3D involute gear evaluation - part II: deviations - basic algorithms for modern software validation

The fundamental equations for the evaluation of cylindrical involute gear measurements on 3D gear measuring instruments are provided. The computations are based on the principles of gear kinematics and use the system of involute gear coordinates introduced in a previous work of the authors. This holistic approach focuses on significant error sources that only appear since 3D measurement technology is used and that are almost unrecognized till today. The proposed algorithms are beneficial for the description of gear deviations as they allow the use of simple formulas covering profile, helix and pitch evaluation for internal or external and spur or helical gears. The presented equations contain the key fundamentals to complement existing standards. They will become part of reference algorithms used by the Physikalisch-Technische Bundesanstalt, the national metrology institute of Germany, to certify gear evaluation software.