Vector-matrix analysis method for designing disk-shaped milling-tool outlines in forming helical surfaces

The manufacturing technique of helical surfaces is one of important tasks in developing single screw hydraulic machines. Using vector and matrix theory, a geometric relationship of contact points located at the contiguous curve between the spiral curved surface of workpiece and the disk shaped milling-tool rotary camber, is analyzed thoroughly. The common point equation and the perpendicular equation located at contact points are established according to the conjugate mesh theory. Then a new effective method based on vector-matrix analysis theory is derived for designing the disk-shaped milling tool outlines in forming spiral curved surfaces. Finally a special CAD software package of machining cylindrical spiral curved surfaces is developed.