KINEMATIC APPROXIMATION ALGORITHM HAVING A RULED SURFACE

摘要

The present invention relates to a method for producing at least one surface on a workpiece by means of a material removal tool and a corresponding material removal device. The problem addressed by the present invention is to provide a method for producing any surface on a workpiece in such a way that the surface is produced quickly and at low cost. An error between any surface to be produced and a produced ruled surface should be small. The invention is characterized in that based on any surface to be produced, a movement path of the material removal tool is controlled to produce a ruled surface approximating to said surface to be produced, the movement path being provided in the form of a curve on a dual unit sphere, wherein a point on the curve corresponds to a location and an orientation of the material removal tool. The curve can be produced based on ruling lines, which are converted into points on the dual unit sphere by means of mathematical transformations. Said points are interpolated by means of a dual sphere spline interpolation algorithm to produce the curve. Said curve can then be transformed back into the ruled surface to be produced or can be used directly to follow the movement path of the material removal tool. Likewise, directrix curves of the ruled surface can be determined by means of the dual sphere spline interpolation algorithm. The method is suited in particular for producing the surfaces of components of turbomachinery, such as impellers. Any surfaces can be produced on any materials.