Dynamic Hybrid Modeling of the Vertical $Z$ Axis in a High-Speed Machining Center: Towards Virtual Machining

This paper describes the modeling and simulation of the $Z$ axis of a five axis machining center for high-speed milling. The axis consists of a mechanical structure: machine head and electro-mandrel, a CNC system interfaced with the feed drive, and a pneumatic system to compensate for the weight of the vertical machine head. These subsystems were studied and modeled by means of: (1) finite element method modeling of the mechanical structure; (2) a concentrated parameter model of the kinematics of the axis; (3) a set of algebraic and logical relations to represent the loop CNC-$Z$ feed drive; (4) an equation set to represent the functioning of the pneumatic system; and (5) a specific analytical model of the friction phenomena occurring between sliding and rotating mechanical components. These modeled subsystems were integrated to represent the dynamic behavior of the entire $Z$ axis. The model was translated in a computer simulation package and the validation of the model was made possible by comparing the outputs of simulation runs with the records of experimental tests on the machining center. The firm which promoted and financed the research now has a virtual tool to design improved machine-tool versions with respect to present models, designed by traditional tools.