Research Papers

Parametric Flexible Multibody Model for Material Removal During Turning

[+] Author and Article Information
Achim Fischer

Research Assistant
e-mail: afischer@itm.uni-stuttgart.de

Peter Eberhard

e-mail: eberhard@itm.uni-stuttgart.de
Institute of Engineering and
Computational Mechanics (ITM),
University of Stuttgart,
Pfaffenwaldring 9,
Stuttgart 70569, Germany

Jorge Ambrósio

Instituto de Engenharia Mecânica (IDMEC),
Instituto Superior Técnico,
Av. Rovisco Pais,
Lisboa 1048-001, Portugal
e-mail: jorge@dem.ist.utl.pt

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 9, 2013; final manuscript received July 20, 2013; published online October 9, 2013. Assoc. Editor: Johannes Gerstmayr.

J. Comput. Nonlinear Dynam 9(1), 011007 (Oct 09, 2013) (10 pages) Paper No: CND-13-1003; doi: 10.1115/1.4025283 History: Received January 09, 2013; Revised July 20, 2013

This work presents a flexible multibody system model for the inside turning of thin-walled cylinders. The model accounts for the varying input and output behavior of the workpiece due to workpiece rotation and tool feed, as well as the changing workpiece dynamics due to material removal. A parametric approach is used to incorporate the effect of material removal. Hereby, a number of systems are precalculated for different machined states that are then interpolated to obtain the model for the desired machined state. As different systems typically have different vectors of degrees of freedom, a preprocessing step must be added to guarantee compatibility and thus a meaningful interpolation. In this work, two ways of obtaining a parametric model are presented that lead to similar results. The parametric model is then used to analyze stability of an inside turning operation. By taking into account the varying workpiece dynamics, an improved tool feed is suggested that would allow to greatly reduce the cycle time.

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Tobias, S. A., 1965, Machine-Tool Vibration, Blackie and Sons, London, UK.
Bathe, K.-J., 1996, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ.
Shabana, A. A., 1998, Dynamics of Multibody Systems, Cambridge University Press, Cambridge, England.
Heisel, U., and Kang, C., 2010, “Model-Based Form Error Compensation in the Turning of Thin-Walled Cylindrical Parts,” Prod. Eng. Res. Develop., 5(2), pp. 151–158. [CrossRef]
Fischer, A., and Eberhard, P., 2011, “Simulation-Based Stability Analysis of a Thin-Walled Cylinder During Turning With Improvements Using an Adaptronic Turning Chisel,” Arch. Mech. Eng., 58(4), pp. 367–391.
Olivier Brüls, P., and Duysinx, J.-C. G., 2007, “The Global Modal Parameterization for Nonlinear Methods in Engineering,” Int. J. Numer. Methods Eng., 69(5), pp. 948–977. [CrossRef]
Tamarozzi, T., Ziegler, P., Eberhard, P., and Desmet, W., 2013, “Static Modes Switching in Gear Contact Simulation” Mech. Mach. Theory, 63, pp. 89–106. [CrossRef]
Ambrósio, J. A. C., 2009, “Advanced Design of Mechanical Systems: From Analysis to Optimization,” Distributed Deformation: A Finite Element Method, Springer, Berlin, pp. 351–374.
Wallrapp, O., 1993, “Standard Input Data of Flexible Bodies for Multibody System Codes,” German Aerospace Establishment, Institute for Robotics and System Dynamics, Oberpfaffenhofen, Report No. IB 515-93-04.
Fehr, J., 2011,“Automated and Error-Controlled Model Reduction in Elastic Multibody Systems,” Ph.D. thesis, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Stuttgart, Germany.
Lehner, M., 2007, “Modellreduktion in Elastischen Mehrkörpersystemen,” Ph.D. thesis, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Germany (in German).
Antoulas, A., 2005, Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, PA.
Kienzle, O., 1952, “Die Bestimmung von Kräften und Leistungen an Spanenden Werkzeugen und Werkzeugmaschinen (in German),” Zeitschrift des Vereines Deutscher Ingenieure, 94, pp. 299–305.
Paucksch, E., Holsten, S., Linß, M., and Tikal, F., 2008, Zerspantechnik (in German), Vieweg+Teubner, Wiesbaden.
König, W., Essel, K., and Witte, L., 1981, Specific Cutting Force Data for Metal-Cutting, Verlag-Stahleisen, Düsseldorf.
Ratchev, S., Liu, S., Huang, W., and Becker, A. A., 2007, “Machining Simulation and System Integration Combining FE Analysis and Cutting Mechanics Modelling,” Int. J. Adv. Manuf. Technol., 35(1–2), pp. 55–65. [CrossRef]
Mañé, I., Gagnol, V., Bouzgarroua, B. C., and Raya, P., 2008, “Stability-Based Spindle Speed Control During Flexible Workpiece High-Speed Milling,” Int. J. Mach. Tools Manuf., 48(2), pp. 184–194. [CrossRef]
Panzer, H., Mohring, J., Eid, R., and Lohmann, B., 2010, “Parametric Model Order Reduction by Matrix Interpolation,” Automatisierungstechnik, 58(8), pp. 475–484. [CrossRef]
Merrit, H. E., 1965, “Theory of Self-Excited Machine-Tool Chatter,” ASME J. Eng. Industry, 87(4), pp. 447–454. [CrossRef]
Budak, E., and Altintas, Y., 1998, “Analytical Prediction of Chatter Stability in Milling – Part I: General Formulation,” J. Dyn. Sys., Meas., Control, 120(1), pp. 22–30. [CrossRef]
Henninger, C., and Eberhard, P., 2009, “Computation of Stability Bounds for Milling Processes With Parallel Kinematic Machine Tools,” Inst. Eng. Comput. Mech., 223(1), pp. 117–129. [CrossRef]
Hale, J. K., and Lunel, S.M.V., 1993, Introduction to Functional Differential Equations, Springer, New York.
Insperger, T., and Stépán, G., 2012, Semi-Discretization for Time-Delay Systems: Stability and Engineering Applications, Springer, New York.
Henninger, C., 2009, “Methoden zur Simulationsbasierten Analyse der Dynamischen Stabilität von Fräsprozessen (in German),” Ph.D. thesis, Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart.
Insperger, T., and Stépán, G., 2002, “Semi-Discretization Method for Delayed Systems,” Int. J. Numer. Methods Eng., 55, pp. 503–518. [CrossRef]
Insperger, T., and Stépán, G., 2004, “Updated Semi-Discretization Method for Periodic Delay-Differential Equations With Discrete Delay,” Int. J. Numer. Methods Eng., 61, pp. 117–141. [CrossRef]


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Fig. 1

Schematic of workpiece, tool and coupling process force

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Fig. 2

Surface element and acting process force

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Fig. 3

Cylinder and tool during machining

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Fig. 4

Eigenfrequencies of the machined workpiece

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Fig. 5

Determination of the permutation matrix for DOF reordering

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Fig. 6

Interpolated eigenvectors of the reduced systems

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Fig. 7

Displacement perpendicular to the workpiece surface for a constant process force

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Fig. 8

Difference between displacements of the two parametric models

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Fig. 9

Frequency response of the interpolated systems and the exact model and zoom on the first eigenfrequency

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Fig. 10

Discretization of the system past and approximation as time-discrete system

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Fig. 11

Stability chart given in terms of feed and machined length




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