Calculation of the Heat Flux from a Ball Screw Nut to the Nut Raceway

Abstract

In the field of precision machining, temperature fluctuation tends to cause the most significant machining errors. In particular, heat, which is generated in the nut of the ball screw feed system during movement, can deform the screw shaft significantly. In order to calculate and evaluate the thermal deformation of the ball screw shaft, the rate of the heat transfer from the nut to the screw shaft must be known. This rate can be calculated by subtracting the heat transfer rate to the nut raceway from the heat generation rate of the nut. Hence, it is necessary to calculate the heat flux from the nut to the nut raceway. This paper introduces a novel method to calculate the heat flux from the nut to the nut raceway. The new approach also enables calculations for different operating conditions. Furthermore, an experimental setup is established to measure the temperature increase, from 0 to 180 s after the nut starts moving, for various operating conditions. It is then theoretically shown that the 0–180 s temperature increase/heat flux curves for the nut are “universal”, i.e., the curve remains unchanged for the different operating conditions. Subsequently, a thermal model using the finite element method (FEM) is developed to simulate the nut temperature increase over time, which is then compared with the experimental data. As a result, it becomes possible to determine the heat flux from the nut to the nut raceway and calculate the 0–180 s temperature increase/heat flux curve (ΔT˜0~180s,Training Data) for the training group. Finally, the heat flux from the nut to the nut raceway is calculated for ten different operating conditions in the test group using the 0–180 s temperature increase/heat flux curve of the training group (ΔT˜0~180s,Training Data). The corresponding temperature curves are then calculated by inputting the values of the heat fluxes into the FEM model. The highest root mean square error (RMSE) between the calculated and experimentally measured temperature increase was 0.16 °C for Test 7 (the error was 10.7%). This result indicates that the new method is valid and feasible for calculating the heat flux from a ball screw nut to the nut raceway.