Analytical prediction of chatter stability for variable pitch and variable helix milling tools

Regenerative chatter is a self-excited vibration that can occur during milling and other machining processes. It leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Variable pitch and variable helix milling tools have been previously proposed to avoid the onset of regenerative chatter. Although variable pitch tools have been considered in some detail in previous research, this has generally focussed on behaviour at high radial immersions. In contrast there has been very little work focussed on predicting the stability of variable helix tools. In the present study, three solution processes are proposed for predicting the stability of variable pitch or helix milling tools. The first is a semi-discretisation formulation that performs spatial and temporal discretisation of the tool. Unlike previously published methods this can predict the stability of variable pitch or variable helix tools, at low or high radial immersions. The second is a time-averaged semi-discretisation formulation that assumes time-averaged cutting force coefficients. Unlike previous work, this can predict stability of variable helix tools at high radial immersion. The third is a temporal-finite element formulation that can predict the stability of variable pitch tools with a constant uniform helix angle, at low radial immersion. The model predictions are compared to previously published work on variable pitch tools, along with time-domain model simulations. Good agreement is found with both previously published results and the time-domain model. Furthermore, cyclic-fold bifurcations were found to exist for both variable pitch and variable helix tools at lower radial immersions

Dual-hop transmissions with fixed-gain relays over Generalized-Gamma fading channels

In this paper, a study on the end-to-end performance of dual-hop wireless communication systems equipped with fixed-gain relays and operating over Generalized-Gamma (GG) fading channels is presented. A novel closed form expression for the moments of the end-to-end signal-to-noise ratio (SNR) is derived. The average bit error probability for coherent and non-coherent modulation schemes as well as the end-to-end outage probability of the considered system are also studied. Extensive numerically evaluated and computer simulations results are presented that verify the accuracy of the proposed mathematical analysis.\u

Level Crossing Rate and Average Fade Duration of the Multihop Rayleigh Fading Channel

We present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one, which can be modelled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and AFD of the product of N Rayleigh fading envelopes, or of the recently so-called N*Rayleigh channel. Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

Multilevel Converters: An Enabling Technology for High-Power Applications

| Multilevel converters are considered today as the state-of-the-art power-conversion systems for high-power and power-quality demanding applications. This paper presents a tutorial on this technology, covering the operating principle and the different power circuit topologies, modulation methods, technical issues and industry applications. Special attention is given to established technology already found in industry with more in-depth and self-contained information, while recent advances and state-of-the-art contributions are addressed with useful references. This paper serves as an introduction to the subject for the not-familiarized reader, as well as an update or reference for academics and practicing engineers working in the field of industrial and power electronics.Ministerio de Ciencia y Tecnología DPI2001-3089Ministerio de Eduación y Ciencia d TEC2006-0386

ZF DFE transceiver design for MIMO relay systems with direct source-destination link

In this paper we consider a non-linear transceiver design for non-regenerative multiple-input multiple-output (MIMO) relay networks where a direct link exists between the source and destination. Our system utilises linear processors at the source and relay as well as a zero-forcing (ZF) decision feedback equaliser (DFE) at the receiver. Under the assumption that full channel state information (CSI) is available the precoding and equaliser matrices are designed to minimise the arithmetic mean square error (MSE) whilst meeting transmit power constraints at the source and destination. The source, relay, and destination processors are provided in closed form solution. In the absence of the direct link our design particularises to a previous ZF DFE solution and as such can be viewed as a generalisation of an existing work. We demonstrate the effectiveness of the proposed solution through simulation and show that it outperforms existing techniques in terms of bit error ratio (BER)

On the Second Order Statistics of the Multihop Rayleigh Fading Channel

Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N*Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations

Tomlinson Harashima precoding design for non-regenerative MIMO relay networks

In this paper we consider the design of minimum mean square error (MMSE) transceivers for non-regenerative multiple input multiple output (MIMO) relay systems. Our design utilises Tomlinson Harashima precoding (THP) at the source along with linear processors in each stage of the network. Assuming full channel state information (CSI) is available at each node in the network the various processors are jointly optimised to minimise the system arithmetic mean square error (MSE) whilst abiding by average power constraints at both the source and relay terminals in the network. Simulations show that the proposed schemes outperform existing methods in terms of bit error ratio (BER)

Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems

Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur as well in other signal processing applications and are typically solved using different modifications of the branch-and-bound method. This method, however, does not have any polynomial time complexity guarantees. In this paper, we show that a class of DC programming problems, to which the sum-rate maximization in two-way MIMO relaying belongs, can be solved very efficiently in polynomial time, and develop two algorithms. The objective function of the problem is represented as a product of quadratic ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial-Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We also derive an upper-bound for the optimal values of the corresponding optimization problem and show by simulations that this upper-bound can be achieved by both algorithms. The proposed methods for maximizing the sum-rate in the two-way AF MIMO relaying system are shown to be superior to other state-of-the-art algorithms.Comment: 35 pages, 10 figures, Submitted to the IEEE Trans. Signal Processing in Nov. 201