Among the strategic sectors in French industry, aeronautics takes a special place both in terms of image and innovation and the number of jobs involved despite a still economic context unfavorable. To preserve this force and dynamic facing the increased competition from emerging countries, it is essential to maintain the competitiveness of our industries and the capacity for innovation. This requires the continuous development of new production processes and alloys with high added value. In the case of titanium alloys, machining is identified by industry in this sector as a critical operation despite significant technological progress over the last decade. Indeed, many finished parts are machined integrally in the mass causing a significant financial cost due to poor machinability compared to a large number of other alloys such as aluminum alloys. To improve the machinability of titanium alloys, the traditional approach is to optimize the machining process by focusing, for example, on tool geometry or cutting forces based on turning or milling models. Our approach focuses on the role of the microstructural parameters of the material and their interaction with the cutting tool on the integrity of surfaces. The research project is devoted to the understanding and the quantification of the role of the microstructure of titanium alloys on the machinability and wear of cutting tool. The originality of our approach is based on the design of a set "model" microstructures to understand the basic physical, chemical and mechanical mechanisms. This study will include a fine analysis of the material/tool chemical reactivity and expertize of the machining chips according to the starting microstructure as well as a crystalline scale modeling. This project is challenging because it is at the limits of the state of art, and because it is based on a multi-scale and quantitative approach taking into account fundamental physics, metallurgy, mechanical and modeling, and finally because it deals with high added value materials that are used in a competitive international business. To achieve the goal will allow establishing the best link between the microstructure and the machinability properties and contributing through this approach to the design of "ideal" microstructures as a function of requirement specification and to provide the required material data for the simulation of the machining process. The expected progress will also help tool manufacturers to develop new coatings and even new tools to improve surface quality and reduce wear, leading to reduced cutting tool consumption.