Comprehensive knowledge and information about the static and dynamic behaviour of machine tools, cutting processes and their interaction is essential for machining system design, simulation, control and robust operation in safe conditions. The very complex system of a machine tool, fixture and cutting tools during the machining of a part is almost impossible to model analytically with sufficient accuracy. In combination with increasing demands for precision and efficiency in machining call for new control strategies for machining systems. These strategies need to be based on the identification of the static and dynamic stability under both the operational and off-operational conditions. To achieve this it is necessary to monitor and analyze the real system at the factory floor in full production. Design information and operational data can then be linked together to make a realistic digital model of a given machining system. Information from such a model can then be used as input in machining simulation software to find the root causes of instability. The work presented in this thesis deals with the static and dynamic capability of machining systems. The main focus is on the operational stability of the machining system and structural behaviour of only the machine tool, as well. When the accuracy of a machining system is measured by traditional techniques, effects from neither the static stiffness nor the cutting process are taken into account. This limits the applicability of these techniques for realistic evaluation of a machining system’s accuracy. The research presented in this thesis takes a different approach by introducing the concept of operational dynamic parameters. The concept of operational dynamic parameters entails an interaction between the structural elements of the machining systems and the process parameters. According to this concept, the absolute criterion of damping is used to evaluate the dynamic behaviour of a machining system. In contrast to the traditional theory, this methodology allows to determine the machining system's dynamic stability, in real time under operating conditions. This framework also includes an evaluation of the static deformations of a machine tool.  In this context, a novel concept of elastically linked system is introduced to account for the representation of the cutting force trough an elastic link that closes the force loop. In addition to the elastic link which behaves as a static element, a dynamic non-contact link has been introduced. The purpose is to study the non-linear effects introduced by variations of contact conditions in joints due to rotational speed. / QC 20111123