Smart machines promise increased functionality, such as conditioning monitoring and vibration control. Several technologies are relevant to smart machines including magnetic bearings, Shape Memory Alloys (SMA) and piezoelectric activation. A range of solutions is available for rigid rotors, usually based on smart or active bearings or pedestals. However, the control of flexible rotors requires some modification on the rotor itself. In this paper, equations of motion are developed to describe a rotor with a strain actuator (for example, a piezoelectric element) mounted on it. It is shown that such a system may be used to compensate for imbalance by inducing a rotor bend. This paper discusses the optimum control strategies for such a system.

The underlying reason for pursuing Condition Monitoring activities is to enhance the overall performance of plant either by accurately predicting the end of effective life or by diagnosis and location of incipient faults. The achievement of both these objectives requires the use of a combination of measurement, modelling and statistical techniques, but the balance of these three strands varies with the plant under study. Practitioners of these different disciplines sometimes develop rivalries, but in reality all three are essential. The fundamental problem involved is the determination of the physical process within a machine which cannot be measured directly and so must be inferred from external measurements, the most common of which is vibration. This inference from measurement to diagnosis requires some form of model, whether physics or statistics based. The paper describes some work on the monitoring of large turbines and in particular, the ways in which measurements and models can be combined to enhance insight into a machine’s operation. Similarly, our understanding of complex data can be enhanced by the use of Artificial Neural Networks and these can be used to enhance understanding. Combining various approaches leads to some new possibilities which are briefly outlined.

The concept of smart machinery is of current interest. Several technologies are relevant in this quest including magnetic bearings, shape memory alloys (SMA) and piezoelectric activation. Recently a smart bearing pedestal was proposed based on SMAs and elastomeric O-rings. However, such a device is clearly relevant only for the control of rigid rotors; for flexible rotors there is a need for some modification on the rotor itself. In this paper, equations of motion are developed to describe a rotor with a force generator (for example, a piezoelectric element) mounted on it. It is shown that such a system may be used to compensate for imbalance by inducing a rotor bend. This leads to some questions as to the optimum control strategies, and the paper discusses some of the possibilities.

We examine the dynamics of the elastic inverted pendulum with a tip mass under horizontal harmonic excitation. In particular, we study the conditions when the potential barrier is overcome by the tip mass, and large amplitude oscillations occur, by means of the Melnikov criterion. The results have been confirmed by numerical simulations.

Rolling contact bearing failures are simulated using four-ball machine experiments to generate acoustic emission (AE) signals for a naturally developing fault. Experiments are modified by introducing a weakness to the ball race component in an attempt to reduce test duration. AE is recorded periodically in a customised DAQ system using LabVIEW software. A study of the four-ball geometry and kinematics determines the optimal data sampling parameters and the modulating frequencies associated with faults. Analysis using envelope techniques demonstrates that AE clearly indicates the presence of a subsurface fault approximately 30 seconds before a surface defect develops in the current tests.

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 work reported in this paper represents research performed at Swansea University in collaboration with SKF Engineering & Research Centre as part of a continuing investigation into the early detection of potential bearing faults using high frequency Acoustic Emission (AE). The aim is to identify the nature of AE associated with subsurface cracking in a complex dynamic environment, which may help in the development of a system which could identify such a risk in a real life application. The experimental technique involves a modified four-ball lubricant tester at loads intended to produce a failure (spall) within a period of several hours. Constant AE arises from surface wear due to high loads, however as the majority of failures occur within the top ball it is hoped that AE arising from subsurface cracking can be identified at stress increases where cyclic contact occurs with the lower balls in the system.This involves an understanding of the rotational nature of the four-ball system, and appropriate timing of the data acquisition in order to collect data for a known number of rotations of the top ball and system of lower balls. Cross-correlation and cyclostationary techniques can then be used in post-processing to help identify these properties

Vibration and noise induced by errors and faults in gear meshes are key concerns for the performance of many rotating machines and the prediction of developing faults. Of particular concern are displacement errors in the gear mesh and for rigid gears these may be modelled to give a linear set of differential equations with forced excitation. Other faults, such as backlash or friction, may also arise and give non-linear models with rich dynamics. This paper considers the particular case of gear errors modelled as a Fourier series based on the tooth meshing frequency, leading immediately to non-linear equations of motion, even without the presence of other non-linear phenomena. By considering the perturbed response this system may be modelled as a parametrically excited system. This paper motivates the analysis, derives the equations of motion for the case of a single gear mesh, and provides example response simulations of a boiler feed pump including phase portraits and power spectra.

This paper reports research currently in progress at Swansea University in collaboration with SKF Engineering & Research Centre as part of a continuing investigation into high frequency Acoustic Emission. The primary concerns are experimentally producing subsurface cracks, the type of which would occur in a service failure of a ball bearing, within a steel ball and to closely monitor the properties of this AE from crack initiation to the formation of a ball on the ball surface. It is worth noting that there is evidence that the frequency content of the AE changes during this period, although this has yet to be proved consistent or even fully explained. Conclusive evidence could lead to a system which detects such cracks in a bearing operating in real life conditions, advantageous for many reasons including safety, downtime and maintenance and associated costs.The results from two experimental procedures are presented, one of which loads a single ball held stationary in a test rig to induce subsurface cracks, which are in turn detected by a pair of broadband AE sensors and recorded via a Labview based software system. This approach not only allows detailed analysis of the AE waveforms but also approximate AE source location from the time difference between two sensors.The second experimental procedure details an adaptation of a four-ball lubricant tester in an attempt to produce naturally occurring subsurface cracks from rolling contact whilst minimising the AE arising from surface wear. This thought behind this experiment is reinforced with 3D computational modelling of the rotating system.

In Chapters 3 and 5, methods are presented to determine the dynamic characteristics of a rotor–bearing system, such as the natural frequencies, damping factors, and mode shapes. In this chapter, we examine how rotor–bearing systems respond to forces and moments. The most common forces acting in rotating machines are lateral forces and moments whose frequencies are locked to the rotor speed or multiples of rotor speed. A force whose frequency is identical to rotor speed is said to be a synchronous force. We also examine how rotor–bearing systems respond to forces the frequency of which is unrelated to rotor speed, called asynchronous forces – for example, external forces acting on the rotor via the bearings and foundation.

This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.

Damping in the stator of a rotating machine is able to reduce the unbalance response, and increase the speed where the stability limit is reached. However, damping in the rotor is destablising and the analysis of rotors with internal viscous damping is well established. The drive towards composite and laminated rotors mean that the viscous damping model is not always appropriate, and viscoelastic material models whose properties depend on frequency should be used. These properties may be measured experimentally and the analysis of structures containing viscoelastic material materials may be performed in the time domain using the ADF, ATF or GHM methods. This paper extends this analysis to rotors containing viscoelastic materials using the ATF approach. Other internal variable formulations for viscoelastic material may be used following the approach adopted in this paper with only slight modifications. Viscous damping in the rotor produces a skew-symmetric component in the ‘stiffness’ matrix; for viscoelastic models the skew-symmetric term appears in the internal variable equations. This paper gives an example to demonstrate the calculation of the stability limit speed for a machine.

In this chapter, the stability of rotating machinery is considered. In stable systems, an initial disturbance decays to zero in the absence of excitation forces. By contrast, in an unstable system, the response grows, producing a large and undesirable response that may damage a machine. A simple example of instability is the motion of a pendulum. One equilibrium position is when the pendulum hangs vertically downward. This position is stable because if the pendulum is slightly displaced, it returns to the equilibrium position. In contrast, there is an equilibrium position when the pendulum is balanced vertically upward. This position is unstable because any slight disturbance from the vertical causes the pendulum to move away from the vertical and, in fact, rotate to the lower equilibrium position. For a linear system with constant coefficients, instability may be determined by considering the eigenvalues, computed in the usual way. Thus, the same or similar calculations used to determine eigenvalues of a system also provide a user with information about the stability of the system. As demonstrated in Chapter 2, the imaginary part of the eigenvalue gives the frequency of free oscillations, whereas the real part determines how rapidly the oscillations decay. The oscillations decay only if the real part of the eigenvalue is negative. A zero real part of the eigenvalue gives an undamped response in which the magnitude of the free oscillation remains constant and a positive real part causes the oscillation to grow.

This experimental study examines the detailed Nusselt number (Nu) distributions for a tilted reciprocating square-sectioned thermosyphon duct with a jet entry flow. Detailed heat transfer measurements over the thermosyphon wall at the jet Reynolds numbers of 15,000, 20,000, 25,000, 30,000, 35,000 with the reciprocating frequencies of 0, 0.33, 0.5, 0.67 and 0.83Hz are performed using the steady-state infrared thermo-graphic method. The coupling effects of jet-inertial, reciprocating and buoyancy forces in the tilted reciprocating thermosyphon exhibit synergistic influences on heat transfer performances. A selection of experimental data illustrates the full-field Nu variations responding to the changes of jet Reynolds (Rej), pulsating (Pu) and reciprocating Grashof (Grp) numbers. Parametric analysis is subsequently followed to identify the individual and interdependent Re, Pu and Grp effects on the area-averaged Nusselt number (Nu¯) in the attempt to generates the physically consistent Nu¯ correlation to assist the design of the shaker-jet piston cooling system. Within the parametric ranges tested, Nu¯ over the tilted reciprocating thermosyphon is raised to 1.25–2.85 times of the heat transfer levels in the static thermosyphon, which confirm the improved heat transfer performance by reciprocation for such cooling configuration.

This comparative study examines the detailed Nusselt number (Nu) distributions, pressure drop coefficients (f) and thermal performance factors (η) for two furrowed rectangular channels with transverse and skewed sinusoidal wavy walls. Detailed heat transfer measurements over these transverse and skewed sinusoidal wavy walls at the Reynolds numbers (Re)=1000, 1500, 2000, 5000, 10,000, 15,000, 20,000, 25,000 and 30,000 are performed using the steady-state infrared thermo-graphic method. Impacts of Re on Nu and f for two tested furrowed channels with transverse and skewed waviness are individually examined. In addition to the macroscopic mixing between the near-wall recirculations and core flows due to the shear layer instabilities in each wavy channel, the secondary flows tripped by the skewed wall-waves further elevate heat transfer performances and distinguish their Nu distributions from those over the transverse wavy wall. The area-averaged Nusselt numbers (Nu¯) for two tested furrowed channels with transverse and skewed waviness with 5000<Re<30000 fall, respectively, in the ranges of 3.45–3.71 and 3.98–4.2 times of the Dittus–Boelter levels. A set of Nu¯ and f correlations for each tested furrowed channel is individually derived using Re as the controlling parameter. By way of comparing the thermal performance factors (η) with a selection of rib-roughened channels, the η factors for the present skewed wavy channel are compatible with those in the channel roughened by the compound V-ribs and deepened scales due to the relative low pressure drop penalties with the equivalent heat transfer augmentations to those offered by V-ribs.