Multibody dynamic modeling of five-axis machine tools with improved efficiency

Predicting the dynamics between the tool and the workpiece is crucial for simulating the control performance and vibration of a machine tool as it changes its pose during machining. This paper presents a computationally efficient multibody dynamic model to simulate the pose-dependent dynamics of machine tool structures from the reduced-order elastic models of its substructures. The flexible substructures are assembled with a Jacobian-based kinematics formulation at the joints without needing to use Lagrange multipliers and constraint equations to define the five-axis dynamics of a machine tool, leading to a significant reduction in the number of unknowns. The frequency response of the machine is quickly updated as the machine changes its kinematic configuration and position by adjusting the sliding and rotating joint parameters in a geometric Jacobian matrix instead of calculating a new set of joint forces between the substructures. The order of the multibody model is further reduced by only including the most dominant vibration modes of the machine tool which are identified based on their contributions to the total kinetic energy. Identification of the most dominant modes is carried out directly on the multibody model of the assembled machine tool instead of individual full-order substructure models which substantially increases the number of excluded vibration modes. The proposed multibody model is demonstrated to predict the frequency response of a five-axis machine tool with a 90% faster computation than the existing multibody models based on reduced-order substructures.