Ball-screw thermal errors - a finite element simulation for on-line estimation

Ball-screws are often used in machine tools with only a rotary encoder feedback on the end of the screw. Since this provides position feedback to the controller, any errors in the screw affect the accuracy of the machine. Also, these errors may change significantly when heating of the screw occurs during machining. This is often overcome by using a linear scale to provide the feedback. Unfortunately, fitting such scales to many machines may be mechanically difficult and costly. This paper describes the development of a system that utilises a minimum of temperature measurements as inputs to a thermal simulation model of the ballscrew. Thus it is possible to estimate on-line the thermal errors of the ball-screw, assuming that position measurements of the nut are available from the rotary encoder. From these positions and the temperatures of the nut and bearings it is possible to estimate the speed of the screw and hence, assuming a knowledge of the frictional and heat transfer characteristics, the heat generated in the nut, bearings and screw. The thermal model constitutes a one-dimensional finite analysis of the whole length of the screw. The output of the model is a temperature distribution along the screw and an estimate of the thermal errors along the screw. Also described is an experimental test rig, which provides facilities to test the model on-line. A laser position measurement is used to compare with the estimated position derived from the model. The results are graphically displayed and saved for future use in optimisation software to determine the parameters of the thermal model which best fit the experimental data. Improvements of better than 90% in the thermal error have been obtained.