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Model for the prediction of whirling vibrations in drilling processes through semi-discretization of the drill motion equation

  • Amaia JiménezEmail author
  • Miguel Arizmendi
  • Wilmer E. Cumbicus
ORIGINAL ARTICLE
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Abstract

In this work, a model for the prediction of drilling stability against low-frequency lateral vibrations, named as whirling in the literature, is proposed. These vibrations are lateral displacements of the tool that arise at frequencies near multiples of the rotation frequency of the drill. The appearance of whirling vibrations leads to the generation of lobe-shaped holes. In order to predict whirling vibrations, the motion equation of the drill is deduced taking into account the modal characteristics of the drill and the cutting and process damping forces that act on it. In this paper, forces that arise in two different regions of the drill are considered: (1) forces on the main cutting edges and (2) forces on the chisel edge. Different force models are presented for each region that include both the regenerative effect of the vibration on the cutting area and the process damping. An oblique cutting model and an orthogonal model are employed for the calculation of cutting forces acting on the main cutting edges and on the chisel edge, respectively. The cutting force model for the main cutting edges takes into account the cutting angle (inclination angle, rake angle, and chip flow angle) variation along the main cutting edges. For the chisel edge region, where the feed speed is no longer negligible with respect to the cutting speed, the dynamic cutting angles are employed for the force model development. Concerning the process damping force model, previous works in the literature consider a constant value of the clearance angle for the calculation of the process damping coefficient. However, in this work, the variation of the normal clearance angle along the main cutting edges is considered. It is shown that, depending on the clearance face grinding parameters employed, the clearance angle can double its value along the main cutting edges. Considering the force models and through the semi-discretization of the motion equation of the drill, the appearance of low-frequency lateral vibrations is predicted regarding the drill geometry and cutting conditions such as drill rotation speed and feed. In addition, given cutting conditions at which whirling vibrations are expected to occur, the model is able to predict the vibration frequencies that are excited. The drilling model and the stability predictions are experimentally validated by means of drilling tests with different drill diameters and cutting conditions. In comparing the experimentally obtained results and the predictions obtained by the model, it is concluded that the model can reasonably predict the appearance of whirling vibrations as a function of drill geometry and cutting conditions. Generated hole shape is also analyzed through the measurement of hole roundness and bottom surface geometry. It is observed that, when drilling in the presence of whirling vibrations, holes with lobed shape and polygonal bottom surface are generated. It is also noticed that both the number of lobes and the number of sides of the polygonal bottom surface are directly related to the vibration frequencies that arise.

Keywords

Drilling Whirling Vibrations Modeling Stability 

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Notes

Acknowledgments

The authors would like to thank the Basque Government for supporting the Elkartek BASQUETECH (Ref. KK-2015/00081) project.

References

  1. 1.
    Kato M, Enomoto S, Saito Y, Hanaoka T (1988) Whirling action of drill at the beginning of cutting. J Mech Work Technol 17:187–193CrossRefGoogle Scholar
  2. 2.
    Reinhall PG, Storti DW (1986) Modeling and analysis of the dynamics of a drill penetrating a thin plate. J Appl Mech 53(86):690–694CrossRefGoogle Scholar
  3. 3.
    Bayly PV, Metzler SA, Schaut AJ, Young KA (2001) Theory of torsional chatter in twist drills: model, stability analysis and composition to test. J Manuf Sci Eng 123(4):552CrossRefGoogle Scholar
  4. 4.
    Stone E, Askari A (2002) Nonlinear models of chatter in drilling processes. Dyn Syst Int J 17(1):65–85MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Basile SA (1993) Modeling transverse motions of a drill bit for process understanding. Precis Eng 15(4):258–265CrossRefGoogle Scholar
  6. 6.
    Fujii H, Marui E, Ema S (1986) Whirling vibration in drilling. Part 1: cause of vibration and role of chisel edge. J Eng Ind 108(3):157CrossRefGoogle Scholar
  7. 7.
    Lee SJ, Eman KF, Wu SM (1987) Analysis of drill wandering motion. J Eng Ind 109:297–305CrossRefGoogle Scholar
  8. 8.
    Bayly PV, Lamar MT, Calvert SG (2002) Low-frequency regenerative vibration and the formation of lobed holes in drilling. J Manuf Sci Eng 124(2):275CrossRefGoogle Scholar
  9. 9.
    Giasin K, Hodzic A, Phadnis V, Ayvar-soberanis S (2016) Assessment of cutting forces and hole quality in drilling Al2024 aluminium alloy: experimental and finite element study. Int J Adv Manuf Technol 87:2041–2061CrossRefGoogle Scholar
  10. 10.
    Abdelhafeez AM, Soo SL, Aspinwall DK, Dowson A, Arnold D (2015) Burr formation and hole quality when drilling titanium and aluminium alloys. Procedia CIRP 37:230–235CrossRefGoogle Scholar
  11. 11.
    Zhou Y, Yang W, Xu Z, Shi X (2017) Consistency evaluation of hole series surface quality using vibration signal. Int J Adv Manuf Technol 92:1069–1079CrossRefGoogle Scholar
  12. 12.
    Fujii H, Marui E, Ema S (1986) Whirling vibration in drilling. Part 2: influence of drill geometries, particularly of the drill flank, on the initiation of vibration. J Eng Ind 108:163–168CrossRefGoogle Scholar
  13. 13.
    Abele E, Elsenheimer J, Hohenstein J, Tschannerl M (2005) Influence of drill dynamics on bore quality. CIRP Ann Manuf Technol 54(1):83–86CrossRefGoogle Scholar
  14. 14.
    Abele E, Tschanner M, Schramm B (2008) Triangular holes - origination, identification and influencing parameters. Adv Prod Eng Manag 3:111–118Google Scholar
  15. 15.
    Chandrasekharan V (1996) A model to predict the three-dimensional cutting force system for drilling with arbitrary point geometry. University of Illinois, Urbana-ChampaignGoogle Scholar
  16. 16.
    Yang JA, Jaganathan V, Du R (2002) A new dynamic model for drilling and reaming processes. Int J Mach Tools Manuf 42(2):299–311CrossRefGoogle Scholar
  17. 17.
    Gong Y, Lin C, Ehmann KF (2005) Dynamics of initial penetration in drilling: part 1 - mechanistic model for dynamic forces. J Manuf Sci Eng Trans ASME 127(2):280–288CrossRefGoogle Scholar
  18. 18.
    Roukema JC, Altintas Y (2006) Time domain simulation of torsional-axial vibrations in drilling. Int J Mach Tools Manuf 46(15):2073–2085CrossRefGoogle Scholar
  19. 19.
    Roukema JC, Altintas Y (2007) Generalized modeling of drilling vibrations. Part I: time domain model of drilling kinematics, dynamics and hole formation. Int J Mach Tools Manuf 47(9):1455–1473CrossRefGoogle Scholar
  20. 20.
    Roukema JC, Altintas Y (2007) Generalized modeling of drilling vibrations. Part II: chatter stability in frequency domain. Int J Mach Tools Manuf 47(9):1474–1485CrossRefGoogle Scholar
  21. 21.
    Ahmadi K, Altintas Y (2013) Stability of lateral, torsional and axial vibrations in drilling. Int J Mach Tools Manuf 68:63–74CrossRefGoogle Scholar
  22. 22.
    Ahmadi K, Savilov A (2015) Modeling the mechanics and dynamics of arbitrary edge drills. Int J Mach Tools Manuf 89:208–220CrossRefGoogle Scholar
  23. 23.
    Chiou RY, Liang SY (1998) Chatter stability of a slender cutting tool in turning with tool wear effect. Int J Mach Tools Manuf 38(4):315–327CrossRefGoogle Scholar
  24. 24.
    M. Eynian and Y. Altintas, “Chatter stability of general turning operations with process damping,”. J Manuf Sci Eng, vol 131, , pp. 1–10, 2009Google Scholar
  25. 25.
    J. C. Roukema, Mechanics and dynamics of drilling. The University of British Columbia Vancouver, 2006Google Scholar
  26. 26.
    Armarego EJA, Brown RH (1969) The machining of metals. Prentice-Hall, Inc., Upper Saddle RiverGoogle Scholar
  27. 27.
    Kachanov LM (1971) Foundations of the theory of plasticity. North-Holland Publishing Company, AmsterdamzbMATHGoogle Scholar
  28. 28.
    Jiménez A, Arizmendi M, Cumbicus WE (2018) Model for the prediction of low-frequency lateral vibrations in drilling process with pilot hole. Int J Adv Manuf Technol 96:1971–1990CrossRefGoogle Scholar
  29. 29.
    Dilley DN, Bayly PV, Whitehead BT, Calvert SG (2005) An analytical study of the effect of process damping on reamer vibrations. J Sound Vib 280(3–5):997–1015CrossRefGoogle Scholar
  30. 30.
    Tsai WD, Wu SM (1979) A mathematical model for drill. Point design and grinding. ASME 101(August):333–340Google Scholar
  31. 31.
    Tsai WD, Wu SM (1979) Computer analysis of drill point geometry. Int J Mach Tool Des Res 19(2):95–108CrossRefGoogle Scholar
  32. 32.
    Fugelso MA (1990) Conical flank twist drill points. Int J Mach Tools Manufact 30(2):291–295CrossRefGoogle Scholar
  33. 33.
    Armarego EJA, Wright JD, Factory A (1980) An analytical study of three point grinding methods for general purpose twist drills. Ann CIRP 29(1):5–10CrossRefGoogle Scholar
  34. 34.
    Insperger T, Stépán G (2004) Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Numer Methods Eng 61(1):117–141MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Insperger T, Stépán G (2011) Semi-Discretization for Time-Delay Systems, vol. 178. Springer, BerlinCrossRefzbMATHGoogle Scholar
  36. 36.
    Uhlmann E, Richarz S (2016) Twisted deep hole drilling tools for hard machining. J Manuf Process 24:225–230CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Amaia Jiménez
    • 1
    Email author
  • Miguel Arizmendi
    • 1
  • Wilmer E. Cumbicus
    • 1
  1. 1.TECNUN Escuela de IngenierosUniversidad de NavarraSan SebastiánSpain

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