Arthur W. Lees

Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass

A common energy harvesting device uses a piezoelectric patch on a cantilever beam with a tip mass. The usual configuration exploits the linear resonance of the system; this works well for harmonic excitation and when the natural frequency is accurately tuned to the excitation frequency. A new configuration is proposed, consisting of a cantilever beam with a tip mass that is mounted vertically and excited in the transverse direction at its base. This device is highly non-linear with two potential wells for large tip masses, when the beam is buckled. The system dynamics may include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. The electromechanical equations of motion for this system are developed, and its response for a range of parameters is investigated using phase portraits and bifurcation diagrams. The model is validated using an experimental device with three different tip masses, representing three interesting cases: a linear system; a low natural frequency, non-buckled beam; and a buckled beam. The most practical configuration seems to be the pre-buckled case, where the proposed system has a low natural frequency, a high level of harvested power and an increased bandwidth over a linear harvester.

The influence of cracks in rotating shafts

In this paper, the influence of transverse cracks in a rotating shaft is analysed. The paper addresses the two distinct issues of the changes in modal properties and the influence of crack breathing on dynamic response during operation. Moreover, the evolution of the orbit of a cracked rotor near half of the first resonance frequency is investigated. The results provide a possible basis for an on-line monitoring system. In order to conduct this study, the dynamic response of a rotor with a breathing crack is evaluated by using the alternate frequency/time domain approach. It is shown that this method evaluates the nonlinear behaviour of the rotor system rapidly and efficiently by modelling the breathing crack with a truncated Fourier series. The dynamic response obtained by applying this method is compared with that evaluated through numerical integration. The resulting orbit during transient operation is presented and some distinguishing features of a cracked rotor are examined.

Fault diagnosis of rotating machinery

A tutorial discussion is given of some of the main faults which may be detected and diagnosed using observed vibrational data of a rotating machine. The paper is written with large turbo-machinery in view but many of the results discussed have relevance to other types of machine. The examination begins with the simplest, yet perhaps the most important, fault namcly mass unbalance. The elementary procedure for locating the source of unbalance will be reviewed and procedures for balancing will be briefly summarised. The distinction between unbalance and a shaft bend will be discussed and the consequences of permanent and temporary bends will be examined. A fault which is sometimes connected with rotor bends is rubbing and the characteristics of this phenomena will be outlined including some recent developments in the theory and the classification of the different categories of rub which can occur in practice. An overview will be given of the characteristics of a cracked rotor and examples of cracks which have been detected using vibration measurements will be described. No discussion of the dynamics of large machines would be complete without a description of the effects of misalignment. Both static and dynamic types are discussed together with their consequences.

Identification of dynamic bearing parameters: A review

In this paper, we present a review of the experimental identification of dynamic parameters of bearings in a rotating machine. Major emphasis is given to vibration-based identification methods and the review encompasses descriptions of experimental measurement techniques, mathematical modeling, parameter extraction algorithms and uncertainty in the estimates applied to a variety of bearings. The parameter extraction algorithms include the descriptions of governing equations of the rotor-bearing system and identification methods in both time and frequency domains. The identification techniques have been classified based on methods used to excite the system. The review includes a variety of bearings and similar components, which play an active link between the rotating and stationary parts of a machine. Based on the state of the art in bearing identification, conclusions are made and future directions are suggested.

Detection of severe sliding and pitting fatigue wear regimes through the use of broadband acoustic emission

Abstract Acoustic emission techniques have been used to monitor severe sliding and pitting fatigue processes during four-ball testing. Results are presented that arose from a collaborative programme between the Naval Research Laboratory (Washington, DC) and the University of Wales Swansea, sponsored by the US Office of Naval Research. The ultimate aim of the research is to develop a systematic fusion technology approach to condition-based maintenance of wear-related surface distress of critical components in naval air and surface combatant engine and transmission systems. The principal monitoring technique utilized in this investigation was acoustic emission (AE). A custom data acquisition system was developed using a novel approach to collect AE signals. Post-test analysis of the data, in the frequency domain, demonstrates the advantage of analysing continuous AE and not just AE pulses.

ENERGY HARVESTING IN PIEZOELASTIC SYSTEMS DRIVEN BY RANDOM EXCITATIONS

The inverted elastic beam is proposed as an energy harvester. The beam has a tip mass and piezoelectric layers which transduce the bending strains induced by the stochastic horizontal displacement into electrical charge. The efficiency of this nonlinear device is analyzed, focusing on the region of stochastic resonance where the beam motion has a large amplitude. Increasing the noise level allows the motion of the beam system to escape from single well oscillations and thus generate more power.

Estimating turbogenerator foundation parameters: model selection and regularization

Estimating a model of the foundation of large machines, such as turbogenerators, is vital for tasks such as fault diagnosis and modal balancing. Unfortunately, it is rarely possible to perform a modal test on the foundations without the rotor present. This paper considers a method to estimate a foundation model using response data from a run–down, using the inherent unbalance of the rotor to excite the foundations. The method requires an accurate model of the rotor and an approximate model of the bearings. Of critical importance is the quality of the model, which may be defined as the ability of the model to predict the response to unbalance excitations that are different from that present for the identification. It is shown in this paper that correct model selection and regularization are vital to produce a foundation model that meets this predictability criterion. The method is validated using simulated data and also experimental data from a test rig with a 4 m long rotor with four fluid film bearings.

The identification of the unbalance of a flexible rotating machine from a single rundown

The reliable estimation of a flexible foundation model and the state of unbalance (both amplitude and phase) of a turbogenerator from machine rundown measured vibration data is an active research area. Earlier studies on the estimation of both these quantities used the whole frequency range of the rundown as a single band. However, such an identification may be inaccurate for large flexible foundations having many modes in the rundown frequency range. For reliable identification, the whole frequency range has to be divided into a number of frequency bands and the frequency-dependent foundation models have to be estimated together with the unbalance. This paper combines the unbalance estimation with the split frequency range for the foundation model, and the highlights the limitations observed during estimation of foundation models and the state of unbalance. It is shown that the accuracy of the method may be enhanced by judicious choice of a weighting function. Having established the method in simulation, experimental data from a 3-m long test rig, with four journal bearings, is used to test the method. The approach seems to give reliable estimates of the machine unbalance.

Estimating turbogenerator foundation parameters

Abstract Turbogenerators in power stations are often placed on foundation structures that are flexible over the running range of the machine and can therefore contribute to its dynamics. Established methods of obtaining structural models for these foundations, such as the finite element method or modal testing, have proved unsuccessful because of complexity or cost. Another method of foundation system identification, using the unbalance excitation applied by the rotor itself during maintenance run-downs, has previously been proposed but has not yet been experimentally verified. In this paper the necessary theory is developed and certain issues critical to the success of the estimation are examined. The method is tested in both simulation and experiment using a two-bearing rotor rig and good fits between model and measurement are obtained. The predictive capacity of the estimated models when the system is excited with a different unbalance is not as good, and it is surmised that this may be due among other things to inaccurate bearing models.

Robust balancing for rotating machines

Abstract The balancing of rotors divides broadly into two categories: balancing in situ and balancing in a balancing machine. In the latter case, the most common practice is to arrange balance corrections on the rotor such that the net excitations of each of the four in-plane rigid-body modes of the free rotor is zero by deploying balance corrections on two independent planes. In a small proportion of cases, the net excitations of the first pair of flexural modes are also zeroed using a third correction plane. This paper proposes that, when rotors are balanced in a balancing machine (not similar to the machine stator), substantially more utility can be gained from the balancing operation by combining a suitably weighted account of the specific balancing requirements of the machine with knowledge of the expected machine characteristics than can be achieved by ignoring this knowledge. A single cost function is established based on a numerical model of the machine. Then, depending on circumstances, either the expected value of this cost function or its worst possible value can be minimized. The methods proposed require that relatively detailed knowledge of the distribution of residual unbalance be obtained experimentally. The paper briefly discusses some practical methods for how such information might be extracted. The definition of the cost function as a matrix quadratic form provides potentially valuable information about the necessary number and the optimal location of balance planes on a given rotor, and methods for determining an optimal set of balance planes are outlined.