Abstract With the rapid progress of science and technology, many applications of hard and brittle materials require advanced and suitable machining-techniques. One technique in particular, ultrasonic vibration-assisted polishing (UVAP), has been studied intensively by researchers worldwide. These studies indicate that UVAP has the capability to improve the surface quality as well as the machining efficiency. However, few studies focus on the deterministic material-removal of UVAP. The difference between generated and theoretical surface profiles determines the surface accuracy. Therefore, this paper focuses on predicting the generated local surface profile and providing a theoretical basis to reduce this error by controlling the polishing parameters. In addition to the axial ultrasonic vibration of polishing tool, ultrasonic atomization was adopted to provide uniformly distributed polishing slurry. To ensure sufficient surface-accuracy, it is necessary to predict the generated surface profile for a fixed spot as a basis research. This means, to enable accurate predictions the following improvements are realized: (i) A novel model for the elastic spherical contact-deformation of the polishing tool is used to calculate both the polishing force and contact radius. It takes into account the nonlinear elasticity of the polishing tool and the lateral extension of the contact area, which makes it more consistent with the actual deformation. (ii) A novel model for the material-removal distribution function for UVAP is proposed, based on the Preston equation. It considers the periodic changes of polishing force and contact radius caused by ultrasonic vibration. (iii) A series of fixed-spot polishing experiments on BK7 glass are carried out to verify the proposed models. The results show that the Preston coefficient is affected by axial ultrasonic amplitude, and large ultrasonic amplitude improves the polishing ability. In addition, the generated local surface profile, the maximum contact radius, as well as the material-removal depth and material-removal rate (MRR) can be predicted well. The new models not only provide a possibility to realize deterministic material removal but also enables in-depth-understanding of UVAP. It also represents a basic theoretical foundation for future, flat or free-form surface-polishing.

中文翻译：

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BK7光学玻璃超声振动辅助抛光局部表面轮廓建模与预测

摘要 随着科学技术的飞速进步，硬脆材料的许多应用都需要先进和合适的加工技术。特别是一种技术，超声波振动辅助抛光 (UVAP)，已被世界各地的研究人员深入研究。这些研究表明，UVAP 具有提高表面质量和加工效率的能力。然而，很少有研究关注 UVAP 的确定性材料去除。生成的表面轮廓和理论表面轮廓之间的差异决定了表面精度。因此，本文的重点是预测生成的局部表面轮廓，并为通过控制抛光参数来减少这种误差提供理论依据。除了抛光工具的轴向超声波振动外，采用超声波雾化，提供均匀分布的抛光液。为了确保足够的表面精度，有必要预测固定点的生成表面轮廓作为基础研究。这意味着，为了能够准确预测，实现了以下改进：（i）抛光工具的弹性球形接触变形的新模型用于计算抛光力和接触半径。它考虑了抛光工具的非线性弹性和接触面积的横向延伸，使其更符合实际变形情况。(ii) 基于 Preston 方程，提出了一种新的 UVAP 材料去除分布函数模型。它考虑了超声波振动引起的抛光力和接触半径的周期性变化。(iii) 在 BK7 玻璃上进行了一系列定点抛光实验以验证所提出的模型。结果表明，Preston系数受轴向超声振幅的影响，较大的超声振幅提高了抛光能力。此外，生成的局部表面轮廓、最大接触半径以及材料去除深度和材料去除率（MRR）可以很好地预测。新模型不仅提供了实现确定性材料去除的可能性，而且可以深入了解 UVAP。它还代表了未来、平面或自由形式的表面抛光的基本理论基础。结果表明，Preston系数受轴向超声振幅的影响，较大的超声振幅提高了抛光能力。此外，生成的局部表面轮廓、最大接触半径以及材料去除深度和材料去除率（MRR）可以很好地预测。新模型不仅提供了实现确定性材料去除的可能性，而且可以深入了解 UVAP。它还代表了未来、平面或自由形式的表面抛光的基本理论基础。结果表明，Preston系数受轴向超声振幅的影响，较大的超声振幅提高了抛光能力。此外，生成的局部表面轮廓、最大接触半径以及材料去除深度和材料去除率（MRR）可以很好地预测。新模型不仅提供了实现确定性材料去除的可能性，而且可以深入了解 UVAP。它还代表了未来、平面或自由形式的表面抛光的基本理论基础。新模型不仅提供了实现确定性材料去除的可能性，而且可以深入了解 UVAP。它还代表了未来、平面或自由形式的表面抛光的基本理论基础。新模型不仅提供了实现确定性材料去除的可能性，而且可以深入了解 UVAP。它还代表了未来、平面或自由形式的表面抛光的基本理论基础。