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Research Papers

Frequency Domain Updating of Thin-Walled Workpiece Dynamics Using Reduced Order Substructuring Method in Machining

[+] Author and Article Information
Oguzhan Tuysuz

Manufacturing Automation Laboratory (MAL),
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: oguzhan.tuysuz@alumni.ubc.ca

Yusuf Altintas

Professor
Fellow ASME
Manufacturing Automation Laboratory (MAL),
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: altintas@mech.ubc.ca

1Corresponding author.

Manuscript received October 16, 2016; final manuscript received February 20, 2017; published online April 10, 2017. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 139(7), 071013 (Apr 10, 2017) (16 pages) Paper No: MANU-16-1551; doi: 10.1115/1.4036124 History: Received October 16, 2016; Revised February 20, 2017

The structural dynamics of thin-walled parts vary as the material is removed during machining. This paper presents a new, computationally efficient reduced order dynamic substructuring method to predict the frequency response function (FRF) of the workpiece as the material is removed along the toolpath. The contribution of the removed mass to the dynamics of the workpiece is canceled by adding a fictitious substructure having the opposite dynamics of the removed material. The equations of motion of the workpiece are updated, and workpiece FRFs are evaluated by solving the hybrid set of assembled equations of motion in frequency domain as the tool removes the material between two consecutive dynamics update steps. The orders of the initial workpiece structure and the removed substructures are reduced using a model order reduction method with a newly introduced automatic master set selection criterion. The reduced order FRF update model is validated with peripheral milling tests and FRF measurements on a plate-shaped workpiece. It is shown that the proposed model provides ∼20 times faster FRF predictions than the full order finite element (FE) model.

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References

Budak, E. , and Altintas, Y. , 1995, “ Modeling and Avoidance of Static Form Errors in Peripheral Milling of Plates,” Int. J. Mach. Tools Manuf., 35(3), pp. 459–476. [CrossRef]
Elbestawi, M. A. , and Sagherian, R. , 1991, “ Dynamic Modeling for the Prediction of Surface Errors in the Milling of Thin-Walled Sections,” J. Mater. Process. Technol., 25(2), pp. 215–228. [CrossRef]
Seguy, S. , Dessein, G. , and Arnaud, L. , 2008, “ Surface Roughness Variation of Thin Wall Milling, Related to Modal Interactions,” Int. J. Mach. Tools Manuf., 48(3–4), pp. 261–274. [CrossRef]
Bravo, U. , Altuzarra, O. , López de Lacalle, L. N. , Sánchez, J. A. , and Campa, F. J. , 2005, “ Stability Limits of Milling Considering the Flexibility of the Workpiece and the Machine,” Int. J. Mach. Tools Manuf., 45(15), pp. 1669–1680. [CrossRef]
Mañé, I. , Gagnol, V. , Bouzgarrou, B. C. , and Ray, P. , 2008, “ Stability-Based Spindle Speed Control During Flexible Workpiece High-Speed Milling,” Int. J. Mach. Tools Manuf., 48(2), pp. 184–194. [CrossRef]
Song, Q. , Ai, X. , and Tang, W. , 2011, “ Prediction of Simultaneous Dynamic Stability Limit of Time–Variable Parameters System in Thin-Walled Workpiece High-Speed Milling Processes,” Int. J. Adv. Manuf. Technol., 55(9–12), pp. 883–889. [CrossRef]
Thevenot, V. , Arnaud, L. , Dessein, G. , and Cazenave–Larroche, G. , 2006, “ Influence of Material Removal on the Dynamic Behaviour of Thin-Walled Structures in Peripheral Milling,” Mach. Sci. Technol., 10(3), pp. 275–287. [CrossRef]
Adetoro, O. B. , Sim, W. M. , and Wen, P. H. , 2010, “ An Improved Prediction of Stability Lobes Using Nonlinear Thin Wall Dynamics,” J. Mater. Process. Technol., 210(6–7), pp. 969–979. [CrossRef]
Campa, F. J. , Lopez de Lacalle, L. N. , and Celaya, A. , 2011, “ Chatter Avoidance in the Milling of Thin Floors With Bull-Nose End Mills: Model and Stability Diagrams,” Int. J. Mach. Tools Manuf., 51(1), pp. 43–53. [CrossRef]
Zhou, X. , Zhang, D. , Luo, M. , and Wu, B. , 2014, “ Toolpath Dependent Chatter Suppression in Multi-Axis Milling of Hollow Fan Blades With Ball-End Cutter,” Int. J. Adv. Manuf. Technol., 72(5), pp. 643–651. [CrossRef]
Le Lan, J.-V. , Marty, A. , and Debongnie, J.-F. , 2007, “ Providing Stability Maps for Milling Operations,” Int. J. Mach. Tools Manuf., 47(9), pp. 1493–1496. [CrossRef]
Kolluru, K. , and Axinte, D. , 2013, “ Coupled Interaction of Dynamic Responses of Tool and Workpiece in Thin Wall Milling,” J. Mater. Process. Technol., 213(9), pp. 1565–1574. [CrossRef]
Eksioglu, C. , Kilic, Z. M. , and Altintas, Y. , 2012, “ Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems,” ASME J. Manuf. Sci. Eng., 134(6), p. 061006. [CrossRef]
Ismail, F. , and Ziaei, R. , 2002, “ Chatter Suppression in Five-Axis Machining of Flexible Parts,” Int. J. Mach. Tools Manuf., 42(1), pp. 115–122. [CrossRef]
Meshreki, M. , Attia, H. , and Kövecses, J. , 2011, “ Development of a New Model for the Varying Dynamics of Flexible Pocket-Structures During Machining,” ASME J. Manuf. Sci. Eng., 133(4), p. 041002. [CrossRef]
Budak, E. , Tunç, L. T. , Alan, S. , and Özgüven, H. N. , 2012, “ Prediction of Workpiece Dynamics and Its Effects on Chatter Stability in Milling,” CIRP Ann. Manuf. Technol., 61(1), pp. 339–342. [CrossRef]
Fischer, A. , Eberhard, P. , and Ambrósio, J. , 2013, “ Parametric Flexible Multibody Model for Material Removal During Turning,” ASME J. Comput. Nonlinear Dyn., 9(1), p. 011007. [CrossRef]
Kersting, P. , and Biermann, D. , 2014, “ Modeling Techniques for Simulating Workpiece Deflections in NC Milling,” CIRP J. Manuf. Sci. Technol., 7(1), pp. 48–54. [CrossRef]
Craig, R. R., Jr. , and Kurdila, A. J. , 2006, Fundamentals of Structural Dynamics, Wiley, Hoboken, NJ.
Vanc Der Valk, P. L. C. , 2010, “ Model Reduction and Interface Modeling in Dynamic Substructuring: Application to a Multi-Megawatt Wind Turbine,” M.Sc. thesis, Delft University of Technology, Delft, The Netherlands.
D'Ambrogio, W. , and Fregolent, A. , 2010, “ The Role of Interface DoFs in Decoupling of Substructures Based on the Dual Domain Decomposition,” Mech. Syst. Signal Process., 24(7), pp. 2035–2048. [CrossRef]
Voormeeren, S. N. , and Rixen, D. J. , 2012, “ A Family of Substructure Decoupling Techniques Based on a Dual Assembly Approach,” Mech. Syst. Signal Process., 27, pp. 379–396. [CrossRef]
Braun, S. G. , and Ram, Y. M. , 2001, “ Modal Modification of Vibrating Systems: Some Problems and Their Solutions,” Mech. Syst. Signal Process., 15(1), pp. 101–119. [CrossRef]
Duarte, M. L. M. , 1996, “ Experimentally-Derived Structural Models for Use in Further Dynamic Analysis,” Ph.D. thesis, Imperial College of Science, Technology and Medicine, London.
Zhao, Y.-Q. , Chen, S.-H. , Chai, S. , and Qu, Q.-W. , 2002, “ An Improved Modal Truncation Method for Responses to Harmonic Excitation,” Comput. Struct., 80(1), pp. 99–103. [CrossRef]
Wilkinson, J. H. , 1965, The Algebraic Eigenvalue Problem, Oxford University Press, London.
Ewins, D. J. , 1984, Modal Testing: Theory, Practice, and Application, Research Studies Press, Letchworth, Hertfordshire, UK.
Kammer, D. C. , 1991, “ Sensor Placement for On-Orbit Modal Identification and Correlation of Large Space Structures,” J. Guid. Control Dyn., 14(2), pp. 251–259. [CrossRef]
Li, D. S. , Li, H. N. , and Fritzen, C. P. , 2007, “ The Connection Between Effective Independence and Modal Kinetic Energy Methods for Sensor Placement,” J. Sound Vib., 305(4–5), pp. 945–955. [CrossRef]
O'Callahan, J. , Avitabile, P. , and Riemer, R. , 1989, “ System Equivalent Reduction Expansion Process (SEREP),” 7th International Modal Analysis Conference (IMAC), Las Vegas, NV, pp. 29–37.
Sastry, C. V. S. , Roy Mahapatra, D. , Gopalakrishnan, S. , and Ramamurthy, T. S. , 2003, “ An Iterative System Equivalent Reduction Expansion Process for Extraction of High Frequency Response From Reduced Order Finite Element Model,” Comput. Methods Appl. Mech. Eng., 192(15), pp. 1821–1840. [CrossRef]
Friswell, M. I. , Garvey, S. D. , and Penny, J. E. T. , 1995, “ Model Reduction Using Dynamic and Iterated IRS Techniques,” J. Sound Vib., 186(2), pp. 311–323. [CrossRef]
Guyan, R. J. , 1965, “ Reduction of Stiffness and Mass Matrices,” AIAA J., 3(2), pp. 380–380. [CrossRef]
Cho, M. , and Kim, H. , 2004, “ Element-Based Node Selection Method for Reduction of Eigenvalue Problems,” AIAA J., 42(8), pp. 1677–1684. [CrossRef]

Figures

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Fig. 3

(a) Machined workpiece Bi−1 at machining step (i – 1), (b) the interaction between the substructure Ai and in-process workpiece Bi−1 by interface coupling forces, fictitiously added substructure −Ai, and the associated opposite interface coupling forces, and (c) interface force equilibrium after addition of the fictitious substructure

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Fig. 2

Equivalent dynamics removal from a blank by coupling of a fictitious substructure

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Fig. 1

Time invariant tool dynamics and varying workpiece dynamics at different stages of machining

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Fig. 4

Flow chart of the overall simulation scheme

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Fig. 6

(a) Experimental setup and (b) measurement (comparison) locations (points 1–6) and removed nine segments in roughing

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Fig. 5

(a) Initial workpiece geometry and (b) FE mesh of the initial thin-walled workpiece

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Fig. 8

Comparison of the measured and predicted direct FRFs along the x-direction at points #7, #8, #10, and #11 in semifinishing

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Fig. 9

Comparison of the measured and predicted direct FRFs along the x-direction at points #13, #14, #16, and #17 in finishing

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Fig. 10

(a) Variation of the first bending mode frequency at all FRF comparison points in experiment and simulation and (b) comparison of the prediction error in full and reduced order dynamics decoupling for the first bending mode

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Fig. 11

(a) Variation of the first torsional mode frequency at all FRF comparison points in experiment and simulation and (b) comparison of the prediction error in full and reduced order dynamics decoupling for the first torsional mode

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Fig. 12

Schematic illustration of the master DOF selected due to (a) the first bending (shaded region) and (b) the first torsional (shaded region) modes of the initial workpiece

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Fig. 7

Comparison of the measured and predicted direct FRFs along the x-direction at points #1, #2, #4, and #5 in roughing

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Fig. 13

Comparison of the experimentally measured and predicted static stiffness of the plate in the x-direction at all FRF measurement points

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