目的 针对BK7玻璃抛光中工具易损、材料去除率低及表面质量难控等问题,提出一种基于IWP（I-graph-wrapped Package）晶胞构型的柔性抛光工具优化设计方法,以实现非牛顿流体动压下的高效低损伤加工。方法 构建具有互补特性的IWP-1与IWP-2内部结构,采用SLA光固化3D打印制备不同硬度的柔性工具。耦合Hertz理论、Preston方程与有效磨粒数,建立修正的材料去除函数。利用有限元静力学分析揭示内部构型对接触压力场及工具影响函数的调控规律;构建CFD-DPM/DEM流固耦合模型,评估IWP结构对流场分布及磨粒输运特性的影响。随后,以结构类型、压缩量和硬度为因素开展三因素三水平的正交抛光实验。结果 相比传统工具,IWP优化工具显著改善了接触区压力分布,减弱了应力集中,并提升了抛光液与磨粒的输运及循环更新能力。其中,IWP-1工具在压缩量2 mm、硬度60 A下获得最佳表面粗糙度Ra=0.033 μm;IWP-2工具在压缩量2 mm、硬度35 A下最佳Ra为0.075 μm,两者均在维持高材料去除率的同时实现了纳米级表面质量。结论 IWP晶胞柔性工具通过协同优化拓扑结构、接触压力场与流体动压行为,有效平衡了BK7玻璃的材料去除率与表面质量,为硬脆光学元件的非牛顿流体动压抛光提供了极具潜力的结构设计思路与理论基础。
Abstract
To address the widely observed problems of rapid tool wear, low material removal rates and unstable surface quality in polishing BK7 optical glass, this study proposes an internal-configuration optimization strategy for flexible polishing tools based on I-graph-wrapped package (IWP) triply periodic minimal surface (TPMS) unit cells. Starting from an implicit-function representation of the IWP unit cell, two complementary internal architectures are constructed, namely a skeletal lattice (IWP-1) and a perforated lattice (IWP-2), and flexible polishing tools with different Shore A hardness levels are fabricated via stereolithography (SLA) photocuring additive manufacturing. The use of SLA-based 3D printing not only enables the direct manufacture of architected tools with complex internal lattices that would be extremely difficult to realize by conventional subtractive routes, but also provides a practical "design-for-additive-manufacturing" pathway for embedding mechanically tailorable architectures into flexible polishing tools. To quantitatively characterize macroscopic material removal behaviour under non-Newtonian hydrodynamic polishing conditions, a corrected material removal function is developed according to the coupling Hertzian contact theory, the Preston equation and the effective number of active free abrasives, in conjunction with an elastic-plastic deformation analysis of individual abrasive particles. This model links local contact pressure, relative sliding velocity and abrasive engagement to the global removal footprint, allowing the influence of internal tool topology to be mapped onto observable polishing performance. Static finite element analysis of the tool-workpiece contact region are carried out in Abaqus to elucidate how different IWP-based internal structures regulate the contact pressure field and reshape the tool influence function, thereby improving contact-pressure uniformity and mitigating local stress concentration at the tool-workpiece interface. On this basis, a CFD-DPM/DEM fluid-solid coupling model is established in Ansys Fluent to simulate the flow-field distribution and abrasive-particle dynamics within the polishing gap. The simulation results show that the IWP cell architecture promotes a more homogeneous spatial distribution of abrasives in the contact region, enhances the renewal efficiency of the polishing slurry and stabilizes the hydrodynamic film, all of which are beneficial for reducing local fluctuations in the removal rate and improving process consistency over repeated runs. Guided by these numerical insights, orthogonal experimental design with three factors (structural type, tool compression and tool hardness) and three levels is implemented for BK7 glass polishing tests, enabling the systematic exploration of the combined effects of internal architecture and macroscopic loading conditions on both efficiency and surface integrity. The experimental data demonstrate that flexible polishing tools optimized with IWP unit cells can significantly improve both the contact-pressure distribution uniformity and the material removal homogeneity compared with conventional internally solid tools. In particular, the IWP-1 tool achieves an optimal surface roughness of Ra = 0.033 μm at a compression of 2 mm and a hardness of 60 on the Shore A scale, while the IWP-2 tool attains a best surface roughness of Ra = 0.075 μm under a compression of 2 mm and a hardness of 35 Shore A. These findings indicate that IWP-1, with its more compliant yet highly uniform stress-transmission characteristics, is more suitable for high-precision finishing stages, whereas IWP-2, offering higher effective stiffness and stronger abrasive retention, is better suited to higher-efficiency pre-polishing or intermediate conditioning stages, highlighting their complementary roles within a multi-step process chain. Overall, the results confirm that IWP unit-cell-based flexible polishing tools, enabled by SLA-based additive manufacturing, offer clear advantages in simultaneously balancing polishing efficiency and surface quality, and provide a feasible structural design concept and theoretical basis for high-efficiency, low-damage polishing of hard-brittle optical glass and, by extension, other advanced optical materials with stringent surface-quality requirements.
关键词
IWP晶胞结构 /
柔性抛光工具 /
流体动压抛光 /
工具影响函数 /
BK7玻璃 /
工艺优化
Key words
IWP unit cell structure /
flexible polishing tool /
hydrodynamic polishing /
tool influence function /
BK7 glass /
process optimization
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基金
国家自然科学基金（51805044）; 中国博士后科学基金（2024M762450）; 陕西省自然科学基础研究项目（2025JC-YBMS-389）; 陕西省秦创原“科学家+工程师”队伍建设项目（2022KXJ-150）
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