微靶球是激光核聚变点火工程的关键元件，高精度高一致性的批产是微靶球面临的主要加工难题。本项目提出一种基于自转一阶非连续式微小球体超精密加工方法。通过设计变摩擦系数的研磨盘或研磨盘沟槽曲线形状，使微小球体在加工时，其自转运动函变量的一阶导数呈非连续。这可使微小球体的研磨轨迹均匀全包络，从而实现其高精度高一致性的批产。本项目采用数学建模、仿真和实验相结合的方式，建立微小球体基于自转一阶非连续式超精密加工过程的运动学模型和研磨轨迹方程。进而研究在这种新型加工方式下影响微小球体加工精度和一致性的关键因素，从而获得优化的自转一阶非连续式研磨盘结构和加工装置。通过对自转一阶非连续式微小球体加工工艺的优化，最终建立微小球体高精度高一致性的加工理论，形成具有自主知识产权的高精度微小球体批产新工艺。项目实施对发展我国微小球体超精密加工技术，特别是激光核聚变微靶球的高精度加工具有重要科学意义和工程应用价值。

Ignition capsules are the key components for laser inertial confinement fusion. A key challenge in batch manufacturing of capsules is the high shape accuracy and the high processing consistency. A novel ultra-precision processing method based on rotation function first-order discontinuity for batch processing small diameter balls is proposed in this project. The groove curve or the different coefficient of friction of the lapping plate is designed, and the first derivative of the rotation function of the lapped small diameter ball is discontinuous. As a result, the entire surface of small diameter ball can be processed evenly. High shape accuracy and high uniformity small diameter balls are obtained for the reasons. Theoretic analyses, numerical simulations and machining experiments are employed to establish dynamical model and lapping trajectory model of rotation function first-order discontinuity processing method. Sphere-shaping mechanism of the processing method, and analyzing the key factors affecting processing consistency and making the effective geometric accuracy are researched. The optimized design structure of rotation function first-order discontinuity lapping plate will be obtained. This project will provide a theoretical and process foundation for the new batch processing method of small diameter ball. It has a great scientific importance and engineering value towards ignition capsule for laser inertial confinement fusion and high precision ball manufacturing in our country.