Measurement uncertainty of non-incremental, non-contact, in-situ shape measurements

Abstract

Abstract Optical measurement systems work fast and non-contact and can achieve sub-micron precision. Thus they appear to be well suited for in-situ shape measurement of fast rotating objects such as cutting processes in metal working lathes. Most optical measurement systems, however, allow an axial position measurement only. In order to retrieve the shape of the object from a distance measurement, the distance between the sensor and the centre of the object has to be known. Otherwise, deviations of this distance, for instance due to temperature effects or vibrations, will result in a measurement deviation. In order to allow an absolute shape measurement, which is independent of the sensor position, the mean radius of the rotating object can be retrieved from the object's circumferential velocity. The laser Doppler distance sensor with phase evaluation (P-LDD sensor) allows a simultaneous velocity and distance measurement with high temporal resolution. Thus, the P-LDD sensor allows to measure the mean radius as well as the spatially resolved deviation of the radius independently of the sensor position. In order to quantify the achievable measurement uncertainty, and especially the influence of the temperature the measurement uncertainty budget is derived and considers random as well as systematic errors. It is shown that the P-LDD sensor allows an absolute, three-dimensional shape measurement of fast rotating objects with sub-micron uncertainty. The systematic measurement uncertainty of the absolute shape due to the temperature amounts to only 200 nm/K. Thus the P-LDD sensor is not dependent on temperature-controlled laboratories but can be employed directly in the production process (in-situ or in-process).