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Coupling dynamics of a geared multibody system supported by ElastoHydroDynamic lubricated cylindrical joints

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Abstract

A comprehensive computational methodology to study the coupling dynamics of a geared multibody system supported by ElastoHydroDynamic (EHD) lubricated cylindrical joints is proposed throughout this work. The geared multibody system is described by using the Absolute-Coordinate-Based (ACB) method that combines the Natural Coordinate Formulation (NCF) describing rigid bodies and the Absolute Nodal Coordinate Formulation (ANCF) characterizing the flexible bodies. Based on the finite-short bearing approach, the EHD lubrication condition for the cylindrical joints supporting the geared system is considered here. The lubrication forces developed at the cylindrical joints are obtained by solving the Reynolds’ equation via the finite difference method. For the evaluation of the normal contact forces of gear pair along the Line Of Action (LOA), the time-varying mesh stiffness, mesh damping and Static Transmission Error (STE) are utilized. The time-varying mesh stiffness is calculated by using the Chaari’s methodology. The forces of sliding friction along the Off-Line-Of-Action (OLOA) are computed by using the Coulomb friction models with a time-varying coefficient of friction under the EHD lubrication condition of gear teeth. Finally, two numerical examples of application are presented to demonstrate and validate the proposed methodology.

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References

  1. Muvengei, O., Kihiu, J., Ikua, B.: Numerical study of parametric effects on the dynamic response of planar multi-body systems with differently located frictionless revolute clearance joints. Mech. Mach. Theory 53, 30–49 (2012)

    Article  Google Scholar 

  2. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behaviour of planar rigid multibody systems including revolute joints with clearance. Proc. Inst. Mech. Eng, Part K: J. Multibody Dyn. 221(2), 161–174 (2007)

    Article  Google Scholar 

  3. Tian, Q., Zhang, Y., Chen, L., Flores, P.: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87, 913–929 (2009)

    Article  Google Scholar 

  4. Erkaya, S., Uzmay, İ.: Experimental investigation of joint clearance effects on the dynamics of a slider–cranker mechanism. Multibody Syst. Dyn. 20, 69–83 (2010)

    Article  MathSciNet  Google Scholar 

  5. Flores, P.: Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44(6), 1211–1222 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Flores, P., Lankarani, H.M., Ambrósio, J., Claro, J.C.P.: Modelling lubricated revolute joints in multibody mechanical systems. Proc. Inst. Mech. Eng, Part K: J. Multibody Dyn. 218(4), 183–190 (2004)

    Google Scholar 

  7. Tian, Q., Liu, C., Machado, M., Flores, P.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64, 25–67 (2011)

    Article  MATH  Google Scholar 

  8. Flores, P., Lankarani, H.M.: Spatial rigid-multi-body systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. 60, 99–114 (2010)

    Article  MATH  Google Scholar 

  9. Stefanelli, R., Valentini, P.P., Vita, L.: Modeling of hydrodynamic journal bearing in spatial multibody systems. In: ASME International Design Engineering Technical Conference, California, USA, DETC2005-84858 (2005)

    Google Scholar 

  10. Brutti, C., Coglitore, G., Valentini, P.P.: Modeling 3D revolute joint with clearance and contact stiffness. Nonlinear Dyn. 66, 531–548 (2011)

    Article  Google Scholar 

  11. Liu, C., Tian, Q., Hu, H.: Dynamics and control of a spatial rigid–flexible multibody system with multiple cylindrical clearance joints. Mech. Mach. Theory 52, 106–129 (2012)

    Article  Google Scholar 

  12. Pinkus, O., Sternlicht, S.A.: Theory of Hydrodynamic Lubrication. McGraw Hill, New York (1961)

    MATH  Google Scholar 

  13. Tian, Q., Zhang, Y., Chen, L., Yang, J.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60(4), 489–511 (2010)

    Article  MATH  Google Scholar 

  14. Dowson, D., Ehret, P.: Past, present and future studies in elastohydrodynamics. Proc. Inst. Mech. Eng. 213(5), 317–333 (1999)

    Article  Google Scholar 

  15. Lugt, P.M., Morles-Espejel, G.E.: A review of Elasto-Hydrodynamic lubrication theory. Tribol. Trans. 54, 470–496 (2011)

    Article  Google Scholar 

  16. Liu, H.P., Xu, H., Ellision, P.J., Jin, Z.M.: Application of computational fluid dynamics and Fluid–Structure Interaction method to the lubrication study of a rotor bearing System. Tribol. Lett. 38(3), 325–336 (2010)

    Article  Google Scholar 

  17. Shenoy, B.S., Pai, R.S., Rao, D.S., Pai, R.: Elasto-hydrodynamic lubrication analysis of full 360° journal bearing using CFD and FSI techniques. World J. Model. Simul. 5(4), 315–320 (2009)

    Google Scholar 

  18. Attia, H.M., Bouziz, S., Maatar, M., Fakhfakh, T., Haddar, M.: Hydrodynamic and elastohydrodynamic studies of a cylindrical journal bearing. J. Hydrodyn. 22(2), 155–163 (2010)

    Article  Google Scholar 

  19. Slim, B., Tahar, F., Mohamed, H.: Acoustic analysis of hydrodynamic and elasto-hydrodynamic oil lubricated journal bearings. J. Hydrodyn. 24(2), 250–256 (2012)

    Article  Google Scholar 

  20. Tian, Q., Sun, Y.L., Liu, C., Hu, H., Flores, P.: ElastoHydroDynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Comput. Struct. 114–115, 106–120 (2013)

    Article  Google Scholar 

  21. García De Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems the Real-Time Challenge. Springer, New York (1994)

    Book  Google Scholar 

  22. Shabana, A.A.: An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies. Technical Report. No. MBS96-1-UIC, University of Illinois at Chicago (1996)

  23. Schiehlen, W.: Research trends in multibody system dynamics. Multibody Syst. Dyn. 18, 3–13 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Shabana, A.A.: Flexible multibody dynamics review of past and recent developments. Multibody Syst. Dyn. 1, 189–222 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  25. Özgüven, H.N., Houser, D.R.: Mathematical models used in gear dynamics a review. J. Sound Vib. 121(3), 383–411 (1988)

    Article  Google Scholar 

  26. Kahraman, A., Singh, R.: Nonlinear dynamics of a geared rotor bearing system with multiple clearances. J. Sound Vib. 144(3), 469–506 (1991)

    Article  Google Scholar 

  27. Kahraman, A., Singh, R.: Interactions between time-varying mesh stiffness and clearance nonlinearities in a geared system. J. Sound Vib. 146(1), 135–156 (1991)

    Article  Google Scholar 

  28. Theodossiades, S., Natsiavas, S.: On geared rotordynamic systems with oil journal bearings. J. Sound Vib. 243(4), 721–745 (2001)

    Article  Google Scholar 

  29. Shiau, T.N., Chou, Y.W., Chang, J.R., Nelson, H.D.: A study on the dynamic characteristics of geared rotor-bearing system with hybrid method. In: International Gas Turbine and Aeroengine Congress and Exposition, The Hague, Netherlands (1994)

  30. Fernandez del Rincon, A., Viadero, F., Iglesias, M., García, P., de-Juan, A., Sancibrian, R.: A model for the study of meshing stiffness in spur gear transmissions. Mech. Mach. Theory 61, 30–58 (2013)

    Article  Google Scholar 

  31. Rao, J.S., Shiau, T.N., Chang, J.R.: Theoretical analysis of lateral response due to torsional excitation of geared rotors. Mech. Mach. Theory 33, 761–783 (1998)

    Article  MATH  Google Scholar 

  32. Machado, M., Moreira, P., Flores, P., Lankarani, H.M.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012)

    Article  Google Scholar 

  33. Baguet, S., Jacquenot, G.: Nonlinear coupling in a gear-shaft-bearing system. Mech. Mach. Theory 45, 1777–1796 (2010)

    Article  MATH  Google Scholar 

  34. Wan, C., Jian, C.: Nonlinear analysis for gear pair system supported by long journal bearings under nonlinear suspension. Mech. Mach. Theory 45, 569–583 (2010)

    Article  MATH  Google Scholar 

  35. Vinayak, H., Singh, R.: Multibody dynamics and model analysis of compliant gear bodies. J. Sound Vib. 210, 171–214 (1998)

    Article  Google Scholar 

  36. Wang, Y., Cheung, H.M.E., Zhang, W.J.: Finite element modelling of geared multibody system. Commun. Numer. Methods Eng. 18, 765–778 (2002)

    Article  MATH  Google Scholar 

  37. Chang, J.R.: Coupling effect of flexible geared rotor on quick-return mechanism undergoing three-dimensional vibration. J. Sound Vib. 300, 139–159 (2007)

    Article  Google Scholar 

  38. Martin, K.F.: A review of friction predictions in gear teeth. Wear 49, 201–238 (1978)

    Article  Google Scholar 

  39. Vaishya, M., Singh, R.: Strategies for modeling friction in gear dynamics. J. Mech. Des. 125, 383–393 (2003)

    Article  Google Scholar 

  40. Vaishya, M., Singh, R.: Analysis of periodically varying gear mesh systems with coulomb friction using Floquet theory. J. Sound Vib. 243(3), 525–545 (2001)

    Article  Google Scholar 

  41. Vaishya, M., Singh, R.: Sliding friction-induced non-linearity and parametric effects in gear dynamics. J. Sound Vib. 248(4), 671–694 (2001)

    Article  Google Scholar 

  42. Xu, H., Kahraman, A., Anderson, N.E., Maddock, D.G.: Prediction of mechanical efficiency of parallel-axis gear pairs. ASME J. Mech. Des. 129, 58–68 (2007)

    Article  Google Scholar 

  43. Xu, H.: Development of a generalized mechanical efficiency prediction methodology for gear pairs. Ph.D. Dissertation, The Ohio State University, Columbus, Ohio (2005)

  44. He, S., Cho, S., Singh, R.: Prediction of dynamic friction forces in spur gears using alternate sliding friction formulations. J. Sound Vib. 309, 843–851 (2008)

    Article  Google Scholar 

  45. García-Vallejo, D., Mayo, J., Escalona, J.L., Domínguez, J.: Three-dimensional formulation of rigid-flexible multibody systems with flexible beam elements. Multibody Syst. Dyn. 20, 1–28 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  46. Liu, C., Tian, Q., Hu, H.Y., García-Vallejo, D.: Simple formulations of imposing moments and evaluating joint reaction forces for rigid-flexible multibody systems. Nonlinear Dyn. 69, 127–147 (2012)

    Article  MATH  Google Scholar 

  47. Shabana, A.A., Yakoub, R.Y.: Three-dimensional absolute nodal coordinate formulation for beam elements: theory. J. Mech. Des. 123, 606–613 (2001)

    Article  Google Scholar 

  48. Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. J. Mech. Des. 123, 614–621 (2001)

    Article  Google Scholar 

  49. He, S., Gunda, R., Singh, R.: Effect of sliding friction on the dynamics of spur gear pair with realistic time-varying stiffness. J. Sound Vib. 301, 927–949 (2007)

    Article  Google Scholar 

  50. Weber, C.: The Deformation of Loaded Gears and the Effect on Their Load-carrying Capacity. Sponsored Research. British Dept. Sci. and Ind. Res. Report No. 3, Germany (1949)

  51. Cornell, R.W.: Compliance and stress sensitivity of spur gear teeth. ASME J. Mech. Des. 103, 447–459 (1981)

    Article  Google Scholar 

  52. Attia, Y.: Deflection of spur gear teeth cut in thin rims. ASME Paper 63-WA-14 (1963)

  53. Baud, S., Velex, P.: Static and dynamic tooth loading in spur and helical geared systems-experiments and model validation. J. Mech. Des. 124, 334–346 (2002)

    Article  Google Scholar 

  54. Sainsot, P., Velex, P., Duverger, O.: Contribution of gear body to tooth deflections a new bidimensional analytical formula. J. Mech. Des. 126, 748–752 (2004)

    Article  Google Scholar 

  55. Wang, Y.: Dynamic modelling of flexible geared multibody system: A finite element approach. Ph.D. Thesis, City University of Hong Kong (1999)

  56. Yang, D.C.H., Sun, Z.S.: A rotary model for spur gear dynamics. ASME J. Mech., Trans. Aut. Des. 107, 529–535 (1985)

    Article  Google Scholar 

  57. Chaari, F., Fakhfakh, T., Haddar, M.: Analytical investigation on the effect of gear teeth faults on the dynamic response of a planetary gear set. Noise Vib. Worldw. 37, 9–15 (2006)

    Article  Google Scholar 

  58. Chaari, F., Baccar, W., Abbes, M.S., Haddar, M.: Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission. Eur. J. Mech. A, Solids 27, 691–705 (2008)

    Article  MATH  Google Scholar 

  59. Chaari, F., Fakhfakh, T., Haddar, M.: Analytical modeling of spur gear tooth crack and influence on gear mesh stiffness. Eur. J. Mech. A, Solids 28, 461–468 (2009)

    Article  MATH  Google Scholar 

  60. Wang, J., Zheng, J.H., Yang, A.: An analytical study of bifurcation and chaos in a spur gear pair with sliding friction. Proc. Eng. 31, 563–570 (2012)

    Article  Google Scholar 

  61. He, S., Singh, R.: Dynamic transmission error prediction of helical gear pair under sliding friction using Floquet theory. J. Mech. Des. 130, 052603 (2008)

    Article  Google Scholar 

  62. Xu, H., Kahraman, A.: Prediction of friction-related power losses of hypoid gear pairs. Proc. Inst. Mech. Eng. Part K: J. Multibody Dyn. 221, 387–400 (2007)

    Google Scholar 

  63. Bathe, K.J.: Finite Element Procedures. Prentice Hall, New Jersey (1996)

    Google Scholar 

  64. Shabana, A.A.: Computational Dynamics, 3rd edn. Wiley, New York (2010)

    Book  MATH  Google Scholar 

  65. Shabana, A.A.: Computational Continuum Mechanics. Cambridge University Press, Cambridge (2008)

    Book  MATH  Google Scholar 

  66. Liu, C., Tian, Q., Hu, H.Y.: Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates. Multibody Syst. Dyn. 26, 283–305 (2011)

    Article  MATH  Google Scholar 

  67. Arnold, M., Brüls, O.: Convergence of the generalized-a scheme for constrained mechanical systems. Multibody Syst. Dyn. 18, 185–202 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  68. Liu, C., Tian, Q., Hu, H.Y.: Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF. Comput. Methods Appl. Mech. Eng. 258, 81–95 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  69. Seo, J.H., Jung, I.H., Park, T.W., Chai, J.B.: Dynamic analysis of a multibody system including a very flexible beam element. JSME Int. J. Ser. C 48(2), 224–233 (2005)

    Article  Google Scholar 

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Acknowledgements

This work is supported in part by National Natural Science Foundations of China under Grant 11290151, 11221202 and 11002022. The work is also supported in part by the Beijing Higher Education Young Elite Teacher Project under Grant YETP1201.

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Authors and Affiliations

  1. Ministry of Education (MOE) Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Qiang Tian, Qianfei Xiao, Yanlei Sun & Haiyan Hu

  2. School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Hui Liu

  3. Department of Mechanical Engineering, University of Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Paulo Flores

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  1. Qiang Tian
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  2. Qianfei Xiao
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Correspondence to Qiang Tian.

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Tian, Q., Xiao, Q., Sun, Y. et al. Coupling dynamics of a geared multibody system supported by ElastoHydroDynamic lubricated cylindrical joints. Multibody Syst Dyn 33, 259–284 (2015). https://doi.org/10.1007/s11044-014-9420-0

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