Third-order chord error estimation for freeform contour in computer-aided manufacturing and computer numerical control systems

Abstract

The chord error employed in computer-aided manufacturing and computer numerical control systems is a crucial index to evaluate the machining accuracy of machined parts. It is usually estimated by the second-order method, that is, the osculating circle method. The second-order estimation only takes the curvature of the curve into account, which will bring about great estimation error when applying to freeform curves. In this article, a third-order method that estimates the chord error using conical helices is proposed. By investigating the geometric properties of the conical helix, it is found that there exists a conical helix that has third-order contact with the freeform curve. With the aid of this conical helix, a third-order model for estimating the chord error of freeform curves is developed. Numerical examples of three freeform curves are provided to verify the effectiveness of the proposed estimation model.