Sébastien Seguy

Toolpath dependent stability lobes for the milling of thin-walled parts

The milling of thin-walled parts can become a seriously complex problem because the parts have variable dynamics. Firstly, the dynamics evolution of the part has been calculated through Finite Element Method (FEM) analysis. Then, the 3D stability lobes have been calculated for the thin walls and the thin floor. Finally, several milling tests have been performed in order to validate the predictions made by the model.

Experimental Investigation and Design Optimization of Targeted Energy Transfer Under Periodic Forcing

In this paper, the dynamic response of a harmonically forced Linear Oscillator (LO) strongly coupled to a Nonlinear Energy Sink (NES) is investigated both theoretically and experimentally. The system studied comprises a LO with an embedded, purely cubic NES. The behavior of the system is analyzed in the vicinity of 1 : 1 resonance. The complexification-averaging technique is used to obtain modulation equations and the associated fixed points. These modulation equations are analyzed using asymptotic expansion to study the regimes related to relaxation oscillation of the slow flow called Strongly Modulated Response (SMR). The zones where SMR occurs are computed using a mapping procedure. The Slow Invariant Manifolds (SIM) is used to derive a proper optimization procedure. It is shown that there is an optimal zone in the forcing amplitude-nonlinear stiffness parameter plane, where SMR occurs without having a high amplitude detached resonance tongue. Two experimental setups are presented. One is not optimized and has a relatively high mass ratio (≈ 13%) and the other one is optimized and exhibits strong mass asymmetry (mass ratio ≈ 1%). Different frequency response curves and associated zones of SMR are obtained for various forcing amplitudes. The reported experimental results confirm the design procedure, and the possible application of NES for vibration mitigation under periodic forcing.

Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments

Recently, it has been demonstrated that a vibro-impact type nonlinear energy sink (VI-NES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of a LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equation of motion are analyzed using the method of multiple scales in the case of 1 : 1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR response regimes. A good agreement between theoretical and experimental results is observed.

SUPPRESSION OF PERIOD DOUBLING CHATTER IN HIGH-SPEED MILLING BY SPINDLE SPEED VARIATION

Spindle speed variation is a well known technique to suppress regenerative machine tool vibrations, but it is usually considered to be effective only for low spindle speeds. In the current paper, spindle speed variation is applied to the high speed milling process, at the spindle speeds where the constant speed cutting results in period doubling chatter. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. It is shown that the milling process can be stabilized by increasing the amplitude of the spindle speed variation, while the frequency of the variation has no significant effect on the dynamic behaviour. The results are validated by experiments. Based on the analysis of the machined workpieces, it is shown that the surface roughness can also be decreased by the spindle speed variation technique.

Chatter Control in Turning Process with a Nonlinear Energy Sink

This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.

Dynamics of Cubic and Vibro-Impact Nonlinear Energy Sink: Analytical, Numerical, and Experimental Analysis

This paper is devoted to study and compare dynamics of primary Linear Oscillator (LO) coupled to cubic and Vibro-Impact (VI) Nonlinear Energy Sink (NES) under transient and periodic forcing. The classic analytical procedure combining the approach of invariant manifold and multiple scales is extended from the analysis of steadystate resonance to other regimes, especially Strongly Modulated Response (SMR). A general equation governing the variation of motion along the Slow Invariant Manifold (SIM) is obtained. Numerical results show its convenience to explain the transition from steady-state response to SMR and the characteristics of SMR for periodic forcing. Targeted energy transfer under transient forcing can also be well understood. Experimental results from LO coupled to VI NES under periodic forcing confirm the existence of SMR and its properties (e.g. chaotic). They also verify the feasibility of the general equation to explain complicated case like SMR in experiments.

Control of Chatter by Spindle Speed Variation in High-Speed Milling

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area.

Critical thickness and dynamic stiffness for chatter avoidance in thin floors milling

A common problem in the aeronautical industry is the chatter vibration due to the lack of dynamic stiffness in the milling of thin walls and thin floors. The present work proposes a method for chatter avoidance in the milling of flexible thin floors with a bull nose end mill. It allows the calculation of the thickness previous to finish milling or the minimum dynamic stiffness that the floor must have to avoid the chatter vibration appearance. To obtain these values, the stability model algorithm has been inverted to estimate the thickness or the dynamic stiffness required in a floor to allow a stable milling. This methodology has been validated satisfactorily in several experimental tests.

Tuned nonlinear energy sink with conical spring: design theory and sensitivity analysis

This paper is devoted to the study of a Nonlinear Energy Sink (NES) intended to attenuate vibration induced in a harmonically forced linear oscillator (LO) and working under the principle of Targeted Energy Transfer (TET). The purpose motivated by practical considerations is to establish a design criterion that first ensures that the NES absorber is activated and second provides the optimally tuned nonlinear stiffness for efficient TET under a given primary system specification. Then a novel NES design yielding cubic stiffness without a linear part is exploited. To this end, two conical springs are specially sized to provide the nonlinearity. To eliminate the linear stiffness, the concept of a negative stiffness mechanism is implemented by two cylindrical compression springs. A small-sized NES system is then developed. To validate the concept, a sensitivity analysis is performed with respect to the adjustment differences of the springs and an experiment on the whole system embedded on an electrodynamic shaker is studied. The results show that this type of NES can not only output the expected nonlinear characteristics, but can also be tuned to work robustly over a range of excitation, thus making it practical for the application of passive vibration control.

Experimental Investigation and Theoretical Analysis of a Nonlinear Energy Sink Under Harmonic Forcing

In the present works, we examine experimentally and theoretically the dynamic behavior of linear oscillator strongly coupled to a nonlinear energy sink under external periodic forcing. The nonlinear oscillator has a nonlinear restoring force realized geometrically with two linear springs that extend axially and are free to rotate. Hence, the force-displacement relationship is cubic. The linear oscillator is directly excited via an electrodynamic shaker. Experiments realized on the test bench consist of measuring the displacement of the oscillators while increasing and decreasing frequencies around the fundamental resonance of the linear oscillator. Many nonlinear dynamical phenomena are observed on the experimental setup such as jumps, bifurcation, and quasiperiodic regimes. The retained nonlinear model is a two degree of freedom system. The behavior of the system is then explained analytically and numerically. The complexification averaging technique is used to derive a set of modulation equation governing the evolution of the complex amplitude at the frequency of excitation, and a stability analysis is performed.Copyright