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Research Papers

Surface Location Error and Surface Roughness for Period-N Milling Bifurcations

[+] Author and Article Information
Andrew Honeycutt

Department of Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
9201 University City Boulevard,
Charlotte, NC 28223
e-mail: ahoney15@uncc.edu

Tony L. Schmitz

Mem. ASME
Department of Mechanical Engineering
and Engineering Science,
University of North Carolina at Charlotte,
9201 University City Boulevard,
Charlotte, NC 28223
e-mail: tony.schmitz@uncc.edu

1Corresponding author.

Manuscript received September 7, 2016; final manuscript received November 28, 2016; published online January 30, 2017. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 139(6), 061010 (Jan 30, 2017) (8 pages) Paper No: MANU-16-1490; doi: 10.1115/1.4035371 History: Received September 07, 2016; Revised November 28, 2016

This paper provides time domain simulation and experimental results for surface location error (SLE) and surface roughness when machining under both stable (forced vibration) and unstable (period-2 bifurcation) conditions. It is shown that the surface location error follows similar trends observed for forced vibration, so zero or low error conditions may be selected even for period-2 bifurcation behavior. The surface roughness for the period-2 instability is larger than for stable conditions because the surface is defined by every other tooth passage and the apparent feed per tooth is increased. Good agreement is observed between simulation and experiment for stability, surface location error, and surface roughness results.

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References

Arnold, R. N. , 1946, “ The Mechanism of Tool Vibration in the Cutting of Steel,” Proc. Inst. Mech. Eng., 154(1), pp. 261–284.
Doi, S. , and Kato, S. , 1956, “ Chatter Vibration of Lathe Tools,” Trans. ASME, 78, pp. 1127–1134.
Tobias, S. A. , and Fishwick, W. , 1958, “ The Chatter of Lathe Tools Under Orthogonal Cutting Conditions,” Trans. ASME, 80, pp. 1079–1088.
Tlusty, J. , and Polacek, M. , 1963, “ The Stability of Machine Tools Against Self-Excited Vibrations in Machining,” ASME International Research in Production Engineering Conference, Pittsburgh, PA, pp. 465–474.
Tobias, S. A. , 1965, Machine Tool Vibration, Wiley, New York.
Merritt, H. E. , 1965, “ Theory of Self-Excited Machine-Tool Chatter,” ASME J. Eng. Ind., 87(4), pp. 447–454. [CrossRef]
Shridar, R. , Hohn, R. E. , and Long, G. W. , 1968, “ A General Formulation of the Milling Process Equation,” ASME J. Eng. Ind., 90(2), pp. 317–324. [CrossRef]
Hohn, R. E. , Shridar, R. , and Long, G. W. , 1968, “ A Stability Algorithm for a Special Case of the Milling Process: Contribution to Machine Tool Chatter Research—6,” ASME J. Eng. Ind., 90(2), pp. 326–329. [CrossRef]
Shridar, R. , Hohn, R. E. , and Long, G. W. , 1968, “ A Stability Algorithm for the General Milling Process: Contribution to Machine Tool Chatter Research—7,” ASME J. Eng. Ind., 90(2), pp. 330–334. [CrossRef]
Hanna, N. H. , and Tobias, S. A. , 1974, “ A Theory of Nonlinear Regenerative Chatter,” ASME J. Eng. Ind., 96(1), pp. 247–255. [CrossRef]
Tlusty, J. , and Ismail, F. , 1981, “ Basic Non-Linearity in Machining Chatter,” Ann. CIRP, 30(1), pp. 299–304. [CrossRef]
Tlusty, J. , and Ismail, F. , 1983, “ Special Aspects of Chatter in Milling,” ASME J. Vib., Stress Reliab. Des., 105(1), pp. 24–32. [CrossRef]
Tlusty, J. , 1985, “ Machining Dynamics,” Handbook of High-Speed Machining Technology, R. I. King , ed., Chapman and Hall, New York, pp. 48–153.
Tlusty, J. , 1986, “ Dynamics of High-Speed Milling,” ASME J. Eng. Ind., 108(2), pp. 59–67. [CrossRef]
Minis, I. , and Yanusevsky, R. , 1993, “ A New Theoretical Approach for Prediction of Chatter in Milling,” ASME J. Eng. Ind., 115(1), pp. 1–8. [CrossRef]
Altintas, Y. , and Budak, E. , 1995, “ Analytical Prediction of Stability Lobes in Milling,” Ann. CIRP, 44(1), pp. 357–362. [CrossRef]
Davies, M. A. , Dutterer, B. S. , Pratt, J. R. , and Schaut, A. J. , 1998, “ On the Dynamics of High-Speed Milling With Long, Slender Endmills,” Ann. CIRP, 47(1), pp. 55–60. [CrossRef]
Moon, F. C. , and Kalmár-Nagy, T. , 2001, “ Nonlinear Models for Complex Dynamics in Cutting Materials,” Philos. Trans. R. Soc., A, 359(1781), pp. 695–711. [CrossRef]
Davies, M. A. , Pratt, J. R. , Dutterer, B. S. , and Burns, T. J. , 2000, “ The Stability of Low Radial Immersion Milling,” Ann. CIRP, 49(1), pp. 37–40. [CrossRef]
Moon, F. C. , 1994, “ Chaotic Dynamics and Fractals in Material Removal Processes,” Nonlinearity and Chaos in Engineering Dynamics, J. Thompson , and S. Bishop , ed., Wiley, New York, pp. 25–37.
Bukkapatnam, S. , Lakhtakia, A. , and Kumara, S. , 1995, “ Analysis of Senor Signals Shows Turning on a Lathe Exhibits Low-Dimensional Chaos,” Phys. Rev., E, 52(3), pp. 2375–2387. [CrossRef]
Stépán, G. , and Kalmár-Nagy, T. , 1997, “ Nonlinear Regenerative Machine Tool Vibrations,” Proceedings of the ASME Design Engineering Technical Conference on Vibration and Noise, Sacramento, CA, Sept. 14–17.
Nayfey, A. , Chin, C. , and Pratt, J. , 1998, “ Applications of Perturbation Methods to Tool Chatter Dynamics,” Dynamics and Chaos in Manufacturing Processes, F. C. Moon , ed., Wiley, New York, pp. 193–213.
Minis, I. , and Berger, B. S. , 1998, “ Modelling, Analysis, and Characterization of Machining Dynamics,” Dynamics and Chaos in Manufacturing Processes, F. C. Moon , ed., Wiley, New York, pp. 125–163.
Moon, F. C. , and Johnson, M. , 1998, “ Nonlinear Dynamics and Chaos in Manufacturing Processes,” Dynamics and Chaos in Manufacturing Processes, F. C. Moon , ed., Wiley, New York, pp. 3–32.
Smith, K. S. , and Tlusty, J. , 1991, “ An Overview of Modeling and Simulation of the Milling Process,” ASME J. Eng. Ind., 113(2), pp. 169–175. [CrossRef]
Campomanes, M. L. , and Altintas, Y. , 2003, “ An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions,” ASME J. Manuf. Sci. Eng., 125(3), pp. 416–422. [CrossRef]
Zhao, M. X. , and Balachandran, B. , 2001, “ Dynamics and Stability of Milling Process,” Int. J. Solids Struct., 38(10–13), pp. 2233–2248. [CrossRef]
Davies, M. A. , Pratt, J. R. , Dutterer, B. , and Burns, T. J. , 2002, “ Stability Prediction for Low Radial Immersion Milling,” ASME J. Manuf. Sci. Eng., 124(2), pp. 217–225. [CrossRef]
Mann, B. P. , Insperger, T. , Bayly, P. V. , and Stépán, G. , 2003, “ Stability of up-Milling and Down-Milling, Part 2: Experimental Verification,” Int. J. Mach. Tools Manuf., 43(1), pp. 35–40. [CrossRef]
Mann, B. P. , Insperger, T. , Bayly, P. V. , and Stépán, G. , 2003, “ Stability of up-Milling and Down-Milling—Part 1: Alternative Analytical Methods,” Int. J. Mach. Tools Manuf., 43(1), pp. 25–34. [CrossRef]
Insperger, T. , Stépán, G. , Bayly, P. V. , and Mann, B. P. , 2003, “ Multiple Chatter Frequencies in Milling Processes,” J. Sound Vib., 262(2), pp. 333–345. [CrossRef]
Insperger, T. , and Stépán, G. , 2004, “ Vibration Frequencies in High-Speed Milling Processes or A Positive Answer to Davies, Pratt, Dutterer, and Burns,” ASME J. Manuf. Sci. Eng., 126(3), pp. 481–487. [CrossRef]
Mann, B. P. , Bayly, P. V. , Davies, M. A. , and Halley, J. E. , 2004, “ Limit Cycles, Bifurcations, and Accuracy of the Milling Process,” J. Sound Vib., 277(1–2), pp. 31–48. [CrossRef]
Merdol, S. D. , and Altintas, Y. , 2004, “ Multi Frequency Solution of Chatter Stability for Low Immersion Milling,” ASME J. Manuf. Sci. Eng., 126(3), pp. 459–466. [CrossRef]
Govekar, E. , Gradišek, J. , Kalveram, M. , Insperger, T. , Weinert, K. , Stepan, G. , and Grabec, I. , 2005, “ On Stability and Dynamics of Milling at Small Radial Immersion,” Ann. CIRP, 54(1), pp. 357–362. [CrossRef]
Gradišek, J. , Kalveram, M. , Insperger, T. , Weinert, K. , Stépán, G. , Govekar, E. , and Grabec, I. , 2005, “ On Stability Prediction for Milling,” Int. J. Mach. Tools Manuf., 45(7–8), pp. 769–781. [CrossRef]
Mann, B. P. , Garg, N. K. , Young, K. A. , and Helvey, A. M. , 2005, “ Milling Bifurcations From Structural Asymmetry and Nonlinear Regeneration,” Nonlinear Dyn., 42(4), pp. 319–337. [CrossRef]
Stépán, G. , Szalai, R. , Mann, B. P. , Bayly, P. V. , Insperger, T. , Gradisek, J. , and Govekar, E. , 2005, “ Nonlinear Dynamics of High-Speed Milling–Analyses, Numerics, and Experiments,” ASME J. Vib. Acoust., 127(2), pp. 197–203. [CrossRef]
Zatarain, M. , Muñoa, J. , Peigné, G. , and Insperger, T. , 2006, “ Analysis of the Influence of Mill Helix Angle on Chatter Stability,” Ann. CIRP, 55(1), pp. 365–368. [CrossRef]
Insperger, T. , Munoa, J. , Zatarain, M. A. , and Peigné, G. , 2006, “ Unstable Islands in the Stability Chart of Milling Processes Due to the Helix Angle,” CIRP 2nd International Conference on High Performance Cutting, Vancouver, Canada, June 12–13, Vancouver, BC, Canada, pp. 12–13.
Patel, B. R. , Mann, B. P. , and Young, K. A. , 2008, “ Uncharted Islands of Chatter Instability in Milling,” Int. J. Mach. Tools Manuf., 48(1), pp. 124–134. [CrossRef]
Moradi, H. , Vossoughi, G. , and Movahhedy, M. , 2014, “ Bifurcation Analysis of Nonlinear Milling Process With Tool Wear and Process Damping: Sub-Harmonic Resonance Under Regenerative Chatter,” Int. J. Mech. Sci., 85, pp. 1–19. [CrossRef]
Honeycutt, A. , and Schmitz, T. , 2015, “ The Extended Milling Bifurcation Diagram,” Proc. Manuf., 1, pp. 466–476.
Honeycutt, A. , and Schmitz, T. , 2016, “ A Numerical and Experimental Investigation of Period-n Bifurcations in Milling,” ASME J. Manuf. Sci. Eng., 139(1), p. 011003. [CrossRef]
Kline, W. , DeVor, R. , and Shareef, I. , 1982, “ The Prediction of Surface Accuracy in End Milling,” ASME J. Eng. Ind., 104(3), pp. 272–278. [CrossRef]
Kline, W. , DeVor, R. , and Lindberg, J. , 1982, “ The Prediction of Cutting Forces in End Milling With Application to Cornering Cuts,” Int. J. Mach. Tool Des. Res., 22(1), pp. 7–22. [CrossRef]
Tlusty, J. , 1985, “ Effect of End Milling Deflections on Accuracy,” Handbook of High Speed Machining Technology, R. I. King , ed., Chapman and Hall, New York, pp. 140–153.
Sutherland, J. , and DeVor, R. , 1986, “ An Improved Method for Cutting Force and Surface Error Prediction in Flexible End Milling Systems,” ASME J. Eng. Ind., 108(4), pp. 269–279. [CrossRef]
Montgomery, D. , and Altintas, Y. , 1991, “ Mechanism of Cutting Force and Surface Generation in Dynamic Milling,” ASME J. Eng. Ind., 113(2), pp. 160–168. [CrossRef]
Altintas, Y. , Montgomery, D. , and Budak, E. , 1992, “ Dynamic Peripheral Milling of Flexible Structures,” ASME J. Eng. Ind., 114(2), pp. 137–145.
Tarng, Y. , Liao, C. , and Li, H. , 1994, “ A Mechanistic Model for Prediction of the Dynamics of Cutting Forces in Helical End Milling,” Int. J. Model. Simul., 14(2), pp. 92–97.
Schmitz, T. , and Ziegert, J. , 1999, “ Examination of Surface Location Error Due to Phasing of Cutter Vibrations,” Prec. Eng., 23(1), pp. 51–62. [CrossRef]
Altintas, Y. , 2000, Manufacturing Automation, Cambridge University Press, Cambridge, UK.
Mann, B. P. , Bayly, P. V. , Davies, M. A. , and Halley, J. E. , 2004, “ Limit Cycles, Bifurcations, and Accuracy of the Milling Process,” J. Sound Vib., 277(1–2), pp. 31–48. [CrossRef]
Schmitz, T. , Couey, J. , Marsh, E. , Mauntler, N. , and Hughes, D. , 2007, “ Runout Effects in Milling: Surface Finish, Surface Location Error, and Stability,” Int. J. Mach. Tools Manuf., 47(5), pp. 841–851. [CrossRef]
Yun, W.-S. , Ko, J. , Cho, D.-W. , and Ehmann, K. , 2002, “ Development of a Virtual Machining System—Part 2: Prediction and Analysis of a Machined Surface Error,” Int. J. Mach. Tools Manuf., 42(15), pp. 1607–1615. [CrossRef]
Schmitz, T. , and Mann, B. , 2006, “ Closed-Form Solutions for Surface Location Error in Milling,” Int. J. Mach. Tools Manuf., 46(12–13), pp. 1369–1377. [CrossRef]
Schmitz, T. , and Smith, K. S. , 2009, Machining Dynamics: Frequency Response to Improved Productivity, Springer, New York.
Dombovari, Z. , and Stépán, G. , 2015, “ On the Bistable Zone of Milling Processes,” Philos. Trans. R. Soc., A, 373(2051), p. 20140409. [CrossRef]
Bachrathy, D. , Munoa, J. , and Stépán, G. , 2016, “ Experimental Validation of Appropriate Axial Immersions for Helical Mills,” Int. J. Adv. Manuf. Technol., 84(5), pp. 1295–1302.
Mann, B. P. , Insperger, T. , Bayly, P. V. , and Stépán, G. , 2003, “ Stability of Up-Milling and Down-Milling—Part 2: Experimental Verification,” Int. J. Mach. Tools Manuf., 43(1), pp. 35–40. [CrossRef]
Ransom, T. , Honeycutt, A. , and Schmitz, T. , 2016, “ A New Tunable Dynamics Platform for Milling Experiments,” Prec. Eng., 44, pp. 252–256. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Cutting force geometry. The normal and tangential direction cutting forces, Fn and Ft, are displayed. The fixed x (feed) and y directions, as well as the rotating normal direction, n, are also shown. The angle ϕ defines the tooth angle. The tool feed is to the right for the clockwise tool rotation and the axial depth is in the z direction.

Grahic Jump Location
Fig. 2

(Left) Feed direction (x) vibration versus time with once-per-tooth sampled points (circles) for b= 0.5 mm. (Right) Poincaré map with once-per-tooth sampled points. Because the cut is stable, all sampled points appear at the same location.

Grahic Jump Location
Fig. 3

(Left) Feed direction (x) vibration versus time with once-per-tooth sampled points (circles) for b= 2.5 mm. (Right) Poincaré map with once-per-tooth sampled points. The period-2 bifurcation behavior shows two sampled point locations. Because the solution alternates between two values, this is referred to as a flip bifurcation.

Grahic Jump Location
Fig. 4

(Left) Feed direction (x) vibration versus time with once-per-tooth sampled points (circles) for b= 5 mm. (Right) Poincaré map with once-per-tooth sampled points. The secondary Hopf instability yields an elliptical distribution of sampled points.

Grahic Jump Location
Fig. 5

(Left) Spatial trajectory of the cutter tooth for b= 2.5 mm. (Right) Magnified view of upper surface of tooth trajectory. The machined surface is defined by the points at the top of the trajectory for the up milling cut. The period-2 behavior gives upper and lower tooth paths. The upper path defines the final surface, although material is removed for each tooth passage.

Grahic Jump Location
Fig. 6

Flexure-based experimental setup with laser vibrometer (LV), laser tachometer (LT), and capacitance probe (CP). The feed direction and the flexible direction for the single degree-of-freedom flexure are also identified. The setup was located on a Haas TM-1 CNC milling machine.

Grahic Jump Location
Fig. 7

The workpiece included four ribs that were initially machined to the same dimensions. The {5 mm axial depth, 2 mm radial depth} cuts were then performed on one edge at a different spindle speed for each rib. The SLE was calculated as the difference between the commanded, C, and measured, M, rib widths. The flexible direction for the flexure is identified.

Grahic Jump Location
Fig. 8

Predicted (left) and measured (right) Poincaré maps for 3180 rpm. Period-2 behavior is seen. Note that x indicates the flexible direction for the flexure. The feed direction was y for these experiments.

Grahic Jump Location
Fig. 9

Predicted (left) and measured (right) Poincaré maps for 3300 rpm. Stable behavior is seen.

Grahic Jump Location
Fig. 10

Predicted (left) and measured (right) Poincaré maps for 3600 rpm. Stable behavior is seen with increased amplitude relative to 3300 rpm (Fig. 9).

Grahic Jump Location
Fig. 11

SLE prediction from time domain simulation (line) and experimental results from rib cutting tests (circles). The four period-2 bifurcation tests are identified.

Grahic Jump Location
Fig. 12

Commanded surface (dashed line), CMM scan (solid line), and simulation result (circles) for 3180 rpm (period-2). These results correspond to Fig. 8.

Grahic Jump Location
Fig. 13

Commanded surface (dashed line), CMM scan (solid line), and simulation result (circles) for 3300 rpm (stable). These results correspond to Fig. 9.

Grahic Jump Location
Fig. 14

Commanded surface (dashed line), CMM scan (solid line), and simulation result (circles) for 3600 rpm (stable). These results correspond to Fig. 10.

Grahic Jump Location
Fig. 15

Scanning white light interferometer line scan (line) and simulation results (circles) for 3180 rpm (period-2)

Grahic Jump Location
Fig. 16

Scanning white light interferometer line scan (line) and simulation results (circles) for 3300 rpm (stable)

Grahic Jump Location
Fig. 17

Scanning white light interferometer line scan (line) and simulation results (circles) for 3600 rpm (stable)

Grahic Jump Location
Fig. 18

Combined stability and SLE map for rib cutting process dynamics. The secondary Hopf instability is represented by the dark zone, the period-2 behavior is identified by the dotted zone, and the SLE is given by the contours (i.e., lines of constant SLE).

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