Modelling and simulation of the milling action

Abstract

The paper describes the mathematical modelling and simulation of the whole milling action in a milling machine. The mathematical model includes: (a) a model of the dynamics of the X axis drive, (b) a model of the dynamics of the spindle drive, (c) a model of the dynamics of the cutting process itself with cutting forces and torques and (d) the interconnection of (a), (b) and (c) to form the complete model of the milling action. The model uses both z and s plane transfer functions in order to model discrete and continuous parts of the system. The models of the X axis drive dynamics and spindle drive dynamics include models of the digital filter and analog converter in the velocity and position loop control. Friction is modelled in the machine table (part of the X axis drive) as a combination of stiction, coulomb and viscous friction. The model of the X axis drive dynamics is explained in detail whereas the model of the spindle drive dynamics is derived from the former. The model of the cutting process dynamics, which connects the other two models, is based upon a relatively simple analysis of the forces generated during face milling. The model is designed to be simulated by an existing computer simulation package and for this reason some dynamic equations are reoriented in order to avoid differentiation. This part of the paper concludes with an overall block diagram to represent the model of the whole milling action. The simulation of the mathematical model is then described, as are the tests carried out on the model and the actual machine in order to validate the model.