Polar pixel layout method for obtaining the profile of the spiral groove end section of end mill

The profile of the end section of the flute is an important factor in tool design, machining and performance analysis. In this paper, a new method, polar pixel layout method (PPM), is proposed to obtain the profile of the flute end section of an end mill by combining the spiral motion of the grinding wheel with polar coordinate transformation and mathematical morphology. PPM extracts the section profile directly through the polar coordinate binary image of the point cloud combined with the erosion and dilation algorithm of mathematical morphology. It does not need to solve the contact line equation, nor do Boolean operations. PPM can stably obtain the high-precision profile of the flute of the end mill. Finally, PPM calculation results are compared with the analytical method. These comparison errors are within the allowable range, thus verifying the correctness and effectiveness of PPM.