RESEARCH PAPER
Algebraic parameterization-based spiral machining toolpath generation for C1-continuous compound surfaces
1
Hefei University of Technology, China
Submission date: 2025-09-03
Final revision date: 2026-01-25
Acceptance date: 2026-03-01
Publication date: 2026-03-05
KEYWORDS
TOPICS
ABSTRACT
In the CAM machining of complex surfaces such as open blisk blades, unsmooth tool paths often occur at the common boundaries of compound surfaces. Conventional parameter alignment cannot guarantee C1continuity in the Euclidean parameter domain. To generate boundary-consistent spiral tool paths on compound or trimmed surfaces, a method based on Coons reparameterization is proposed for computing the control lines required to generate spiral tool paths. On the unfolded Coons compound surfaces, spiral tool paths are generated directly by connecting the start and end points, avoiding the need to compute 3D points one by one. However, this may still fail to ensure C1 continuity at surface boundaries. Therefore, a 2D compound parameter domain is reconstructed via Coons mapping, which maintains the geometric features of the part and ensures C1-continuous tool paths at common boundaries. Simulation and machining of an open blisk blade verify the effectiveness of the method, showing improved contour accuracy and an 18% reduction in surface roughness after optimization.
REFERENCES (27)
1.
Liang Q, Wang Y, Fu H, Han Z. Cutting path planning for ruled surface impellers. Chinese Journal of Aeronautics 2008; 21(5): 462–471. https://doi:10.1016/S1000-9361....
2.
Zhang K, Tang K. An efficient greedy strategy for five-axis tool path generation on dense triangular mesh. The International Journal of Advanced Manufacturing Technology 2014; 74: 1539–1550. https://doi: 10.1007/s00170-014-6083-1.
3.
Feng H, Teng Z. Iso-planar piecewise linear NC tool path generation from discrete measured data points. Computer-Aided Design 2005; 37(1): 55–64. https://doi: 10.1016/j.cad.2004.04.001.
4.
He W, Lei M, Bin H. Iso-parametric CNC tool path optimization based on adaptive grid generation. The International Journal of Advanced Manufacturing Technology 2009; 41: 538–548. https://doi.org/10.1007/s00170....
5.
Feng H, Li H. Constant scallop-height tool path generation for three-axis sculptured surface machining. Computer-Aided Design 2002; 34(9): 647–654. https://doi:10.1016/S0010-4485....
6.
Lee E. Contour offset approach to spiral toolpath generation with constant scallop height. Computer-Aided Design 2003; 35(6): 511-518. https://doi: 10.1016/S0010-4485(01)00185-3.
7.
Sun Y, Guo D, Jia Z, Wang H. Iso-parametric tool path generation from triangular meshes for free-form surface machining. The International Journal of Advanced Manufacturing Technology 2006; 28(7): 721–726. https://doi.org/10.1007/s00170....
8.
Xu J, Ji Y, Sun Y, Lee Y. Spiral tool path generation method on mesh surfaces guided by radial curves. Journal of Manufacturing Science and Engineering 2018; 140(7): 071016. https://doi.org/10.1115/1.4039....
9.
Guo J, Ding F, Jia X, Yan D. Automatic and high-quality surface mesh generation for CAD models. Computer-Aided Design 2019; 109: 49–59. https://doi.org/10.1016/j.cad.....
10.
Suresh K, Yang D C H. Constant scallop-height machining of free-form surfaces. Journal of engineering for industry 1994; 116(2): 253–259. https://doi: 10.1115/1.2901938.
11.
Yang, D C H, Chuang J, OuLee T H. Boundary-conformed toolpath generation for trimmed free-form surfaces. Computer-Aided Design 2003; 35(2): 127–139. https://doi: 10.1016/S0010-4485(02)00047-7.
12.
Chuang J, Yang D C H. A laplace-based spiral contouring method for general pocket machining. In ASME International Mechanical Engineering Congress and Exposition 2004; 47136: 227–236. https://doi: 10.1115/IMECE2004-60138.
13.
Takasugi K, Asakawa N. Parameter-based spiral tool path generation for free-form surface machining. Precision Engineering 2018; 52: 370–379. https://doi: 10.1016/j. precisioneng.2018.01.013.
14.
Xu J, Sun Y, Wang S. Tool path generation by offsetting curves on polyhedral surfaces based on mesh flattening. The International Journal of Advanced Manufacturing Technology 2013; 64: 1201–1212. https://doi: 10.1007/s00170-012-4075-6.
15.
Han J, Du H, Tian X, Xia L. Research on spiral finishing path generation for integral blade disc composite surface blades based on coons reparameterization. Chinese Journal of Mechanical Engineering 2025; 1–19. https://link.cnki.net/urlid/42....
16.
Randrianarivony M. On global continuity of Coons mappings in patching CAD surfaces. Computer-Aided Design 2009; 41(11): 782–791. https://doi: 10.1016/j.cad.2009.04.012.
17.
Kapl M, Vitrih V, Jüttler B, Birner K. Isogeometric analysis with geometrically continuous functions on two-patch geometries. Computers & Mathematics with Applications 2015; 70(7): 1518–1538. https://doi: 10.1016/j.camwa.2015.04.004.
18.
Collin A, Sangalli G, Takacs T. Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces. Computer Aided Geometric Design 2016; 47: 93–113. https://doi: 10.1016/j.cagd.2016.05.009.
19.
Kapl M, Sangalli G, Takacs T. Construction of analysis-suitable G1 planar multi-patch parameterizations. Computer-Aided Design 2018; 97: 41–55. https://doi: 10.1016/j.cad.2017.12.002.
20.
Elber G, Cohen E. Tool path generation for freeform surface models. In Proceedings on the second ACM symposium on Solid modeling and applications 1993; 419–428. https://doi: 10.1145/164360.164500.
21.
Feng H, Li H. Constant scallop-height tool path generation for three-axis sculptured surface machining. Computer-Aided Design 2002; 34(9): 647–654. https://doi: 10.1016/S0010-4485(01)00136-1.
22.
Yazıcı İ, Yaylacı E K, Yalçın F. Modified golden section search based MPPT algorithm for the WECS. Engineering Science and Technology, an International Journal 2021; 24(5): 1123–1133. https://doi: 10.1016/j.jestch.2021.02.006.
23.
Zhang Y, Ji Y, Zhu C. Multi-patch parameterization method for isogeometric analysis using singular structure of cross-field. Computers & Mathematics with Applications 2024; 162: 61–78. https://doi.org/10.1016/j.camw....
24.
Sun Y, Sun S, Xu J, Guo D. A unified method of generating tool path based on multiple vector fields for CNC machining of compound NURBS surfaces. Computer-Aided Design 2017; 91: 14–26. https://doi: 10.1016/j.cad.2017.04.003.
25.
Wang L, Zhu X, Tang Z. Coons type blended B-spline (CNSBS) surface and its conversion to NURBS surface. Computers & Graphics 1997; 21(3): 297–303. https://doi: 10.1016/S0097-8493(97)00006-X.
26.
Peters J. Geometric Continuity. In: Handbook of computer aided geometric design. Amsterdam: North-Holland 2002; 193–227.
27.
Buchegger F, Jüttler B. Planar multi-patch domain parameterization via patch adjacency graphs. Computer-Aided Design 2017; 82: 2–12. https://doi: 10.1016/j.cad.2016.05.019.
| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
