Error motion of an ultraprecision axis of rotation has great influences on form error of machined parts. This paper gives a complete error analysis for the measurement procedure including nonlinearity error of capacitive displacement probes, misalignment error of the probes, eccentric error of artifact balls, environmental error, and error caused by different error separation methods. Nonlinearity of the capacitive displacement probe targeting a spherical surface is investigated through experiments. It is found that the additional probe output caused by lateral offset of the probe relative to the artifact ball greatly affects the measurement accuracy. Furthermore, it is shown that error motions in radial and axial directions together with eccentric rotation of the artifact lead to lateral offset. A novel measurement setup which integrates an encoder and an adjustable artifact is designed to ensure measurement repeatability by a zero index signal from the encoder. Moreover, based on the measurement setup, once roundness of the artifact is calibrated, roundness of the artifact can be accurately compensated when radial error motion is measured, and this method improves measurement efficiency while approaches accuracy comparable to that of error separation methods implemented alone. Donaldson reversal and three-probe error separation methods were implemented, and the maximum difference of the results of the two methods is below 14 nm. Procedure of uncertainty estimation of radial error motion is given in detail by analytical analysis and Monte Carlo simulation. The combined uncertainty of radial error motion measurement of an aerostatic spindle with Donaldson reversal and three-probe methods is 14.8 nm and 13.9 nm (coverage k = 2), respectively.

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