750 research outputs found
Estimates of the bistable region in metal cutting
No full textThe classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics. The standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature. The proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point. In the case of the one degree-of-freedom model of orthogonal cutting, the existence of unstable self-excited vibrations is proven along the stability limits, which is strongly related to the force characteristic at its inflexion point. An analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist. It is shown how this domain of bistability depends on the theoretical chip thickness. The comparison of these results with the experimental observations and also with the subcritical Hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearit
Stochastic semi‐discretization for linear stochastic delay differential equations
No full textAn efficient numerical method is presented to analyze the moment stability and stationary behavior of linear stochastic delay differential equations. The method is based on a special kind of discretization technique with respect to the past effects. The resulting approximate system is a high dimensional linear discrete stochastic mapping. The convergence properties of the method is demonstrated with the help of the stochastic Hayes equation and the stochastic delayed oscillator
Analytical investigation of single and double Neimark-Sacker bifurcations
No full textThe analytical investigation of bifurcations is a very challenging task for many applied scientists and engineers. Often, numerical simulations cannot clarify the complicated dynamics of mechanical systems, in this cases, preprogrammed softwares can be of valid help during the investigation. Also, in the literature, methodology to study bifurcations are presented for most of the cases. However, the presented procedures, are often very hard to be understood from applied scientists with low mathematical background. In this paper we present in details the typical procedure to analyze single and double Neimark-Sacker bifurcations. Especially regarding the double Neimark-Sacker bifurcations of maps, very few sources can be found in the literature, although this kind of bifurcation is very common in many dynamical systems. © Periodica Polytechnica 2012
Bifurcation analysis of a two-DoF mechanical system subject to digital position control. Part II. Effects of asymmetry and transition to chaos
No full textConsidering a two DoF system subject to digital position control, of interest for robotic application, we analyze the dynamics of the system at the intersection of two loci of Neimark-Sacker bifurcations, where a double Neimark-Sacker bifurcation is taking place. In the system, the saturation of the control force is the only nonlinear term considered, other than this, the system is piecewise linear. Starting from the analytical investigation already performed in Part I (Habib et al. in Nonlin. Dyn., under review, 2013), in this paper the effects of an asymmetry of the saturation of the control force are investigated, both analytically and numerically. The results show the increasing complexity of the dynamics for a more and more asymmetric system. First, the asymmetry is making the bifurcation transit from supercritical to subcritical, then it generates a stable torus that breaks down into a strange attractor, associated with a chaotic motion. In the last part of the paper, the torus breakdown and the onset of chaos are investigated, furthermore the evolution of complex dynamics through regions of phase locking and higher-dimensional chaos is outlined
Nonlinear bifurcation analysis of a single-dof model of a robotic arm subject to digital position control
No full textPrecision and stability in position control of robots are critical parameters in many industrial applications where high accuracy is needed. It is well known that digital effect is destabilizing and can cause instabilities. In this paper, we analyze a single DoF model of a robotic arm and we present the stability limits in the parameter space of the control gains. Furthermore we introduce a nonlinearity relative to the saturation of the control force in the model, reduce the dynamics of the nonlinear map to its local center manifold, study the bifurcation along the stability border and identify conditions under which a supercritical or subcritical bifurcation occurs. The obtained results explain some of the typical instabilities occurring in industrial applications. We verify the obtained results through numerical simulations. [DOI: 10.1115/1.4006430
BIFURCATION ANALYSIS OF A TWO-DOF SYSTEM SUBJECT TO DIGITAL POSITION CONTROL
No full textThis paper analyzes the stability of a two-DoF system, subject to PD digital position control. In the model the control force is considered piecewise constant. Introducing the nonlinearity related to the saturation of the control force, the bifurcations occurring in the system are analyzed. The system is generally loosing stability through Neimark-Sacker bifurcations, with a relatively simple dynamics. However; the interaction of two different Neimark-Sacker bifurcations steers the system to much more complicated behaviors. About this kind of bifurcation, namely double Neimark-Sacker bifurcation, there are very few studies in the literature. Our analysis is carried out using the method proposed by Kuznetsov. The performed investigation shows the appearance of quasiperiodic motions and the existence of regions with coexisting periodic stable attractors, in the space of the control gains. Numerical simulations validate the results obtained analytically
Why is it hard to identify the onset of chatter? A stochastic resonance perspective
No full textA stochastic dynamical model is presented to identify the difficulties in chatter detection during cutting processes. The theoretical implications are based on measurements related to the stochastic character of the cutting force. The stochastic model is validated in a Hardware-In-the-Loop (HIL) environment where the multiplicative component of the stochastic cutting force is varied parametrically. In case of an industrial machine tool, the stochastic resonance effect is also demonstrated quantitatively by means of high-resolution vibration measurements for various spindle speeds in full immersion milling. The proposed method predicts the noise induced peaks in the spectrum of the vibration signals, which occur already within the chatter-free parameter domains and might be misjudged as chatter
Sloshing dynamics estimation for liquid-filled containers under 2-dimensional excitation
No full textMany industrial applications require the displacement of liquid-filled containers on planar paths, by means of linear transport systems or serial robots. The movement of the liquid inside the container, known as sloshing, is usually undesired, so there is the necessity to keep under control the peaks that the liquid free surface exhibits during motion. This paper aims at validating a model for estimating the liquid sloshing height, taking into account 2-dimensional planar motions of a cylindrical container, with accelerations up to 9.5 m/s^2. This model can be exploited for assessment or optimization purposes. Experiments performed with a robot following three paths, each one of them with different motion profiles, are described. Comparisons between experimental results and model predictions are provided and discussed
Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in L2(ℝ)
No full textSampled Gabor phase retrieval — the problem of recovering a square-integrable signal from the magnitude of its Gabor transform sampled on a lattice — is a fundamental problem in signal processing, with important applications in areas such as imaging and audio processing. Recently, a classification of square-integrable signals which are not phase retrievable from Gabor measurements on parallel lines has been presented. This classification was used to exhibit a family of counterexamples to uniqueness in sampled Gabor phase retrieval. Here, we show that the set of counterexamples to uniqueness in sampled Gabor phase retrieval is dense in L2(ℝ), but is not equal to the whole of L2(ℝ) in general. Overall, our work contributes to a better understanding of the fundamental limits of sampled Gabor phase retrieval.Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Analysi
Sampling Delay and Backlash in Balancing Systems
No full textA mechanical model of a digital balancing system is constructed and its stability analysis is presented. This model considers experimental problems like backlash and sampling delay. The conditions of existence of stable stationary and periodic solutions are determined for the case of the system without delay. Phase diagrams and bifurcation diagrams are revealed after simulations and bifurcation analysis. Adding sampling delay to the system, the stability conditions are changed and above a critical value of the delay, the balancing is impossible. The stability conditions and the stability chart are determined again and the critical sampling delay is calculated versus the parameters describing the system
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