Helisel Bir Yörüngede Hareket Eden Dairesel Paraboloit Parmak Frezenin Süpürme Hacmi

Talaşlı imalat yöntemlerini kullanarak tek pasoda karmaşık parça geometrileri elde etmek için, geleneksel olmayan geometrilere sahip takımların kullanılması önemlidir. Dairesel paraboloit, bir parabolün döndürülmesiyle elde edilebilen katı bir cisimdir. Bir parmak frezenin süpürme hacmi, takım hareket ettikçe üzerindeki tüm noktaların her an için birleştirilmesi olarak tanımlanabilir ve bunun elde edilmesi gerçek bir talaşlı imalat işleminden önce işlenmiş parça geometrisini belirlemek için bir zorunluluktur. Takımın süpürme hacminin türetilmesinden sonra, işlenmiş parça geometrisi takımın süpürme hacminin ilk iş parçasının hacminden çıkarılmasıyla elde edilir. Ancak takım süpürme hacminin elde edilmesi basit değildir. Bu çalışmada, iyi tanımlanmış ve kısıtlanmış takım geometrisi ve takım yolu kullanılarak işlenmiş parça üzerindeki tüm noktaları elde etmek için analitik bir model sunulmuştur. Modelde takımın helisel yörünge boyunca hareket ederken anlık kesitini gözlemlemek için vida ekseninden geçen bir düzlem kullanılmıştır. Bu düzlemde takımın anlık kesitleri üst üste getirilerek, son kesit elde edilmiştir. Vida ekseninden geçen tüm kesitler özdeş olduğundan, yöntem işlenmiş parça yüzeyi üzerindeki noktaların kümesini vermektedir. Modeli doğrulamak için bilgisayar destekli tasarım programı kullanılmıştır.

Anahtar Kelimeler:

Frezeleme, Dairesel paraboloit parmak freze, Helisel yörünge, Süpürme hacmi

The Swept Volume of a Circular Paraboloid End Mill Moving Along a Helical Path

To obtain complex part geometries at one pass using machining processes, it is important to employ the tools with non-conventional geometries. A circular paraboloid is a solid of revolution, which can be obtained by rotating a parabola. The swept volume of an end mill can be defined as the unification of all sets of points on the tool for every instant as it moves, and its derivation is an obligation to determine the machined part geometry prior to an actual machining process. After derivation of the swept volume of the tool, machined part geometry is obtained by subtracting the swept volume of the tool from the volume of the initial workpiece. However, derivation of the swept volume of the tool is not a straightforward task. In this work, an analytical model was introduced to derive a complete set of points on the machined part by means of well-defined and constrained tool geometry and tool path. In the model, a plane that passes through the screw axis was used to observe the instant cross-section of the tool as it moves along the helical path. By overlapping the instant cross-sections of the tool in the plane, the final cross-section was derived. Since all cross-sections that pass through the screw axis are identical, the method gives an entire set of points on the machined surface. To validate the model, a computer-aided design program was utilized.

Keywords:

Milling, Circular paraboloid end mill, Helical path, Swept volume,

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Bruno Dutra Pereira R., Brandão L., Paiva A., Ferreira J. and Davim J. (2017). A review of helical milling process. International Journal of Machine Tools and Manufacture, 120, 27-48.
Araujo A. C., Silveira J. L., Jun M. B., Kapoor S. G. and DeVor R. (2006). A model for thread milling cutting forces. International Journal of Machine Tools and Manufacture, 46, 2057–65.
Fromentin G. and Poulachon G. (2010). Geometrical analysis of thread milling—part 1: evaluation of tool angles. The International Journal of Advanced Manufacturing Technology, 49, 73–80.
Fromentin G. and Poulachon G. (2010). Modeling of interferences during thread milling operation. The International Journal of Advanced Manufacturing Technology, 49, 41–51.
Perrin N., Stasse O., Baudouin L., Lamiraux F. and Yoshida E. (2011). Fast humanoid robot collision-free footstep planning using swept volume approximations. IEEE Transactions on Robotics, 28, 427–39.
Täubig H., Bäuml B. and Frese U. (2011). Real-time swept volume and distance computation for self collision detection. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, San Francisco, CA, USA, 25-30 September 2011.
Weinert K., Du S., Damm P. and Stautner M. (2004). Swept volume generation for the simulation of machining processes. International Journal of Machine Tools and Manufacture, 44, 617–28.
Abdel-Malek K., Yang J. and Blackmore D. (2001). On swept volume formulations: implicit surfaces. Computer-Aided Design, 33, 113–21.
Abdel-Malek K. and Yeh H-J. (1997). Geometric representation of the swept volume using Jacobian rank-deficiency conditions. Computer-Aided Design, 29, 457–68.
Blackmore D, Leu M-C. and Wang L. P. (1997). The sweep-envelope differential equation algorithm and its application to NC machining verification. Computer-Aided Design, 29, 629–37.
Pottmann H. and Peternell M. (2000). Envelopes-computational theory and applications. Proceedings of Spring Conference on Computer Graphics, 3-23, Comenius University, Bratislava, Slovakya.
Aras E. (2019). Tracing sub-surface swept profiles of tapered toroidal end mills between level cuts. Journal of Computational Design and Engineering, 6(4), 629-649.
Boz Y., Erdim H. and Lazoglu I. (2015). A comparison of solid model and three-orthogonal dexelfield methods for cutter-workpiece engagement calculations in three- and five-axis virtual milling. The International Journal of Advanced Manufacturing Technology, 81, 811–23.
Nishida I., Okumura R., Sato R. and Shirase K. (2018). Cutting force simulation in minute time resolution for ball end milling under various tool posture. Journal of Manufacturing Science and Engineering, 140(2), 021009.