SGER: Implementation and Performance Analysis of Real-Time Pythagorean-Hodograph (PH) Curve CNC Interpolators for Precision Machining Applications

这个探索性研究的小拨款(SGER)项目将研究一种新的方法，直接从基于毕达哥拉斯-速度图(PH)曲线的路径的解析描述来驱动数控机床。这项探索性研究的主要目标是通过在一个商用开放式数控软件产品的框架内实现和测试PH曲线插补算法的优势，给出一个实际的演示。为此，将使用MDSI开放式数控系统。PH曲线数控插补器在位置精度、进给速度平稳性、连续可变进给速度能力等方面的性能将与线性/圆形G代码零件程序和近似Bezier/B-Spline插补算法进行比较。PH曲线包含一种特殊的代数结构，这使得它们非常适合通过开放式结构的数控插补器和控制器进行实时处理。除了不需要中间的直线/圆形刀具轨迹近似外，PH曲线还提供了一种以连续变化的进给速度驱动数控机床的新能力。该项目为数控机床的性能改进提供了极大的潜力。

This Small Grant for Exploratory Research (SGER) project will investigate a novel approach to driving CNC machines directly from the analytic descriptions of paths based on the use of Pythagorean-hodograph (PH) curves. The principal goal of this exploratory study is to give a practical demonstration of the advantages of PH curve interpolator algorithms by implementing and testing them within the framework of a commercial open-architecture CNC software product. The MDSI OpenCNC system will be used for this purpose. The performance of the PH curve CNC interpolators in terms of positional accuracy, feedrate smoothness, continuously-variable feedrate capability, and other characteristics will be compared with both linear/circular G code part programs and approximate Bezier/B-spline interpolation algorithms. The PH curves incorporate a special algebraic structure, which renders them well suited to real-time processing by open-architecture CNC interpolators and controllers. In addition to bypassing the need for intermediate linear/circular tool path approximations, PH curves offer a new ability to drive CNC machines at continuously-varying feedrates. This project offers the potential for very significant performance improvements in CNC machines.