A novel dynamic model for multiple configurations of machine tools using a coordinate transformation method

Virtual machine tools have been used widely for simulating designs in computer environments to determine optimal design parameters without the need for manufacturing prototypes. Machine tools include different multiple configurations that are designed to be suitable for the differing requirements of production. To date, studies on dynamic analysis have been limited to a few-axis machine tools of a specific configuration, such as a 3-axis milling machine or a 4-axis grinding machine. Here, we propose a novel method to focus on the dynamic analyses of multi-axis machines with differing multiple configurations. The motion equations for multiple degrees of freedom of linear and rotary axes are established by a Lagrange energy method, equilibrium equations, and Newton's second law. This technique formulates the motion equations for each axis, and then further develops them for a multi-axis machine through a combination process and a transformation matrix. The library includes five dynamic model components, built to simulate 1236 different configurations of a machine tool. A dynamic analysis was applied to a control system to simulate the control signals of a virtual machine, which include stepped, ramped, curved, sinusoidal, and circular responses, and frequency response functions. The simulated and experimental results demonstrated that the method has high accuracy and reliability for one-, two-, and four-axis machine tools. Thus, this method can simulate the dynamic analyses of multi-axis machines and different multi-configurations without the need to build a specific configuration for each machine. It is recommended for selecting optimal motors, design parameters, and control parameters of the multiple configurations in a machine tool.