Krzysztof Kecik

Autoparametric vibrations of a nonlinear system with pendulum

Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It has been found that the motion of the oscillator, forced by an external harmonic force, has been dynamically eliminated by the pendulum oscillations. Influence of a nonlinear spring on the vibration absorption near the main parametric resonance region has been carried out analytically, whereas the transition from regular to chaotic vibrations has been presented by using numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.

Cutting force response in milling of Inconel: analysis by wavelet and Hilbert-Huang Transforms

We study the milling process of Inconel. By continuously increasing the cutting depth we follow the system response and appearance of oscillations of larger amplitude. The cutting force amplitude and frequency analysis has been done by means of wavelets and Hilbert-Huang transform. We report that in our system the force oscillations are closely related to the rotational motion of the tool and advocate for a regenerative mechanism of chatter vibrations. To identify vibrations amplitudes occurrence in time scale we apply wavelet and Hilbert-Huang transforms.

Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension

This paper presents vibration analysis of an autoparametric pendulum-like mechanism subjected to harmonic excitation. To improve dynamics and control motions, a new suspension composed of a semiactive magnetorheological damper and a nonlinear spring is applied. The influence of essential parameters such as the nonlinear damping or stiffness on vibration, near the main parametric resonance region, are carried out numerically and next verified experimentally in a special experimental rig. Results show that the magnetorheological damper, together with the nonlinear spring can be efficiently used to change the dynamic behaviour of the system. Furthermore, the nonlinear elements applied in the suspension of the autoparametric system allow to reduce the unstable areas and chaotic or rotating motion of the pendulum.

Modeling of high-speed milling process with frictional effect

This article deals with the problem of chatter vibrations in high-speed milling process taking into account both regeneration and frictional chatter. In this aim, a nonlinear model of high-speed down milling is developed. The proposed model includes friction force produced between an edge of a tool and a workpiece, modeled by nonlinear and nonsmooth function and also the time delay effect, which is responsible for a vibration regeneration. The influence of friction on the process stability is compared with results obtained in a classical way using a commercial software. Finally, numerical tests are compared with the stability lobe diagrams obtained experimentally during real machining of nickel superalloys.

Chatter control in the milling process of composite materials

In this paper, a model of the milling process of fibre reinforced composite material is shown. This classical one degree of freedom model of the milling process is adjusted for composite materials by variable specific cutting forces, which describe the fibre resistance. The stability lobe diagrams are determined numerically. Additionally, to eliminate the chatter vibration, small relative oscillations between the workpiece and the tool are introduced. Basing on numerical simulations the range of amplitude and the frequency of excitation is found for chatter reduction.

Autoparametric Vibrations of a Nonlinear System with a Pendulum and Magnetorheological Damping

The chapter deals with autoparametric vibrations of a system composed of a nonlinear oscillator with an attached pendulum. Dynamics of the mechanical structure is studied analytically around the principal parametric resonance region, numerically and experimentally for a wide range of parameters. The influence of damping, nonlinear stiffness (hard and soft), amplitude and frequency of excitation on the system’s behaviour is analysed in details. The obtained results show that the pendulum can be applied as a dynamical absorber. However, for selected parameters, near the main parametric resonance, instability, which transits the pendulum to chaotic oscillations or to a full rotation, occurs. Therefore, the application of a magnetorheological (MR) damper and a nonlinear spring is proposed to improve the dynamics and to control the response online. Periodic vibrations, chaotic motions or a full rotation of the pendulum obtained numerically are confirmed by the experiment. The chaotic nature of motion is determined from real signals by the attractor reconstruction and the recurrence plot calculation. The results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one.

Parametric Analysis of Magnetorheologically Damped Pendulum Vibration Absorber

This paper presents numerical and experimental study of an autoparametric pendulum absorber attached to a vertically moving Duffing oscillator. The absorber can be highly efficient for slightly damped systems, when correctly tuned. In the suspension of pendulum absorber, the magnetorheological damper (MR) is installed to allow control. The influence of system parameters: Viscous and magnetorheological damping, stiffness of the spring, parameter which couples both systems on the suppression effectiveness are studied. Additionally, the influence of system parameters on periodic solutions and stability are analyzed using continuation techniques.

Dynamic model of cutting process with modulated spindle speed

The paper presents classical regenerative one degree of freedom model of cutting. The model is enriched in an additional friction phenomenon which generates frictional chatter. A mutual interaction between regeneration and frictional effects is analysed to find stability regions. In the second part of the paper a spindle speed variation method is applied for chatter suppression both for classical regenerative model and also for regenerative model with the friction effect. Finally, the map of spindle speed variation parameters is drawn.

Non-Linear Dynamics and Optimization of a Harvester–Absorber System

In this paper, we propose a novel concept of a harvester-absorber system. The idea is based on usage of the dynamic absorber for energy harvesting. The device consists of three elements: a main system (damped body), a pendulum (tuned mass absorber) and an electromagnetic harvester. The ultimate goal of this investigation is to achieve simultaneous mitigation of vibrations and energy harvesting. We show the dynamics of the system and ranges of parameters where we observe good damping properties and high energy recovery. Additionally, an optimization of the harvester device parameters has been performed.

Energy Recovery from a Non-Linear Electromagnetic System

Abstract The paper presents study of a pseudo-magnetic levitation system (pseudo-maglev) dedicated for energy harvesting. The idea rely on motion of a pseudo-levitating magnet in a coil’s terminal. The study based on real prototype harvester system, which in the pendulum dynamic vibration absorber is applied. For some parameters, the stability loss caused by the period doubling bifurcation is detected. The coexistence of two stable solutions, one of which is much better for energy harvesting is observed. The influence of the pseudo-maglev parameters on the recovered current and stability of the periodic solutions is presented in detail. The obtained results show, that the best energy recovery occurs for the high pseudo-maglev stiffness and close to the coil resistance. The amplitude’s excitation, the load resistances and the coupling coefficient strongly influence on the system’s response.