Dynamic Analysis of Abrasive Filaments in Contact with Different Workpiece Geometries
Eckart Uhlmann and Christian Sommerfeld
Institute for Machine Tools and Factory Management, Technische Universität Berlin
Pascalstraße 8-9, 10587 Berlin, Germany
Abrasive brushes are often used for surface finishing and deburring and consist of a brush body with fixed, highly flexible abrasive filaments. During the brushing process the highly flexible abrasive filaments deform tangentially and axially and adapt to the shape of the workpiece. The contact behaviour of abrasive brushes in the machining process is very complex and has been insufficiently investigated so far. Abrasive brushes consist of a brush body with fixed, highly flexible abrasive filaments and are often used for surface finishing and deburring. During the brushing process, the highly flexible abrasive filaments deform tangential and axial and adapt to the shape of the workpiece. The mentioned contact behavior of the abrasive brush during the machining process is complex, and has not yet been sufficiently investigated. To better understand the contact behavior and, thus, the brushing process, a model of an abrasive filament is proposed in this study. The model describes the dynamic behavior of a single filament in contact with different workpiece geometries. The filament is discretized into a multi-body system of rigid links connected with rotational springs and rotational dampers, and the workpiece is approximated by using a polynomial. The contact of the multi-body system representing the filament with the surface of the workpiece is described by using Hertz’s theory of elastic contact and Coulomb’s law of friction. Based on this, a system of equations of motion for the multi-body system is obtained by using Lagrangian mechanics. A numerical solution of the equation of motion system was calculated by using experimentally determined material and contact properties of the filament as a composite of a plastic matrix and abrasive grains. A comparison of the calculated results with experimental data yielded satisfactory agreement for the contact between the filament and different workpiece geometries.
-  R. J. Stango, S. M. Heinrich, and C. Y. Shia, “Analysis of constrained filament deformation and stiffness properties of brushes,” J. Eng. for Ind., Vol.111, pp. 238-243, 1989.
-  E. Uhlmann, C. Sommerfeld, M. Renner, and M. Baumann, “Bürstspanen von Profilen,” Wt online, Vol.107, No.6, pp. 238-243, 2017.
-  S. M. Heinrich, R. J. Stango, and C. Y. Shia, “Effect of workpart curvature on the stiffness Properties of circular filamentary brushes,” J. of Engineering for Industry, Vol.113, No.6, pp. 276-282, 1991.
-  C. Y. Shia and R. J. Stango, “On the frictional response of a filamentary brush in contact with a curved workpart,” Int. J. Machine Tools and Manufacture, Vol.34, pp. 573-589, 1994
-  R. J. Stango, V. Capriapa, A. Prasad, and S. K. Lian, “Measurement and analysis of brushing tool performance characteristics, Part 1: Stiffness response,” J. of Eng. for Ind., Vol.113, pp. 283-289, 1991.
-  D. Kono, S. Weikert, A. Matsubara, and K. Yamazaki, “Estimationof mechanical error for evaluation of machine tool structures,” Int. J. Automation Technol., Vol.6, No.2, pp. 147-153, 2012.
-  D. Isobe and Y. Moriya, “A finite element schewme for impact force prediction of robotic mechanisms,” J. Robot. Mechatron., Vol.18, No.3, pp. 340-346, 2006.
-  C. Y. Shia, R. J. Stango, and S. M. Heinrich, “Analysis of contact mechanics for a circular filamentary brush/ workpart system: Part 1 – Modelling and Formulation,” Contact Problems and Interactions in Manufacturing and Tribological Systems, Vol.67, pp. 171-179, 1993.
-  C. Y. Shia, R. J. Stango, and S. M. Heinrich, “Analysis of contact mechanics for a circular filamentary brush/workpart system,” J. Man. Sc. and Eng., Vol.120, pp. 715-721, 1998.
-  L. V. Vanegas Useche, “Dynamics and performance of oscillatory gutter brushes for street sweeping,” Ph.D. Thesis, The University of Surrey, 2007.
-  L. V. Vanegas Useche, M. M. Abdel Wahab, and G. A. Parker, “Determination of friction coefficients for cutting brush-road surface interaction through FEM,” Proc. of IEEE Southeast Conf., pp. 77-80, March 18-21, 2010.
-  L. V. Vanegas Useche, M. M. Abdel Wahab, and G. A. Parker, “Determination of friction coefficient, brush contact arcs and brush penetration for gutter brush-road interaction through FEM,” Acta. Mech., Vol.221, pp. 119-132, 2011.
-  L. V. Vanegas Useche, M. M. Abdel Wahab, and G. A. Parker, “Dynamic finite element model of oscillatory brushes,” Finite Elements in Analysis and Design, Vol.47, pp. 771-783, 2011.
-  M. M. Abdel Wahab, G. A. Parker, and C. Wang, “Modelling rotary sweeping brushes and analyzing brush characteristic using finite element method,” Finite Elements in Analysis and Design, Vol.43, pp. 521-532, 2007.
-  M. M. Abdel Wahab, C. Wang, and L. V. Vanegas Useche, “Finite element models for brush-debris interaction in road sweeping,” Acta. Mech., Vol.215, pp. 71-84, 2010.
-  J. L. Lagrange, “Mécanique Analytique,” Jacques Gabay, 1989.
-  J. G. Hayes and J. Halliday, “The least-squares fitting of cubic spline surface to general data sets,” J. Inst. Maths. Applics., Vol.14, pp. 89-103, 1974.
-  H. Hertz, “Über die Berührung fester elastsicher Körper,“ J. für die Reine und Angewandte Mathematik, Vol.92, pp. 156-171, 1881.
-  G. Szego, “Orthogonal polynomials,” American Mathematical Society Providence, 4th ed., 1975.
-  K. E. Atkinson, “An introduction to numerical analysis,” Wiley, 2nd ed., 1989.
-  DIN EN ISO 527-1, Teil 1, “Kunststoffe-Bestimmung der Zugeigenschaften-Teil 1: Allgemeine Grundsätze,” Berlin, 1996.
-  K. U. Kainer, “Metallische Verbundwerkstoffe,” Wiley, 2003.
-  U. Naumann, “Zum Gefüge-Elastizitätsmodul-Zusammenhang poröser Oxid-Cermets,” Kernforschungszentrum Karlsruhe, 1987.
-  DIN EN ISO 14577-1, Teil 1, “Metallische Werkstoffe-Instrumentierte Eindringprüfung zur Bestimmung der Härte und anderer Werkstoffparameter-Prüfverfahren,” Berlin, 2015.
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