The master’s thesis deals with building mechatronics model of machine tool head delivered by company TOSHULIN,a.s. for purpose of damping vibration. Mechanical part of the model is based on modeling of system of flexible bodies. Components are modeled in FEM program ANSYS and subsequently reduced using Craig-Bampton method. The system of flexible bo-dies is created in MBS program ADAMS. Model is linearized and subsequently reduced. As a element of active damping is used linearized model of magnetic bearing. For control is desig-ned PID controller. The comparison of damped and undamped model is conducted in the end.

In multibody systems, mechanical components (bodies) can be assumed rigid (non-deformable), if their deformation is negligible. For components with non-negligible deformations several methods were developed to represent their deformation. The most widely used method is the floating frame of reference. In this formulation the deformable body is represented by a finite element model whose deformation is described with respect to a local body-fixed frame. Unfortunately, finite element models can include many degrees-of-freedom, which stand in contradiction to the requirements of multibody dynamics. System truncation is therefore inevitable to support computational efficiency. The use of modal data in representing a deformable body is well understood in the multibody community. By truncating modes associated with higher frequencies, the total degrees-of-freedom of the deformable body can be reduced while preserving its dynamic eigen-properties. However, since the finite element model may be in contact with other moving bodies, the reduction technique needs to address the issue of moving boundary conditions. The component mode synthesis reduction methods are such techniques that describe the deflection of all the nodes as a superposition of different types of modes. However, it is limited in the fact that the nodes in contact need to remain in contact throughout a simulation. In some applications these nodes may change, i.e. a node that is in contact with another body or the ground at one instant may become free at the next instant. The present methodologies in multibody modeling of a deformable body with modal data have not yet addressed the issue of changing contact nodes. This research highlights the usefulness of orientation invariant characteristics of some deformable bodies. It proposes to define orientation invariant degrees-of-freedom of the reduced model in Eulerian space, while the remaining degrees-of-freedom are defined in Lagrangian space. In some circumstances, this approach can resolve the issue of changing contact nodes. The combination of Eulerian and Lagrangian formulation for component mode synthesis reduced finite element models is a new concept in deformable multibody dynamics.

The thesis deals with building and utilization of mechatronic models which are based on modeling of system of rigid and flexible bodies. Such models are then used for analysis of behavior of complex systems, for instance machine tools. The work is concentrated on analysis of self-excitation of a machine tool. The appearance of the self-excitation during the machining may be influenced by several methods described in the work. The evaluation of the appearance of the self-excitation is analyzed via so called lobe diagram. It is necessary to know transfer function describing the impact of acting forces on the deformation of the system (machine tool in this case) for compilation of the lobe diagram. The whole structure of the model shows compliant behavior which dramatically influences the transfer function thus the approach to the modeling of mechanical parts as flexible bodies is proposed. There are created models of modally reduced flexible bodies based on modified CAD models which have same modal properties as non-reduced FEM models up to the maximal excitation frequency. The reduced models have significantly lower number of degrees of freedom and it is possible to work with them in multi-body simulation tools and at the same time they contain the information about the deformations. The work utilizes Graig-Bamton method which is implemented to the ANSYS. The whole model is consequently built and analyzed in ADAMS. It is possible to export the linearized model of the system in form of state matrices which are used for writing of the transfer function. The conditions of stability of the machining process are then evaluated via the lobe diagram. The proposed thesis presents the modeling of mechatronic systems with stiff and rigid bodies. The approach may be used for analysis of machining tools as well as for development of advanced mechatronic systems with active damping, etc.