Abstract: Misalignment of multi-bearing rotor systems is one of the most common fault conditions
yet it is still not fully understood. There are numerous (and sometimes confusing) accounts in the
literature asserting the presence of harmonics in the vibration signal, but no quantitative
descriptions are offered. Harmonics may arise, of course, from the nonlinearities in fluid film
journal bearings or from the kinematics of flexible couplings, but in this paper only rigidly coupled
rotors mounted on idealised linear bearings. It is shown that even for this case, excitation at twice
synchronous speed is developed and an expression for the magnitude and phase of the response is
derived. Several examples are then studied to give some insight into the magnitude of these
harmonic terms which can arise. It is argued that it is precisely because the harmonic terms can
arise from diverse sources, a full description of the phenomena has proved somewhat elusive.
A brief discussion of the type of rig required to validate the model is given. There is a need to
separate the phenomena discussed here from the nonlinearities found in real machines. Some
features of the new facility are described.
Abstract: This paper is concerned with the modelling of gear rattle in Roots blower vacuum
pumps. Analysis of experimental data reveals that the source of the noise and vibration problem
is the backlash nonlinearity due to gear teeth losing and re-establishing contact.We develop non-
smooth ordinary differential equation models for the dynamics of the pump. The models include
a time-dependent forcing term which arises from the imperfect, eccentric mounting of the gears.
We use a combination of explicit construction, asymptotic methods and numerical techniques
to classify complicated dynamic behaviour in realistic parametric regimes. We first present a
linear analysis of motions where the gears do not lose contact, and develop upper bounds on
eccentricity for quiet operation. We then develop a nonlinear analysis of ‘backlash oscillations’,
where the gears lose and re-establish contact, corresponding to noisy pump operation. It is
found that noisy solutions can coexist with silent ones, explaining why geared systems can rattle
intermittently. We then consider several possible design solutions, and show their implications
for pump design in terms of the existence and stability of silent and noisy solutions. Finally,
we present conclusions and possibilities for future work.
Abstract: Recent EPSRC funded research at Glasgow University, Swansea University, and Virginia
Polytechnic and State University, and collaborative work with the Karlsruhe University of Applied
Sciences, on the application of shape memory alloy (SMA) elements integrated within glass epoxy
composite plates and shells is currently leading to the design of a novel smart bearing based on the
principle of antagonistic action. In this system a ball bearing is fitted halfway down a glass epoxy
composite tube, entering through one end of the tube. The tube has both ends rigidly built in to the
support frame. The tube is divided into two regions, one on each side of the centrally located
bearing. SMA strips are bonded in two independent sets of four, each set running axially along half
the length of the tube and separated by 90 º around the tube. The four strips in each set are
electrically connected in series to a high current power supply that can be switched in or out, and
the current set, as required. This provides a convenient and fast way of heating each set of SMA
strips through the martensite-to-austenite transformation temperature, and provides a significant
axial contraction load on the tube in either direction. Previous FE analysis has provided predictions
for converting an axial contraction load into useful stiffening of the structure in the radial and hoop
directions. This introduces the potential for modification of the dynamic performance of the
flexible rotor. In addition to separate heating each half of the active bearing has its own
independent forced-air cooling system. Previous work by one of the authors, and others, has shown
that a single SMA/composite active bearing can be very effective in both altering the natural
frequency of the fundamental whirl mode as well as the modal amplitude. The drawback with that
design has been the disparity in the time constant between the relatively fast heating phase and the
much slower cooling phase which is reliant on forced air, or some other form of cooling. This form
of design means that the cooling phase of one half, still using forced air, is significantly assisted by
switching the other half into its heating phase, and vice versa, thereby equalising the time constants,
and giving a faster push-pull load on the centrally located bearing; a loading which is termed
‘antagonistic’ in this paper. The experimental system is discussed in terms of potential performance
and control issues.
Abstract: Adaptive time-frequency representations have many advantages compared with
conventional methods. In this paper, a new method is proposed to adapt Smoothed Pseudo Wigner-
Ville distribution to match signal’s time-frequency content. It is based on maximizing a local timefrequency
concentration measure for different time and frequency smoothing window lengths.
Subsequently, the optimized values are used for constructing an adaptive kernel over time. The
proposed transform is then applied to vibration signals of healthy and cracked shafts which are
acquired through run-up, and the crack signature is obtained. Results show that enhanced
improvement in resolution is obtained while the computational cost is not very high.
Abstract: The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the
membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with
a view to their biological implications and as a test bed for numerical methods, which can be
applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the
dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the
membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of
Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev
polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F
Abstract: Boundary element (BE) analysis is well known as a tool for assessing the stiffness and
strength of engineering components, but, along with finite element (FE) techniques, it is also finding
new applications as a means of simulating the behaviour of deformable objects within virtual reality
simulations since it exploits precisely the same kind of surface-only definition used for visual
rendering of three-dimensional solid objects. This paper briefly reviews existing applications of BE
and FE within virtual reality, and describes recent work on the BE-based simulation of aspects of
surgical operations on the brain, making use of commercial hand-held force-feedback interfaces
(haptic devices) to measure the positions of the virtual surgical tools and provide tactile feedback to
the user. The paper presents an overview of the project then concentrates on recent developments,
including the incorporation of simulated tumours in the virtual brain.
Abstract: Thermoelastic Stress Analysis (TSA) is a non-contacting technique that provides full
field stress information and can record high-resolution measurements from small structures. The
work presented in this paper summarises the application of TSA to two types of small medical
devices that are used to treat diseased arteries; angioplasty balloons and vascular stents. The use of
high resolution optics is described along with a calibration methodology that allows quantitative
stress measurements to be taken from the balloon structure. A brief account of a study undertaken to
characterise the thermoelastic response from Nitinol is also included and it is demonstrated that
thermoelastic data can be obtained from a stent at high resolutions.
Abstract: In this paper delay differential equations approach is used to model a real-time
dynamic substructuring experiment. Real-time dynamic substructuring involves dividing the
structure under testing into two or more parts. One part is physically constructed in the lab-
oratory and the remaining parts are being replaced by their numerical models. The numerical
and physical parts are connected via an actuator. One of the main difficulties of this testing
technique is the presence of delay in a closed loop system. We apply real-time dynamic sub-
structuring to a nonlinear system consisting of a pendulum attached to a mass-spring-damper.
We will show how a delay can have (de)stabilising effect on the behaviour of the whole system.
Theoretical results agree very well with experimental data.