On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing

his paper deals with the implementation in 3D of the constrained natural element method (CNEM) in order to simulate material forming involving large strains. The CNEM is a member of the large family of mesh-free methods, but is at the same time very close to the finite element method. The CNEM’s shape function is built using the constrained Voronoï diagram (the dual of the constrained Delaunay tessella- tion) associated with a domain defined by a set of nodes and a description of its border. The use of the CNEM involves three main steps. First, the constrained Voronoï diagram is built. Thus, for each node, a Voronoï cell is geometrically defined, with respect of the boundary of the domain. Then, the Sibson-type CNEM shape functions are computed. Finally, the discretization of a generic variational for- mulation is defined by invoking an ‘‘stabilized conforming nodal integration’’. In this work, we focus especially on the two last points. In order to compute the Sibson shape function, five algorithms are pre- sented, analyzed and compared, two of them are developed. For the integration task, a discretization strategy is proposed to handle domains with strong non-convexities. These approaches are validated on some 3D benchmarks in elasticity under the hypothesis of small transformations. The obtained results are compared with analytical solutions and with finite elements results. Finally, the 3D CNEM is applied for addressing two forming processes: high speed shearing and machining

Analysis and modeling of green wood milling: Chip production by slabber

During the primary transformation of wood, logs are faced with slabber heads. Chips produced are raw materials for pulp paper and particleboard industries. Efficiency of these industries is partly due to particle size distribution. Command of this distribution is no easy matter because of great dependence on cutting conditions and variability in material. This study aimed a better understanding and predictionof chip fragmentation. It starts with a detailed description of cutting kinematic and interaction between knife and log. This leads to the numerical development of a generic slabber head. Chip fragmentation phenomena were studied through experiments in dynamic conditions. These experiments were carried out thanks to a pendulum (Vc = 400 m/min). It was instrumented with piezoelectric force sensors and high speed camera. Obtained results agreed very well with previous quasi-static experiments

High Speed Blanking: An Experimental Method to Measure Induced Cutting Forces

Lien vers la version éditeur: http://link.springer.com/article/10.1007/s11340-013-9738-1A new blanking process that involves punch speed up to 10 ms −1 has obvious advantages in increased productivity. However, the inherent dynamics of such a process makes it difficult to develop a practical high speed punch press. The fracture phenomenon governing the blanking process has to be well understood to correctly design the machine support and the tooling. To observe this phenomenon at various controlled blanking speeds a specific experimental device has been developed. The goal is to measure accurately the shear blanking forces imposed on the specimen during blanking. In this paper a new method allowing the blanking forces to be measured and taking into account the proposed test configuration is explained. This technique has been used to determine the blanking forces experienced when forming C40 steel and quantifies the effect of process parameters such as punch die clearance, punch speed, and sheet metal thickness on the blanking force evolution

Simulation of a finishing operation : milling of a turbine blade and influence of damping

Milling is used to create very complex geometries and thin parts, such as turbine blades. Irreversible geometric defects may appear during finishing operations when a high surface quality is expected. Relative vibrations between the tool and the workpiece must be as small as possible, while tool/workpiece interactions can be highly non-linear. A general virtual machining approach is presented and illustrated. It takes into account the relative motion and vibrations of the tool and the workpiece. Both deformations of the tool and the workpiece are taken into account. This allows predictive simulations in the time domain. As an example the effect of damping on the behavior during machining of one of the 56 blades of a turbine disk is analysed in order to illustrate the approach potential

Solving Stefan problem through C-NEM and level-set approach

Numerical methods to solve problems involving discontinuities (jumps, kinks or singularities) on moving internal boundaries have received much attention over the last decade. Among them, the most suitable is probably the extended finite element method (XFEM) in tandem with the level-set technique due to its ability to take into account these discontinuities without matching meshes [1]. The present contribution aims to elaborate a numerical approach to model interfacial discontinu- ities within a meshless context. This approach couples the constrained natural element method (C-NEM) [2] and the level-set technique. In the former, the natural neighbours interpolation, based on a Voronoi diagram, is locally enriched through the partition of unity concept. This enrichment is built from level-set functions that represent and track implicitly discontinuities inside the domain [3]. Like in XFEM, key features of the proposed approach is (i) to determine the intersection between Voronoi cells and discontinuities and (ii) to integrate numerically the weak form over cells containing discontinuities. After testing the proposed method on classical benchmarks, both accuracy and efficiency are examined on the two phase Stefan problem that deals with heat flow involving a solid-liquid phase boundary on which a jump condition must be satisfied [4]. [1] Chessa J., Smolinski P. and Belytschko T. The extended finite element method (XFEM) for solidification problems. Int. J. Numer. Meth. Engng 53:1959–1977 (2002). [2] Yvonnet J., Chinesta F., Lorong P. and Ryckelynck D. The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces. Int. J. Therm. Sci. 44:559–569 (2005). [3] LiuJ.T.,GuS.T.,MonteiroE.andHeQ.C.Aversatileinterfacemodelforthermalconduc- tion phenomena and its numerical implementation by XFEM. Comp. Mech. 53:825–843 (2014). [4] Carslaw H.S. and Jaeger J.C. Conduction of Heat in Solids. 2th Edition, Clarendon Press, (1959)

Simulation of green wood milling with discrete element method

This work was carried out in LaBoMaP and PIMM at Arts et Metiers ParisTech. We acknowledge I2M laboratory for their technical support in Discret Element Method; Robert Collet, Louis Denaud, Guillaume Pot; PIMM and LaBoMaP technicians and Morgane Pfeiffer-Laplaud for their availability and advice.During the primary transformation in wood industry, logs are faced with conical rough milling cutters commonly named slabber or canter heads. Chips produced consist of raw materials for pulp paper and particleboard industries. The process efficiency of these industries partly comes from particle size distribution. However, chips formation is greatly dependent on milling conditions and material variability. Numerical simulation of chip fragmentation can allow some useful chip thickness prediction. In this complex situation in wood cutting, the utilization of the Discrete Element Method (DEM) is relevant. In this method, solids are modeled with spherical discrete elements linked by cohesive bonds. However the Discrete Element Method requires a previous calibration step with simple mechanical loading. For example the nature and the mechanical properties of the cohesive bonds must be determined. After an analysis of the different mechanical loadings in green wood milling, a complete study of green wood compression is carried out. This experimental study covers the strain rates range of 10-3 to 103 s-1 using a hydraulic compression machine and the Split Hopkinson Pressure Bar technique. Wood specimens at different moisture content states are compressed longitudinally. This study enables us to observe the viscoelastic and hygroscopic behaviour of wood. The experimental and qualitative simulation results show that elastic brittle beams are not well adapted to be used in quantitative green wood milling simulations

Dynamic Study of Thin Wall Part Turning

The numerical simulation of machining process is a key factor in the control of parts machining process. Its development aims at improving the process reliability and reduces the time spent during the process planning stage. In this context, we use a specific time domain simulation allowing modeling the dynamics of a thin wall part turning operation. After having introduced the basics of the proposed approach we present a specific cutting test that has been designed to specifically measure and control the dynamics of the part and the cutting conditions of a finishing toolpath. The influences of the cutting speed and damping coefficient on the chatter occurrence are discussed. In order to better control the simulation uses, an analysis of the simulation parameters influences on the simulated results is proposed

Etude du comportement dynamique de broche d'un centre d'usinage dans son espace de travail : application en fraisage

Une méthodologie est proposée dans cet article dans le but de faciliter l’évaluation de la stabilité d’une opération de fraisage, pour une broche, un outil et une position connue de la broche dans son espace de travail. L’approche se base sur une procédure d’indentification du comportement dynamique de la broche qui se suit par un couplage des FRF du système (broche et attachement) avec le tronçon avant de l’outil d’usinage pour prédire la FRF en sa pointe. Celle-ci permet à l’aide d’une résolution analytique de l’équation caractéristique de la dynamique de fraisage dans le domaine fréquentiel de prédire la limite de stabilité critique. Dans le but d’étudier la variabilité du comportement dynamique du système usinant dans son espace de travail, la même démarche est appliquée dans différentes positions. Les profondeurs de passe critiques obtenu pas simulations sont comparées à celles qui sont obtenues par fraisage.The aim of this work is to provide a methodology helping on the evaluation of the milling process stability for a given spindle, tool and work space position of the spindle. The proposed approach is based on the spindle dynamic behavior identification. Then, a FRF coupling is made between the identified system and the tool model in order to obtain the FRF at the tool tip. Therefore, the critical depth of cut can analytically be calculated from the characteristic equation of the dynamic milling process in the frequency domain. In order to study the variability of the dynamic behavior of the spindle in the work space, the same approach is then, applied at different positions and compared against experimental milling.Financement de thèse CIFR

On some aspects of the CNEM implementation in 3D in order to simulate high speed machining or shearing

his paper deals with the implementation in 3D of the constrained natural element method (CNEM) in order to simulate material forming involving large strains. The CNEM is a member of the large family of mesh-free methods, but is at the same time very close to the finite element method. The CNEM’s shape function is built using the constrained Voronoï diagram (the dual of the constrained Delaunay tessella- tion) associated with a domain defined by a set of nodes and a description of its border. The use of the CNEM involves three main steps. First, the constrained Voronoï diagram is built. Thus, for each node, a Voronoï cell is geometrically defined, with respect of the boundary of the domain. Then, the Sibson-type CNEM shape functions are computed. Finally, the discretization of a generic variational for- mulation is defined by invoking an ‘‘stabilized conforming nodal integration’’. In this work, we focus especially on the two last points. In order to compute the Sibson shape function, five algorithms are pre- sented, analyzed and compared, two of them are developed. For the integration task, a discretization strategy is proposed to handle domains with strong non-convexities. These approaches are validated on some 3D benchmarks in elasticity under the hypothesis of small transformations. The obtained results are compared with analytical solutions and with finite elements results. Finally, the 3D CNEM is applied for addressing two forming processes: high speed shearing and machining

Identification of the heat input during dry or MQL machining

Machining with minimum quantity lubrication (MQL) has been the focus of many scientific investigations since the last 20 years. Nevertheless an acceptable method of predicting the thermal influences on the workpiece quality has still not been developed. This paper describes a simulation approach to estimate the distribution of the cutting energy during machining. During machining, the cutting power is measured to calculate the specific cutting power for each machining process – here drilling, tapping and milling of aluminum. In parallel, the warm-up of the part is measured by fast response thermocouples implanted closed of the machined zone. These thermocouples identify the cutting energy entering into the work piece