Different techniques are used to obtain approximate solutions for delayed functional differential equations (RFDEs). All these models used the so-called stability lobe diagrams, to choose the maximum axial depth of cut for a given spindle speed associated with a free chatter in machining. In this research paper, the ZOA (Zeroth Order Approximation) and SD (Semi Discretization) methods are explained, developed and used to obtain the stability lobe diagrams for a milling cutting system with two degree of freedom, in high speed machining case.

his paper presents a combined experimental and theoretical investigation and proposes a mechanical load modeling of a multidirectional layer CFRP drilling to avoid fibers delamination by a better choice of their orientations. A first step consists in working with unidirectional CFRP to correlate cutting mode (opening, shear and bending) with force level depending on the angular tool position. The discretisation of the cutting edge is employed to know the exact contribution of each elementary part of the edge, resulting in a complete drill operation modeling (tip penetration, full engagement and exit). A second step consists in using this unidirectional approach to model a multidirectional layer CFRP drilling. In this case, layers are cut simultaneously which induce brutal mechanical load variation. A summation method is used to estimate the force level depending on fiber arrangement. Optimal orientation combinations are underlined by this approach, in order to improve the CFRP design, by considering the manufacturing concerns.

The machining of the complex forms is a characteristic of moulds and matrices manufacturing. Owing to the fact that these forms became increasingly complicated, the production of moulds and matrices require tolerances which are particularly severe. One of the principal objectives to be reached is the precision of machining and the improvement of the micro geometrical state of machined surfaces, for the minimization of polishing operations after machining which still necessary to obtain a good finished part, which is required by the car industry and the aeronautic industry. To reach these goals, it is important to choose a tool which fulfils the requirements of a machining which could be carried out in various orientations. This will make possible the machining of complex forms by using a milling machine with several axes. Among the tools allowing the realization of these complex forms, there is the ball-end mill. The goal of this work is to study the geometry of the mill's spherical part, in order to determine the contact zones between the part of complex form and the tool which is following a trajectory in space.

We have determined in which conditions we have a regenerative vibration cases (chatter). We have used the simulation of a machining system dynamic behaviour. A cutting force law was obtained by an indirect method, by comparing between simulation results and experimental ones.

During manufacturing process of mechanical parts, the method of material remove by cutting tools have a significant importance, according to the matter of the part manufacturing process and to its raw elaboration method. On one hand, the characteristics of machining operations depend on the “studies office” choices during the part conception (the shape, the material, ...). On the other hand, they also depend on the “methods office” choices (machining gamut, choice of: machines, tools, cutting parameters, and tools paths, ...). For the “methods office”, some bad choices of cutting forces could change the final quality of the machined part. In this order, we have studied the dynamic cutting law evaluation problem. This consists in developing a simplified phenomenological cutting force model, in a case of turning under orthogonal machining conditions in presence of vibrations.