Refining gear measurement uncertainty calculations by using the WelchSatterthwaite equation for effective degrees of freedom

When carrying out any form of precision measurement, early consideration should be given to the uncertainty of the measurement results. The primary reference document for evaluation is the "ISO Guide to the expression of uncertainty in measurement". When dealing with variable measurement data on a continuous scale, the structure and mathematical methods will remain similar over different instruments, however the specific sources of error and uncertainty will be dependent upon the instrument and nature of the quantity under study. Various mathematical models are used to calculate uncertainty (such as partial derivatives and the MonteCarlo method). In gear measurement BS ISO 18653:2003 addresses traceability, calibration intervals, sources of measurement uncertainty or errorsincluding mechanical alignment and drift (among others). Basic instrument checks include environmental factors and methods to evaluate gear uncertainty. The UK National Gear Metrology Laboratory (NGML) utilises the "spreadsheet model"to evaluate measurement uncertainty. The evaluation of gear dimensions defined in ISO 1328-1:2013 requires specific elements of the gear (profile, lead or helix, and pitch) to be considered independently, so a series of spreadsheets are utilised. Since each of the various sources of uncertainty generally have a small number of repeat checks (if any), applying the Welch-Satterthwaite equation allows effective degrees of freedom (veff) to be calculated for all the sources related to the specific element under study. This will result in a working model which can calculate a coverage factor (k) based on a confidence interval that will compensate for any number of repeat measurements (n) from each source, and therefore result in a more statistically sound outcome.