A General Numerical Method to Calculate Cutter Profiles for Formed Milling of Helical Surfaces with Machinability Analysis

Formed milling is one of the most commonly used methods for machining the helical surfaces of various screw rotors. The profile of a formed cutter is designed according to the profile of the helical surface, which is usually represented by discrete points. The most widely used analytical method is rather complex, and it is easy to obtain singular points. To obtain a reliable cutter profile and simplify the solution procedure, a general numerical method suited for rotors with an arbitrary tooth profile is proposed. The proposed method does not need to establish and solve the complex nonlinear contact equation and can determine the contact point accurately. Firstly, a series of intersection planes that are perpendicular to the revolving axis of the cutter is constructed. The searching of the contact points of the selected tooth curves with each intersection plane is achieved using the subdivision method. By this means, the plane–curve intersection is simplified to a straight line–curve intersection that can easily be solved via Newton iteration. Meanwhile, the machinability related to the profile of the formed cutter can also be analyzed. Two cutter profiles are used to validate the proposed method. The cutter profiles generated by the proposed method are compared with the profiles generated by the analytical method. The results indicate that the accuracy and computational efficiency increase significantly. Furthermore, the proposed method can also be applied to the design of formed grinding wheels.