Pascal Ray

von Kármán vortex street within an impacting drop.

The splashing of a drop impacting onto a liquid pool produces a range of different sized microdroplets. At high impact velocities, the most significant source of these droplets is a thin liquid jet emerging at the start of the impact from the neck that connects the drop to the pool. We use ultrahigh-speed video imaging in combination with high-resolution numerical simulations to show how this ejecta gives way to irregular splashing. At higher Reynolds numbers, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von Kármán vortex street, thus breaking the ejecta sheet as it forms.

Bspline approximation of circle arc and straight line for pocket machining

This article proposes a new method of 2D curve interpolation using non-uniform cubic B-splines particularly adapted to the interpolation of sequences of straight lines and circle arcs. The purpose of this method is to calculate C2 continuous curves adapted to high feedrate pocket machining. Industrially machined pockets usually present simple forms. Generally, the tool path is defined by circle arcs and line segments that introduce slowdowns during machining. Thus, a method for approximating a sequence of line segments and circle arcs using Bspline curves is proposed. The proposed method ensures exact line interpolation, to approach the tool path precisely, to reduce the number of control points and to avoid thickening and oscillation at the connections between line segments and circle arcs. Various applications are presented and numerous tests on machine tools allow the advantages of this method to be illustrated.

Stability-Based Spindle Design Optimization

Prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency-response measurements of the tool-holder-spindle set obtained from a nonrotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic high-speed spindle-bearing system model is elaborated on the basis of rotor dynamics prediction and readjusted on the basis of experimental modal identification. The dependency of dynamic behavior on speed range is then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. They show that dynamic effects due to high rotational speed and elastic deformations, such as gyroscopic coupling and spin softening, have a significant influence on spindle behavior. By integrating the modeled speed-dependent spindle transfer function in the chatter vibration stability approach ofAltintas and Budak (1995, CIRPS Ann, 44(1), pp. 357-362), a new dynamic stability lobe diagram is predicted. Significant changes are observed in the stability limits constructed using the proposed approach and allow accurate prediction of cutting conditions to be established. Finally, optimization studies are performed on spindle design parameters in order to obtain a chatter vibration-free cutting operation at the desired speed and depth of cut for a given cutter.

Scaling laws for the slumping of a Bingham plastic fluid

Bingham plastics exhibit complex behaviors, depending on both geometrical and rheological factors, and are difficult to characterize systematically. This is particularly true in the case of transient flows, where solidlike and fluidlike behaviors coexist in an intermittent fashion. The aim of this contribution is to study the slump of Bingham columns under gravity, while varying systematically and independently both the geometry of the system and the rheological parameters. To do so, numerical experiments are carried out in two dimensions with a non-Newtonian Navier–Stokes code, the Gerris flow solver, using a volume-of-fluid approach. We are able to determine the slump height and the spreading of the column after motion ceased. These characteristics are related to the rheological properties and initial shape through scaling relationships. The results are compared with previous scalings and prediction from the literature. A discussion ensues on the importance of the normalization choice and of unambiguous...

Droplet impact on a thin liquid film: anatomy of the splash

We investigate the dynamics of drop impact on a thin liquid film at short times in order to identify the mechanisms of splashing formation. Using numerical simulations and scaling analysis, we show that the splashing formation depends both on the inertial dynamics of the liquid and the cushioning of the gas. Two asymptotic regimes are identified, characterized by a new dimensionless number

The spreading of a granular column from a Bingham point of view

J

Seismic fragility curves based on the probability density evolution method

: when the gas cushioning is weak, the jet is formed after a sequence of bubbles are entrapped and the jet speed is mostly selected by the Reynolds number of the impact. On the other hand, when the air cushioning is important, the lubrication of the gas beneath the drop and the liquid film controls the dynamics, leading to a single bubble entrapment and a weaker jet velocity.

Dynamic model of high speed machining spindle associated to a self-vibratory drilling head influence of drill torsional-axial coupling

The collapse and spreading of granular columns has been the subject of sustained interest in the last years from both mechanical and geophysical communities. Yet, in spite of this intensive research, the adequate rheology allowing for a reliable continuum modeling of the dynamics of granular column collapse is still open to discussion. Essentially, continuum models rely on shallow‐water approximation for which dissipation and sedimentation processes are taken into account through the introduction of ad hoc laws. However, the rheological origin of the experimental scaling laws exhibited by the granular columns when spreading remains unclear. On these grounds, we adopt an alternative approach consisting of studying the collapse of columns of material obeying a Bingham rheology. Therefore we carried out series of numerical simulations using the Gerris Flow Solver solving the time dependent incompressible Navier‐Stokes equation in two dimensions for the specified rheology. We first check that the mass exhibit similar scaling laws as those shown by granular columns. Then we investigate in which extent rheological parameters do reflect on these scaling laws. A comparative analysis of Bingham and granular flow characteristics ensues.The collapse and spreading of granular columns has been the subject of sustained interest in the last years from both mechanical and geophysical communities. Yet, in spite of this intensive research, the adequate rheology allowing for a reliable continuum modeling of the dynamics of granular column collapse is still open to discussion. Essentially, continuum models rely on shallow‐water approximation for which dissipation and sedimentation processes are taken into account through the introduction of ad hoc laws. However, the rheological origin of the experimental scaling laws exhibited by the granular columns when spreading remains unclear. On these grounds, we adopt an alternative approach consisting of studying the collapse of columns of material obeying a Bingham rheology. Therefore we carried out series of numerical simulations using the Gerris Flow Solver solving the time dependent incompressible Navier‐Stokes equation in two dimensions for the specified rheology. We first check that the mass exhibit...

Integration of Drill Torsional-Axial Coupling in Spindle-Vibratory Drilling Head Model for Stability Analysis

A seismic fragility curve that shows the probability of failure of a structure in function of a seismic intensity, for example peak ground acceleration (PGA), is a powerful tool for the evaluation of the seismic vulnerability of the structures in nuclear engineering and civil engineering. The common assumption of existing approaches is that the fragility curve is a cumulative probability log-normal function. In this paper, we propose a new technique for construction of seismic fragility curves by numerical simulation using the Probability Density Evolution Method (PDEM). From the joint probability density function between structural response and random variables of a system and/or excitations, seismic fragility curves can be derived without the log-normal assumption. The validation of the proposed technique is performed on two numerical examples.

Influence of adapted five-axis tool paths on the machine behaviour

The drilling of deep holes with small diameters remains an unsatisfactory technology, since its productivity is rather limited. The main limit to an increase in productivity is directly related to the poor chip evacuation, which induces frequent tool breakage and poor surface quality. Retreat cycles and lubrication are common industrial solutions, but they induce productivity and environmental drawbacks. An alternative response to the chip evacuation problem is the use of a vibratory drilling head, which enables the chips to be fragmented thanks to the axial self-excited vibration. Contrary to conventional machining processes, axial drilling instability is sought, thanks to an adjustment of head design parameters and appropriate conditions of use. In this paper, self-vibratory cutting conditions are established through a specific stability lobes diagram. A dynamic high-speed spindle/drilling head/tool system model is elaborated on the basis of rotor dynamics predictions. The model-based tool tip Frequency Response Function (FRF) is integrated into an analytical stability approach. The torsional-axial coupling of the twist drill is investigated and consequences on drilling instability are established.