Uncertainty analysis of phase and amplitude of harmonic components of bearing inner ring four-point roundness measurement

The four-point roundness measurement method enables the measurement of roundness without a requirement for a precise rotating motion of the workpiece or a measurement sensor. The four-point roundness measurement method can separate the roundness profile and the motion of the rotating axis of the workpiece. In the present study, the uncertainty of the four-point roundness measurement of a bearing inner ring was analysed. The bearing inner ring was installed in its operating position on the shaft of a large rotor during the measurement in order to investigate the bearing inner ring roundness profile in operating conditions. Since the measurement evaluation using the four-point method is complex, the uncertainty analysis was conducted through a Monte-Carlo simulation, using realistic error sources in typical measurement conditions. The uncertainty of both the amplitude and phase of the harmonic components of the roundness profile was analysed for the 2nd till the 30th harmonic component. Attention was directed especially towards the phase of the harmonic components, since the uncertainty of the phase is analysed very little in existing research studies. In addition, the phase of the harmonic components of the roundness profile is important when considering compensative precision grinding applications of round workpieces. The results show that below the 10th harmonic component, the maximum amplitude standard uncertainty was circa 0.5 μm, and the maximum phase standard uncertainty was circa 5°. The standard uncertainties of the amplitudes for the complete harmonic component range were below 1.3 μm for odd components and 0.2 μm for even components. The maximum standard uncertainties of the phases for the complete harmonic component range were circa 15° for odd components and circa 5° for even components. The measured roundness profile itself did not have an effect on the uncertainty of the method.