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Optimal tool orientation in 3 + 2-axis machining considering machine kinematics

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Abstract

In 5-axis machining, the initial orientation and position of the part in the fixture on the machine table are chosen to avoid collisions and to ensure that axes ranges are respected. However, kinematics of the machine is rarely considered for workpiece setup optimization although it affects the tool path execution and machining time. Indeed, for complex surfaces, actual feedrate is often lower than the programmed one and can present strong slowdowns, which are critical for the tool cutting conditions and therefore the part quality. This article investigates the use of kinematic manipulability criteria to determine the best orientation of the workpiece setup to maximize the actual feedrate and reduce machining time. The modelling of maximum velocity, acceleration, and jerk of each axis by means of polytopes makes it possible to take advantage of the whole kinematic space of the machine more intuitively. Simulations and experiments are carried out in 3 + 2-axis machining on test parts with a ball-end tool. For stretched surfaces, while the tool centre motion is given by the machining strategy, the tool axis orientation is optimized jointly with the workpiece setup. Experiments confirm that actual feedrate raises faster to better respect the programmed cutting conditions along each path. As feedrate is also higher, machining time is reduced significantly.

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References

  1. Gupta P, Janardan R, Majhi J, Woo T (1996) Efficient geometric algorithms for workpiece orientation in 4- and 5-axis NC machining. Comput Aided Des 28(8):577–587. https://doi.org/10.1016/0010-4485(95)00071-2

    Article  MATH  Google Scholar 

  2. Kang JK, Suh SH (1997) Machinability and set-up orientation for five-axis numerically controlled machining of free surfaces. Int J Adv Manuf Technol 13(5):311–325. https://doi.org/10.1007/BF01178251

    Article  Google Scholar 

  3. Tang K, Chen LL, Chou SY (1998) Optimal workpiece setups for 4-axis numerical control machining based on machinability. Comput Ind 37(1):27–41. https://doi.org/10.1016/S0166-3615(98)00067-0

    Article  Google Scholar 

  4. Hu P, Tang K, Lee CH (2013) Global obstacle avoidance and minimum workpiece setups in five-axis machining. Comput Aided Des 45(10):1222–1237. https://doi.org/10.1016/j.cad.2013.05.007

    Article  Google Scholar 

  5. Chiou CJ, Lee YS (2002) A machining potential field approach to tool path generation for multi-axis sculptured surface machining. Comput Aided Des 34(5):357–371. https://doi.org/10.1016/S0010-4485(01)00102-6

    Article  MATH  Google Scholar 

  6. Barakchi Fard MJ, Feng HY (2010) Effective determination of feed direction and tool orientation in five-axis flat-end milling. J Manuf Sci Eng 132(6). https://doi.org/10.1115/1.4002766

  7. Zȩbala W, Plaza M (2014) Comparative study of 3- and 5-axis CNC centers for free-form machining of difficult-to-cut material. Int J Prod Econ 158:345–358. https://doi.org/10.1016/j.ijpe.2014.08.006

    Article  Google Scholar 

  8. Kim T, Sarma SE (2002) Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths. Comput Aided Des 34(6):453–468. https://doi.org/10.1016/S0010-4485(01)00116-6

    Article  Google Scholar 

  9. Farouki RT, Han CY, Li S (2014) Inverse kinematics for optimal tool orientation control in 5-axis CNC machining. Comput Aided Geom Des 31(1):13–26. https://doi.org/10.1016/j.cagd.2013.11.002

    Article  MathSciNet  MATH  Google Scholar 

  10. Hu P, Chen L, Tang K (2017) Efficiency-optimal iso-planar tool path generation for five-axis finishing machining of freeform surfaces. Comput Aided Des 83:33–50. https://doi.org/10.1016/j.cad.2016.10.001

    Article  Google Scholar 

  11. Bohez ELJ (2002) Five-axis milling machine tool kinematic chain design and analysis. Int J Mach Tools Manuf 42(4):505–520. https://doi.org/10.1016/S0890-6955(01)00134-1

    Article  Google Scholar 

  12. Tutunea-Fatan OR, Feng HY (2004) Configuration analysis of five-axis machine tools using a generic kinematic model. Int J Mach Tools Manuf 44(11):1235–1243. https://doi.org/10.1016/j.ijmachtools.2004.03.009

    Article  Google Scholar 

  13. Anotaipaiboon W, Makhanov S, Bohez E (2006) Optimal setup for five-axis machining. Int J Mach Tools Manuf 46(9):964–977. https://doi.org/10.1016/j.ijmachtools.2005.07.046

    Article  Google Scholar 

  14. Lin Z, Fu J, Shen H, Gan W (2014) On the workpiece setup optimization for five-axis machining with RTCP function. Int J Adv Manuf Technol 74(1):187–197. https://doi.org/10.1007/s00170-014-5981-6

    Article  Google Scholar 

  15. Yang J, Aslan D, Altintas Y (2018) Identification of workpiece location on rotary tables to minimize tracking errors in five-axis machining. Int J Mach Tools Manuf 125:89–98. https://doi.org/10.1016/j.ijmachtools.2017.11.009

    Article  Google Scholar 

  16. Pessoles X, Landon Y, Segonds S, Rubio W (2013) Optimisation of workpiece setup for continuous five-axis milling: application to a five-axis BC type machining centre. Int J Adv Manuf Technol 65(1):67–79. https://doi.org/10.1007/s00170-012-4151-y

    Article  Google Scholar 

  17. Shaw D, Ou GY (2008) Reducing X,Y and Z axes movement of a 5-axis AC type milling machine by changing the location of the work-piece. Comput Aided Des 40(10):1033–1039. https://doi.org/10.1016/j.cad.2008.09.001

    Article  Google Scholar 

  18. Dong J, Ferreira PM, Stori JA (2007) Feed-rate optimization with jerk constraints for generating minimum-time trajectories. Int J Mach Tools Manuf 47(12):1941–1955. https://doi.org/10.1016/j.ijmachtools.2007.03.006

    Article  Google Scholar 

  19. Sencer B, Altintas Y, Croft E (2008) Feed optimization for five-axis CNC machine tools with drive constraints. Int J Mach Tools Manuf 48(7):733–745. https://doi.org/10.1016/j.ijmachtools.2008.01.002

    Article  Google Scholar 

  20. Bosetti P, Bertolazzi E (2014) Feed-rate and trajectory optimization for CNC machine tools. Robot Comput Integr Manuf 30(6):667–677. https://doi.org/10.1016/j.rcim.2014.03.009

    Article  Google Scholar 

  21. Hu P, Tang K (2011) Improving the dynamics of five-axis machining through optimization of workpiece setup and tool orientations. Comput Aided Des 43(12):1693–1706. https://doi.org/10.1016/j.cad.2011.09.005

    Article  Google Scholar 

  22. Xu K, Tang K (2016) Optimal workpiece setup for time-efficient and energy-saving five-axis machining of freeform surfaces. J Manuf Sci Eng 139(5). https://doi.org/10.1115/1.4034846

  23. Campatelli G, Scippa A, Lorenzini L, Sato R (2015) Optimal workpiece orientation to reduce the energy consumption of a milling process. Int J Precis Eng Manuf Green Technol 2(1):5–13. https://doi.org/10.1007/s40684-015-0001-3

    Article  Google Scholar 

  24. Zhu Y, Chen ZT, Ning T, Xu RF (2016) Tool orientation optimization for 3+2-axis CNC machining of sculptured surface. Comput Aided Des 77:60–72. https://doi.org/10.1016/j.cad.2016.02.007

    Article  Google Scholar 

  25. Vulliez M, Lavernhe S, Bruneau O (2017) Dynamic approach of the feedrate interpolation for trajectory planning process in multi-axis machining. Int J Adv Manuf Technol 88(5):2085–2096. https://doi.org/10.1007/s00170-016-8903-y

    Article  Google Scholar 

  26. Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int J Mach Tools Manuf 41(9):1323–1345. https://doi.org/10.1016/S0890-6955(01)00002-5

    Article  Google Scholar 

  27. Yoshikawa T (1985) Manip of robot mech. Int J Robot Res 4(2):3–9. https://doi.org/10.1177/027836498500400201

    Article  Google Scholar 

  28. Merlet JP (2005) Jacobian, manipulability, condition number, and accuracy of parallel robots. J Mech Des 128(1):199–206. https://doi.org/10.1115/1.2121740

    Article  Google Scholar 

  29. Briot S, Pashkevich A, Chablat D (2010) Optimal technology-oriented design of parallel robots for high-speed machining applications. In: 2010 IEEE Int Conf on Robot and Autom, pp 1155–1161. https://doi.org/10.1109/ROBOT.2010.5509543

  30. Fukuda K (2004) From the zonotope construction to the minkowski addition of convex polytopes. J Symb Comput 38(4):1261–1272. https://doi.org/10.1016/j.jsc.2003.08.007 symbolic Computation in Algebra and Geometry

    Article  MathSciNet  MATH  Google Scholar 

  31. Ziegler GM (1995) Lectures on polytopes, graduate texts in mathematics, vol 152. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4613-8431-1

    Book  Google Scholar 

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Authors and Affiliations

  1. Université Paris-Saclay, ENS Paris-Saclay, LURPA, 91190, Gif-sur-Yvettes, France

    Laureen Grandguillaume, Sylvain Lavernhe & Christophe Tournier

Authors
  1. Laureen Grandguillaume
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  2. Sylvain Lavernhe
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  3. Christophe Tournier
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The submitted work is original and has not been published elsewhere in any form or language.

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Correspondence to Sylvain Lavernhe.

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Grandguillaume, L., Lavernhe, S. & Tournier, C. Optimal tool orientation in 3 + 2-axis machining considering machine kinematics. Int J Adv Manuf Technol 115, 2765–2783 (2021). https://doi.org/10.1007/s00170-021-07036-z

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