A Detailed Uncertainty Analysis of the Displacement Sensors with Three-point Method

We researched an autonomous calibration method of the zero-difference (i.e. the difference between zero values of each sensor probe which brings a serious error to the measurement values) in the three-point method using three displacement sensors for measuring the surface straightness. The outline of the calibration method is as follows. (1) a simple disc gauge made by CNC turning machine, etc. is used for the calibration of the zero-difference between the three sensors. (2) the disc gauge rotates a few revolutions and moves parallel to the three displacement sensors built into a holder. (3) the geometrical parameters between the sensors and the disc gauge are simultaneously acquired at each predetermined movement of the sensors and the zero-differences are determined by our developed algorithm.

In this paper, the detailed uncertainty analysis of the displacement sensors of a surface straightness measurement system with the three-point method is proposed with basic mathematical method. The main uncertainty components are regarded to be the linearity, sensitivity, zero-value, and repeatability of the measurement of the sensors. In particular, the coefficient elements of the uncertainty components arisen from the systematic effect, which cannot be reduced to zero even if both the sampling number for calibrating the system and that for measuring the shape of an object surface are made infinitely large, are investigated with respect to the influence of them on the measurement uncertainty. The derivation and analysis of the equation which describes the expanded uncertainty U of the measured shape considering the above uncertainty components are studied in detail with some numerical simulations.