3D-Surface-like numerical description, alignment, and evaluation of involute cylindrical gears

The classical gear measurement mostly refers to standards which are based o n the measuring paths of conventional mechanical gear measuring devices. Th e mechanical alignment by means of geometric elements and clamping devices is regarded as problematic. On the other hand the correct evaluation of mea sured flanks requires ideally mounted gears to exactly match the profile an d helix (lead) lines. Both requirements can be fulfilled partially only by CMMs using numerical alignment or specialised gear measuring devices, thus errors inevitably occur during the evaluation. Since involute cylindrical g ears can be described both with and without corrections by self-contained m athematical functions it is possible to fit the measuring points according to the nominal surface using a numerical alignment algorithm. This procedur e results in a coordinate transformation for the measured points which may origin from arbitrary tooth flanks in a varying point density and distribut ion. This contribution gives a survey about the theoretical approaches and some results of simulations and evaluations based on simulated alignment er rors. Especially conventional uncorrected evaluations are compared with num erically improved evaluations.