This thesis develops an algorithm to decrease high-curvature sections in tool paths for complex parts to achieve shorter machining times resulting in higher production rates. In the research sample cases, the algorithm decreased machining times by 1% to 9% for design-induced sections of high curvature and by 16% to 75% for CAM induced ripples using high path tolerances. High-curvature sections in tool paths are caused by complex part geometry, noise, and discontinuities in the model. The curvature is decreased by deviating the tool path within an allowable path tolerance. The feedrate along the tool path is directly related to the curvature of the tool path. High-curvature sections cause the NC machine to reduce the feedrate along the tool path due to acceleration and jerk limits. These lower feedrates increase machining time and slow production rates. This new algorithm decreases curvature, which increases feedrates and decreases machining times, thereby increasing production rates for manufacturing companies. The tool paths are represented by cubic B-splines. The algorithm is based on the basic principle that the curvature of a B-spline directly relates to the geometry of its control polygon. If the control polygon's geometry has many tight corners then the B-spline will have high curvature. If the control polygon's geometry is a straight line then the B-spline will be a straight line with zero curvature. The algorithm deviates the control polygon's points so that they move towards forming a straight line. The control polygon will rarely form a straight line because the spline is limited by the path tolerance. However, as the control polygon moves towards forming a straight line, the curvature decreases, which allows the feedrate to increase. Six sample cases are explored in which the machining time is decreased. Three of the cases are tool paths that contain curvature sections with a range of unnecessary curvature from low to high. One sample is the tool path for the complex geometry in a snow tire mold. Another sample tool path contains ripples caused by noise in the CAD model. The last tool path contains ripples caused by tangency discontinuities in the CAD model. The percent of time saved directly relates to the severity of the curvature in the part. This thesis provides a quick and efficient means to reduce curvature in complex parts, resulting in decreased machining times and increased production rates.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





naseath, red, NURBS, B-spline, B-splines, CAM, CAD, curvature, reducing curvature, complex tool paths, tool paths, tolerance, NURB, machine time, machining time