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An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems

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Abstract

This study is focused on dynamic modeling of planar multibody systems with multiple deep groove ball bearing joints, in which the radial clearance, contact deformation, and bearing kinematics are included. By using the approach presented, the variation of the joint reaction force and the dynamic load on each ball element in bearings can be simulated. The deep groove ball bearing joints are modeled by introducing a nonlinear force system, which takes into account the contact elastic deformations between the ball elements and the raceways. The contact force is calculated by the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. A planar slider-crank mechanism with two deep groove ball bearing joints is chosen as an example to demonstrate the application of the methodologies presented in this paper. In this model, one bearing locates at the joint between the ground and crank, while the other one locates at the joint between the crank and connecting rod. By numerical calculation, the dynamic load distribution characteristics of bearings under real mechanism movement conditions are simulated. From the results, it can be concluded that the dynamic load on each rolling element varies differently and belongs to a variable load with the change of mechanism configuration. Load characteristic analysis is the foundation of developing research on the fatigue life and reliability of bearings. This study will provide a key mechanical support for the performance evaluation, dynamic design, and geometrical parameter optimization of the joint rolling element bearings.

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References

  1. Upadhyay, S.H., Harsha, S.P., Jain, S.C.: Analysis of nonlinear phenomena in high speed ball bearings due to radial clearance and unbalanced rotor effects. J. Vib. Control 16(1), 65–88 (2010)

    Article  Google Scholar 

  2. Tiwari, M., Prakash, O., Gupta, K.: Effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor. J. Sound Vib. 238(5), 723–756 (2000)

    Article  Google Scholar 

  3. Kappaganthu, K., Nataraj, C.: Nonlinear modeling and analysis of a rolling element bearing with a clearance. Commun. Nonlinear Sci. Numer. Simul. 16(10), 4134–4145 (2011)

    Article  MATH  Google Scholar 

  4. Choudhury, A., Tandon, N.: Vibration response of rolling element bearings in a rotor bearing system to a local defect under radial load. J. Tribol. 128(2), 252–261 (2006)

    Article  Google Scholar 

  5. Arslan, H., Aktürk, N.: An investigation of rolling element vibrations caused by local defects. J. Tribol. 130(4), 041101 (2008)

    Article  Google Scholar 

  6. Rafsanjania, A., Abbasiona, S., Farshidianfarb, A., Moeenfardc, H.: Nonlinear dynamic modeling of surface defects in rolling element bearing systems. J. Sound Vib. 319(3–5), 1150–1174 (2009)

    Article  Google Scholar 

  7. Kankar, P.K., Sharma, S.C., Harsha, S.P.: Vibration based performance prediction of ball bearings caused by localized defects. Nonlinear Dyn. 69(3), 847–875 (2012)

    Article  Google Scholar 

  8. Patel, V.N., Tandon, N., Pandey, R.K.: A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races. J. Tribol. 132(4), 0411011 (2010)

    Article  Google Scholar 

  9. Patil, M.S., Mathew, J., Rajendrakumar, P.K., Desai, S.: A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing. Int. J. Mech. Sci. 52(9), 1193–1201 (2010)

    Article  Google Scholar 

  10. Nakhaeinejad, M., Bryant, M.D.: Dynamic modeling of rolling element bearings with surface contact defects using bond graphs. J. Tribol. 133(1), 0111021 (2011)

    Article  Google Scholar 

  11. Liu, J., Shao, Y.M., Lim, T.C.: Vibration analysis of ball bearings with a localized defect applying piecewise response function. Mech. Mach. Theory 56, 156–169 (2012)

    Article  Google Scholar 

  12. Tandon, N., Choudhury, A.: A theoretical model to predict the vibration response of rolling bearings in a rotor bearing system to distributed defects under radial load. J. Tribol. 122(3), 609–615 (2000)

    Article  Google Scholar 

  13. Sopanen, J., Mikkola, A.: Dynamic model of a deep-groove ball bearing including localized and distributed defects, Part 1: theory. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 217(3), 201–211 (2003)

    Google Scholar 

  14. Sopanen, J., Mikkola, A.: Dynamic model of a deep-groove ball bearing including localized and distributed defects, Part 2: implementation and results. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 217(3), 213–223 (2003)

    Google Scholar 

  15. Harsha, S.P., Sandeep, K., Prakash, R.: Non-linear behaviors of rolling element bearings due to surface waviness. J. Sound Vib. 272(3–5), 557–580 (2004)

    Article  Google Scholar 

  16. Bai, C.Q., Xu, Q.Y.: Dynamic model of ball bearings with internal clearance and waviness. J. Sound Vib. 294(1–2), 23–48 (2006)

    Google Scholar 

  17. Babu, C.K., Tandon, N., Pandey, R.K.: Vibration modeling of a rigid rotor supported on the lubricated angular contact ball bearings considering six degrees of freedom and waviness on balls and races. J. Vib. Acoust. 134(1), 0110061 (2012)

    Article  Google Scholar 

  18. Weinzapfel, N., Sadeghi, F.: A discrete element approach for modeling cage flexibility in ball bearing dynamics simulations. J. Tribol. 131(2), 0211021 (2009)

    Article  Google Scholar 

  19. Leblanc, A., Nelias, D., Defaye, C.: Nonlinear dynamic analysis of cylindrical roller bearing with flexible rings. J. Sound Vib. 325(1–2), 145–160 (2009)

    Article  Google Scholar 

  20. de Jalon, J.G., Bayo, E.: Kinematic and Dynamic Simulations of Multibody Systems. Springer, New York (1994)

    Book  Google Scholar 

  21. Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University Press, Cambridge (2005)

    Book  MATH  Google Scholar 

  22. Ravn, P.: A continuous analysis method for planar multibody systems with joint clearance. Multibody Syst. Dyn. 2(1), 1–24 (1998)

    Article  MATH  Google Scholar 

  23. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behavior of planar rigid multi-body systems including revolute joints with clearance. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 221(2), 161–174 (2007)

    Google Scholar 

  24. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112(3), 369–376 (1990)

    Article  Google Scholar 

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

    Google Scholar 

  26. Ravn, P., Shivaswamy, S., Alshaer, B.J., Lankarani, H.M.: Joint clearances with lubricated long bearings in multibody mechanical systems. J. Mech. Des. 122(4), 484–488 (2000)

    Article  Google Scholar 

  27. Flores, P., Ambrósio, J., Claro, J.C.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12(1), 47–74 (2004)

    Article  MATH  Google Scholar 

  28. Alshaer, B.J., Nagarajan, H., Beheshti, H.K., Lankarani, H.M., Shivaswamy, S.: Dynamics of a multibody mechanical system with lubricated long journal bearings. J. Mech. Des. 127, 493–498 (2005)

    Article  Google Scholar 

  29. Flores, P., Ambrósio, J., Claro, J.C.P., Lankaranic, H.M., Koshy, C.S.: A study on dynamics of mechanical systems including joints with clearance and lubrication. Mech. Mach. Theory 41(3), 247–261 (2006)

    Article  MATH  Google Scholar 

  30. Flores, P., Ambrósio, J., Claro, J.C.P., Lankaranic, H.M., Koshy, C.S.: Lubricated revolute joints in rigid multibody systems. Nonlinear Dyn. 56(3), 277–295 (2009)

    Article  MATH  Google Scholar 

  31. Machado, M., Costa, J., Seabra, P., Flores, P.: The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems. Nonlinear Dyn. 69(1–2), 635–654 (2012)

    Article  Google Scholar 

  32. Tian, Q., Zhang, Y.Q., Chen, L.P., Flores, P.: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87(13–14), 913–929 (2009)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  34. Imed, K., Lotfi, R.: Dynamic analysis of a flexible slider–crank mechanism with clearance. Eur. J. Mech. A, Solids 27(5), 882–898 (2008)

    Article  MATH  Google Scholar 

  35. 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(1–2), 25–47 (2011)

    Article  Google Scholar 

  36. Brutti, C., Coglitore, C., Valentini, P.P.: Modeling 3D revolute joint with clearance and contact stiffness. Nonlinear Dyn. 66(4), 531–548 (2011)

    Article  Google Scholar 

  37. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamics of multibody systems with spherical clearance joints. J. Comput. Nonlinear Dyn. 1(3), 240–248 (2006)

    Article  Google Scholar 

  38. Flores, P., Lankarani, H.M.: Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. 60(1–2), 99–144 (2010)

    Article  MATH  Google Scholar 

  39. Erkaya, S., Uzmay, I.: Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn. 58(1–2), 179–198 (2009)

    Article  MATH  Google Scholar 

  40. Flores, P.: A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn. 61(4), 633–653 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  41. Flores, P., Lankarani, H.M.: Dynamic response of multibody systems with multiple clearance joints. J. Comput. Nonlinear Dyn. 7(3), 0310031 (2012)

    Article  Google Scholar 

  42. Liu, C., Tian, Q., Hu, H.Y.: 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 

  43. Megahed, S.M., Haroun, A.F.: Analysis of the dynamic behavioral performance of mechanical systems with multi-clearance joints. J. Comput. Nonlinear Dyn. 7(1), 0110021 (2012)

    Article  Google Scholar 

  44. 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 

  45. 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 

  46. Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints. Multibody Syst. Dyn. (2012) doi:10.1007/s11044-012-9309-8. Online first

  47. Gummer, A., Sauer, B.: Influence of contact geometry on local friction energy and stiffness of revolute joints. J. Tribol. 134(2), 0214021 (2012)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  49. Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L., Sawyer, G.W.: Analysis of planar multibody systems with revolute joint wear. Wear 268(5–6), 643–652 (2010)

    Article  Google Scholar 

  50. Olyaei, A.A., Ghazavi, M.R.: Stabilizing slider-crank mechanism with clearance joints. Mech. Mach. Theory 53, 17–29 (2012)

    Article  Google Scholar 

  51. Erkaya, S., Uzmay, I.: Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst. Dyn. 24(1), 81–102 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  52. Flores, P., Koshy, C.S., Lankarani, H.M., Ambrósio, J., Claro, J.C.P.: Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn. 65(4), 383–398 (2011)

    Article  Google Scholar 

  53. Xu, L.X., Yang, Y.H., Li, Y.G., Li, C.N., Wang, S.Y.: Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance. Mech. Mach. Theory 56, 69–88 (2012)

    Article  Google Scholar 

  54. Harris, T.A.: Rolling Bearing Analysis. Wiley, New York (2001)

    Google Scholar 

  55. Dowson, D., Higginson, G.R.: Elasto-Hydrodynamic Lubrication. Pergamon, Elmsford (1977)

    Google Scholar 

  56. Cameron, A.: Basic Lubrication Theory. Wiley, New York (1987)

    Google Scholar 

  57. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints. Springer, Berlin (2008)

    MATH  Google Scholar 

  58. Baumgarte, J.: Stabilization of constraints and integral of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1(1), 1–16 (1972)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to express their sincere thanks to the referees for their valuable suggestions. This project is supported by the National High Technology Research and Development Program of China (Grant No. 2011AA04A102) and National Natural Science Foundation of China (Grant No. 51005164). This support is gracefully acknowledged.

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  1. School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin, 300222, China

    Li-xin Xu & Yong-gang Li

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Correspondence to Li-xin Xu.

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Xu, Lx., Li, Yg. An approach for calculating the dynamic load of deep groove ball bearing joints in planar multibody systems. Nonlinear Dyn 70, 2145–2161 (2012). https://doi.org/10.1007/s11071-012-0606-9

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  • DOI: https://doi.org/10.1007/s11071-012-0606-9

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