Definitions and correlations of 3D volumetric positioning errors of CNC machining centers

The worldwide competition and quality standards such as ISO 9000 and QS 9000, demanded tighter tolerance and regular maintenance of all machine tools. To generate good quality or accurate parts, the measurement of true 3 dimensional volumetric positioning accuracy of a machine tool is critical. However, the 3D volumetric accuracy has not been defined in the standards. Currently, both the ASME B5(TC52) and ISO 230(TC39) are working on a new definition of volumetric accuracy. There are many possible definitions, such as the root mean square of the 3 axes displacement errors, the root mean square of the total errors in the 3-axis directions, the maximum 4 body diagonal displacement errors without squareness and the maximum 4 body diagonal displacement errors with squareness errors. Reported here are some definitions of 3D volumetric positioning errors and their correlations. We have measured the positioning errors of 10 CNC machine tools, representing a selection of modern mid-size CNC machining centers. Based on these measurement results, the 3D volumetric errors using various definitions can be calculated. It is concluded that the 4 body diagonal displacement errors with squareness errors correlate with the true 3D volumetric errors very well. It may be used as a quick check of 3D volumetric accuracy of CNC machine tools.