Automatic polishing process of plastic injection molds on a 5-axis milling center

The plastic injection mold manufacturing process includes polishing operations when surface roughness is critical or mirror effect is required to produce transparent parts. This polishing operation is mainly carried out manually by skilled workers of subcontractor companies. In this paper, we propose an automatic polishing technique on a 5-axis milling center in order to use the same means of production from machining to polishing and reduce the costs. We develop special algorithms to compute 5-axis cutter locations on free-form cavities in order to imitate the skills of the workers. These are based on both filling curves and trochoidal curves. The polishing force is ensured by the compliance of the passive tool itself and set-up by calibration between displacement and force based on a force sensor. The compliance of the tool helps to avoid kinematical error effects on the part during 5-axis tool movements. The effectiveness of the method in terms of the surface roughness quality and the simplicity of implementation is shown through experiments on a 5-axis machining center with a rotary and tilt table

Random walks in Dirichlet environment: an overview

Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized by a family of positive weights $(\alpha_i)_{i=1, \ldots, 2d}$, one for each direction of $\Bbb{Z}^d$. In this case, the annealed law is that of a reinforced random walk, with linear reinforcement on directed edges. RWDE have a remarkable property of statistical invariance by time reversal from which can be inferred several properties that are still inaccessible for general environments, such as the equivalence of static and dynamic points of view and a description of the directionally transient and ballistic regimes. In this paper we give a state of the art on this model and several sketches of proofs presenting the core of the arguments. We also present new computation of the large deviation rate function for one dimensional RWDE.Comment: 35 page

Stable fluctuations for ballistic random walks in random environment on Z

We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitting time of level $n$, after proper centering and normalization, converges to a completely asymmetric stable distribution, but does not describe its scale parameter. Following a previous article by three of the authors, where the (non-critical) zero speed case was dealt with, we give a new proof of this result in the subdiffusive case that provides a complete description of the limit law. The case of Dirichlet environment turns out to be remarkably explicit

Usinage de formes gauches : génération de trajectoires outils à hauteur de crête constante

National audienceWe present in this communication a method to generate constant scallop height tool paths in 3-axis milling with ball endmill. This machining strategy is interesting because it minimises the number of tool paths for a given geometrical specification of form deviation and surface roughness. Our approach is based on the concept of the machining surface which provides a surface representation of the tool paths and an exact model of the scallop generated by the tool path. This approach is confronted with the methods previously developed in the literature in term of precision and more particularly on the processing of curvature discontinuities. Then the constant scallop height tool path planning is evaluated on surfaces of great curvature variations.Nous présentons une méthode de génération de trajectoires à hauteur de crête constante en fraisage à trois axes avec outil hémisphérique. Cette stratégie d'usinage est intéressante dans la mesure où elle minimise le nombre de passes pour des spécification géométriques de défaut de forme et d'état de surface données. Notre approche s'appuie sur le concept de la surface d'usinage qui procure une représentation surfacique des trajets de l'outil et permet une modélisation exacte de la crête laissée par l'usinage. Cette approche est comparée aux méthodes usuelles développées dans la littérature selon des critères de précision et de capacité à traiter les discontinuités en courbure des surfaces. Le problème de la planification des trajectoires iso-crêtes sur une surface présentant d'importantes évolutions de courbure est abordé par la suite

A surface based approach for constant scallop height tool path generation

International audienceThe machining of sculptured surfaces like molds and dies in 3-axis milling relies on the chordal deviation, the scallop height parameter and the planning strategy. The choice of these parameters must ensure that manufacturing surfaces respect the geometrical specifications. The current strategies of machining primarily consist in driving the tool according to parallel planes which generates a tightening of the tool paths and over quality. The constant scallop height planning strategy has been developed to avoid this tightening. In this paper, we present a new method of constant scallop height tool path generation based on the concept of the machining surface. The concept of the machining surface is exposed and its use to generate constant scallop height tool paths. The approach is confronted with existing methods in terms of precision and in particular its aptitude to treat curvature discontinuities

Stratégies d'usinage et productivité en fraisage des surfaces complexes

National audienceThe manufacturing process of molds and dies has been largely modified by the use of new techniques like high-speed machining and polynomial interpolation. Its optimization imposes a complete integration between CAM, numerical controller and machining to take best account of the dynamic performance of the machine used. To illustrate this problem, we study in this communication the influence of the choice of the machining strategy and the type of interpolation over quality and machining time. Thus, we compare the constant scallop height machining strategy which optimizes surface covering, with the traditional machining strategy using parallel planes and the polynomial interpolation, which returns continues C2 tool paths to the usual linear interpolation.The analysis of tool path lengths, the machining time and the tool real mean speed along the path, makes it possible to define a classification of employment according to the geometrical form of the tool path.Le processus de réalisation des moules et des matrices a largement été modifié par l'utilisation de nouvelles techniques comme l'usinage à grande vitesse et l'interpolation polynomiale. Son optimisation impose une intégration complète entre la FAO, la commande numérique et l'usinage de manière à tenir compte au mieux de la performance dynamique de la machine utilisée. Pour illustrer ce problème, nous étudions dans cette communication l'influence du choix de la stratégie d'usinage et du mode d'interpolation sur la qualité et le temps d'usinage. Ainsi, nous comparons la stratégie d'usinage à hauteur de crête constante qui optimise la couverture de la surface, à la stratégie d'usinage classique par plans parallèles et l'interpolation polynomiale, qui rend continue C2 les trajets d'usinage à l'interpolation linéaire usuelle. L'analyse des longueurs de trajets, du temps d'usinage et des vitesses moyennes réelles de parcours permet de définir une classification d'emploi en fonction de la forme géométrique de la trajectoire. Abstract

Integrability of exit times and ballisticity for random walks in Dirichlet environment

We consider random walks in Dirichlet environment, introduced by Enriquez and Sabot in 2006. As this distribution on environments is not uniformly elliptic, the annealed integrability of exit times out of a given finite subset is a non-trivial property. We provide here an explicit equivalent condition for this integrability to happen, on general directed graphs. Such integrability problems arise for instance from the definition of Kalikow auxiliary random walk. Using our condition, we prove a refined version of the ballisticity criterion given by Enriquez and Sabot

FVPM simulation of scratching induced by a spherical indenter

International audienceThis article presents a single particle scratching simulation using the Finite Volume Particle Method (FVPM). FVPM is a variant of the well-known Smooth Particles Hydrodynamics method (SPH) which is locally conservative and consistent, what's more it features advantages of mesh-free methods for handling moving interfaces and multi-scale interpolation. The test material is represented by overlapping particles and data exchanges occur through the interfaces. The indenter is modeled as a rigid sphere whose path is a straight horizontal line. The resulting surface topography as well as constraints and scratching efforts have been numerically studied. The FVPM simulation code assessed in this article has been found suitable for the scratching simulation based on a comparison with other results from the literature. The presented results suggest the possibility to simulate more complex surface finishing operations. Manufacturing processes based on abrasion material removal, such as the grinding process, will be considered in the future

Opto-mechanical modelling of an additive manufacturing laser scanning head including assembly defects

International audienceAdditive manufacturing (AM) machines used in SLM or SLA are composed of galvanometric scanning system in order to focus and steer a laser beam to melt raw materials. A major problematic in these AM processes is to master the laser spot position which essentially depends on the machine geometry and the galvanometers angular positions. In literature, most of existing models make strong assumptions concerning the geometry of the laser scanning system. Moreover, the position of the laser spot is often obtained by interpolating a table of correspondence, experimentally determined, between the angular positions of the galvanometers and the cartesian coordinates in the working plane. All these approximations induce deviations of the laser spot compared to the desired position and affect machine performance. This article presents two kinematic models of the galvanometric laser scanning system in an AM machine: a nominal model of the system and a model with assembly defects consideration. These kinematic models, often used for machine tools and robots, are here applied to create a virtual AM machine. Thereby, the laser spot position can be simulated knowing the geometry of the machine, the possible assembly defects, and the orientation of the galvanometers. The second kinematic model is then used to extract the influence of assembly defects on the laser spot position. The work described in this paper allows us to highlight and quantify the theoretical impact of an assembly defect on the precision of the laser spot position in an AM machine