Modelling the dynamic behaviour of a ballscrew system taking into account the changing position of the ballscrew nut

An understanding of the dynamic characteristics of a machine tool is a vital element in the control of the machine which has a direct affect on the precision of the machining which can be undertaken. The torsional behaviour of the motor, coupling drive (belt, chain, gear or direct) and ballscrew coupled with the axial movement of the table or saddle and the ballscrew nut have the most direct effect on machining accuracy. Nevertheless transverse dynamic movement of drive system components can have an affect on machine performance and system component life especially if vibration problems occur. This paper discusses the development of an approach to investigating the dynamic characteristics of an axis drive on a CNC milling machine in which all six degrees of freedom are taken into consideration. The mechanical elements of the drive are modelled as point inertias coupled by springs and dampers. The ways in which energy is dissipated, such as friction and damping, also are taken into account. The solution technique includes a series method which can cope with non-linearities in the stiffness and damping behaviour of the system components as well as the changes in the relative orientation of parts of the machine as a duty cycle unfolds. Comparison with measurements taken from a ballscrew test rig demonstrate some of the capabilities of the method.