Analytical estimation of measurement uncertainty in surface plate calibration by the Moody method using differential levels

Surface plate quality influences the calibration of artifacts, instruments, working gauges and, by extension, the quality of manufactured parts. A statement of uncertainty for the surface plate calibration is needed for conformance testing and for estimating uncertainty in calibrations that rely on the surface plate. An analytical approach to the estimate of uncertainty for a common measurement method is given. The residual height at each position on the surface is expressed in terms of the measurement parameters and the measured angles. Uncertainty of each residual height value is then derived following the common methods for propagation of uncertainty. The maximum uncertainty is at the center of the surface and the calculated bounds on error compare well with values of closure from actual measurements. The uncertainty of height values is proportional to the spacing of the measurement positions and to the squareroot of the number of positions. Using data from many plates of various size and quality, a generalized uncertainty in flatness for the measurement method was estimated. The derivations also allow calculations for specific applications. Finally, a method is proposed for reporting uncertainty in surface slope which is required for estimating uncertainties of items calibrated on a surface plate.