Envelope to a Two-Parameter Family of Point Vectors Method for Surface Swept by Form Wheel

Abstract

The form wheel generating curve is always a composited curve which is composed of lines and arcs, and the calculation of the envelope surface is more complex than conventional rotary cutter. Therefore, a method of envelope to a two-parametric family of point vectors is proposed, which defines the point and its normal vector on the wheel generating curve as a point vector. Each point vector corresponds to a virtual ball uniquely. The rotation of point vector forms latitude circle and the valid envelopment movement forms sectional circle. The intersection of latitude circle and sectional circle is grazing point; The analytical calculation model is established, in which the geometry parameters of virtual ball can be directly calculated from point vector; An example is presented to demonstrate the effectiveness of the method which can be used for form grinding geometry simulation, accuracy evaluation and optimization of the wheel path.