Improving Stability Prediction in Peripheral Milling of Al7075T6

Chatter is an old enemy to machinists but, even today, is far from being defeated. Current requirements around aerospace components call for stronger and thinner workpieces which are more prone to vibrations. This study presents the stability analysis for a single degree of freedom down-milling operation in a thin-walled workpiece. The stability charts were computed by means of the enhanced multistage homotopy perturbation (EMHP) method, which includes the helix angle but also, most importantly, the runout and cutting speed effects. Our experimental validation shows the importance of this kind of analysis through a comparison with a common analysis without them, especially when machining aluminum alloys. The proposed analysis demands more computation time, since it includes the calculation of cutting forces for each combination of axial depth of cut and spindle speed. This EMHP algorithm is compared with the semi-discretization, Chebyshev collocation, and full-discretization methods in terms of convergence and computation efficiency, and ultimately proves to be the most efficient method among the ones studied.The authors wish to acknowledge the financial support received from HAZITEK program, from the Department of Economic Development and Infrastructures of the Basque Government and from FEDER funds. Additional support was provided by the Tecnologico de Monterrey, through the Research Group in Nanomaterials and Devices Design

Analytical and numerical investigation of mixed-type functional differential equations

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of computational and applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of computational and applied mathematics, 234 (2010), doi: 10.1016/j.cam.2010.01.028This journal article is concerned with the approximate solution of a linear non-autonomous functional differential equation, with both advanced and delayed arguments

Is the jet-drive flute model able to produce modulated sounds like Flautas de Chinos ?

Flautas de chinos - prehispanic chilean flutes played during ritual celebrations in central Chile - are known to produce very particular beating sounds, the so-called sonido rajado. Some previous works have focused on the spectral analysis of these sounds, and on the input impedance of the complex resonator. However, the beating sounds origin remains to be investigated. Throughout this paper, a comparison is provided between the characteristics of both the sound produced by flautas de chinos and a synthesis sound obtained through time-domain simulation of the jet-drive model for flute-like instruments. Jet-drive model appears to be able to produce quasiperiodic sounds similar to sonido rajado. Finally, the analysis of the system dynamics through numerical continuation methods allows to explore the production mechanism of these quasiperiodic regimes.Comment: Stockholm Music Acoustics Conference, Stockholm : Sweden (2013

Spectrum-based stability analysis and stabilization of a class of time-periodic time delay systems

We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet multipliers can be characterized as eigenvalues of the monodromy operator and by the solutions of a finite-dimensional non-linear eigenvalue problem, where the evaluation of the characteristic matrix involves solving an initial value problem. We demonstrate that such a dual interpretation can be exploited in a two-stage approach for computing dominant Floquet multipliers, where global approximation is combined with local corrections. Correspondingly, we also propose two novel characterizations of left eigenvectors. Finally, from the nonlinear eigenvalue problem formulation, we derive computationally tractable expressions for derivatives of Floquet multipliers with respect to parameters, which are beneficial in the context of stability optimization. Several numerical examples show the efficacy and applicability of the presented results

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given

A Taylor series-based continuation method for solutions of dynamical systems

International audienceThis paper describes a generic Taylor series based continuation method, the so-called Asymptotic Numerical Method, to compute the bifurcation diagrams of nonlinear systems. The key point of this approach is the quadratic recast of the equations as it allows to treat in the same way a wide range of dynamical systems and their solutions. Implicit Differential-Algebraic Equations, forced or autonomous, possibly with time-delay or fractional order derivatives are handled in the same framework. The static, periodic and quasi-periodic solutions can be continued as well as transient solutions

Collocation methods for complex delay models of structured populations

openDottorato di ricerca in Informatica e scienze matematiche e fisicheopenAndo', Alessi