Angular-Dependent Radius Measurements at Rotating Objects Using Underdetermined Sensor Systems

Precise and contactless shape measurements of rotating objects is important, e.g., for monitoring and controlling the manufacturing quality in lathes. For this purpose, multisensor and single-sensor approaches based on optical distance and surface velocity measurements are state-of-the-art techniques. Two- and single-sensor systems are particularly promising to measure the angular-dependent radius of the cross section of the rotating object in a scanning regime with minimal optical access. Since a comparison between the different sensor systems is missing, the potential of these underdetermined sensor systems is unclear. In addition, displacements of the rotational axis and sensor misalignments are suspected to be crucial error sources, but the error is unknown. For this reason, an error analysis is performed regarding the resulting systematic error and the random error for the two- and single-sensor systems. As a result, the different sensor systems have an equal cross-sensitivity with respect to lateral displacements of the rotational axis from the sensor axes, but the two-sensor approach has the lowest sensitivity regarding sensor misalignments. For the studied measurement conditions, the systematic error dominates the sensor noise for the two-sensor system and the single-sensor system with combined distance and velocity measurement at an object mean radius >6 mm. The smallest total measurement uncertainty is obtained with the two-sensor system. Finally, the relevance of systematic error depends on the utilization, i.e., for instance on the absolute rotor radius, the stability of the rotor axis, the sensor position, the accuracy of the sensor alignment, and the uncertainty of the distance and/or velocity measurements.