A hybrid three-probe method for measuring the roundness error and the spindle error

• The formulation for determining the suppressed harmonics is derived.
• The harmonic measurement errors are investigated.
• A hybrid three-probe method is developed.
• Cross-correlation is applied to measure the unknown probe angles.

The three-probe method is the most widely used technique for separating the artifact roundness error from the spindle error, with the superiority available for in situ measurement. For further improving the measurement accuracy of the three-probe method, in this paper, the harmonic measurement errors are investigated analytically and experimentally. To achieve this aim, firstly, according to the transfer matrices W(k), the harmonics are classified into two types: the suppressed harmonics with zero W(k) and the unsuppressed harmonics with no-zero W(k). Then, on one hand, through mathematical deduction, the formulation for determining the suppressed harmonics is derived; on the other hand, the measurement errors to the unsuppressed harmonics are experimentally acquired, and the experimental results demonstrate that the measurement errors to the unsuppressed harmonics are greatly related to the determinant of the transfer matrix |W(k)|, but not rigorously in inverse proportion to |W(k)|. Based on the conclusions drawn from the investigations, a hybrid three-probe method is constructed, where several conventional three-probe measurements are performed for optimizing individual harmonic coefficients. Experiments verify that the hybrid three-probe method is more robust to the error sources than the conventional method.