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Stability of milling with non-uniform pitch and variable helix Tools

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Abstract

We study mechanical vibrations in milling with non-uniform pitch and variable helix tools. The process is modeled by a periodic delay differential equation with distributed delay, which takes into account, for example, the nonlinear cutting force behavior, the effect of runout, and the exact delay distribution due to the unequally spaced flutes. We present a new method for the identification of the chatter stability lobes from the linearized system that is based on the multifrequency solution. We give detailed remarks on the truncation of the resulting infinite dimensional matrices and the efficient numerical implementation of the method. Cutting tests for steel milling with a customary end mill with non-uniform pitch and variable helix angle and a conventional end mill with uniform pitch and constant helix angle are performed. The numerical and experimental results coincide well. They reveal a significant increase of the limiting depth of cut for the variable helix tool compared to the conventional tool. Moreover, we show that in contrast to conventional tools, for non-uniform pitch and variable helix tools, an exact model with time-varying coefficients, nonlinear cutting force behavior, and runout is necessary for an accurate prediction of the stability lobes.

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References

  1. Tobias SA (1961) Schwingungen an Werkzeugmaschinen. Hanser, München

  2. Danek O, Polacek M, Spacek J, Tlusty J (1962) Selbsterregte Schwingungen an Werkzeugmaschinen. VEB Technik Berlin, Berlin

    Google Scholar 

  3. Altintas Y (2012) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. Cambridge University Press

  4. Insperger T, Lehotzky D, Stepan G (2015) Regenerative delay, parametric forcing and machine tool chatter: a review. IFAC-PapersOnLine 48(12):322–327

    Article  Google Scholar 

  5. Altintas Y, Weck M (2004) Chatter stability of metal cutting and grinding. CIRP Ann 53:619–642

    Article  Google Scholar 

  6. Otto A, Radons G (2013) Application of spindle speed variation for chatter suppression in turning. CIRP J Manuf Sci Technol 6(2):102–109

    Article  Google Scholar 

  7. Otto A, Rauh S, Kolouch M, Radons G (2014) Extension of Tlusty’s law for the identification of chatter stability lobes in multi-dimensional cutting processes. Int J Mach Tools Manuf 82–83:50–58

    Article  Google Scholar 

  8. Zatarain M, Muñoa J, Peigné G, Insperger T (2006) Analysis of the influence of mill helix angle on chatter stability. CIRP Ann 55:365–368

    Article  Google Scholar 

  9. Zatarain M, Bediaga I, Muñoa J, Insperger T (2010) Analysis of directional factors in milling: importance of multi-frequency calculation and of the inclusion of the effect of the helix angle. Int J Adv Manuf Techn 47:535–542

    Article  Google Scholar 

  10. Altıntas Y, Engin S, Budak E (1999) Analytical stability prediction and design of variable pitch cutters. ASME J Manuf Sci Eng 121:173–178

  11. Turner S, Merdol D, Altintas Y, Ridgway K (2007) Modelling of the stability of variable helix end mills. Int J Mach Tools Manuf 47(9):1410–1416

    Article  Google Scholar 

  12. Olgac N, Sipahi R (2007) Dynamics and stability of variable-pitch milling. J Vibr Control 13(7):1031–1043

    Article  MATH  Google Scholar 

  13. Sellmeier V, Denkena B (2011) Stable islands in the stability chart of milling processes due to unequal tooth pitch. Int J Mach Tools Manuf 51:152–164

    Article  Google Scholar 

  14. Budak E (2003) An analytical design method for milling cutters with nonconstant pitch to increase stability, part i: theory. ASME J Manuf Sci Eng 125:29–34

    Article  Google Scholar 

  15. Wan M, Zhang WH, Dang JW, Yang Y (2010) A unified stability prediction method for milling process with multiple delays. Int J Mach Tools and Manuf 50(1):29–41

    Article  Google Scholar 

  16. Compeán F, Olvera D, Campa F, López de Lacalle LN, Elías-Zúñiga A, Rodríguez C (2012) Characterization and stability analysis of a multivariable milling tool by the enhanced multistage homotopy perturbation method. Int J Mach Tools Manuf 57:27–33

    Article  Google Scholar 

  17. Guo Q, Jiang Y, Zhao B, Ming P (2016) Chatter modeling and stability lobes predicting for non-uniform helix tools. Int J Adv Manuf Technol:1–16

  18. Sims ND, Mann B, Huyanan S (2008) Analytical prediction of chatter stability for variable pitch and variable helix milling tools. J Sound Vibr 317(3–5):664–686

    Article  Google Scholar 

  19. Yusoff AR (2016) Identifying bifurcation behavior during machining process for an irregular milling tool geometry. Measurement 93:57–66

    Article  Google Scholar 

  20. Yusoff AR, Sims ND (2011) Optimisation of variable helix tool geometry for regenerative chatter mitigation. Int J Mach Tools and Manuf 51(2):133–141

    Article  Google Scholar 

  21. Otto A, Radons G (2012b) Frequency domain stability analysis of milling processes with variable helix tools. 9th Int Conf on High Speed Machining, San Sebastian, Spain, March 7-8 doi:10.13140/2.1.1253.8882

  22. Bachrathy D, Stepan G (2013) Improved prediction of stability lobes with extended multi frequency solution. CIRP Ann 62(1):411–414

    Article  Google Scholar 

  23. Stepan G, Munoa J, Insperger T, Surico M, Bachrathy D, Dombovari Z (2014) Cylindrical milling tools: comparative real case study for process stability. CIRP Ann 63(1):385–388

    Article  Google Scholar 

  24. Sims ND (2016) Fast chatter stability prediction for variable helix milling tools. Proc Inst Mech Eng C J Mech Eng Sci 230(1):133–144

    Article  Google Scholar 

  25. Otto A, Radons G (2012a) The effect of runout on the stability of milling with variable helix tools. Proc 23th ICTAM, 9-24 August, Beijing, China doi:10.13140/RG.2.2.17228.62080

  26. Otto A, Radons G (2015) The influence of tangential and torsional vibrations on the stability lobes in metal cutting. Nonlin Dyn 82:1989–2000

    Article  Google Scholar 

  27. Sellmeier V, Denkena B (2012) High speed process damping in milling. CIRP J Manuf Sci Technol 5(1):8–19

    Article  Google Scholar 

  28. Tyler C, Schmitz T (2013) Analytical process damping stability prediction. J Manuf Proc 15(1):69–76

    Article  Google Scholar 

  29. Wan M, Ma YC, Feng J, Zhang WH (2016) Study of static and dynamic ploughing mechanisms by establishing generalized model with static milling forces. Int J Mech Sci 114:120– 131

    Article  Google Scholar 

  30. Stepan G, Dombovari Z, Muñoa J (2011) Identification of cutting force characteristics based on chatter experiments. CIRP Ann 60(1):113–116

    Article  Google Scholar 

  31. Wan M, Wang YT, Zhang WH, Yang Y, Dang JW (2011) Prediction of chatter stability for multiple-delay milling system under different cutting force models. Int J Mach Tools Manuf 51(4):281–295

    Article  Google Scholar 

  32. Rott O, Hömberg D, Mense C (2006) A comparison of analytical cutting force models. WIAS Preprint:1151

  33. Insperger T, Mann BP, Surmann T, Stépán G (2008) On the chatter frequencies of milling processes with runout. Int J Mach Tools Manuf 48(10):1081–1089

    Article  Google Scholar 

  34. Engelborghs K, Luzyanina T, Roose D (2002) Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Trans Math Softw 28(1):1–21

    Article  MathSciNet  MATH  Google Scholar 

  35. Sieber J, Engelborghs K, Luzyanina T, Samaey G, Roose D (2014) DDE-BIFTOOL Manual - Bifurcation analysis of delay differential equations arXiv:1406.7144

  36. Khasawneh F, Barton D, Mann B (2012) Periodic solutions of nonlinear delay differential equations using spectral element method. Nonlin Dyn 67(1):641–658

    Article  MathSciNet  MATH  Google Scholar 

  37. Dombovari Z, Stepan G (2012) The effect of helix angle variation on milling stability. ASME J Manuf Sci Eng 134(051015): 1–6

    Google Scholar 

  38. Wan M, Ma YC, Zhang WH, Yang Y (2015) Study on the construction mechanism of stability lobes in milling process with multiple modes. Int J Adv Manuf Technol 79(1):589–603

    Article  Google Scholar 

  39. Farkas M (1994) Periodic Motions. Springer New York

  40. Hill G (1886) On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon. Acta Math 8(1):1–36

    Article  MathSciNet  MATH  Google Scholar 

  41. Insperger T, Stépán G (2024) Stability chart for the delayed Mathieu equation. Phil Trans Royal Soc A 458:1989–1998

    MathSciNet  MATH  Google Scholar 

  42. Lampe B, Rosenwasser E (2011) Hill method for linear periodic systems with delay. Proc 16th Int Conf MMAR August 22-25, Miedzyzdroje, Poland:100–106

  43. Hall SR, Wereley NM (1990) Generalized Nyquist stability criterion for linear time periodic systems. In: Amer. Control Conf. , San Diego, CA, May 1990, pp 1518–1525

  44. López de Lacalle LN, Lamikiz A, Sanchez JA, de Bustos IF (2005) Simultaneous measurement of forces and machine tool position for diagnostic of machining tests. IEEE Trans Instrum Meas 54(6):2329–2335

    Article  Google Scholar 

  45. Otto A, Khasawneh FA, Radons G (2015) Position-dependent stability analysis of turning with tool and workpiece compliance. Int J Adv Manuf Technol 79:1453–1463

    Article  Google Scholar 

  46. Just W (2000) On the eigenvalue spectrum for time-delayed Floquet problems. Phys D 142(1–2):153–165

    Article  MathSciNet  MATH  Google Scholar 

  47. Jaurigue L, Schöll E, Lüdge K (2016) Suppression of noise-induced modulations in multidelay systems. Phys Rev Lett 117:154101

    Article  Google Scholar 

  48. Jüngling T, Gjurchinovski A, Urumov V (2012) Experimental time-delayed feedback control with variable and distributed delays. Phys Rev E 86:046213

    Article  Google Scholar 

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Authors and Affiliations

  1. Insitute of Physics, TU Chemnitz, 09107, Chemnitz, Germany

    Andreas Otto & Günter Radons

  2. Fraunhofer Institute for Machine Tools and Forming Technology IWU, Reichenhainer Straße 88, 09126, Chemnitz, Germany

    Stefan Rauh & Steffen Ihlenfeldt

  3. Institute for Machine tools and Control Engineering, TU Dresden, 01062, Dresden, Germany

    Steffen Ihlenfeldt

Authors
  1. Andreas Otto
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  2. Stefan Rauh
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  3. Steffen Ihlenfeldt
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  4. Günter Radons
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Correspondence to Andreas Otto.

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Otto, A., Rauh, S., Ihlenfeldt, S. et al. Stability of milling with non-uniform pitch and variable helix Tools. Int J Adv Manuf Technol 89, 2613–2625 (2017). https://doi.org/10.1007/s00170-016-9762-2

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  • DOI: https://doi.org/10.1007/s00170-016-9762-2

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