A study of B-splines and their applications to surface design and manufacture

Sanjeev Bedi
Compound curved surfaces are frequently encountered in engineering applications, such as marine propellers, turbines, ship hulls, aeroplane fuselages and automobile bodies. In the manufacture of such items the surface definition is required in a smoothly changing form without surface oscillations and irregularities. Frequently, however, the surfaces are defined by measured prototype data, which may be sparse in nature and have attendant measurement errors. In such instances the data has to be
more » ... proximated and possibly smoothed by a series of curves of some known form. There are a number of types of curves available for curve fitting in CAD/CAM work. In this work the basis and properties of B-spline curve fitting are established and evaluated in relation to other curve fitting techniques. A series of trial shapes, or bench marks, were devised which showed that B-splines generated the smoothest curves and are very suitable for computer-aided-design applications. B-splines, with other types of spline curves, form the basis of a new computer-aided-machining program called G-SURF. The surface is defined within G-SURF as a grid of orthogonal space curves and is machined using an end milling cutter inclined at a predetermined angle to the surface normals. The end mill thus cuts on the leading or trailing edge (as appropriate) and is able to remove material very efficiently at a full and preselected material cutting speed. Within this work G-SURF has been used to design and produce a series of trial objects, including a 3ft. ship hull and a chain-saw guide bar. They have served to prove and test the G-SURF program.
doi:10.14288/1.0080806 fatcat:u4eckleibvgqzhdirg3n76ym5e