The modelling and correction of ball-screw geometric, thermal and load errors on CNC machine tools

In the modern global economy, there is a demand for high precision in manufacture as competitive pressures drive businesses to seek greater productivity. This results in a demand for a reduction in the errors associated with CNC machine tools. To this end, it is useful to develop a greater understanding of the mechanisms which give rise to errors in machine tool drives.
This programme of research covers the geometric, thermal and load errors commonly encountered on CNC machine tools. Several mathematical models have been developed or extended which enable a deeper understanding of the interaction between these errors, various details of ballscrew design and the dynamic behaviour of ballscrew driven systems.
Some useful models based on the discrete matter or “lumped mass” approach have been devised. One extends the classical eigenvalue method for finding the natural frequencies and other dynamic characteristics of ballscrew systems to include viscous damping effects using a generalised eigenvalue approach. This gives the damping coefficient of each predicted vibration mode along with the estimates of the natural frequencies, enabling many of the natural frequencies predicted by standard undamped natural frequency analyses to be dismissed as being of little consequence to the vibratory behaviour of the system.
A development of this modelling method gives the sensitivity of the system to changes in stiffness and damping characteristics, which is helpful at the preliminary design stage of a ballscrew system, and is an aid in deciding the most convenient remedy to vibration problems which may occur in service.
The second set of lumped-mass models is specially developed to take account of the changes in the configuration of the system with time as the nut moves along the screw while taking into account the non-linear phenomena of backlash and Coulomb friction. These can deal with the axial, torsional and transverse degrees of freedom of the system and predict many aspects of the dynamic behaviour of a ballscrew system which have an effect on the errors arising from such systems. They also include features which calculate the energy converted to heat by all the energy dissipative mechanisms in the model which can be used in conjunction with models already developed at the University of Huddersfield to predict thermal errors.
Further, a strategy for compensation of some of these errors has been devised