Piecewise compensation of thermal errors of a ball screw driven CNC axis

The article presents compensation of thermal errors of a computerized numerical control (CNC) axis. A partial differential equation (PDE) model of ball screw temperature distribution was utilized. The model takes into account non-steady-state localized heat sources and the effect of heat conduction between the screw and the machine body. To tune and validate the model, temperature distribution of the axis was measured on-line during its operation. The change of the model parameters related to the change of the axis movement velocity was presented. The article shows, that utilization of the thermal PDE model to compensate thermal errors, though effortful, is beneficial, but noticeably less accurate than the utilization of compensation based on the measured temperature values.