Research on the numerical fitting method of the spiral surface cross-section

The screw rod is widely used in the oil drilling, chemical industry, light industry and so on. Its machining accuracy affects directly the quality and efficiency of instruments. Thus a deep research on the machining process of the screw rod is urgently needed. The fitting method of the spiral surface cross-section is one of the key issues. It was proposed that cubic spline and parametric cubic spline interpolation function were taken to approximate the spiral surface cross-section by comparing different methods of curve fitting. Coefficients of them were derived, fitting equations were presented and examples were taken to verify the fitting results. At the same time, key issues on the skewness, tangent vectors of ends and so on were involved both in the process of cubic spline and in parametric cubic spline fittings. Corresponding fitting function can be chosen on the basis of foregone data points, so as to provide smooth curves to generate accurate tool path.