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

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

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)

The Basics of Time-Domain-Based Milling Stability Prediction Using Frequency Response Function

This study presents the fundamentals of the usage of frequency response functions (FRF) directly in time-domain-based methods. The methodology intends to combine the advantages of frequency- and time-domain-based techniques to determine the stability of stationary solutions of a given milling process. This is achieved by applying the so-called impulse dynamic subspace (IDS) method, with which the impulse response function (IRF) can be disassembled to separated singular IRFs that form the basis of the used transformation. Knowing the IDS state, the linear stability boundaries can be constructed and a measure of stability can be determined using the Floquet multipliers via the semidiscretization method (SDM). This step has a huge importance in parameter optimization where the multipliers can be used as objective functions, which is hardly achievable using frequency-domain-based methods. Here we present the basic idea of utilizing the IDS method and analyze its convergence properties

Estimates of the bistable region in metal cutting

The 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

Non-smooth torus to identify domain of attraction of stable milling processes

International audienceThe presented work shows a possible model dealing with the non-smooth flyover effect in milling processes. The excitation force of the general modal model of milling process is delayed, nonlinear, time-periodic and piecewise smooth. Apart from a state independent switch originated from the so-called radial immersion, flyover causes difficulties in connection with accurate depiction of the anyway quasi-periodic solution. From industrial point of view, the ’size’ of this non-smooth quasi-periodic solution is essential to predict approximately the attraction zone of the stable time-periodic stationary solution calculated using linear theories

Chatter formation during milling due to stochastic noise-induced resonance

In this paper, the stochastic dynamical model of a single-degree-of-freedom milling operation is formulated, where a Gaussian white noise process models the high-frequency variation in the cutting force. With the help of this stochastic model, it is shown, that large-amplitude stable vibrations can occur near the critical machining parameters, due to stochastic noise-induced resonance. During the analysis, the second moment stability and stationary first and second moment behavior of the periodic stochastic delay differential equation (SDDE) describing the milling operation are investigated. The behavior of these quantities are then compared to the evolution of the so-called “chatter peak” in the Fourier-spectrum of the vibrations, that is used to experimentally determine the presence of chatter, in the stable machining parameter domain. Furthermore, it is discussed, how the statistical properties of the resonant vibrations can be used to predict the stability boundary and the formulation of chatter, while the machining parameters are kept in the safe region. The theoretical calculations are supported by experiments performed on a single-degree-of-freedom system