An accurate calculation method of side mill profile from the coordinates of discrete points of helicoid section curve

According to the gearing principle, the side mill for machining the helicoid (cylindrical helical surfaces of constant pitch) can be calculated from the parametric equation of the helicoid section curve. However, in practice, only a series of discrete point coordinates on the work-piece section curve were measured, which lead to the low calculation accuracy, especially when the section curve is composed of multi-segments, the calculation accuracy at the connection point (cusp) is lower. To improve the calculation accuracy, this paper first deduced the contact condition formula, and pointed out that the first derivation of discrete points had a great impact on the calculation accuracy. Then, an improved curve fitting method was proposed to calculate the first derivation of discrete points. In order to further improve the calculation accuracy at the cusp, a method of piecewise solving the cutter profile was proposed. Finally, calculation examples of the side mill profile of the main screw of a three screw pump, as well as a screw pump rotor, were carried out. The results show that the calculation accuracy of the improved curve fitting method is high, and the method of piecewise solving the cutter profile of discrete points is feasible.