Estimate of uncertainty for thread-measurement standards

Measuring threads poses very specific problems for the metrologist. While the conditions for obtaining traceability of measurements remain fairly simple and analogous to measurements of plain rings and plugs, the assessment of uncertainty requires particular attention when defining the measurand and the mathematical expression modelling the measurement process.

The very nature of thread geometry has led the standardizer to define a certain number of dimensional characteristics, more or less functional, taking into account all or part of the geometric parameters defining the thread and their manufacturing defects.

This specificity obliges the metrologist to define the measurand in compliance with current standards. On the other hand, he has a certain amount of latitude as to the operating mode and the means to be used, it being up to him to carry out a pertinent and exhaustive analysis of his measurement process and to establish the appropriate mathematical model.

This last point is particularly delicate due to the complex geometry of a thread. The November 2003 edition of standard XP E 03-110 highlights this complexity, which leads to the solution of a system of non-linear equations to obtain the value of the flank diameter.

The aim of this dossier is therefore to present, for the most common cases, the approach to analyzing the measurement process and dealing with the propagation and composition of the various uncertainty components, based on the exact formulas for calculating flank diameter.

It should be noted that the developments presented below relate to measurement principles that enable a good level of uncertainty to be achieved. This study therefore excludes all measurements using jaw gauges, knurled gauges, threaded micrometers, etc.