Optimisation of five-axis machining G-codes in the angular space

Reducing the kinematic errors is an important problem in five-axis machining. Errors of this type substantially affect the quality of the five-axis manufacturing. In this paper, we propose and analyse a new numerical algorithm to reduce the kinematic errors of a five-axis tool path using minimisation of the variation of the rotation angles. Our algorithm finds the locations of the cutter contact points (CC points) in the angular space and the orientation/location of the target surface relative to the mounting table that minimise the angle variation. We show through the numerical experiments and cutting simulations that the proposed method is efficient and accurate.

[1]  Stanislav S. Makhanov,et al.  Optimization of rotations of a five-axis milling machine near stationary points , 2004, Comput. Aided Des..

[2]  Manfred Weck,et al.  Handbook of machine tools , 1984 .

[3]  Taejung Kim,et al.  Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths , 2002, Comput. Aided Des..

[4]  Hsi-Yung Feng,et al.  The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction , 1995 .

[5]  Stanislav S. Makhanov,et al.  Advanced Numerical Methods to Optimize Cutting Operations of Five Axis Milling Machines , 2007 .

[6]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[7]  Placid Mathew Ferreira,et al.  Analysis of the Influence of Fixture Locator Errors on the Compliance of Work Part Features to Geometric Tolerance Specifications , 2003 .

[8]  Gustavo Belforte,et al.  Systematic geometric rigid body error identification of 5-axis milling machines , 2007, Comput. Aided Des..

[9]  A. Geddam,et al.  Error compensation in the end milling of pockets: a methodology , 2003 .

[10]  Marnix Nuttin,et al.  Compensation of thermal deformations in machine tools with neural nets , 1995 .

[11]  Joung-Hahn Yoon,et al.  Tool tip gouging avoidance and optimal tool positioning for 5-axis sculptured surface machining , 2003 .

[12]  Radha Sarma,et al.  On local gouging in five-axis sculptured surface machining using flat-end tools , 2000, Comput. Aided Des..

[13]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[14]  W. Anotaipaiboon,et al.  Tool path generation for five-axis NC machining using adaptive space-filling curves , 2005 .

[15]  Knut Sørby,et al.  Inverse kinematics of five-axis machines near singular configurations , 2007 .

[16]  Yuan-Shin Lee,et al.  Admissible tool orientation control of gouging avoidance for 5-axis complex surface machining , 1997, Comput. Aided Des..

[17]  Erik L.J. Bohez,et al.  Compensating for systematic errors in 5-axis NC machining , 2002, Comput. Aided Des..

[18]  Chia-Hsiang Menq,et al.  The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification , 1995 .

[19]  Edwin K. P. Chong,et al.  An Introduction to Optimization: Chong/An Introduction , 2008 .

[20]  Yuan-Shin Lee,et al.  Surface interrogation and machining strip evaluation for 5-axis CNC die and mold machining , 1997 .

[21]  Andrew Honegger,et al.  Analysis of thermal errors in a high-speed micro-milling spindle , 2010 .

[22]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[23]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[24]  Aun-Neow Poo,et al.  Thermal error measurement and modelling in machine tools. Part II. Hybrid Bayesian Network—support vector machine model , 2003 .

[25]  O. Remus Tutunea-Fatan,et al.  Comparing the kinematic efficiency of five-axis machine tool configurations through nonlinearity errors , 2011, Comput. Aided Des..

[26]  Erik L.J. Bohez,et al.  Optimal setup for five-axis machining , 2006 .

[27]  Mud-Armeen Munlin,et al.  Optimal sequencing of rotation angles for five-axis machining , 2007 .

[28]  Yang Jianguo,et al.  Simulation of thermal behavior of a CNC machine tool spindle , 2007 .

[29]  Hsi-Yung Feng,et al.  Configuration analysis of five-axis machine tools using a generic kinematic model , 2004 .

[30]  Yuan-Shin Lee,et al.  Optimizing tool orientations for 5-axis machining by configuration-space search method , 2003, Comput. Aided Des..

[31]  Erik L.J. Bohez,et al.  Five-axis milling machine tool kinematic chain design and analysis , 2002 .

[32]  Y. Altintas,et al.  Generalized kinematics of five-axis serial machines with non-singular tool path generation , 2013 .

[33]  Hiroyasu Iwabe,et al.  Study on corner cut by end mill: analysis of cutting mechanism and new cutting method at inside corner , 1989 .

[34]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[35]  Kai Tang,et al.  Improving the dynamics of five-axis machining through optimization of workpiece setup and tool orientations , 2011, Comput. Aided Des..

[36]  Manfred Weck.  Metrological analysis and performance tests , 1984 .

[37]  Tamara G. Kolda,et al.  Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods , 2003, SIAM Rev..

[38]  Chih-Ching Lo,et al.  Efficient cutter-path planning for five-axis surface machining with a flat-end cutter , 1999, Comput. Aided Des..

[39]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[40]  Bert Lauwers,et al.  Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machine simulation , 2003, Comput. Aided Des..

[41]  Min Wang,et al.  Kinematic error separation on five-axis NC machine tool based on telescoping double ball bar , 2010 .

[42]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[43]  Stanislav S. Makhanov,et al.  Adaptable geometric patterns for five-axis machining: a survey , 2010 .

[44]  Esther M. Arkin,et al.  Optimal covering tours with turn costs , 2001, SODA '01.

[45]  Aun-Neow Poo,et al.  Thermal error measurement and modelling in machine tools.: Part I. Influence of varying operating conditions , 2003 .

[46]  Soichi Ibaraki,et al.  Machining tests to identify kinematic errors on five-axis machine tools , 2010 .

[47]  Masaomi Tsutsumi,et al.  Enhancement of geometric accuracy of five-axis machining centers based on identification and compensation of geometric deviations , 2013 .

[48]  Stanislav S. Makhanov,et al.  Grid generation as applied to optimize cutting operations of the five-axis milling machine , 2003 .

[49]  J. Jung,et al.  Machining accuracy enhancement by compensating for volumetric errors of a machine tool and on-machine measurement , 2006 .

[50]  Pierre Bourdet,et al.  Avoiding 5-axis singularities using tool path deformation , 2004 .

[51]  A. Geddam,et al.  A process-design approach to error compensation in the end milling of pockets , 1999 .

[52]  William B. Langdon,et al.  Genetic Algorithms—Principles and Perspectives, A Guide to GA Theory by Colin R. Reeves and Jonathan E. Rowe, Kluwer Academic Publishers, 332 pp., $120.00, ISBN 1-4020-7240-6 , 2004, Knowledge engineering review (Print).

[53]  Tony L. Schmitz,et al.  Case study: A comparison of error sources in high-speed milling , 2008 .

[54]  Jian Gao,et al.  Adaptive restoration of complex geometry parts through reverse engineering application , 2006, Adv. Eng. Softw..

[55]  M A. Donmez,et al.  A Novel Cooling System to Reduce Thermally-Induced Errors of Machine Tools☆ , 2007 .