Envelope to a two-parameter family of point vectors method for surface swept by wheel during 5-axis gear form grinding
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Abstract:
The wheel generating curve for gear grinding 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. 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 grazing point is determined by the geometry parameters of virtual ball and the velocity of virtual ball center，and the geometry parameters of virtual ball can be directly calculated from point vector. The kinematic geometry of 5-axis form gear grinder is analyzed. The coordinate transformation between fixed frame and moving frame is conducted，and the velocity of virtual ball center based on NC codes is obtained. An example is presented to demonstrate the effectiveness of the method which can be used for 5-axis gear grinding geometry simulation，accuracy evaluation and optimization of the wheel path.
