The main difficulty of pitch diameter calculation arises during the determination of the coordinates of the probing element and screw surface contact. This paper proposes a mathematical model for pitch diameter calculation of thread gauges using a two-ball stylus for internal thread calibration and three wires for external thread calibration. To describe the geometry of the thread and probing element, a non-linear equation system has been established and solved numerically. The solution of this system gives the actual contact points of the probing element with the thread profile. Pitch diameter is calculated directly without any further corrections. This mathematical model can be applied to parallel threads without any restrictions regarding lead and flank angles. Calculation of the rake correction is therefore avoided completely. The authors provide functional PHP/HTML code that can be easily integrated into any PHP-based website. Additionally, an open-access web tool has been developed that enables the direct calculation of thread pitch diameter from measured values, as well as the coordinates of the actual contact points between the thread profile and the measuring elements.
Šimunović et al. (Tue,) studied this question.