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3D model for gears

Holistic characterization of helical machine elements

PTB-News 2.2022
Especially interesting for

manufacturers of gears and screw threads

operators and manufacturers of coordinate measuring machines and evaluation software

In conventional gear and screw thread metrology, measurements for evaluating the quality of components are performed only pointwise or linewise in selected transverse and axial sections, respectively. In light of tighter manufacturing tolerances and new challenges brought on by modern production processes, this procedure is not sufficient. At PTB, a universal procedure has been developed to conduct areal measurements of helical machine elements and to evaluate them holistically by means of a parameterized 3D model.

Best-fit 3D model illustrated on an involute gear. The data points are represented in false colors as residuals of this best-fit geometry.

Gears and screw threads of the most varied types are important components in all areas of mechanical engineering. Tight manufacturing tolerances define the requirements placed on the measuring equipment used for quality assurance purposes along the entire scale of quantities and across diverse sectors. To ensure that the evaluation of a component’s quality is reliable and relevant to its function, the measurement processes used must be not only fast and accurate, but also, and most importantly, holistic. This means for one thing that the geometry must be acquired along all function surfaces and, for another, that all characteristics be evaluated in a single geometry element based on only one reference coordinate system.

Modern coordinate measurement systems provide areal information fast and reliably with regard to the dimension, form and position errors of helical machine elements. Up to now, however, standard evaluation procedures required reducing this data to individual lines. A major share of the data points thus had to be discarded. The new procedure enables the evaluation of areal measurement data distributed anywhere along the entire external surface. This procedure is based on a universal 3D model that allows helical machine elements to be described by means of a unique set of geometry parameters. The model is best-fitted into the data point cloud using a foot-point iteration algorithm. The actual values of the geometry parameters yielded in this way can then be converted into the determinants already established in conventional procedures.

It is planned to enhance this new procedure to characterize additional types of machine elements (such as those of bevel gears). Moreover, we are working to incorporate the procedure into standards in order to promote its use in industry.


Martin Stein
Department 5.3
Coordinate Metrology
Phone: +49 531 592-5335
Opens local program for sending emailmartin.stein(at)ptb.de

Scientific publication

M. Stein, F. Keller, A. Przyklenk: A unified theory for 3D gear and thread metrology. Appl. Sci. 11, 7611 (2021)