Novel Framework for Optimizing Non-Uniform Pitch Milling

本研究的主要目的是研究用于优化使用非均匀螺距刀具的铣削过程的分析工具，并通过实验验证分析结果。分析研究的重点主要是多时滞效应对动力学颤振稳定性的影响。该问题产生了具有合理无关时滞的超越特征方程，需要从稳定性的角度在时滞域内求解。最佳的刀具设计将根据颤振抑制能力和提高生产率之间的权衡进行研究。并推导出相应的最佳切削条件。该方法将基于首席研究员最近的数学范式，称为“特征根的聚类处理”。这种模式将创建一个显示，类似于传统的稳定叶，除了全套的俯仰角变化。将使用各种刀具几何形状进行广泛的实验研究，并在每种情况下调查分析和实验结果的对应关系。如果成功，这项研究将产生一种新的分析方法，可用于机床科学。该程序将有助于选择最佳切削参数，以避免颤振和提高生产率。这种优化的加工条件将转化为生产成本优势。研究成果也将透过各种传播渠道，用于培养研究生及实操制造工程师。

The main objectives of this research are to investigate analytical tools for optimizing a milling process that uses non-uniform pitch cutters, and to validate the analytical findings experimentally. The focus in the analytical investigation is primarily on the multiple time-delay effects on the chatter stability of the dynamics. The problem gives rise to transcendental characteristic equations with rationally unrelated time delays, which have to be resolved in the domain of the delays from the perspective of stability. Optimum cutter design will be investigated based on a trade-off between the chatter rejection ability and increased productivity. Corresponding optimum cutting conditions will also be derived. The approach will be based on a recent mathematical paradigm of the principal investigator , which is called the "Cluster Treatment of Characteristic Roots". This paradigm will create a display that is analogous to the conventional stability lobes, except for the complete set of pitch angle variations. Broad ranging experimental studies will be performed using various cutter geometries and the correspondence of the analytical and experimental findings will be investigated in each case.If successfull, this research will yield a new analytical procedure that will be available to the machine tools science. This procedure will facilitate the selection of optimum cutting parameters to avoid chatter and increase productivity. Such optimized machining conditions will translate into a production cost advantage. The outcome of the research will also be used to train graduate students as well as the practicing manufacturing engineers through various channels of dissemination.