On initialization of milling paths for 5-axis flank CNC machining of free-form surfaces with general milling tools

Abstract We propose a path-planning algorithm for 5-axis flank CNC machining with general tools of varying curvature. Our approach generalizes the initialization strategy introduced for conical tools Bo et al. (2017) to arbitrary milling tools. Given a free-form (NURBS) surface and a rotational milling tool, we look for its motion in 3D to approximate the input reference surface within a given tolerance. We show that for a general shape of the milling tool, there exist locally and generically four 3D directions in which the point-surface distance follows the shape of the tool up to second order. These directions form a 3D multi-valued vector field and its integration gives rise to a set of integral curves. Among these integral curves, we seek straight line segments that correspond to good initial positions of the axes of the milling tool. We validate our method against synthetic examples with known exact solutions and, on industrial datasets, we detect approximate solutions that meet fine machining tolerances. We also demonstrate applicability of our method for efficient flank milling of convex regions that is not possible using traditional conical tools.

[1]  Knut Sørby,et al.  Improving High Speed Flank Milling Operations in Multi-Axis Machines , 2000 .

[2]  Helmut Pottmann,et al.  Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining , 2017, Comput. Aided Des..

[3]  Pengbo Bo,et al.  Highly accurate 5-axis flank CNC machining with conical tools , 2018, The International Journal of Advanced Manufacturing Technology.

[4]  Chih-Hsing Chu,et al.  Machining accuracy improvement in five-axis flank milling of ruled surfaces , 2008 .

[5]  Johanna Senatore,et al.  Optimising positioning of the axis of a milling cutter on an offset surface by geometric error minimisation , 2008 .

[6]  Xavier Beudaert,et al.  Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path , 2012 .

[7]  Dinesh Manocha,et al.  Fast continuous collision detection for articulated models , 2004, SM '04.

[8]  Robert B. Jerard,et al.  5-axis Machining of Sculptured Surfaces with a Flat-end Cutter , 1994, Comput. Aided Des..

[9]  Jianhua Fan,et al.  Flat-end cutter orientation on a quadric in five-axis machining , 2014, Comput. Aided Des..

[10]  Daniel Cohen-Or,et al.  DSCarver: decompose-and-spiral-carve for subtractive manufacturing , 2018, ACM Trans. Graph..

[11]  Yusuf Altintas,et al.  Simulation of flank milling processes , 2005 .

[12]  Yusuf Altintas,et al.  Mechanics and dynamics of general milling cutters.: Part I: helical end mills , 2001 .

[13]  Wenping Wang,et al.  Efficient collision detection using a dual OBB-sphere bounding volume hierarchy , 2010, Comput. Aided Des..

[14]  Johanna Senatore,et al.  Correlation between machining direction, cutter geometry and step-over distance in 3-axis milling: Application to milling by zones , 2012, Comput. Aided Des..

[15]  Sanjeev Bedi,et al.  Flank milling of a ruled surface with conical tools—an optimization approach , 2006 .

[16]  Sanjeev Bedi,et al.  Flank Millable Surface Design with Conical and Barrel Tools , 2008 .

[17]  Jie Sun,et al.  Modeling of cutting force under the tool flank wear effect in end milling Ti6Al4V with solid carbide tool , 2013 .

[18]  Li-Min Zhu,et al.  Five-axis flank milling of impellers: Optimal geometry of a conical tool considering stiffness and geometric constraints , 2016 .

[19]  Michael Barton,et al.  Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution , 2016, Comput. Aided Des..

[20]  S. K. Ghosh,et al.  Curvature catering-a new approach in manufacture of sculptured surfaces (part 1. theorem) , 1993 .

[21]  Ke Xu,et al.  Cutting force and machine kinematics constrained cutter location planning for five-axis flank milling of ruled surfaces , 2017, J. Comput. Des. Eng..

[22]  Ieee Xplore,et al.  IEEE Transactions on Pattern Analysis and Machine Intelligence Information for Authors , 2022, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Xing Zhang,et al.  An accurate prediction method of cutting forces in 5-axis flank milling of sculptured surface , 2016 .

[24]  Jian Liu,et al.  Improved positioning of cylindrical cutter for flank milling ruled surfaces , 2005, Comput. Aided Des..

[25]  Gershon Elber,et al.  Accessibility in 5-axis milling environment , 1994, Comput. Aided Des..

[26]  B. Ravani,et al.  Cylindrical milling of ruled surfaces , 2008 .

[27]  Pierre Alliez,et al.  Eurographics Symposium on Geometry Processing (2007) Voronoi-based Variational Reconstruction of Unoriented Point Sets , 2022 .

[28]  Gershon Elber,et al.  Automatic generation of globally assured collision free orientations for 5-axis ball-end tool-paths , 2018, Comput. Aided Des..

[29]  Satoshi Sakamoto,et al.  Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis , 2001 .

[30]  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..

[31]  Alain Bernard,et al.  5-axis flank milling: A state-of-the-art review , 2013, Comput. Aided Des..

[32]  Gershon Elber,et al.  Precise algebraic-based swept volumes for arbitrary free-form shaped tools towards multi-axis CNC machining verification , 2017, Comput. Aided Des..

[33]  H. Pottmann,et al.  Approximation by ruled surfaces , 1999 .

[34]  Ning Wang,et al.  Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface , 2009, Comput. Aided Des..

[35]  Aitzol Lamikiz,et al.  Selection of cutting conditions for a stable milling of flexible parts with bull-nose end mills , 2007 .

[36]  Charlie C. L. Wang,et al.  Multi-dimensional dynamic programming in ruled surface fitting , 2014, Comput. Aided Des..

[37]  Pierre-Yves Pechard,et al.  Geometrical deviations versus smoothness in 5-axis high-speed flank milling , 2009 .

[38]  Linda M. Wills,et al.  Reverse Engineering , 1996, Springer US.

[39]  Josef Hoschek,et al.  Handbook of Computer Aided Geometric Design , 2002 .

[40]  M. Rautenberg,et al.  The vibration behavior of impeller blades in the five-axis CNC flank milling process , 2010 .

[41]  Johanna Senatore,et al.  5-Axis Flank Milling of Sculptured Surfaces , 2012 .

[42]  Han Ding,et al.  Global optimization of tool path for five-axis flank milling with a cylindrical cutter , 2009, Comput. Aided Des..

[43]  Helmut Pottmann,et al.  Geometry of architectural freeform structures , 2008, SPM '08.

[44]  D.M. Mount,et al.  An Efficient k-Means Clustering Algorithm: Analysis and Implementation , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[45]  Sanjeev Bedi,et al.  PII: S0890-6955(99)00058-9 , 1999 .

[46]  Johanna Senatore,et al.  Analytical estimation of error in flank milling of ruled surfaces , 2008, Comput. Aided Des..

[47]  Walter Rubio,et al.  Side milling of ruled surfaces: Optimum positioning of the milling cutter and calculation of interference , 1998 .

[48]  Gershon Elber,et al.  5-Axis Freeform Surface Milling Using Piecewise Ruled Surface Approximation , 1997 .

[49]  Gershon Elber,et al.  Precise gouging-free tool orientations for 5-axis CNC machining , 2015, Comput. Aided Des..

[50]  Helmut Pottmann,et al.  Ruled Surfaces for Rationalization and Design in Architecture , 2010, Proceedings of the 30th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA).

[51]  Aitzol Lamikiz,et al.  Experimental and numerical investigation of the effect of spray cutting fluids in high speed milling , 2006 .

[52]  Kathryn A. Ingle,et al.  Reverse Engineering , 1996, Springer US.