目的 具有中心凹凸形貌特征的光学曲面在光束整形、能量重分布及像差校正等应用中,能够实现紧凑高效的光场调控,然而其非单调的高度分布与局部几何突变,导致慢刀伺服车削过程中刀具路径存在大量无效切削行程。传统螺旋线路径策略要求刀具在每一切削层完整遍历整个径向区域,即便局部轨迹不产生实际材料去除,仍需执行相应联动运动,严重制约加工效率。方法 针对上述问题,本文提出一种基于曲面特征自适应的动态路径截断优化方法。该方法首先依据曲面中心与边缘的凹凸特性构建分层刀具路径,进而通过空切临界离散点搜索识别各加工阶段的无效切削区,最终在不改变精加工轨迹、刀具路径连续性与最终设计面形的前提下,对螺旋加工路径实施径向截断重构。结果 本文以典型塔形环面为例,在Nanoform X超精密机床上开展慢刀伺服车削验证,并采用PGI Optics轮廓仪与Zygo NewView白光干涉仪分别表征面形精度与表面质量。实验结果表明,所提优化方法使总加工时间缩短约31%;优化前后表面粗糙度Sa分别为12.008 nm与11.464 nm,平均Sz值分别为0.216 μm与0.139 μm。结论 可见,动态截断策略在未牺牲面形精度与表面完整性的前提下,显著提升了慢刀伺服车削效率。该研究为复杂光学曲面高效、确定性的超精密加工提供了一种可行的路径规划方案。
Abstract
Optical surfaces with central convex-concave features, such as tower-shaped toroids with a central protrusion or depression and compound aspheres with inflection zones, are essential for compact light-field manipulation in laser beam shaping, energy redistribution, and aberration correction. However, their non-monotonic radial height profiles and abrupt geometric transitions at the center-to-periphery boundaries cause severe air-cutting redundancy in slow tool servo (STS) diamond turning. In conventional Archimedean spiral tool paths, the diamond tool is forced to traverse the entire radial range during every cutting layer, including extensive regions where the tool hovers above the workpiece surface without material engagement. These non-productive motions nevertheless demand fully synchronized C-, X-, and Z-axis movements, significantly degrading machining efficiency, with the redundancy escalating for larger apertures and stronger undulations.
To overcome this intrinsic limitation, the work aims to propose a feature-adaptive dynamic path truncation optimization method. Firstly, the surface was partitioned radially into effective cutting and air-cutting zones based on the characteristic height distribution around the central convex-concave boundary, constructing a layered tool path structure. A discrete-point search was then executed along the planned spiral under the instantaneous tool-workpiece contact criterion, precisely identifying the critical transition points where air-cutting begins and ends. Finally, the roughing and semi-finishing spiral paths were radially truncated: only the effective cutting segments were retained and reconnected via smooth, machine-dynamics-compliant transition arcs that maintained C-axis continuity, respected acceleration and jerk limits, and guaranteed interference-free clearance. Crucially, the final finishing pass remained an unmodified full-coverage Archimedean spiral, ensuring the machined surface faithfully replicated the design form.
Experimental validation was performed on a representative tower-shaped toric surface by a Nanoform X ultra-precision lathe with a round-nose single-crystal diamond tool. Spindle speed, feed rate, and depth of cut were held constant. Two complete machining sequences were executed: one with conventional full-spiral roughing and semi-finishing, the other with the proposed truncated strategy, both followed by an identical full-coverage finishing pass. Surface form was measured with a Taylor Hobson PGI Optics contact profilometer, and areal micro-topography was characterized with a Zygo NewView 8000 white light interferometer. Results show that the dynamic truncation strategy reduces total machining time by approximately 31%, directly due to the elimination of extensive air-cutting motions. The areal surface roughness Sa values are 12.008 nm for the conventional path and 11.464 nm for the truncated path, while average maximum peak-to-valley heights Sz are 0.216 µm and 0.139 µm, respectively. Form accuracy remains at the same sub-micrometer level without statistically significant difference. The slightly lower Sz obtained under the truncated path confirms that no additional vibration or surface damage is introduced, preserving surface integrity. This work provides a practical and deterministic path optimization strategy for high-efficiency STS machining of central convex-concave optical surfaces, readily extendable to broader complex free forms.
关键词
超精密切削 /
慢刀伺服车削 /
光学自由曲面 /
中心凹凸特征 /
刀具路径优化 /
空切截断 /
加工效率
Key words
ultra-precision cutting /
slow tool servo turning /
optical free form surfaces /
central convex-concave features /
tool path optimization /
air-cut truncation /
machining efficiency
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基金
国家自然科学基金（52305445,22FAA01871,U24A20126）; 吉林省科技发展计划项目（YDZJ202401338ZYTS）
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