Effect of Thermal Changes on the Squareness Error Between Linear Axes of Machine Tools

The international standard ISO 230-3 generally specifies four different tests to characterise the thermal behaviour of machine tools. All these tests quantify performance of a single linear or a single rotary axis/component of the machine tool under certain thermal conditions. However, this standard does not address the influence of thermal changes in the assembly of machine tools’ linear axes, namely all their mutual squareness, EC0X, EA0Y, and EB0Z. This study examines the variation of squareness error between each pair of linear axes of machine tools. The mutual squareness errors between all three linear axes of a 3-axis vertical machining centre (VMC) with kinematic chain of [w X’ Y’ b Z (C) t] were measured using the Renishaw QC-20W ballbar. Reasons for this choice of instrument, supported by an analysis of the associated uncertainty contributors are provided to show that this is a robust and convenient method to measure these thermal effects. The measurements were repeated over a period of two weeks, where the ambient temperature naturally varied by 4.5 °C. Findings of this study indicate significant changes of 12 μm/m and 14 μm/m in squareness error in two vertical planes, YZ and ZX, respectively, whereas the squareness in the horizontal XY plane shows negligible variation. The reasons for these differences are explained by the mechanical construction of the machine. Monitoring the temperature of the machine reveals a significant correlation between the temperature of elements of the Z-axis and the squareness of this axis with respect to both horizontal axes, X and Y of this machine. An uncertainty analysis based on GUM for squareness measurements using a ballbar in the three principal planes reveals that the expanded uncertainties are ± 2.2 μm/m, ± 7.1 μm/m, and ± 7.5 μm/m in the XY, YZ, and ZX planes, respectively. The paper concludes by proposing a suitable outline method of test for the thermal influences on the squareness error of precision machines, in line with other parts of the ISO 230 series of standards.