Research on geometric model of grinding large and medium scales optical aspheric surfaces

摘要

Aspheric optics have been used in optical systems widely because of their excellent optical properties. At present, the manufacture of small scale aspheric surfaces has been industrialized. However the manufacture of large and medium aspheric surfaces still follows the procedure of grinding, lapping and polishing. Generally speaking, increasing the working efficiency is the key of machining large and medium scale aspheric surfaces. As we know, lapping and polishing have relatively low efficiencies. Therefore prior to lapping and polishing, NC grinding is often used to shape large and medium scale optical aspheric surfaces, so as to reduce the subsequent process time. Current approaches to grinding aspheric surfaces differ from each other because the wheels and methods used are different, which is inconvenient for programming. To facilitate programming, a unified mathematical formulation is proposed for calculation of the wheel center trajectory when grinding axisymmetric aspheric surfaces based on the principle of shaping aspheric surfaces. Certain geometric models are derived from the unified formulation for the cases of parallel grinding wheel, spherical grinding wheel and cup grinding wheel, according to their features of process. The condition of avoiding overcutting is also derived. The step length of cutting is adaptively selected with accuracy control so as to reduce the program codes. After analyze all the factors affecting the shape accuracy of the curved surface, the major factors are found to be the tool setting error and the radius error of the grinding wheel, then the corresponding influence coefficients of the errors are calculated and the simulation results are given. Finally an example is shown in order to prove the analysis.