| The flute is the important part of the drill which provides space for chip, chip ejection and controlling the direction of chip ejection. The shape and size of the drill's flute affects the strength and rigidity of the drill, so that affects the particularity during drilling. Besides, the complexity degree of the flute's shape relates with the shape of the tool machining the drill's flute and the machining methods. Generally, there are two basic problems related to the mathematical model of the flute. The first problem solves the flute radial cross-section by the given tool axial cross-section (known as the direct problem). The other concerns the tool axial cross-section for the desired flute radial cross-section (known as the inverse problem). The paper studies fully on the profiles of the drill's flute and the using tool (the grinding wheel) from the inverse problem.There are the graph method and the calculation method, but the precision of the graph method is low, so that the calculation method is often used. Solving the contact equation in the numeration introduced by the literature is very complicated. Besides, the introduction about the arithmetic for the inverse problem, the establishing of the CAD and simulation system, the optimization for the parameters of the flute cross-section is not comprehensive. The paper expresses the kinematic relationship by the geometric relationship between the tool and flute and obtains the contact equation, so that the solving process become simply. Then the paper developes the CAD system which can optimize the parameters of the cross-section of the flute and solve the cross-section of the grinding wheel. The precision and efficiency of the design is highly improved.Applying the principles of differential geometry and kinematics, The paper formulates the mathematical model solving the grinding wheel axial cross-section by the given drill's flute radial cross-section on the basic engagement condition between the generating flute and the generated grinding wheel. Parameter equations of the end section curve for front blade of standard twist drills and the arc instead of the end section curve are established. With the parameter of the drill changed, the relative error of the arc instead of the end section curve of front blade is calculated.Furthermore, the mathematical model of the flute radial cross section with three pieces of arc is established. The CAD system solving the cross-section of the grinding... |
