MODELLING AND UNCERTAINTY FOR HIGH-ACCURACY ROUNDNESS MEASUREMENT

摘要

High-accuracy roundness measurements of a component made with an instrument having a precision rotary stage are considered. The measurements comprise a superimposition of the component form deviation and the instrument spindle deviation, the latter being a consequence of the imperfect but highly repeatable rotation of the sensor. These effects need to be separated in order to determine the departure from roundness of the component, and also of the spindle deviation. Separation is possible by using the rotary stage to take several sets of measurements, corresponding to different angular positions of the component with respect to the rotary stage, which introduces phase differences relative to these effects. The evaluation of the uncertainty associated with the departures from roundness is the main concern. When the measurements are uncorrelated, the evaluation provides specific formulae for the uncertainty. For the instrument of concern, the presence of serial correlations in the measurements means that the uncertainties so evaluated would be too small. An approach based on the use of bootstrap re-sampling is given that permits the correlation effects to be taken into account. Results are provided for comparison with those obtained based on the assumption that the measurements are uncorrelated.