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Static condensation in modeling roller guides with preload

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Języki publikacji
EN
Abstrakty
EN
This article presents the methodology for modeling the stiffness of a machine tool load-bearing system using the finite element method. A new, simplified model of stiffness of the linear guide with a preload based on equivalent contact model was proposed. An equivalent contract model was developed where the ball was replaced with four rod elements of equivalent stiffness, interconnecting the opposite ends of the face of cuboidal finite ele- ments. To shorten the computation time and facilitate modeling reduction and substructur-ing methods was used. The accuracy of the proposed model was compared with experimental results. In addition, the computation times were evaluated by comparing the simplified model with the full model and other equivalent models. Then, the model was used to determine the stiffness of the machine load-bearing system on the example of a machining table using the aforementioned methods and the obtained results were com-pared in terms of accuracy (less than 1% difference in maximum displacement value) and computation time with the classic approach (up to 97% in time reduction). This paper demonstrated the validity of the proposed model, allowing accurate and fast determination of the stiffness of machine tool load-bearing system.
Rocznik
Strony
1072--1082
Opis fizyczny
Bibliogr. 28 poz., rys., wykr.
Twórcy
autor
  • Institute of Mechanical Technology, West Pomeranian University of Technology, Szczecin, Poland
  • Institute of Mechanical Technology, West Pomeranian University of Technology, Szczecin, Poland
  • Institute of Mechanical Technology, West Pomeranian University of Technology, Szczecin, Poland
  • Maritime University of Szczecin, Poland
  • Institute of Mechanical Technology, West Pomeranian University of Technology, Szczecin, Poland
Bibliografia
  • [1] G. Szwengier, T. Goduński, S. Berczyński, Identification of physical parameters in contact joints models of machines supporting systems, Adv. Eng. Softw. 31 (2) (2000) 149–155.
  • [2] E. Chlebus, B. Dybala, Modelling and calculation of properties of sliding guideways, Int. J. Mach. Tools Manuf. 39 (12) (1999) 1823–1839.
  • [3] D. Jastrzebski, M. Dolata, Modeling the carrying system of the machine tool under the condition of variable configurations of its motion units, Adv. Manuf. Sci. Technol. 39 (3) (2015).
  • [4] D. Jastrzebski, P. Pawełko, G. Szwengier, Modeling the effect of geometric errors on the static characteristics of guide rail systems, Adv. Manuf. Sci. Technol. 34 (4) (2010) 23–33.
  • [5] X. Kong, et al., Dynamic and stability analysis of the linear guide with time-varying, piecewise-nonlinear stiffness by multi-term incremental harmonic balance method, J. Sound Vib. 346 (2015) 265–283.
  • [6] H. Hertz, On the contact of elastic solids, Z. Reine Angew. Mathematik 92 (1881) 156–171.
  • [7] W. Tao, et al., Model for wear prediction of roller linear guides, Wear 305 (1) (2013) 260–266.
  • [8] A. Palmgren, The service life of ball bearings, Zeitschrift des Vereines Deutscher Ingenieure 68 (14) (1924) 339–341.
  • [9] H. Ohta, K. Tanaka, Vertical stiffnesses of preloaded linear guideway type ball bearings incorporating the flexibility of the carriage and rail, J. Tribol. 132 (1) (2010) 011102.
  • [10] H.T. Zou, B.L. Wang, Investigation of the contact stiffness variation of linear rolling guides due to the effects of friction and wear during operation, Tribol. Int. 92 (2015) 472–484.
  • [11] C.Y. Lin, J.P. Hung, T.L. Lo, Effect of preload of linear guides on dynamic characteristics of a vertical column–spindle system, Int. J. Mach. Tools Manuf. 50 (8) (2010) 741–746.
  • [12] P. Pawełko, S. Berczyński, Z. Grządziel, Modeling roller guides with preload, Arch. Civil Mech. Eng. 14 (4) (2014) 691–699.
  • [13] M. Jasiewicz, B. Powałka, Receptance coupling for turning with a follower rest, advances is mechanics: theoretical, computational and interdisciplinary issues, in: Kleiber, et al. (Eds.), Proceedings of the 3rd Polish Congress of Mechanics (PCM) and 21st International Conference on Computer Methods in Mechanics (CMM), Gdansk, Poland, 8–11 September 2015, CRC Press Taylor & Francis Group, London, 2016 245–248.
  • [14] M. Law, H. Rentzsch, S. Ihlenfeldt, Predicting mobile machine tool dynamics by experimental dynamic substructuring, Int. J. Mach. Tools Manuf. 108 (2016) 127–134.
  • [15] T.L. Schmitz, R.R. Donalson, Predicting high-speed machining dynamics by substructure analysis, CIRP Ann. Manuf. Technol. 49 (1) (2000) 303–308.
  • [16] M. Pajor, K. Marchelek, B. Powałka, Method of reducing the number of DOF in the machine tool-cutting process system from the point of view of vibrostability analysis, Modal Anal. 8 (4) (2002) 481–492.
  • [17] M. Pajor, K. Marchelek, B. Powalka, Experimental verification of method of machine tool-cutting process system model reduction in face milling, WIT Trans. Model. Simul. 22 (1999).
  • [18] K. Kaliński, The finite element method application to linear closed loop steady system vibration analysis, Int. J. Mech. Sci. 39 (3) (1997) 315–330.
  • [19] K.J. Kaliński, et al., Modelling and simulation of a new variable stiffness holder for milling of flexible details, Pol. Marit. Res. 24.s1 (2017) 115–124.
  • [20] I. Garitaonandia, et al., Prediction of dynamic behavior for different configurations in a drilling–milling machine based on substructuring analysis, J. Sound Vib. 365 (2016) 70–88.
  • [21] R. Craig, M. Bampton, Coupling of substructures for dynamic analyses, AIAA J. 6 (7) (1968) 1313–1319.
  • [22] Rexroth Star GMBH, Linear Motion and Assembly Technologies, 2007.
  • [23] MSC Nastran 2014 Quick Reference Guide, 2014.
  • [24] M. Gonzalez, A.M. Cuitiño, A nonlocal contact formulation for confined granular systems, J. Mech. Phys. Solids 60 (2) (2012) 333–350.
  • [25] J.S. Sun, K.H. Lee, H.P. Lee, Comparison of implicit and explicit finite element methods for dynamic problems, J. Mater. Process. Technol. 105 (1-2) (2000) 110–118.
  • [26] P. Majda, Modeling of geometric errors of linear guideway and their influence on joint kinematic error in machine tools, Precis. Eng. 36 (3) (2012) 369–378.
  • [27] M. Rahmani, F. Bleicher, Experimental and analytical investigations on normal and angular stiffness of linear guides in manufacturing systems, Proc. CIRP 41 (2016) 795–800.
  • [28] R.J. Guyan, Reduction of stiffness and mass matrices, AIAA J. 3.2 (1965) 380.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0172f8f0-49d1-47a3-b3d5-be54930b4bbd
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