异形螺杆的数学建模与数据拟合

The mathematical model established and data fitting of an abnormal screw-rod

由于各式螺杆转子在工程中应用很广泛,因此,为实现螺杆螺旋面的数控加工而提供的有效加工轨迹是一个非常重要和关键的问题,而生成螺杆加工轨迹的一个重要条件就是已知螺杆螺旋曲面的方程。针对已知螺杆端截形方程和端截形型线离散点不同的两种情况,分别用直接法和三次样条插值函数法解决了如何建立螺杆螺旋曲面方程。论文重点讨论三次样条插值函数的建立过程,并阐述如何得到的三次样条函数的系数,进而可以确定三次样条插值函数。最后对三次样条插值函数法得到的螺杆端截形进行数据拟合后建立实体模型。

Due to various screw-rod is widely applied in the project. Therefore, in order to achieve the NC machining the helical-surface of a screw-rod, it provides effective processing track is a very important and key problem. It is an important condition that has been known the equation of the helical-surface of a screw-rod before it generates the helical-surface machining track. According to two different situations, one is known the equation of the end sectional profile of a screw-rod, the other is known points of the end sectional profile. This paper used respectively direct method and cubic spline interpolation function method to solve the problem how to establish the helical-surface equation of a screw-rod. This paper focuses on the procedure of building the cubic spline interpolation function, and expounds how to get the cubic spline function＇s coefficients. Then, the cubic spline interpolation function can be confirmed. Finally, computer simulated the data fitting of screw-rod sectional profile through gotten cubic spline interpolation function and built the 3D models ofmultihead rod.