2010

Sascha Merz

Passive and active control of the sound radiated by a submerged vessel due to propeller forces

Abstract:

An important cause of sound radiation from a submarine in the low frequency range is fluctuating forces at the propeller. The forces arise from the operation of the propeller in a non-uniform wake and are transmitted from the propeller to the submarine hull through both the shaft and the fluid. The sound radiated from the submarine is due to the combination of sound radiation caused by hull and propeller vibrations as well as dipole sound radiation from the propeller. To improve the stealth of a submarine, the radiated sound power can be reduced using passive and active noise and vibration control mechanisms. In this thesis, dynamic models of a submarine hull and propeller/shafting system are developed. To reduce the radiated sound fields, passive control is introduced using a hydraulic vibration attenuation device known as a resonance changer, which is implemented in the propeller/shafting system. Active control techniques are implemented using either tuned actuators or a control moment. To initially obtain the structural and acoustic responses of a submarine hull, an analytical model and fully coupled finite element/boundary element model are developed, for a simplified physical model of the hull. The submerged body under axial excitation is modelled as a ring-stiffened cylindrical shell with finite rigid end closures and separated by bulkheads into a number of compartments. Lumped masses are located at each end to maintain a condition of neutral buoyancy. In the low frequency range, only the axial hull modes in accordion motion and axial vibration of the propeller/shafting system are examined, which gives rise to an axisymmetric case. The frequency responses, axial and radial responses of the cylinder and the radiated sound pressure from both the analytical and computational models are compared. A dynamic model of the propeller/shafting system developed computationally and including the resonance changer is then coupled to the FE/BE model of the hull which is subject to both structural excitation from the propeller/shafting system and acoustic excitation from the propeller. The influence of tailcone properties on the structural and acoustic responses of the submarine are investigated. Passive control is implemented to attenuate the hull responses using a resonance changer. It is demonstrated that the performance of the resonance changer is negatively influenced at frequencies above the fundamental axial resonance of the hull by the effect of forces transmitted through the fluid. When the resonance changer is optimised to minimise excitation of the hull via the propeller shaft, the increased axial movement of the propeller results in an additional sound field that excites the submarine hull in a similar manner to the fluid forces that arise directly from the hydrodynamic mechanism. Cost functions that represent the submarine radiated sound power are developed, where the virtual stiffness, damping and mass of the resonance changer were chosen as design parameters. The minima of the cost functions are found by applying gradient based optimisation techniques. The adjoint operator is employed to calculate the sensitivity of the cost function to the design parameters. The influence of sound radiation due to propeller vibration on the optimisation of the resonance changer is investigated. The influence of the reduction in amplitude for higher harmonics of the blade passing frequency on the control performance is also examined. Different active control strategies are investigated, in which active control is applied to the propeller/shafting system and/or to the submarine hull. Active vibration control and discrete structural acoustic sensing based on the far field radiated sound power were considered in the development of the cost functions. In addition, the performance of a of a combined passive and active control system is investigated. Significant reduction of radiated sound power is achieved when an active control system using tuned actuators is combined with a resonance changer. The structural responses of a model scale, free flooded submarine tailcone are investigated computationally and experimentally. The tailcone is represented by a thin-walled conical shell attached to a stiff plate. The stiff plate represents the pressure hull end plate of the submarine and is subject to axial excitation correlated to propeller forces. Good agreement between the computational and experimental results are found for the tailcone in air as well as for the submerged tailcone.

Gareth Forbes

Non-contact gas turbine blade vibration monitoring using internal pressure and casing response measurements

Abstract:

This thesis addresses the non-contact measurement of rotor blade vibrations in gas turbines. Specifically, use is made of internal casing wall pressure, and external casing vibration measurements. Non-contact measurement of gas turbine blade vibrations has made significant progress over recent years; however, there still exist some limitations in the current techniques available. The current dominant non-contact method uses proximity probes to measure blade arrival time, to be used for blade vibration monitoring. Distinctly with these blade tip timing methods, some of the limitations are: the requirement of a large number of sensors for each engine stage, difficulties in dealing with multiple excitation frequencies, and sensors being located in the gas path. Alternative techniques are examined here, utilising the unsteady casing wall pressure, and external casing vibration measurements which have the potential to rectify some of these limitations. Simulated internal pressure measurements are used in the proposal of a technique for direct rotor blade vibration amplitude estimation. A novel phase demodulation procedure was developed to obtain the blade vibration amplitude estimates from the simulated internal pressure signal. This demodulation technique has the potential to find further application with phase modulated signals, often present in rotating machinery, where the modulating frequency is higher than the carrier frequency. Although the use of internal pressure measurements showed great potential in the direct measurement of rotor blade vibrations, the use of external sensors outside of the flow path has a more discernible advantage. Thus, the development of the response of the external casing of a gas turbine under the internal pressure forces was undertaken, with the unique response of an axi-symmetric structure under moving loads being presented. Once the response of the casing structure is determined, it can then be used in understanding how external casing vibration measurements could be correlated to rotor blade vibrations. It is shown that the stochastic portion of the external casing vibration measurements will contain narrowband peaks located at multiples of shaft speed plus and minus rotor blade natural frequencies. These results, significantly, demonstrated that blade vibration information can be obtained from casing vibration measurements at a single engine running speed.

2009

Mauro Caresta

Structural and acoustic responses of a submerged vessel

Abstract:

Excitation of the low frequency vibrational modes of a submerged vessel can generate significant radiated noise levels. Vibrational modes of a submarine hull are excited from the transmission of fluctuating forces through the shaft and thrust bearings due to the propeller rotating in an unsteady fluid. The focus of this work is to investigate the structural and acoustic responses of a submarine hull under axial excitation. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The displacement normal to the surface of the structure in contact with the fluid medium was calculated by assembling the boundary/continuity matrix. The far field radiated sound pressure was then calculated by means of the Helmholtz integral. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model. The individual and combined effects of the various influencing factors, corresponding to the ring stiffeners, bulkheads, conical end closures and fluid loading, on the structural and acoustic responses are characterised by examining the contribution by the circumferential modes. It is shown that equally spaced internal bulkheads generate a periodic structure thus creating a grouping effect for the higher circumferential modes, but do not have strong influence on the sound radiation. Stiffeners are found to have an important effect on both the dynamic and acoustic responses of the hull. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is also clearly observed. This work shows the importance of the bending modes when evaluating the sound pressure radiated by a submarine under harmonic excitation from the propulsion system.

2008

Geoffrey Lucas

Vibrational Characteristics of Structures with Uncertainty

Abstract:

This thesis is concerned with the prediction of the vibro-acoustic response of structures with uncertain properties in the mid frequency region. The motivation for this research is the growing need of engineers to understand the responses of a group of similar structures ranging from vehicles, aircraft and aerospace structures, to household whitegood appliances. These structures are complex in geometry and may possess variability in their material or geometric properties, as well as variation arising from the assembly and manufacturing processes. Small variations can have a significant effect on a dynamic response of a structure, and the effect of structural uncertainties increases as the frequency increases. Deterministic modelling techniques such as finite element analysis are only suitable to model complex structures at low frequencies. Furthermore, FEA cannot easily account for uncertainty or randomness in structural parameters. High frequency dynamic predictive techniques such as Statistical Energy Analysis can account for structural uncertainty but is limited to structures with high modal density. There exists a frequency range between the two methods in which neither technique can be applied with great confidence. The objective of this thesis is to investigate predictive techniques for mid frequency vibration analysis of dynamic systems with structural uncertainties. The first part of this work is to numerically characterise the effect of a range of uncertainties on the modal statistics of structures. The degree of uncertainty required to achieve universality of the statistical properties is investigated. This is achieved by examining the modal statistics of dynamic systems with a range of uncertainty, corresponding to uncertainty due to mass and stiffness perturbations, uncertainty at the boundaries of a structure, uncertainty in the coupling between structures, uncertainty in the material properties of a structure and uncertainty in the geometry of a structure. Several structures are examined corresponding to a plate with masses and/or linear springs added at random locations, a plate with torsional springs attached at random locations along its boundary edges, two plates coupled by linear springs at random locations, a mass-loaded coupled L-shaped plate, a mass-loaded frame-plate structure, and a plate with varying Young’s modulus, density and thickness. The natural frequencies of the aforementioned structures have been derived using either the Lagrange-Rayleigh-Ritz technique, finite element analysis, or the use of interval analysis in conjunction with FEA. The natural frequency statistics of structures with uncertain properties are observed using two statistical measures; the statistical overlap factor and the probability density function of the spacing between successive natural frequencies. The statistical overlap factor is defined by the variation in a natural frequency from its mean value measured across an ensemble of nominally identical structures with uncertainty. For a single ensemble member, the probability density function of the spacing between successive natural frequencies is compared to a Rayleigh distribution of the mean frequency spacing. A Rayleigh distribution of modal spacings is a feature of the universality exhibited by structures with uncertainty. To further investigate the effect of structural uncertainty on the vibrational characteristics of structures, the interval analysis is applied to finite element models of a plate with uncertainty in its material properties and dimensions. Using this method, the Young’s modulus, density and thickness of a rectangular plate were set to vary by a small amount within predefined bounds. Using finite element equations, the natural frequencies and modeshapes of the structure were then determined in terms of the Young’s modulus, density and plate thickness. For the mass and spring loaded plates, the springs were shown to affect the lower order modes while the masses had a significant effect on the higher order modes. As the frequency increased, only a small amount of perturbation was sufficient to affect the natural frequencies of a structure. Using the interval analysis method, the variation of the natural frequencies from their deterministic value increased as the frequency increased. An ergodic hypothesis was used to examine the responses statistics of structures with uncertainty. Three structures have been computationally studied corresponding to two plates coupled by springs, an L-shaped plate and a frame plate structure. Uncertainty has been generated for the two coupled plates by locating the springs randomly across the surface of the two plates. For the L-shaped plate and a frame plate structure, uncertainty was generated by randomly positioning small masses across the plates. Using the ergodic hypothesis, the frequency averaged response on one member of an ensemble is compare with the ensemble averaged response. It was found that the ensemble averaged response was well predicted by a frequency averaged response of a single ensemble member. The width of the frequency averaging band was shown to have a large influence on the quality of the match between the frequency and ensemble averaged responses. Results were significantly improved using a frequency averaging bandwidth which varies proportionally to frequency. Finally, experiments have been conducted on an L-shaped plate, a frame plate structure and a vehicle to validate the computational results for the natural frequency and response statistics.

Anne Shen

Optimised reduction of the radiated noise from the casing of a constant speed gearbox

Abstract:

This thesis presents a comprehensive methodology for predicting and minimising the noise radiated from a constant speed gearbox assembly by means of attaching optimally placed stiffening ribs on the casing. The procedure involves building an FE model of the gearbox, which is updated using modal parameters extracted from a modal test. This is followed by synthesis of the required FRFs with respect to the forcing degrees-of-freedom. The forces, which are assumed to act only at the bearings are identified from these FRFs and the measured operational velocities of the casing. The identified forces are then used to excite the updated FE model to re-calculate the vibration velocities. A boundary element method is used to calculate the final radiated sound power to be compared with that measured. The same forces are used later to excite the modified gearbox casing to determine the improvement given by optimised modification. The optimisation study minimises the vibration energy of the casing in 10% bands around critical frequencies, in this case the first two harmonics of the gearmesh frequency. To allow for errors in the model, the excitation is by white noise, so as to produce wide stop bands, rather than minimising the response at particular frequencies. The vibration energy is weighted for radiation efficiency, A-weighting, and relative source strength in the bands. The final optimal stiffener layout is validated through a final vibration and acoustic calculation on the updated gearbox model using the forces identified in the earlier steps. The study of one particular gearbox concludes that i) the proposed hybrid optimisation scheme produces a theoretical effective noise reduction of 3 dBA for the total sound power. ii) Because the gearmesh harmonics were targeted, a further 5 dB improvement was effectively gained by eliminating the tonal penalty which otherwise applied. iii) From plate studies it was demonstrated that the stiffening ribs could be attached using epoxy cement (to avoid welding) and that the properties of the cemented joint could be determined by model updating after attaching one rib, so as to obtain a better prediction of the final optimised result.

Michael Skeen

An investigation of energy flow through coupled plate structures

Abstract:

This PhD thesis presents research aims to improving the dynamic modelling of coupled plate structures across a wide frequency range by using analytical, statistical and experimental methods. The analytical waveguide method is used to model the flexural displacement of coupled plate structures which are simply supported along two parallel edges. A method of quickly predicting the average energy level in a plate from details of the waveguide model is described, and used for comparison with SEA models. The Poynting and Impedance methods of predicting the energy flow in coupled plate structures are investigated. Transmission coefficients for coupled plate structures are evaluated using the analytical waveguide method for both semi-infinite and finite coupled plate structures. Finite transmission coefficients have traditionally been more difficult to evaluate due to the presence of a reverberant field, but in this work a novel method of separating the reverberant field using a scattering matrix method is presented. The transmission coefficients for semi-infinite and finite structures are then compared for L-shaped plates. A modal transmission coefficient is also defined and for the cases considered, and is used to develop an alternative method of deriving the transmission coefficient in a finite structure. Frequency averaged transmission coefficients are also considered, and the transmission coefficients derived for finite and semi-infinite structures are found to be very similar after frequency averaging. Statistical Energy Analysis models of coupled plates are evaluated using transmission coefficients derived from waveguide models. The results of the SEA models are compared to those predicted by the analytical waveguide method. A modal transmission coefficient based SEA model is also investigated. In an attempt to validate the numerical work presented in this thesis, experiments have been conducted. Using a wave extraction technique, both the wave amplitudes and plate properties have been evaluated from experimental data, and are subsequently used to experimentally measure the transmission coefficient for two plates coupled at different angles.

2007

Wee Lee Chia

Multiple-Input Multiple-Output (MIMO) blind system identification for operational modal analysis using the Mean Differential Cepstrum (MDC)

Abstract:

The convenience of Operational Modal Analysis (OMA), over conventional Experimental Modal Analysis (EMA), has seen to its increasing popularity over the last decade for the purpose of evaluating dynamic properties of structures. OMA features an advantage of requiring only output information, which is in tandem with its main drawback of lacking scaled modeshape information. While correctly scaled modeshapes can be assumed under a restrictive assumption of spectrally white inputs, in reality, input spectra are at best broadband in nature. In this thesis, an OMA method for Multiple-Input Multiple-Output (MIMO) applications in mechanical structures is developed. The aim is to separate MIMO responses into a collection of Single-Input Single-Output (SISO) processes (matrix FRF) using cepstral-based methods, under less restrictive and hence more realistic coloured broadband excitation. Existing cepstral curve-fitting techniques can be subsequently applied to give regenerated FRFs with correct relative scaling. This cepstral-based method is based on the matrix Mean Differential Cepstrum (MDC) and operates in the frequency domain. Application of the matrix MDC onto MIMO responses leads to a matrix differential equation which together with the use of finite differences, directly solves or identifies the matrix FRF in a propagative manner. An alternative approach based on whitened MIMO responses can be similarly formulated for the indirect solution of the matrix FRF. Both the direct and indirect approaches can be modified with a Taylor series approximation to give a total of four propagative solution sequences. The method is developed using relatively simple simulated and experimental systems, involving both impulsive and burst random excitations. Detailed analysis of the results is performed using more complicated Single-Input Multiple-Output (SIMO) and MIMO systems, involving both driving and non-driving point measurements. The use of the matrix MDC method together with existing cepstral curve-fitting technique to give correct relative scaling is demonstrated on a simulated MIMO system with coloured inputs. Accurate representation of the actual FRFs is achieved by the matrix MDC technique for SIMO set-ups. In MIMO scenarios, excellent identification was obtained for the case of simulated impulsive input while the experimental and burst random input cases were less favourable. The results show that the matrix MDC technique works in MIMO scenarios, but possible noise-related issues need to be addressed in both experimental and burst random input cases for a more satisfactory identification outcome.

Paul Dylejko

Optimum resonance changer for submerged vessel signature reduction

Abstract:

In maritime vessels, it is desirable to minimise the structural and acoustic responses for several reasons, including passenger comfort, minimisation of crew fatigue, and in the case of military vessels, to avoid detection. The propeller-shafting system represents one of the most critical areas which must be addressed in order to reduce the low frequency acoustic signature. The propeller-shafting system is primarily excited by axial oscillations at the propeller. The force transmitted along the propeller-shafting system from these disturbances results in axial excitation of the hull and subsequent sound radiation. The aim of this thesis is to apply a combination of passive and active control techniques, in order to minimise the low frequency radiated noise signature of a pressure hull submerged in a fluid. Dynamic models of the propeller-shafting system, foundation and cylindrical hull including complicating factors such as fluid loading, bulkheads and onboard equipment are developed and described using the transmission matrix approach. This modular description enables greater flexibility for dynamic modelling of the propeller-shafting system, and can be easily manipulated for future design modifications. The far-field radiated sound pressure from the submarine hull is evaluated and related to the force delivered to the hull by the propeller-shafting system. A passive optimisation scheme involving a genetic and general non-linear constrained algorithm is used to minimise fitness functions associated with the vibration of the propeller, vibration transmission to the hull and far-field radiated sound pressure over a low frequency range. This results in optimal resonance changer parameters for single and multiple resonance changers in a variety of configurations. A new quasi-adaptive resonance changer system is proposed and optimised to minimise the radiated sound pressure or propeller velocity. The optimal use of an adaptive resonance changer is investigated in both the frequency and time domains to reduce the hull velocity and subsequently the far-field radiated sound pressure. Fully active control is also evaluated by introducing a control force to the resonance changer with the aim of minimising either the propeller velocity or the radiated noise level. Finally, the concept of hybrid control is investigated by coupling passive, active and semi-active control techniques together to improve the overall performance.

Nader Sawalhi

Diagnostics, prognostics and fault simulation for rolling element bearings

Abstract:

Vibration signals generated from spalled elements in rolling element bearings (REBs) are investigated in this thesis. A novel signal-processing algorithm to diagnose localized faults in rolling element bearings has been developed and tested on a variety of signals. The algorithm is based on Spectral Kurtosis (SK), which has special qualities for detecting REBs faults. The algorithm includes three steps. It starts by pre-whitening the signal’s power spectral density using an autoregressive (AR) model. The impulses, which are contained in the residual of the AR model, are then enhanced using the minimum entropy deconvolution (MED) technique, which effectively deconvolves the effect of the transmission path and clarifies the impulses. Finally the output of the MED filter is decomposed using complex Morlet wavelets and the SK is calculated to select the best filter for the envelope analysis. Results show the superiority of the developed algorithm and its effectiveness in extracting fault features from the raw vibration signal. The problem of modelling the vibration signals from a spalled bearing in a gearbox environment is discussed. This problem has been addressed through the incorporation of a time varying, non-linear stiffness bearing model into a previously developed gear model. It has the new capacity of modeling localized faults and extended faults in the different components of the bearing. The simulated signals were found to have the same basic characteristics as measured signals, and moreover were found to have a characteristic seen in the measured signals, and also referred to in the literature, of double pulses corresponding to entry into and exit from a localized fault, which could be made more evident by the MED technique. The simulation model is useful for producing typical fault signals from gearboxes to test new diagnostic algorithms, and also prognostic algorithms. The thesis provides two main tools (SK algorithm and the gear bearing simulation model), which could be effectively employed to develop a successful prognostic model.

2006

David Hanson

Operational modal analysis and model updating with a cyclostationary input

Abstract:

This thesis addresses the problem of identifying the modal properties of a system based only on measurements of the system responses. This situation is frequently encountered in structural dynamics and is particularly relevant for systems where the in-service excitation is not artificially reproducible. The inherent non-linearities in these systems mean that the modal properties estimated using traditional input/output techniques will be different to those exhibited in operation. A common example from the literature is an aircraft in flight where the modal properties are heavily influenced by the operating point, i.e. the combination of load, speed, altitude etc., at which the aircraft is travelling. The process of identifying the modal properties of systems in-service is called Operational Modal Analysis (OMA). Not knowing the input complicates the analysis. Most of the techniques in the literature overcome the lack of knowledge about the unmeasured excitations by assuming they are both spatially and frequentially white, i.e. of equal magnitude and with a flat autospectrum. This thesis presents a new technique for OMA which relaxes these constraints, requiring only that the system is excited by a so called cyclostationary input with a unique cyclic frequency, and that the log spectrum of the second order component of this input is frequentially smooth, as will be explained. Such systems include vehicles with internal combustion engines as the vibration from such an engine exhibits cyclostationary statistics. In this thesis, the technique is applied to a laboratory test rig and a passenger train both using an artificial input, and to a race car using the engine as the excitation. By combining cyclostationary signal processing and the concept of the cepstrum, the technique identifies the resonances and anti-resonances in the transfer functions between each response and the cyclostationary source. These resonances and antiresonances can be used to regenerate Frequency Response Functions (FRFs) and it is shown how the unknown scaling of the system can be recovered by employing finite element model updating in conjunction with this regeneration. In addition, the contribution made to model updating by the anti-resonances is also investigated. Finally, the potential of OMA to inform a model updating process is demonstrated using an experimental case study on a diesel railcar.

Xianhua Liu

Blind source separation methods and their mechanical applications

Abstract:

Blind Source Separation is a modern signal processing technique which recovers both the unknown sources and unknown mixing systems from only measured mixtures of signals. It has application in diverse fields such as communication, image processing, geological exploration and biomedical signal processing etc. This project studies the BSS problem, develop separation methods and reveal the potential for mechanical engineering applications. There are two models for blind source separation corresponding to the two ways that the sources are mixed, the instantaneous mixing model and the convolved mixing model. The author carried out a theoretical study of the first model by proposing an idea called Redundant Data Elimination which leads to geometric interpretation of the model, explains that circular distribution property is the reason why Gaussian signal mixtures can not be separated, and showed that this idea can improve separation accuracy for unsymmetrically distributed sources. This new idea enabled evaluation and comparison of two well-known algorithms and proposal of a simplified algorithm based on Joint Approximate Diagonalization of fourth order cumulant matrices, which is further developed by determining an optimized parameter value for separation convergence. Also based on the understanding from the RDE, an outlier spherical projection method is proposed to improve separation accuracy against outlier errors. Mechanical vibration or acoustic problems belong to the second model. After some theoretical study of the problem and the model, a novel application of the Blind Least Mean Square algorithm using Gray’s variable norm as cost function is applied to engine vibration data to separate piston slap, fuel injection noise and cylinder pressure effects. Further, the algorithm is combined with a deflation algorithm for successive subtraction of recovered source responses from the measured mixture to enable the recovery of more sources. The algorithms are verified to be successful by simulation, and the separated engine sources are proved reasonable by analysing the engine operation and physical properties of the sources. The author also studied the relationship between these two models, the problems of different approaches for solving the model such as the frequency domain approach and the Bussgang approach, and sets out future research interests.

Vibration and Acoustics Research Group, UNSW Sydney NSW 2052, Australia
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