5-axis circumference milling's polar problem and polar interpolation algorithm

In the 5-axis machining, the circumference milling is quite useful to improve the quality of the products and machining efficiency, while the plane Interpolation of tool orientation algorithm has the nonlinear error brought by the default linear interpolation of rotation angles eliminated. But the plane interpolation causes another over-cutting & under-cutting when the inclined plane has a little included angle with the rotation axis of the 4th/5th rotation axis (e.g. 1 degree), which is named polar problem (or pole point problem). After analyzing the causing of the polar problem, the position of pole point, the related polar value and its nonlinear error by circumference milling, etc, it has been found that the polar problem will be take place in the circumference milling an inclined plane with a little angle, which is smaller than the polar value. Therefore, a new interpolation algorithm, the polar interpolation algorithm is given out in the paper following with the simulation results and machining test results of the plane interpolation and polar interpolation based on a 5-axis machining center with two swiveling heads (rotation axes: C/A). The results prove that the new interpolation is valid and correct.