The Influence of the Setup on the Result of Measuring the Roundness of an Anuloid Surface

In engineering practice, anuloid surfaces are produced that are subject to strict requirements in terms of accuracy (e.g., in the bearing industry). Roundness is also often measured. The accuracy of the roundness measurement does not only depend on the accuracy of a particular metrological system. The setting of the component on the measuring device can also have a significant influence on the accuracy of the measurement. The axis of the measured surface must be perpendicular to the section in which the roundness is measured. Tilting the measured surface causes a systematic measurement error, which depends on the size of the tilt angle and the parameters of the measured surface. This study presents mathematical relations for the calculation of this error when measuring roundness on an anuloid surface. Mathematical relations for the internal and external surfaces formed by the inner and outer parts of the anuloid are derived herein. There is also a theoretical analysis of the influence of inclination and the parameters of the measured surface on the size of this error. Theoretically calculated values were compared with practically measured values of roundness. The error had a negative effect on the accuracy of the roundness measurement. It affected the roundness value, the second harmonic component, and also the roundness profile itself.