Research On Reverse Problem Of Slender Spiral Curved Surface

Complex curved surface is the important part of mechanical products of various highprecision and sophisticated. However, the complex curved surface often formed by somecurve motion. The shape of the rotor of the screw drill for oil drilling in the industry is a kindof complex spiral curved surfaces. The profile of the work piece should be detailed andconcrete analysis to processing the screw. In recent years, with the diversification of screwtype, many manufacturers began to study the screw profile to improve the efficacy of screwdrill through the factor on the change of screw profile, the head numbers and lead, and hasaccumulated to form a lot of experience, but with the flow of personnel, time and otherreasons, some of the screw profile curve have lost, and only existed the NC program code orthe legacy of the product photos. Manufacturers hope to get the original profile data curvescrew through research on NC program code and pictures.For two kinds of cases about the NC program and product photos, methods areproposed to obtain original profile data curve. For the only case of the NC program, there aretwo ways to get the end section profile curve, the simple method is to set the sectioncurve equation, find out the equation coefficients to obtain profile curve, the general one isthat the information of tool motion includes the profile of workpiece, that needs to simplifythe tool motion and establish mathematical model, the tool nose arc center trajectory curvecan be extracted from the NC program. Then offset the curve to obtain the workpiece profilecurve. For the only case of the product photos, extract screw shaft section offset curve, withthe coordinate equation of cutter in space, contact law, and helical surface projection contactpoint coordinates can be obtained from the cutter contact point coordinates in space, next,convert the cutter contact point coordinate space to plane coordinates, and get the profileof type curve to fit Finally, verify the feasibility of the method through examples. Two kindsof situations about different methods not only make up the blank of the screw surface reverseproblem but increase the application example of mathematical theory in other fields.