数控加工双曲回转面的几何模型研究

Research on geometry models of NC machining of hyperbolic revolving surfaces

双曲回转面因其特有的光学性质而被广泛应用,其高精度制造显然越来越重要。首先给出二轴联动数控加工其内侧的方案,进而证明该回转面最小主曲率半径在其顶点,并依此给出加工用球头铣刀的半径计算模型;证明相同行距下,从顶点开始的第一行距内残留高度最大,并据此给出行距计算模型;还给出实现固定行距的水平和轴向进给控制公式;最后用实例验证方案的可行性和模型、公式、分析结果的可靠性。

Because revolving surfaces own its special optical properties, it is widely used in a lot of fields. So its machining with excellent accuracy is more and more important. Firstly, a method of two-axis NC machining inner surfaces of hyperbolic revolving surfaces is provided and that the minimum main curvature is at the top point is investigated. Thereby, the model of calculating the ball-ended cutter radius of machining inner surfaces is also provided. Secondly, that the biggest actual machining error exits in the first path interval is proved when the path interval are same, from which the model of calculating the path interval is provided. In the meantime, in order to fix the path interval, the formulation of calculating the horizontal and axial feed rates is given. At the end, an example presents the admissibility of the design and the reliability of the models, formulations and resuits.