Uncertainty propagation from probe spacing to Fourier 3-probe straightness measurement

Reliable and precise straightness profile measurements are crucial for manufacturing ultra-precision components and are capable of further enhancing their accuracy. The Fourier three-probe (F3P) straightness measurement allows for precise assessment of the workpiece profile on the machine by eliminating the harmful influence of the error motion of the sliding table. However, the probe spacing uncertainty deteriorates the measurement accuracy remarkably; and, the affecting mechanism behind this phenomenon has not yet been studied in detail. In this context, this paper thoroughly investigated the propagation of the probe spacing uncertainty in the F3P measurement. First, the influence of the probe spacing deviation is analyzed. Next, by calculating the partial differential of Laplace transform of the workpiece profile, we algebraically deduce the probe spacing uncertainty propagation law, especially in the harmonic domain. Subsequently, Monte Carlo simulations are carried out to confirm the derived propagation law. To reduce uncertainty propagation, a hybrid approach is presented: (I) F3P measurements are carried out under changing probe spacings to produce several sets of Fourier coefficients; (II) optimal harmonic estimates are selected individually according to the harmonic uncertainty. Finally, simulations and experimental measurements are performed for verification.