VIRTUAL CONTACT POINT METHOD. SIDE MILL GENERATING A CYLINDRICAL HELICAL SURFACE

Cylindrical helical surfaces with constant pitch can be generated using tools bounded by primary peripheral surfaces of revolution, such as side mills, end mills, cylindrical planing tools, and, less frequently, ring tools. The task of profiling tools for generating such surfaces has been addressed using Olivier’s theorem, treating it as a winding problem between a surface of revolution and a helical surface. Winding involves linear contact and is analyzed based on the first Olivier theorem. Additionally, the problem is addressed using Gohman’s kinematic theorem of surface winding, which applies to mutually winding surfaces that share a common contact curve, along which the normals of the two conjugate surfaces are identical. This curve is called the characteristic curve. Several complementary theorems have been devised to deal with the problem of contact between mutually wrapping surfaces with linear contact: the minimum distance theorem; the in-plane generating trajectory theorem; the theorem of substitution circlesfamily, etc. The issue of profiling the side mill, or the main peripheral surface of this instrument, which is a surface of revolution, is rigorously resolved by all of these complementing approaches. This work presents the "virtual contact point" theorem, a novel complementary theorem about side mill profiling, as a particular application to tools made to process mutually wrapped surfaces with linear contact. The method was originally developed for in-plane winding profiles associated with a rolling centroid couple, and its use has now been extended to winding surfaces with linear contact. Based on the surface enwrapping principles developed by Olivier and Gohman, the complementary theorem of the "virtual contact point" takes a different approach to the problem by utilizing "virtual contact points" between two surfaces: the primary peripheral surface of the intended side mill (a surface of revolution) and the cylindrical helical surface with constant pitch that needs to be created. This complementary theorem has been applied to determine the profile of the generating side mill for a helical surface featuring a circular cross-section in the frontal plane. The application was performed in Matlab program and the results obtained demonstrate the accuracy and simplicity of using the virtual contact point theorem. Obviously, the theorem can also be applied to the profiling of other types of tools and other surface shapes, respectively.