Abstract: It largely depended on the selection of NC interpolation algorithm to improve the accuracy of surface machining on NC machine tools, because circular interpolation algorithm can be up to geometric continuity C1 in the arc joint which made it become widely used. It proposed a step constant double circular interpolation algorithm, and deduce a mathematical model of step constant double circular interpolation algorithm common point of tangency based on the geometric conditions, also establish a mathematical transformation of the local coordinate system and the absolute coordinate system of the double circular constructed by any two points of the basic NC curve, and it give the adjustment method of error analysis of the slope of common point of tangency and error discriminant model. Because the adjustment of interpolation error is not relevant with interpolation step which made the adjustment of interpolation error not need changing the process parameters. This step constant double circular interpolation algorithm could adapt to various requirements of different processing tolerance in different processing environment with good NC machining flexibility and rapid and efficient NC processing. It verifies the feasibility of the algorithm through the example of large-diameter axisymmetric aspheric ultra-precision grinding with the interpolation tolerance range is less than 0.002 μm.

Key words: Double circular, Interpolation algorithm, Numerical control processing, Step constant, Ultra-precision grinding