Research On Interpolation Method For Tool Path In Diamond Turning Of Optical Free-form Surface

Because free-form surface optical components can improve optical performance,and can realize structure lightweight, they are widely used not only in aerospace,aviation, national defense, and many other industries, but also in consumer-orientedindustries, such as fiber-optic communications, mobile phones, digital cameras, imageprocessing, automotive, etc.The key of free-form surface optical components being used inconsumer-oriented industries successfully is to create high performance, precision,low cost optical free-form surfaces. Current optical free-form surface creatingmethods include: copy forming, grinding, lapping and polishing technology, diamondturning based on fast tool servo (FTS) or slow slide servo (S3), diamond fly-cuttingand micro-milling, etc. Diamond turning based on FTS is generally considered themost promising optical free-form surface creating method by international academicsand industry because of its high precision, high efficiency, and low cost.Interpolation function module is a significantly important function module in thewhole CNC system, and the interpolation algorithm will directly affect the machiningaccuracy and speed. Therefore, experts have been trying to look for a interpolationmethod with fast calculating speed and high accuracy, from the initial straight line,circular interpolation to the parabolic line, helix interpolation later, and recently thevery popular spline interpolation. However, there are still some problems so far. Thus,studying the optical surface interpolation technique has not only great theoreticalvalue but also important practical value for improving the performance of CNCsystem.After researching the current NC system and the existing linear interpolation,circular interpolation and non-uniform rational B-spline surfaces (NURBS)interpolation algorithm, and comparing their shortcomings, this thesis proposes a new tool path interpolation algorithm based on FTS, the four points mean valuefdinaetnteer-crpmoolilunametidon n tb hyaa trlg aocdranisit hbrme a.rn edIm toasvn egpdleri b ny c iptoolone l st hisoe n cfterhea teti-:mf oeer; macfi hrs sutlriyfn atucesere p coNolaUrtriReosn point whichBpSo nidnste trop oala tuinointalgorithm to calculate each interpolation point’s X, Y, and Z coordinate values, andthen use the Z coordinate values of the four vertices of each small fan column tocalculated the corresponding interpolation point’s Z coordinate values, ultimatelytransport the Z coordinate values to the control system for machining. That is, throughreducing the surface error of each unit fan-column, improve the surface accuracy ofthe entire free surface, and then improve the optical properties of freeform surface.This thesis takes the loop surface for an example, analyzes and compares thesurface accuracy of free-form surfaces which are processed by NURBS interpolationalgorithm and four-point mean value interpolation algorithm using Matlab, andverifies the validity and reliability of the new four points mean value interpolationalgorithm. The results show that the proposed new interpolation method is simple, itnot only improves the surface accuracy of the free-form surface, but also meets thereal-time requirement.