Unfortunately, when theses individual components are built into assemblies, the level of confidence in the results is reduced, since the joints in the real structure introduce nonlinearity that cannot be reproduced with a linear model. Certain types of nonlinear joints in an aircraft engine, such as underplatform dampers and blade roots, have been investigated in great detail in the past, and their design and impact on the dynamic response of the engine is now well understood. With this increased confidence in the nonlinear analysis, the focus of research now moves towards other joint types of the engine which must be included in an analysis to allow an accurate prediction of the engine behaviour.One such joint is the bolted flange, which is present in many forms on an aircraft engine. Its main use is the connection of different casing components to provide the structural support and gas tightness to the engine. This flange type is known to have a strong influence on the dynamics of the engine carcase. A detailed understanding of the nonlinear mechanisms at the contact is required to generate reliable models and this has been achieved through a combination of an existing non-linear analysis capability and an experimental technique to accurately measure the nonlinear damping behaviour of the flange. Initial results showed that the model could reproduce the correct characteristics of flange behaviour, but the quantitative comparison was poor. From further experimental and analytical investigations it was identified that the quality of the flange model is critically dependent on two aspects: the steady stress/load distribution across the joint and the number and distribution of non-linear elements. An improved modelling approach was developed which led to a good correlation with the experimental results and a good understanding of the underlying nonlinear mechanisms at the flange interface.Copyright

Non-Parametric Identification of Asymmetric Signals and Characterization of a Class of Non-Linear Systems Based on Frequency Modulation

Non-parametric and parametric identification of a non-linear system is often performed by estimating instantaneous amplitude and frequency using the Hilbert transform. However, the Hilbert transform cannot be used for the accurate analysis of asymmetric signals and the reliable estimation of intra-wave frequency modulation. This paper proposes two alternatives to the Hilbert transform which not only avoid some of its mathematical and numerical issues, but also allow the above mentioned analyses. The first method, based on zero-crossing, allows the backbone and damping curves as well as the elastic and damping force characteristics of an asymmetric free decay to be identified. The application and accuracy of this method are demonstrated on the free decay of the system with off-centre clearance. The second method, based on direct quadrature, estimates intrawave frequency modulation frequency with sufficient resolution for characterization of non-linear systems which have stiffness non-linearities. The use of this method is shown on a system with cubic hardening stiffness.Copyright

Detection of nonlinear behaviour of composite components before and after endurance trials

Composite components are being studied by many researchers due to complex nature of their nonlinear dynamic behaviour. This behaviour can be a function of several factors, such as lay-up configuration and/or visco-elastic material properties etc. Recent studies on failure criteria of composite structures under endurance testing have shown that vibration forced responses can be nonlinear because of structural modification occurring during a test. Typically, endurance testing can cause initiation and propagation of a delamination(s) of the test structure, shifting dynamics of composites from quasi linear to non-linear regime. This transition was observed during laboratory experiments but very little effort was made to generate an understanding of the phenomenon. The aim of this paper is to focus on the study of nonlinear behaviour of composites before and after endurance trials. Recently, tools capable of addressing detection, characterisation, localisation and quantification aspects of nonlinearity have been developed. Some of these tools will be used in this exercise with an overall objective of quantifying the level of nonlinearity.

Experimental and Numerical Investigation of Rotating Bladed Disk Forced Response Using Under-Platform Friction Dampers

In this paper we present a methodology and results from an experimental investigation of forced vibration response for a bladed disk with fitted under-platform ‘cottage-roof’ friction dampers, together with the corresponding numerical predictions. A carefully-designed and constructed rotating test rig is used to make precise measurements which involve only the phenomena of interest. For this purpose, the measurement rig is operated under vacuum to eliminate aerodynamic effects on the rotating blisk and non-contact excitation and measurement techniques are employed so as not to modify the bladed disk dynamics. The experimental data measured are used for validation of multi-harmonic balance-based prediction tools developed at Imperial College. Predictions are carried out both with and without taking inherent mechanical mistuning into account, which is identified from measured data. Measured and predicted response curves are compared with each other and the degree of correlation is discussed.© 2007 ASME

Full-field strain measurements on turbomachinery components using 3D SLDV technology

This paper focuses on measurements of 3D Operating Deflection Shapes (ODSs), and subsequently, construction of full-field surface strain maps of a number of turbomachinery components. For this purpose a 3D Scanning Laser Doppler Vibrometer (SLDV) is used. The ODS measurements are performed for a large number of modes and results obtained are compared with the 1-D shapes that are most commonly measured. It is demonstrated that the 3D measurements are a significant improvement over the 1-D case in terms of independent amount of extra information they provide. This is confirmed through comparisons with FE results. Special tests are carried out to recover the full-field strain on scanned faces of the components used. Visual comparison of these measurements with FE counterparts reveal that strain maps can be successfully measured, not only for low frequency modes but also for highly complex high frequency ones. These maps are measured with different levels of input force to assess the linearity of strain resul...

An Experimental Case Study for Nonlinear Model Validation: Effect of Nonlinearities in an Aero-Engine Structure

Linear FE-models are commonly validated with measured data obtained from experimental test conducted under similar FE-simulated boundary conditions. However, measured data at higher or operational amplitudes of vibration often exhibit evidence of nonlinear characteristics. Research has proven that majority of the causes and sources of these nonlinearities are frequently local in nature while a large proportion of the structure can be represented using linear theory. This paper presents the experimental investigations conducted on an aircraft structure ranging from linear to nonlinear regime, the aim of the investigation was to understand the influence of connecting accessories or components to the proposed aircraft structure. Broadband, sine-sweeps and stepped-sine excitations were used to detect and characterise the nature of the nonlinear behaviour in the assembly.

A Distribution-Based Damping Estimation Method for Random Vibration Response and Its Applications

In this paper, a damping estimation method based on distribution of zero-crossing times and its applications are presented. The method is empirically derived and it is based on Rice distribution operating on probability distribution of zero-crossings. The method’s assertion is that a relationship exists between said probability distribution and the bandwidth of a mechanical system and this can be used as a means of increasing confidence in more traditional damping estimation methods. The method is applicable to responses that are due to broadband random excitation featuring a mono-harmonic response. Given that a multitude of modes will be active in aero-engines; its application has to be preceded with a suitable band-pass filter to isolate modes of interest. Such filtering is shown to affect the damping estimates. Some controlled laboratory tests are performed to verify the accuracy of the method and to study the effects of preceding filtering amongst other factors such as modal density, data length etc. The performance of the method is compared with Fourier transform based damping estimation methods. The results of application of the method to real engine measurements and carefully controlled laboratory tests are also presented.

Non-linear System Identification Using the Hilbert-Huang Transform and Complex Non-linear Modal Analysis

Modal analysis is a well-established method for analysis of linear dynamic structures, but its extension to non-linear structures has proven to be much more problematic. A number of viewpoints on non-linear modal analysis as well as a range of different non-linear system identification techniques have emerged in the past, each of which tries to preserve a subset of properties of the original linear theory. The objective of this paper is to discuss how the Hilbert-Huang transform can be used for detection and characterization of non-linearity, and to present an optimization framework which combines the Hilbert-Huang transform and complex non-linear modal analysis for quantification of the selected model. It is argued that the complex non-linear modes relate to the intrinsic mode functions through the reduced order model of slow-flow dynamics. The method is demonstrated on simulated data from a system with cubic non-linearity.

Correlation of Non-contact Full-Field Dynamic Strain Measurements with Finite Element Predictions

It is highly desirable to have the capability to measure strain maps on components directly and in a full-field fashion that addresses shortcomings of conventional approaches. In this paper, use of a 3D laser measurement system is explored for direct and full-field dynamic strain measurements on compressor and turbine rotor blades. More importantly, the results obtained are numerically correlated to corresponding FE predictions in a systematic manner. The ability to measure strain maps on real engine hardware is demonstrated not only for low frequency fundamental modes, but also for challenging high frequency modes. Correlation results show a high degree of agreement between measured and predicted strains, demonstrating the maturity of the technology and the validity of the method of integration used here. The measurements are repeated for a number of different loading amplitudes to assess the variations in strain fields. Although the application of 3D laser systems to measurements of full-field strain were explored in previous studies, to the best knowledge of authors, full-field numerical correlation of full-field strain on a wide range of real, complex components to this extent is presented here for the first time.

Scanning LDV Measurement Technology for Vibration Fatigue Testing

Vibration fatigue testing is a verification method for structural components. It is rapid and cost efficient, and it is often performed for aero-engine components because it replicates closely stresses under normal operation conditions. This testing methodology is well known for metallic components but it can also be applied to composites for studying failure caused by high cycle fatigue. Resonant frequency decay is usually the main parameter used to assess fatigue behaviour of metallic components at a given excitation level. However for composites this alone is not very useful and several measurement parameters need to be monitored in order to understand the behaviour and develop a set of failure criteria. Scanning LDV is an excellent measurement system which enables a variety of options thanks to its non-contact nature. This manuscript will show how this system can be used for monitoring several parameters during vibration fatigue testing. A custom made control panel called MONTEVERDI and the independent use of the scanning mirrors allow the SLDV to perform several tasks: (1) Phase Lock Loop (PLL) to excite the component always at resonance, (2) measuring of Operational Deflection Shape (ODS) using either step or continuous scanning method, (3) custom calibrated strain measurement and (4) phase portrait for nonlinear vibration analysis. This paper will present the great potential of using SLDV for performing time consuming vibration fatigue testing via an automated control panel.