Minimum polynomial degree (root)

The parameters of the NURBS surface for the left and right sides of the pinion and gear can be specified individually for the flank and root using the polynomial degree p and number of control points n. When specifying the polynomial degree and the number of control points, a distinction is made in the width and profile directions according to the coordinates R and θ for the flank and R and u in the root. This allows specific modeling of the surfaces (e.g.; for tip and root relief), as any irregularities generally occur in the profile direction.

Please note:

• The number of control points must be at least 1 greater than the polynomial degree:
  n ≥ p + 1.
• For the tooth flank, the following must apply:
  2 · n_R · n_θ < 2 to 3 · number of flank points from the manufacturing simulation or 3D point cloud.
• For the tooth root, the following must apply:
  2 · n_R · n_u < 2 to 3 · number of root points from the manufacturing simulation or the 3D point cloud.

The default values are: Polynomial degree = 3, Number of control points = 11.

Source: BECAL user manual and program documentation (in German).