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

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

We investigated an autonomous zero-difference calibration method in the three-point method using three displacement sensors for measuring surface straightness (i.e. the difference between zero values of each sensor probe, which introduces a significant error to the measurement values). The following is a description of the calibration procedure. (1) For calibration of the zero-difference between the three sensors, a simple disc gauge made by a CNC turning unit, etc. is used. (2) the gauge for the disc rotates a few times and travels parallel to three built-in displacement sensors in a holder. (3) At each predetermined movement of the sensors, the geometrical parameters between the sensors and the disc gauge are simultaneously acquired, and the zero-differences are calculated by our established algorithm. The three-point approach is used in this paper to suggest a detailed uncertainty study of the displacement sensors of a surface straightness measurement device using a simple mathematical method. The linearity, sensitivity, zero-value, and repeatability of the sensor measurements are considered the key uncertainty components. The coefficient elements of the uncertainty, in particular. The impact of components arising from the systematic effect, which cannot be reduced to zero even if both the sampling number for calibrating the device and that for measuring the shape of an object surface are rendered infinitely high, on measurement uncertainty is investigated. With some numerical simulations, the derivation and analysis of the equation that describes the extended uncertainty U of the measured form considering the above uncertainty components are studied in detail.

Author (s) Details

Ikumatsu Fujimoto
Okuwa Technical Research Center, Yamaguchi, Japan

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