Experimental Study on Free Vibratory Behavior of Nonlinear Structure

The basic behavior of free vibratory nonlinear system is investigated in this work. The main approach was to reveal the order of fitting necessary to properly approximate the actual behavior of a nonlinear mechanical system. Tests were performed in an experimental setup subjected to geometric hardening nonlinearities. The investigation showed that, it is essential to approximate the nonlinearity correctly. Low order approximation can result in large errors in the predicted amplitudes. The nonlinear static stiffness characteristics was measured and fit with polynomial describing function. The free vibratory response was deviated from the one calculated by cubic fitting. The presented higher order approximation of the amplitude-frequency parametric relation is revealed so that, in this particular example, seventh degree approximation is sufficiently closer to the experienced behavior. The analytical solution including the first and second order internal resonances were checked and compared with continuation results of the backbone curve

Upgraded Kalman filtering of cutting forces in milling

Advanced piezoelectric dynamometers with a wide frequency bandwidth are required for cutting force measurement in high-speed milling and micromilling applications. In many applications, the signal bandwidth is limited by the dynamic response of the mechanical system, thus compensation techniques are necessary. The most effective compensation techniques for a full 3D force correction require an accurate and complex identification phase. Extended Kalman filtering is a better alternative for input force estimation in the presence of unknown dynamic disturbances. The maximum bandwidth that can be currently achievable by Kalman filtering is approximately 2 kHz, due to crosstalk disturbances and complex dynamometer\u2019s dynamics. In this work, a novel upgraded Kalman filter based on a more general model of dynamometer dynamics is conceived, by also taking into account the influence of the force application point. By so doing, it was possible to extend the frequency bandwidth of the device up to more than 5 kHz along the main directions and up to more than 3 kHz along the transverse directions, outperforming state-of-the-art methods based on Kalman filtering

Bi-stability induced by motion limiting constraints on boring bar tuned mass dampers

This paper investigates the effect of displacement constraints on the attenuation performance of tuned mass dampers (TMDs) used in boring and turning applications. A simplified piecewise- smooth mechanical model is investigated through time domain simulations and hybrid periodic orbit continuation, first under harmonic excitation, then under regenerative cutting load. A quasi-frequency response function is derived for impacting TMDs through composition of different families of period-1 orbits, then an acceptability map for turning is formulated based on the appearance of cutting-edge contact-loss and fly-over events. The bi-stable domain boundaries are determined through two parameter continuation of contact-loss grazing events. It is shown that in both cases arising rigid body collisions can significantly hinder TMD damping performance and lead to resonance problems or machine tool chatter

Optimum selection of variable pitch for chatter suppression in face milling operations

Cutting capacity can be seriously limited in heavy duty face milling processes due to self-excited structural vibrations. Special geometry tools and, specifically, variable pitch milling tools have been extensively used in aeronautic applications with the purpose of removing these detrimental chatter vibrations, where high frequency chatter related to slender tools or thin walls limits productivity. However, the application of this technique in heavy duty face milling operations has not been thoroughly explored. In this paper, a method for the definition of the optimum angles between inserts is presented, based on the optimum pitch angle and the stabilizability diagrams. These diagrams are obtained through the brute force (BF) iterative method, which basically consists of an iterative maximization of the stability by using the semidiscretization method. From the observed results, hints for the selection of the optimum pitch pattern and the optimum values of the angles between inserts are presented. A practical application is implemented and the cutting performance when using an optimized variable pitch tool is assessed. It is concluded that with an optimum selection of the pitch, the material removal rate can be improved up to three times. Finally, the existence of two more different stability lobe families related to the saddle-node and flip type stability losses is demonstrated

Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation

We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of Fiedler et al. [PRL 98, 114101 (2007)], who demonstrated that such feedback control can stabilize the UPO associated with a two-dimensional subcritical Hopf normal form. Pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization, as well as knowledge of the period of the targeted UPO. We apply feedback in the directions tangent to the two-dimensional center manifold. We parameterize the feedback gain by a modulus and a phase angle, and give explicit formulae for choosing these two parameters given the period of the UPO in a neighborhood of the bifurcation point. We show, first heuristically, and then rigorously by a center manifold reduction for delay differential equations, that the stabilization mechanism involves a highly degenerate Hopf bifurcation problem that is induced by the time-delayed feedback. When the feedback gain modulus reaches a threshold for stabilization, both of the genericity assumptions associated with a two-dimensional Hopf bifurcation are violated: the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied, and the real part of the cubic coefficient of the normal form vanishes. Our analysis of this degenerate bifurcation problem reveals two qualitatively distinct cases when unfolded in a two-parameter plane. In each case, Pyragas-type feedback successfully stabilizes the branch of small-amplitude UPOs in a neighborhood of the original bifurcation point, provided that the phase angle satisfies a certain restriction.Comment: 35 pages, 19 figure

The effects of delay on the HKB model of human motor coordination

Understanding human motor coordination holds the promise of developing diagnostic methods for mental illnesses such as schizophrenia. In this paper, we analyse the celebrated Haken-Kelso-Bunz (HKB) model, describing the dynamics of bimanual coordination, in the presence of delay. We study the linear dynamics, stability, nonlinear behaviour and bifurcations of this model by both theoretical and numerical analysis. We calculate in-phase and anti-phase limit cycles as well as quasi-periodic solutions via double Hopf bifurcation analysis and centre manifold reduction. Moreover, we uncover further details on the global dynamic behaviour by numerical continuation, including the occurrence of limit cycles in phase quadrature and 1-1 locking of quasi-periodic solutions.Comment: Submitted to the SIAM Journal on Applied Dynamical Systems. 27 pages, 8 figure

Improvement of boring operations by means of mode coupling effect

Boring bars are inherently slender tools which are prone to show chatter problems due to their low dynamic stiffness and damping, being this problem their main limitation in productivity. The onset of chatter is mainly related to the dynamic stiffness of the bending mode of the boring bar when the length L to dia-meter D ratio is higher than 4. Tuned mass dampers (TMD) are effective technical solutions to increase the dynamic stiffness of large ratio boring bars. However, there are many applications where 4-6 L/D ratio tools are required, and the avoidance of chatter without the application of TMDs is interesting due to the high cost of damped tools. This work proposes the use of mode coupling effect to increase the damping and stabilise the machining process avoiding the use of any special device. This effect occurs when the fre-quency of one of the machine's modes is similar to the frequency of the dominant mode of the boring bar. As a result, the shape of the critical mode of the boring bar is mixed with the mode originated in the machine, and the damping and stability will be higher than the one that is not subjected to any dynamic coupling. The main contribution of this work is the application of this concept to increase stability in boring operations. This objective has been achieved by optimising the tool length and material by means of a dynamic model based on Receptance Coupling Substructure Analysis (RCSA). The model combines an analytical model of the elastic body of the boring bar with the experimental characterisation of the effect of the rest of the machine. This way, the shape and materials of the boring bar can be optimised to create an increase of damping. The optimisation procedure has been experimentally validated resulting in an increase of cutting stability and demonstrating that not always a shorter bar supposes a higher stability.The authors thank the collaboration of Markel Sanz from IDEKO. This work has been supported by EUROSTARS FORTH E!12998 pro-ject and the EU Horizon 2020 InterQ project (958357/H2020-EU.2.1.5.1)

Self-Tuning Algorithm for Tuneable Clamping Table for Chatter Suppression in Blade Recontouring

The production and repair of blades for aerospace engines and energy turbines is a complex process due their inherently low stiffness and damping properties. The final recontouring operation is usually performed by milling operations where regenerative chatter is one of the main productivity limiting factors. With the objective of avoiding specific stiffening fixtures for each blade geometry, this paper proposes a semi-active tuneable clamping table (TCT) based on mode tuning for blade machining. The active mode of the device can be externally controlled by means of a rotary spring and eddy current damping modules. Its in-series architecture allows damping to be introduced to the critical mode of the thin-walled part without any direct contact in the machining area and enables a more universal clamping. Its chatter suppression capabilities are maximized by means of a novel self-tuning algorithm that iteratively optimizes the tuning for the measured chatter frequency. The benefits of the iterative algorithm are validated through semidiscretization and initial value time-domain simulations, showing a clear improvement in blade recontouring stability compared to regular broad-bandwidth tuning methods.This project has been funded by the MIRAGED: Posicionamiento Estratégico en Modelos Virtuales y Gemelos Digitales para una Industria 4.0 (CER-20191001), supported by CDTI-Acreditación y Concesión de Ayudas Destinadas a Centros Tecnológicos de Excelencia Cervera; the Hungarian NKFI FK 124361 and the TiMachina project (IDI-201904196) from the International Technological Corporation, and by R+d projects program of the Spanish Centre for the Development of Industrial Technology (CDTI)