Structural Engineering and Mechanics

  • 제63권5호
  • /
  • Pages.691-702
  • /
  • 2017
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Characterization of the effect of joint clearance on the energy loss of flexible multibody systems with variable kinematic structure

  • 투고 : 2016.06.03
  • 심사 : 2017.07.26
  • 발행 : 2017.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

Clearances are essential for the assemblage of mechanisms to allow the relative motion between the joined bodies. This clearance exists due to machining tolerances, wear, material deformations, and imperfections, and it can worsen the mechanism performance when the precision and smoothly-working are intended. Energy is a subject which is less paid attention in the area of clearance. The effect of the clearance on the energy of a flexible slider-crank mechanism is investigated in this paper. A clearance exists in the joint between the slider and the coupler. The contact force model is based on the Lankarani and Nikravesh model and the friction force is calculated using the modified Coulomb's friction law. The hysteresis damping which has been included in the contact force model dissipates energy in clearance joints. The other source for the energy loss is the friction between the journal and the bearing. Initial configuration and crank angular velocity are changed to see their effects on the energy of the system. Energy diagrams are plotted for different coefficients of friction to see its influence. Finally, considering the coupler as a flexible body, the effect of flexibility on the energy of the system is investigated.

키워드

참고문헌

  1. Bathe, K.J. (1996), Finite Element Procedures, Prentice-Hall Inc, New Jersey, USA.
  2. Chunmei, J., Yang, Q., Ling, F. and Ling, Z. (2002), "The nonlinear dynamic behavior of an elastic linkage mechanism with clearances", J. Sound Vib., 249(2), 213-226. https://doi.org/10.1006/jsvi.2001.3771
  3. Dubowsky, S. and Freudenstein, F. (1971), "Dynamic analysis of mechanical systems with clearances, Part I: Formation of dynamic model", J. Eng. Indus., 305-309.
  4. Ebrahimi, S., Salahshoor, E. and Moradi, S. (2017a) "Vibration performance evaluation of planar flexible multibody systems with joint clearance", J. Braz. Soc. Mech. Sci. Eng., 1-15.
  5. Ebrahimi, S., Salahshoor, E. and Maasoomi, M. (2017b), "Application of the method of multiple scales for nonlinear vibration analysis of mechanical systems with dry and lubricated clearance joints", J. Theor. Appl. Vib. Acoust., 3(1), 42-61.
  6. Ebrahimi, S. (2007), "A contribution to computational contact procedures in flexible multibody systems", Ph.D. Dissertation, Institute of Engineering and Computational Mechanics, University of Stuttgart, Germany.
  7. Ebrahimi, S. and Eberhard, P. (2008), "Aspects of linear complementarity problems on position and velocity level in normal impact formulation of planar deformable bodies", MMMS Int. J. Multidisc. Model. Mater. Struct., 4, 331-344. https://doi.org/10.1163/157361108785963046
  8. Erkaya, S. and Uzmay, I. (2009), "Optimization of transmission angle for slider-crank mechanism with joint clearances", Struct. Multidisc. Optim., 37, 493-508. https://doi.org/10.1007/s00158-008-0243-6
  9. Erkaya, S. (2012), "Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network", J. Mech. Sci. Technol., 26, 1419-1430. https://doi.org/10.1007/s12206-012-0308-8
  10. Feng, B.Z., Yang, Z. and Gui, W.X. (2013), "Wear analysis of revolute joints with clearance in multibody systems", Phys. Mech. Astron., 56, 1581-1590. https://doi.org/10.1007/s11433-013-5125-2
  11. Flores, P. and Ambrosio, J. (2004), "Revolute joints with clearance in multibody systems", Comput. Struct., 82, 1359-1369. https://doi.org/10.1016/j.compstruc.2004.03.031
  12. Flores, P., Ambrosio, J. and Claro, J.P. (2004), "Dynamic analysis for planar multibody mechanical systems with lubricated joints", Multib. Syst. Dyn., 12, 47-74. https://doi.org/10.1023/B:MUBO.0000042901.74498.3a
  13. Flores, P. (2004), "Dynamic analysis of mechanical systems with imperfect kinematic joints", Ph.D. Dissertation, University of Minho, Braga, Portugal.
  14. Flores, P. and Ambrosio, J. (2010), "On the contact detection for contact-impact analysis in multibody systems", Multib. Syst. Dyn., 24(1), 103-122. https://doi.org/10.1007/s11044-010-9209-8
  15. Gandhi, V.C. Sathish, Kumaravelan, R., Ramesh, S. and Sriram, K. (2015), "Analysis of material dependency in an elastic - plastic contact models using contact mechanics approach", Struct. Eng. Mech., 53(5), 1051-1066. https://doi.org/10.12989/sem.2015.53.5.1051
  16. Garrido, J.A., Foces, A. and Paris, F. (1994), "An incremental procedure for three-dimensional contact problems with friction", Comput. Struct., 50(2), 201-215. https://doi.org/10.1016/0045-7949(94)90296-8
  17. Jablokow, A.G., Nagarajan, S. and Turcic, D.A. (1993), "A modal analysis solution technique to the equations of motion for elastic mechanism systems including the rigid-body and elastic motion coupling terms", Tran. ASME, J. Mech. Des., 115, 314-323. https://doi.org/10.1115/1.2919194
  18. Khemili, I. and Romdhane, L. (2008), "Dynamic analysis of a flexible slider-crank mechanism with clearance", Euro. J. Mech. A Solid., 27, 882-898. https://doi.org/10.1016/j.euromechsol.2007.12.004
  19. Lankarani, H.M. and Nikravesh, P. (1994), "Continuous contact force models for impact analysis in multibody systems", Nonlin. Dyn., 5, 193-207.
  20. Li, C., He, Y. and Ning, X. (2015), "Helical gear multi-contact tooth mesh load analysis with flexible bearings and shafts", Struct. Eng. Mech., 55(4), 839-856. https://doi.org/10.12989/sem.2015.55.4.839
  21. Liu, Z. and Yang, Y. (1998), "Contact surface element method for two-dimensional elastic contact problems", Struct. Eng. Mech., 6(4), 363-375. https://doi.org/10.12989/sem.1998.6.4.363
  22. Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L. and Sawyer, W.G. (2010), "Analysis of planar multibody systems with revolute joint wear", Wear, 268, 643-652. https://doi.org/10.1016/j.wear.2009.10.014
  23. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607
  24. Pei, L., Wei, C. and Bin, Z. A. (2013), "An improved practical model for wear prediction of revolute clearance joints in crank slider mechanisms", Sci. China Press Springer-Verlag Berlin Heidelberg 56(2), 2953-2963. https://doi.org/10.1007/s11431-013-5401-4
  25. Rahmanian, S. and Ghazavi, M.R. (2015), "Bifurcation in planar slider-crank mechanism with revolute clearance joint", Mech. Mach. Theor., 91, 86-101. https://doi.org/10.1016/j.mechmachtheory.2015.04.008
  26. Ravn, P. (1998), "A continuous analysis method for planar multibody systems with joint clearance", Multib. Syst. Dyn., 2, 1-24. https://doi.org/10.1023/A:1009759826529
  27. Rhee, J.K. and Akay, A. (1996), "Dynamic response of a revolute joint with clearance", J. Mech. Mach. Theor., 31, 121-134. https://doi.org/10.1016/0094-114X(95)00061-3
  28. Salahshoor, E., Ebrahimi, S. and Maasoomi, M. (2016), "Nonlinear vibration analysis of mechanical systems with multiple joint clearances using the method of multiple scales", Mech. Mach. Theor., 105, 495-509. https://doi.org/10.1016/j.mechmachtheory.2016.07.020
  29. Sardashti, A., Daniali, H.M. and Varedi, S.M. (2013), "Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm", Meccanica, 48, 1681-1693. https://doi.org/10.1007/s11012-013-9699-6
  30. Schiling, R.J. and Harris, S.L. (1999), Applied Numerical Methods for Engineering, CL Engineering, Brooks/Cole.
  31. Schwab, A.L., Meijaard, J.P. and Meijers, P. (2002), "A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems", Mech. Mach. Theor., 37, 895-913. https://doi.org/10.1016/S0094-114X(02)00033-2
  32. Shabana, A.A. (2001), Computational Dynamics, John Wiley & Sons, Inc, New York, USA.
  33. Shabana, A.A. (2005), Dynamics of Multibody Systems, Cambridge University Press, New York, USA
  34. Tian, Q., Zhang, Y., Chen, L. and Flores, P. (2009) "Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints", Comput. Struct., 87(13-14), 913-929. https://doi.org/10.1016/j.compstruc.2009.03.006
  35. Tian, Q., Zhang, Y., Chen, L. and Yang, J.J. (2010) "Simulation of planar flexible multibody systems with clearance and lubricated revolute joints", Nonlin. Dyn., 60(4), 489-511. https://doi.org/10.1007/s11071-009-9610-0
  36. Tian, Q., Liu, C., Machado, M. and Flores, P. (2011) "A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems", Nonlin. Dyn., 64(1-2), 25-47. https://doi.org/10.1007/s11071-010-9843-y
  37. Tian, Q., Sun, Y., Liu, C., Hu, H. and Flores, P. (2013) "Elastohydrodynamic lubricated cylindrical joints for rigidflexible multibody dynamics", Comput. Struct., 114-115, 106-120. https://doi.org/10.1016/j.compstruc.2012.10.019
  38. Tian, Q., Xiao, Q., Sun, Y., Hu, H., Liu, H. and Flores, P. (2015) "Coupling dynamics of a geared multibody system supported by ElastoHydroDynamic lubricated cylindrical joints", Multib. Syst. Dyn., 33(3), 259-284. https://doi.org/10.1007/s11044-014-9420-0
  39. Vaidya, A.M. and Padole, P.M. (2010), "A performance evaluation of four bar mechanism considering flexibility of links and joints stiffness", Open Mech. Eng. J., 4, 16-28.
  40. Varedi, S.M., Daniali, H.M., Dardel, M. and Fathi, A. (2015), "Optimal dynamic design of a planar slider-crank mechanism with a joint clearance", Mech. Mach. Theor., 86, 191-200. https://doi.org/10.1016/j.mechmachtheory.2014.12.008
  41. Yang, G., Yang, J., Qiang, C., Ge, J. and Chen, Q. (2012), "Natural frequencies of a cantilever beam and block system with clearance while block staying on given position", J. Vib. Control, 19, 262-275.
  42. Zhang, X., Zhang, X. and Chen, Z. (2014), "Dynamic analysis of a 3-RRR parallel mechanism with multiple clearance joints", Mech. Mach. Theor., 78, 105-115. https://doi.org/10.1016/j.mechmachtheory.2014.03.005
  43. Zhang, Z., Xu, L., Tay, Y.Y., Flores, P. and Lankarani, H. (2015), "Multi-objective optimization of mechanisms with clearances in revolute joints", Mech. Mach. Sci., 24, 423-433.
  44. Zhao, B., Zhang, Z.N. and Dai, X.D. (2013), "Prediction of wear at revolute clearance joints in flexible mechanical systems", Procedia Eng., 68, 661-667. https://doi.org/10.1016/j.proeng.2013.12.236
  45. Zhao, Y., Zhang, B., An, G., Liu, Z. and Cai, L. (2016), "A hybrid method for dynamic stiffness identification of bearing joint of high speed spindles", Struct. Eng. Mech., 57(1), 141-159. https://doi.org/10.12989/sem.2016.57.1.141