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

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.

[1]  Yuwen Sun,et al.  A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints , 2015 .

[2]  Han Tong Loh,et al.  Adaptive fairing of digitized point data with discrete curvature , 2002, Comput. Aided Des..

[3]  Ranga Narayanaswami,et al.  A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining , 2003, Comput. Aided Des..

[4]  Rong-Shean Lee,et al.  Tool path generation and error control method for multi-axis NC machining of spatial cam , 1998 .

[5]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[6]  Yuan-Shin Lee,et al.  Adaptive Tool Path Planning for 5-Axis Sculptured Surface Machining by Machining Strip Evaluation , 1998, SSM.

[7]  Christophe Tournier,et al.  A Surface Based Approach for Constant Scallop HeightTool-Path Generation , 2002 .

[8]  Li-Min Zhu,et al.  Geometric conditions for tangent continuity of swept tool envelopes with application to multi-pass flank milling , 2015, Comput. Aided Des..

[9]  An-Chen Lee,et al.  The feedrate scheduling of NURBS interpolator for CNC machine tools , 2011, Comput. Aided Des..

[10]  M. Nategh,et al.  Development of a novel adaptive nonuniform rational basis spline interpolator with limited kinematic error for hexapod machine tools , 2014 .

[11]  Tae Jo Ko,et al.  NURBS interpolator for constant material removal rate in open NC machine tools , 2004 .

[12]  Li-Min Zhu,et al.  Feedrate scheduling for interpolation of parametric tool path using the sine series representation of jerk profile , 2017 .

[13]  Hsi-Yung Feng,et al.  An improved tool path discretization method for five-axis sculptured surface machining , 2007 .

[14]  Naoki Uchiyama,et al.  Contouring controller design based on iterative contour error estimation for three-dimensional machining , 2011 .

[15]  Xianli Liu,et al.  Interpolation using non-uniform rational B-spline for the smooth milling of ruled-surface impeller blades , 2015 .

[16]  Limin Zhu,et al.  Look-ahead interpolation of short line segments using B-spline curve fitting of dominant points , 2015 .

[17]  Han Ding,et al.  Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (I): Third-order approximation of tool envelope surface , 2010 .

[18]  Peihua Gu,et al.  Recent development in CNC machining of freeform surfaces: A state-of-the-art review , 2010, Comput. Aided Des..

[19]  P. Dey,et al.  A new iso-parametric machining algorithm for free-form surface , 2014 .

[20]  Dongming Guo,et al.  Variable feedrate interpolation of NURBS Toolpath with geometric and kinematical constraints for five-axis CNC machining , 2013, J. Syst. Sci. Complex..

[21]  Aun Neow Poo,et al.  Adaptive iso-planar tool path generation for machining of free-form surfaces , 2003, Comput. Aided Des..

[22]  Dongsheng Yang,et al.  A real-time look-ahead interpolation algorithm based on Akima curve fitting , 2014 .

[23]  Gershon Elber,et al.  Tool path generation for freeform surface models , 1993, Solid Modeling and Applications.

[24]  Claire Lartigue,et al.  CNC tool path in terms of B-spline curves , 2001, Comput. Aided Des..

[25]  Yang Zhao,et al.  The feedrate scheduling of parametric interpolator with geometry, process and drive constraints for multi-axis CNC machine tools , 2014 .