Based on the principles of differential geometry and kinematics, a mathematical model is developed to describe the grinding wheel axial cross-section with the radial cross-section of the flute in a given drill under the basic engagement condition between the generating flute and the generated grinding wheel （or disk milling tool）. The mathematical model is good for the flute in the radial cross-section consisting of three arcs. Furthermore, a CAD system is also developed to represent the axial cross-section of the grinding wheel （or disk milling tool）. With the system, the grinding wheel （or disk milling tool） axial cross-section that corresponds to the three-arc flute cross section can be conveniently simulated. Through the grinding experiment of drill flutes, the method and the CAD system are proved to be feasible and reasonable.
