A parametric modeling method for the pose-dependent dynamics of bi-rotary milling head

Bi-rotary milling head is one of the core components of five-axis machining center, and its dynamic characteristics directly affect the machining stability and accuracy. During the sculptured surface machining, the bi-rotary milling head exhibits varying dynamics in various machining postures. To facilitate rapid evaluation of the dynamic behavior of the bi-rotary milling head within the whole workspace, this article presents a method for parametrically establishing dynamic equation at different postures. The rotating and swing shafts are treated as rigid bodies. The varying stiffness of the flexible joints (such as bearings and hirth coupling) affected by gravity and cutting force at different swing angles is analyzed and then a multi-rigid-body dynamic model of the bi-rotary milling head considering the pose-varying joint stiffness is established. The Lagrangian method is employed to deduce the parametric dynamic equation with posture parameters. The static stiffness, natural frequencies and frequency response functions at different postures are simulated using the parametric equation and verified by the impact testing experiments. The theoretical and experimental results show that the dynamics of the bi-rotary milling head vary with the machining postures, and the proposed method can be used for efficient and accurate evaluation of the pose-dependent dynamics at the design stage.