Abstract
Complexity of sculptured surfaces has a great influence on multi-axis computer numerical control (CNC) machining performances such as processing efficiency, surface quality, and energy consumption. A term called surface machining complexity (SMC) is first presented to describe the complexity level of surface geometrical shape features, and its influence on CNC machining performance. Shape features of sculptured surfaces are classified into seven categories based on surface curvature. An innovative method for quantifying SMC using surface subdivision is proposed. Firstly, representation of sculptured surfaces is introduced. Then, three processes of surface subdivision are presented, which are surface discretization based on iso-parameter line sampling, rough partitioning based on surface shape categories, and region grouping based on two criteria. After that calculation, formulas of SMC including formulas of local SMC and global SMC are developed. The proposed formulas utilize three correction factors to describe the influences of surface size, cutter diameter, grouping order, and mode of different surface shape categories. Finally, the proposed method is applied to calculate SMC for a typical sculptured surface and multi-axis CNC machining experiments to demonstrate the ability of our method, which can form a foundation for further research.
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References
Zhou ZX, Zhou QY, Ren YH (2010) Complex curve surface design machining equipment current research trend. J Mech Eng 46(17):105–113
Li BL, Wang XL, Hu YJ (2008) Tool orientation control method based on divided-area algorithm. Chin J Mech Eng-En 21(4):452–457
Li LL, Zhang YF, Li HY, Geng L (2011) Generating tool-path with smooth posture change for five-axis sculptured surface machining based on cutter's accessibility map. Int J Adv Manuf Technol 53(5–8):699–709
Chen ZC, Khan MA (2013) A new approach to generating arc length parameterized NURBS tool paths for efficient three-axis machining of smooth, accurate sculptured surfaces. Int J Adv Manuf Technol. doi:10.1007/s00170-013-5411-1
Li L, Liu F, Chen B, Li CB (2013) Multi-objective optimization of cutting parameters in sculptured parts machining based on neural network. J Intell Manuf. doi:10.1007/s10845-013-0809-z
Subrahmanyam KVR, San WY, Soon HG, Sheng H (2010) Cutting force prediction for ball nose milling of inclined surface. Int J Adv Manuf Technol 48:23–32
Cao QY, Xue DY, Zhao J, Li Y (2011) A cutting force model considering influence of radius of curvature for sculptured surface machining. Int J Adv Manuf Technol 54(5–8):821–835
Piegl L (1991) On NURBS: a survey. IEEE Comput Graph 11(1):55–71
Lin RS, Koren Y (1996) Efficient tool-path planning for machining free-form surfaces. J Eng Ind 118(1):20–28
Hwang JS (1992) Interference-free tool-path generation in the NC machining of parametric compound surfaces. Comput-Aided Des 24(12):667–676
Xie J, ZOU MS, Cui XL (2009) Effect of curvature distribution feature of complex free-form surface on CNC milling performance. J Inst Eng Bangladesh 45(11):158–162
Lin JQ, Wang YQ (2007) Subdivision planning of complex free-form surface. J Jilin Univ Eng Tech Edit 37(2):386–390
Sridharan N, Shah JJ (2004) Recognition of multi axis milling features: part I-topological and geometric characteristics. J Comput Inf Sci Eng 4(3):242–250
Sunil VB, Pand SS (2008) Automat recognition of features from freeform surface CAD models. Comput Aided Des 40(4):502–517
Cicirello V, Regli WC (2001) Machining feature-based comparisons of mechanical parts. Proceedings International Conference on Shape Modeling and Applications 176-185.
Chen CK, Wu CT (2002) The region division and NC machining of compound surfaces. J Mmater Process Tech 121(1):5–14
Stoker JJ (1989) Differential geometry. Wiley-Interscience, Now York
Goldman R (2005) Curvature formulas for implicit curves and surfaces. Comput-Aided Geom Des 22(7):632–658
Chen ZZC, Dong ZM, Geoffrey WV (2003) Automated surface subdivision and tool path generation for 3 0.5 0.5-axis CNC machining of sculptured parts[J]. Comput Ind 50:319–331
Sonthi R, Kunjur G, Gadh R (1997) Shape feature determination using the curvature region representation. Fourth ACM symposium on Solid modeling and applications:285-296.
Tuonga NV, Pokornya P (2010) A practical approach for partitioning free-form surfaces. Int J Comput Integ M 23(11):992–1001
Song Y, Bronsvoort WF (2005) Fitting and manipulating free-form shapes using templates. J Comput Inf Sci Eng 5(2):86–94
Pan RJ (2001) Explicit matrix representation for NURBS curves and surfaces and its algorithm. Chinese J of Comp 24(4):258–288
Benko P, Varady T (2004) Segmentation methods for smooth point regions of conventional engineering objects. Comput-Aided Des 36(6):511–523
Woo H, Kang E, Wang SY, Kwan H (2002) A new segmentation method for point cloud data. Int J Mach Tool Manu 42(2):167–178
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Li, L., Chen, B., Liu, F. et al. Complexity analysis and calculation for sculptured surface in multi-axis CNC machining based on surface subdivision. Int J Adv Manuf Technol 71, 1433–1444 (2014). https://doi.org/10.1007/s00170-013-5544-2
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DOI: https://doi.org/10.1007/s00170-013-5544-2