Capability analysis of the dynamic R-test measuring thermo-elastic errors of a five-axis machine tool

Five-axis machine tools are essential in industrial applications for their ability to efficiently machine complex geometries with high accuracy. The challenge of maintaining accuracy over long machining times is exacerbated by thermal effects that can contribute to significant geometric errors. To analyze these thermally induced geometric errors, also known as thermo-elastic errors, it is first necessary to measure them. Since the thermo-elastic state of the machine can change within a few minutes, the measurement method must have a short measurement time and the capability to measure a large number of geometric errors simultaneously. A potential promising method is the dynamic R-test, which can record the displacements of the sensor nest on the tool center point, synchronized with the actual positioning of the axes during a dynamic movement, and calculate the geometric errors using a kinematic model. The feasibility of the data acquisition method was previously demonstrated, but not the precise analysis and validation of its capability. Therefore, this study analyses the capability of the dynamic R-test to measure thermo-elastic errors in practice considering the influence of method, machine tool, human and environmental measurement uncertainties. For this purpose, numerous relevant measurement uncertainties are quantified, and a comprehensive measurement uncertainty analysis is performed using the Monte Carlo method. The results are then used to optimize the measurement method, striking a balance between time efficiency, measurement uncertainty and the number of measurable errors. They are validated by an experimental study in which thermo-elastic errors are artificially generated using the CNC geometric error compensation function on a demonstrator machine and then measured. This demonstrates the capability of the optimized dynamic R-test to measure thermo-elastic errors in practical settings, as well as a practical approach to the measurement uncertainty analysis and implementation of the dynamic R-test for five-axis machine tools.