On-machine workpiece straightness profile measurement using a hybrid Fourier 3-sensor method

To compensate for the straightness error of the slide of a machine tool efficiently and precisely, on-machine self-calibrating measurement of the manufacturing error is critical. The Fourier 3-sensor (F3S) method proposed by Fung is promising in measuring the straightness profile of a workpiece accurately on a machine. However, it still suffers from two main challenges: the height difference between the second and the third probes and the stochastic uncertainty, both of which can significantly decrease the measurement precision. In this paper, we counter these two challenges, respectively, and propose the solutions accordingly. First of all, by resorting to the Laplace transform, an algorithm for the F3S method is proposed. Second, the adverse effect of the height difference between the second and the third probes is demonstrated. An approach is presented for estimating the height difference, and compensating for this. Third, to alleviate the stochastic uncertainty, a hybrid F3S method is developed: several F3S measurements are first performed under different probe spacings; then, the optimal Fourier coefficients of the straightness profile are individually selected from the candidate estimates in accordance to the determinant of the transfer matrix. Finally, practical straightness profile measurements were performed, respectively, on a grinding machine by adopting the hybrid F3S method and on a Taylor Hobson surface profiler. The results show that compared with the conventional F3S method, the hybrid F3S method reduced the measurement uncertainty significantly, and the straightness profiles estimated by the hybrid method and by the surface profiler were consistent with each other.