Digital modeling for products with helical surface and its corresponding cutter with axial section

According to the forming principle of helical surface and space analytic geometry, the mathematical model of helical surface was established. Based on the principle of coordinate conversion, the space envelope theory of single parameter surface, and theorem that the contact line between the cutter revolution surface and the helical surface is a space curve, the theoretical models of the helical surface and the contact line was derived. Based on the thought of numerical operation with MATLAB, 3D mesh model of helical surface and axial section of cutter have been obtained accurately by discretion and digitalization under the control of the number of discrete points. The current modeling, compared with traditional methods of modeling, provides rapidly and accurately the design of products of helical surface and the design of corresponding cutter with axial section.