Surface modeling method - left tooth root

Mathematical representation of the tooth flank geometry (including the microgeometry) as precisely as possible is the foundation of every local calculation. This requires a manufacturing simulation or the import of 3D data, for example in the KIMoS 3D data format, in order to obtain 3D surface points distributed as evenly and completely as possible over the entire tooth surface. From these 3D surface points, fitting surfaces are calculated for the effective tooth flanks and the tooth root areas. These ensure quick access to each and every point on the flank.

Surface modeling methods are:

• Bezier surface: Only specification of the polynomial degree required; recommended for gears without tip relief, protuberance or end relief; shorter calculation times
  Characteristics: Local changes in the 3D point cloud have a global effect on the Bezier surface. The Bezier surface has a compensating effect on point outliers. However, significant curvature changes due to the polynomials can also lead to fluctuations on the fitting surface (for example, in the flank area as a result of tip relief).
• NURBS surface: Specification of the polynomial degree and number of control points required (whick makes it more difficult to determine an optimal setting); usually necessary for differentials; recommended for gearings with tip relief, protuberance or end relief; recommended for recalculation of gear damage (e.g., pitting entered via 3D measurement data).
  Characteristics: Local changes in the 3D point cloud have only local effect. For this reason, and also due to the fact that the required polynomial degree is usually smaller than for a Bezier surface, NURBS surfaces do not tend to fluctuate.

Standard value: Bezier surface

An evaluation of the quality of the fitting surfaces can be found in the Advanced Gear Calculation report in the tooth flank and root area diagrams. The distribution of the surface points over the flank area and various measures for the deviation of the 3D surface points from the calculated fitting surface are shown.