Modelling of time-variant material removal functions for abrasive subaperture polishing

该项目的目标是开发用于光学和精密零件加工的磨料子孔径抛光的时变材料去除函数。这将使有针对性的形状校正与最小的材料去除，并提高可实现的生产精度和工艺可靠性。以前的方法集中在基于Preston方程的时间一致的材料去除函数上。虽然这种停留时间控制的去除功能可以节省高达35%的工艺时间，但它们的缺点是不可避免的基本去除，这意味着在任何情况下都必须去除材料。为了不去除任何材料，理论上抛光工具必须在工件上无限快速移动。时变去除功能允许最小化甚至避免这种基本去除，这反过来又导致过程时间的减少。为了开发这样的去除函数，有必要对一种新的抛光算法或过程控制进行建模。因此，材料去除必须首先量化，根据重要的工艺参数，如压力，标称去除深度和相对速度。在这些实验结果的基础上，推导出特定的去除函数，并通过建模加以验证。底层模型也是基于Preston方法的。然而，它是由时变项扩展，从而产生时变去除函数。主要重点是变抛光压力和变相对速度的模型描述。抛光工具的磨损也将集成到模型中，因为磨损也描述了去除函数随时间的变化。建模的一部分将包括最小化期望和实际材料去除之间的偏差，即期望和实际表面之间的偏差。该优化任务将为具体情况提供最优的参数组合。由于计算时间较短，在推导出更为复杂、适用的三维模型之前，首先会推导出二维模型。

The objective of this project is the development of time-variant material removal functions for abrasive subaperture polishing for the machining of optics and precision parts. This will enable a targeted shape correction with minimal material removal and increase the achievable production accuracy and process reliability. Previous approaches focus on time-consistent material removal functions based on the Preston equation. Although this dwell time controlled removal functions allow a process time saving of up to 35%, they have the disadvantage of an inevitable basic removal, meaning that material has to be removed in any case. In order to remove no material, the polishing tool would theoretically have to be moved infinitely fast over the workpiece. A time-variant removal function allows minimizing or even avoiding this basic removal, which in turn leads to a reduction of process time. For the development of such a removal function, the modeling of a novel polishing algorithm or process control is necessary. Therefore, the material removal must be quantified first, according to significant process parameters such as pressure, nominal removal depth and relative speed. On the basis of these experimental results, specific removal functions will be derived, which are proven by modeling. The underlying model is also based on the Preston approach. However, it is extended by temporally variable terms and thus a time-variant removal function is generated. Main focus is the model description of the variable polishing pressure as well as the variable relative speed. The wear of the polishing tool will also be integrated into the model, since wear also depicts a change in the removal function over time. Part of the modeling will consist in minimizing the deviation between the desired and the actual material removal, i.e. the deviation between the desired and the actual surface. This optimization task will provide the optimal parameter constellation for the individual case. Due to the short computing times, at first a two-dimensional model will be evolved, before a substantially more complex, applicable three-dimensional model is derived.