Dynamic modelling for the family of 5-axis CNC milling machines with application to feed-rate optimization

• Proof of common special characteristics of all possible 5-axis CNC mechanisms. • Novel explicit forward kinematic equation and closed-form inverse kinematic solution for all possible 5-axis mechanisms. • Novel dynamics model formulation for the class of 5-axis mechanisms. • New feed-rate optimization with dynamic constraints. • Validation by numerical simulations and experimental results. The 5-axis CNC milling machines are complex mechanical systems, and they can be designed with hundreds of 5 degrees of freedom mechanisms. The kinematic and dynamic modelling of machines is crucial for optimising the machine design and the milling process. However, formulating the dynamics model of 5-axis milling machines has never been proposed so far. Moreover, efforts have been made to develop kinematic models for the machines; however, formulating the generalized kinematic model for all possible 5-axis milling machines in closed form is challenging. In this paper, a novel method of kinematic and dynamic modelling for the entire family of 5-axis milling machines is developed. First, the special features of the machines family are fully studied to formulate effectively the generalized forward and inverse kinematic equations in closed-form. Second, by treating each 5-axis mechanism as a closed mechanism subject to a nonlinear kinematic constraint characterizing the machining process, the dynamics model for the whole family of 5-axis milling machines is successfully formulated, and the inverse dynamic equation is derived in closed-form. Finally, to demonstrate the importance and impact of the proposed method, useful applications were conducted; and these were supported by both numerical simulations and actual cutting experiments. Compared with previous works, our study includes new generalized equations of kinematics and dynamics for the family of 5-axis milling machines, and useful applications of the proposed equations for optimization of the 5-axis machining.