Application of Mathematical Morphology in Solving the Profile of Forming Grinding Wheel

In the development of modern tools, the flute (or profiling flute) after design optimization is often obtained by grooving with a forming grinding wheel. At present, the main method of reverse forming wheel profile is the analytical method, which needs to solve the contact line equation according to the contact conditions. It is difficult to solve the equation. The solution value is unstable, which leads to the design error of the grinding wheel profile. In order to solve this problem, this paper proposes a new algorithm, called the pixel matrix method for short. This method is based on the spiral motion envelope method and mathematical morphology. First, the cross-section of the flute is discretized into a point cloud, and then, the envelope motion is carried out in the grinding wheel coordinate system. Second, the point cloud of the grinding wheel radial section is collected and converted into a binary image of pixel points. Finally, the profile of the binary image is extracted by erosion and dilation. The optimized profile of the formed grinding wheel reaches the accuracy requirements of the design and processing in the actual machining verification. This method can accurately reverse the profile of the forming grinding wheel. The calculation process is intuitive, avoiding the solution of the contact line equation, and the solution value is stable. It provides a new way to reverse the profile of the machining tool for cylindrical spiral products.