Active chatter control in high-speed milling processes

In present day manufacturing industry, an increasing demand for highprecision products at a high productivity level is seen. High-speed milling is a manufacturing technique which is commonly exploited to produce highprecision parts at a high productivity level for the aeroplane, automotive and mould and dies industry. The performance of a manufacturing process such as high-speed milling, indicated by the material removal rate, is limited by the occurrence of a dynamic instability phenomenon called chatter. The occurrence of chatter results in an inferior workpiece quality due to heavy vibrations of the cutter. Moreover, a high level of noise is produced and the tool wears out rapidly. Although different types of chatter exist, regenerative chatter is recognised as the most prevalent type of chatter. The occurrence of (regenerative) chatter has such a devastating effect on workpiece quality and tool wear that it should be avoidedat all times. The occurrence of chatter can be visualised in so-called stability lobes diagrams (sld). In an sld the chatter stability boundary between a stable cut (i.e. without chatter) and an unstable cut (i.e. with chatter) is visualised in terms of spindle speed and depth of cut. Using the information gathered in a sld, the machinist can select a chatter free operating point. In this thesis two problems are tackled. Firstly, due to e.g. heating of the spindle, tool wear, etc., the sld may vary in time. Consequently, a stable working point that was originally chosen by the machinist may become unstable. This requires a (controlled) adaptation of process parameters such that stability of the milling process is ensured (i.e. chatter is avoided) even under such changing process conditions. Secondly, the ever increasing demand for high-precision products at a high productivity level requires dedicated shaping of the chatter stability boundary. Such shaping of the sld should render working points (in terms of spindle speed and depth of cut) of high productivity feasible, while avoiding chatter. These problems require the design of dedicated control strategies that ensure stable high-speed milling operations with increased performance. In this work, two chatter control strategies are developed that guarantee high-speed chatter-free machining operations. The goal of the two chatter control strategies is, however, different. The first chatter control strategy guarantees chatter-free high-speed milling operations by automatic adaptation of spindle speed and feed (i.e. the feed is not stopped during the spindle speed transition). In this way, the high-speed milling process will remain stable despite changes in the process, e.g. due to heating of the spindle, tool wear, etc. To do so, an accurate and fast chatter detection algorithm is presented which predicts the occurrence of chatter before chatter marks are visible on the workpiece. Once the onset of chatter is detected, the developed controller adapts the spindle speed and feed such that a new chatter-free working point is attained. Experimental results confirm that by using this control strategy chatter-free machining is ensured. It is also shown experimentally that the detection algorithm is able to detect chatter before it is fully developed. Furthermore, the control strategy ensures that chatter is avoided, thereby ensuring a robust machining operation and a high surface quality. The second chatter control strategy is developed to design controllers that guarantee chatter-free cutting operations in an a priori defined range of process parameters (spindle speed and depth of cut) such that a higher productivity can be attained. Current (active) chatter control strategies for the milling process cannot provide such a strong guarantee of a priori stability for a predefined range of working points. The methodology is based on a robust control approach using µ-synthesis, where the most important process parameters (spindle speed and depth of cut) are treated as uncertainties. The proposed methodology will allow the machinist to define a desired working range (in spindle speed and depth of cut) and lift the sld locally in a dedicated fashion. Finally, experiments have been performed to validate the working principle of the active chatter control strategy in practice. Hereto, a milling spindle with an integrated active magnetic bearing is considered. Based on the obtained experimental results, it can be stated that the active chatter control methodology, as presented in this thesis, can indeed be applied to design controllers, which alter the sld such that a pre-defined domain of working points is stabilised. Results from milling tests underline this conclusion. By using the active chatter controller working points with a higher material removal rate become feasible while avoiding chatter. To summarise, the control strategies developed in this thesis, ensure robust chatter-free high-speed milling operations where, by dedicated shaping of the chatter stability boundary, working points with a higher productivity are attained

Control Theory: On the Way to New Application Fields

Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Recently, deep interactions are emerging with new application areas, such as systems biology, quantum control and information technology. In order to address the new challenges posed by the new application disciplines, a special focus of this workshop has been on the interaction between control theory and mathematical systems biology. To complement these more biology oriented focus, a series of lectures in this workshop was devoted to the control of networks of systems, fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control

Novel sources of near- and mid-infrared femtosecond pulses for applications in gas sensing, pulse shaping and material processing

In this thesis the design, construction process and the performance of two femtosecond optical parametric oscillators and one second–harmonic generation femtosecond pulse shaper is described. One oscillator was applied to gas sensing while potential applications of other devices are outlined. ATi:sapphire oscillator was used to pump a periodically–poled lithium niobate– based optical parametric oscillator. This signal–resonant device was configured to produce broadband idler pulses tunable in the range of 2.7–3.4 μm. This wavelength coverage was matched to the ν3 optical absorption band of methane, and Fourier–transform spectroscopy of a CH4:N2 mixture was implemented by employing a mid–IR silica photonic bandgap fibre simultaneously as a gas cell and an optical waveguide. Methane sensing below a 1% concentration was demonstrated and the main limiting factors were identified and improvements suggested. Another optical parametric oscillator was demonstrated which was pumped by a commercial Yb:fibre master oscillator/power amplifier system and was based on a periodically–poled lithium niobate crystal. The signal was tunable between 1.42–1.57 μm and was intended as a source for a subsequent project for waveguide writing in silicon. The oscillator was a novel long–cavity device operating at 15 MHz. The 130 nJ pump pulse energies allowed for 21 nJ signal pulses at a pump power of 2 W. The performance of the oscillator was characterised via temporal and spectral measurements and the next steps of its development are outlined. Finally a pulse shaper based on second harmonic generation in a grating– engineered periodically–poled lithium niobate crystal was demonstrated. Pulses from a 1.53 μm femtosecond Er:fibre laser were compressed and then used as the input to the shaper. The performance of the shaper was tested by performing cross–correlation frequency–resolved optical gating measurements on the output second harmonic pulses and this confirmed the successful creation of multiple pulses and other tailored shapes including square and chirped pulses, agreeing well with theoretical calculations

Opinion Dynamics and the Evolution of Social Power in Social Networks

A fundamental aspect of society is the exchange and discussion of opinions between individuals, occurring in mediums and situations as varied as company boardrooms, elementary school classrooms and online social media. This thesis studies several mathematical models of how an individual’s opinion(s) evolves via interaction with others in a social network, developed to reflect and capture different socio-psychological processes that occur during the interactions. In the first part, and inspired by Solomon E. Asch’s seminal experiments on conformity, a novel discrete-time model of opinion dynamics is proposed, with each individual having both an expressed and a private opinion on the same topic. Crucially, an individual’s expressed opinion is altered from the individual’s private opinion due to pressures to conform to the majority opinion of the social network. Exponential convergence of the opinion dynamical system to a unique configuration is established for general networks. Several conclusions are established, including how differences between an individual’s expressed and private opinions arise, and how to estimate disagreement among the private opinions at equilibrium. Asch’s experiments are revisited and re-examined, and then it is shown that a few extremists can create “pluralistic ignorance”, where people believe there is majority support for a position but in fact the position is privately rejected by the majority of individuals! The second part builds on the recently proposed discrete-time DeGroot–Friedkin model, which describes the evolution of an individual’s self-confidence (termed social power) in his/her opinion over the discussion of a sequence of issues. Using nonlinear contraction analysis, exponential convergence to a unique equilibrium is established for networks with constant topology. Networks with issue-varying topology (which remain constant for any given issue) are then studied; exponential convergence to a unique limiting trajectory is established. In a social context, this means that each individual forgets his/her initial social power exponentially fast; in the limit, his/her social power for a given issue depends only on the previously occurring sequence of dynamic topology. Two further related works are considered; a network modification problem, and a different convergence proof based on Lefschetz Fixed Point Theory. In the final part, a continuous-time model is proposed to capture simultaneous discussion of logically interdependent topics; the interdependence is captured by a “logic matrix”. When no individual remains attached to his/her initial opinion, a necessary and sufficient condition for the network to reach a consensus of opinions is provided. This condition depends on the interplay between the network interactions and the logic matrix; if the network interactions are too strong when compared to the logical couplings, instability can result. Last, when some individuals remain attached to their initial opinions, sufficient conditions are given for opinions to converge to a state of persistent disagreement

The quantitative analysis of transonic flows by holographic interferometry

This thesis explores the feasibility of routine transonic flow analysis by holographic interferometry. Holography is potentially an important quantitative flow diagnostic, because whole-field data is acquired non-intrusively without the use of particle seeding. Holographic recording geometries are assessed and an image plane specular illumination configuration is shown to reduce speckle noise and maximise the depth-of-field of the reconstructed images. Initially, a NACA 0012 aerofoil is wind tunnel tested to investigate the analysis of two-dimensional flows. A method is developed for extracting whole-field density data from the reconstructed interferograms. Fringe analysis errors axe quantified using a combination of experimental and computer generated imagery. The results are compared quantitatively with a laminar boundary layer Navier-Stokes computational fluid dynamics (CFD) prediction. Agreement of the data is excellent, except in the separated wake where the experimental boundary layer has undergone turbulent transition. A second wind tunnel test, on a cone-cylinder model, demonstrates the feasibility of recording multi-directional interferometric projections using holographic optical elements (HOE’s). The prototype system is highly compact and combines the versatility of diffractive elements with the efficiency of refractive components. The processed interferograms are compared to an integrated Euler CFD prediction and it is shown that the experimental shock cone is elliptical due to flow confinement. Tomographic reconstruction algorithms are reviewed for analysing density projections of a three-dimensional flow. Algebraic reconstruction methods are studied in greater detail, because they produce accurate results when the data is ill-posed. The performance of these algorithms is assessed using CFD input data and it is shown that a reconstruction accuracy of approximately 1% may be obtained when sixteen projections are recorded over a viewing angle of ±58°. The effect of noise on the data is also quantified and methods are suggested for visualising and reconstructing obstructed flow regions

Stability and superconductivity of light-atom systems under extreme pressure

The use of high pressure in physics provides access to unusual chemistry, rich phase behaviour, and various interesting phenomena. One of the most sought after phenomena of recent years is high-temperature superconductivity, which has been predicted in solid hydrogen and experimentally verified in numerous metal hydrides. This thesis adds to the knowledge of these high-pressure light-atom systems and introduces new tools for predicting their superconducting properties. It showcases the calculation of an anharmonic phase diagram of solid hydrogen, demonstrates that current theoretical techniques can produce structures and superconducting critical temperatures (Tc) in agreement with experiment for the record-holding binary hydride LaH10, and reveals a metastable hexagonal phase of this material that provides an explanation for recent experimental observations. It also addresses the real need to reduce the operational pressure of superconducting hydrides and offers a solution through the use of machine learning methods, leading to the discovery of several superconductors inhabiting favourable regions of P-Tc space. It is common for papers in this field to focus on the stability and superconductivity of a limited number of metal hydrides, largely because the electron-phonon calculations involved are computationally expensive and because it is not clear which hydrides are potential high-Tc candidates before performing these calculations. This drastically slows down the rate of discovery. The work presented in this thesis provides a solution to this problem; by identifying physically motivated descriptors from scattering theory and density of states calculations, we are able to construct a model for Tc and therefore obtain a method for cheaply identifying the most promising candidate structures. Incorporating this screening step into a high-throughput workflow allows us to study superconductivity in binary hydrides from across the whole periodic table, resulting in one of the most comprehensive studies of superconductivity in binary hydrides ever produced and leading to the identification of several above- and near-room-temperature candidates. The methods developed in this thesis could be expanded to other classes of materials, including ternary hydrides and other light binaries, and used as a guide to designing high-throughput workflows for other material properties. The findings may bring us closer to the ultimate goal of first-principles material design.PhD studentship provided by the Engineering and Physical Sciences Research Council (EPSRC

Non-linear system identification in structural dynamics: advances in characterisation of non-linearities and non-linear modal analysis

Many new methods for theoretical modelling, numerical analysis and experimental testing have been developed in non-linear dynamics in recent years. Although the computational power has greatly improved our ability to predict non-linear behaviour, non-linear system identification, a central topic of this thesis, still plays a key role in obtaining and quantifying structural models from experimental data. The first part of the thesis is motivated by the industrial needs for fast and reliable detection and characterisation of structural non-linearities. For this purpose a method based on the Hilbert transform in the frequency domain is proposed. The method detects and characterises structural non-linearities from a single frequency response function and does not require a priori knowledge of the system. The second part of the thesis is driven by current research trends and advances in non-linear modal analysis and adaptive time series processing using the Hilbert-Huang transform. Firstly, the alternatives of the Hilbert transform, which is commonly used in structural dynamics for the estimation of the instantaneous frequency and amplitude despite suffering from a number of numerical issues, are compared to assess their potential for non-linear system identification. Then, a possible relation between the Hilbert-Huang transform and complex non-linear modes of mechanical systems is investigated. Based on this relation, an approach to experimental non-linear modal analysis is proposed. Since this approach integrates the Hilbert-Huang transform and non-linear modes, it allows not only to detect and characterise structural non-linearities in a non-parametric manner, but also to quantify the parameters of a selected model using extracted non-linear modes. Lastly, a new method for the identification of systems with asymmetric non-linear restoring forces is proposed. The application of all proposed methods is demonstrated on simulated and experimental data.Open Acces

On the integration of deformation and relief measurement using ESPI

The combination of relief and deformation measurement is investigated for improving the accuracy of Electronic Speckle-Pattern Interferometry (ESPI) data. The nature of sensitivity variations within different types of interferometers and with different shapes of objects is analysed, revealing significant variations for some common interferometers. Novel techniques are developed for real-time measurement of dynamic events by means of carrier fringes. This allows quantification of deformation and relief, where the latter is used in the correction of the sensitivity variations of the former

An investigation into the applicability of the Fourier transform to dispersive water waves and their short term prediction

After many years of slow but progressive development, the wave energy industry is on the cusp of breaking through the economic and technical barriers to full scale deployment of wave energy electrical generating devices. As the major obstacles in device design are solved, and with several devices in the water, the scope for increasing their efficiency through advanced control techniques is now becoming clearer. In some cases, it would be advantageous to integrate an advanced prediction of wave behaviour (of some tens of seconds into the future) into these control methods. Past research on wave prediction has focused on utilising the Fourier theorem to deconstruct wave records and then make predictions ahead in space, with published results indicating promise. However, predicting ahead in time has so far not been achieved. This thesis takes the Fourier theorem method of prediction to its logical conclusion by exploring its limitations in predicting over both time and space. A discussion as to why these limits should exist, and possible work into the solution of the wave prediction problem, are also presented. A review of current devices under development, and the history and emergence of the wave generating industry (which is a comparatively recent technology and still in its infancy), are also included as appendices to the main thesis in order to put the work into context