Modern Practice in Stress and Vibration Analysis VI

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Authors: A.W. Lees
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.
Authors: Joanna F. Mason, Martin E. Homer, R.E. Wilson
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.
Authors: Daniel J. Inman, Matthew P. Cartmell, A.W. Lees, Th. Leize, L. Atepor
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.
Authors: M. Behzad, A.R. Ghias
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.
Authors: Fabio R. Chavarette, N.J. Peruzzi, José Manoel Balthazar, H.A. Hermini
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 transformation).
Authors: I.A. Jones, A.A. Becker, A.T. Glover, P. Wang, S.D. Benford, Michael Vloeberghs, C.M. Greenhalgh
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.
Authors: James Eaton-Evans, Janice M. Dulieu-Barton, Edward G. Little, Ian A. Brown
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.
Authors: Fernando Antunes, C. Pereira, Marcelo Calvete Gaspar
Authors: Y.N. Kyrychko, K.B. Blyuss, A. Gonzalez-Buelga, S.J. Hogan, David J. Wagg
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.

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