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Dynamic modeling and comparative analysis of a 3-PRR parallel robot with multiple lubricated joints

  • Haodong Zhang
  • Xianmin ZhangEmail author
  • Zhenhui Zhan
  • Lixin Yang
Article
  • 82 Downloads

Abstract

This paper presents a methodology to study the dynamic response of a parallel robot with multiple lubricated joints. Based on Gümbel’s boundary conditions, the hydrodynamic force of the journal bearing is calculated with the Pinkus–Sternlicht model. Considering the dynamic loads on the multiple lubricated joints, the Pinkus–Sternlicht model is modified to ensure numerical stability of the solution of the system’s equations. A comparative analysis of four joint force models is presented to show the advantages of the modified model for a 3-PRR (P and R represent prismatic and revolute pairs respectively and the underline of the P represents the actuated joint) parallel robot. The improvement in the numerical stability of the modified Pinkus–Sternlicht model is proven. Subsequently, the dynamic behavior of the 3-PRR parallel robot with multiple lubricated joints is analyzed comprehensively, compared with the 3-PRR parallel robot with multiple dry clearance joints. Simulation results demonstrate the validity of the dynamic methodology containing the modified Pinkus–Sternlicht model for the 3-PRR parallel robot with multiple lubricated joints. This dynamic methodology can illustrate the better periodicity of such parallel robots considering lubricated joints.

Keywords

Multibody dynamics Multiple lubricated joints 3-PRR parallel robot Hydrodynamic force 

Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. U1501247) and the Fundamental Research Funds for the Central Universities of China (2019MS068). These supports are greatly acknowledged.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no conflicts of interest.

References

  1. Alshaer, B., Nagarajan, H., Beheshti, H., Lankarani, H., Shivaswamy, S.: Dynamics of a multibody mechanical system with lubricated long journal bearings. J. Mech. Des. 127(3), 493–498 (2005)Google Scholar
  2. Bannwart, A.C., Cavalca, K.L., Daniel, G.B.: Hydrodynamic bearings modeling with alternate motion. Mech. Res. Commun. 37(6), 590–597 (2010)zbMATHGoogle Scholar
  3. Chen, X., Wu, L., Deng, Y., Wang, Q.: Dynamic response analysis and chaos identification of 4-UPS-UPU flexible spatial parallel mechanism. Nonlinear Dyn. 87(4), 2311–2324 (2017)MathSciNetGoogle Scholar
  4. Chen, X., Jiang, S., Deng, Y., Wang, Q.: Dynamics analysis of 2-DOF complex planar mechanical system with joint clearance and flexible links. Nonlinear Dyn. pp. 1–26 (2018)Google Scholar
  5. Daniel, G.B., Cavalca, K.L.: Analysis of the dynamics of a slider–crank mechanism with hydrodynamic lubrication in the connecting rod–slider joint clearance. Mech. Mach. Theory 46(10), 1434–1452 (2011)zbMATHGoogle Scholar
  6. Daniel, G.B., Machado, T.H., Cavalca, K.L.: Investigation on the influence of the cavitation boundaries on the dynamic behavior of planar mechanical systems with hydrodynamic bearings. Mech. Mach. Theory 99, 19–36 (2016)Google Scholar
  7. Erkaya, S.: Clearance-induced vibration responses of mechanical systems: computational and experimental investigations. J. Braz. Soc. Mech. Sci. Eng. 40(2), 90 (2018a)Google Scholar
  8. Erkaya, S.: Experimental investigation of flexible connection and clearance joint effects on the vibration responses of mechanisms. Mech. Mach. Theory 121, 515–529 (2018b)Google Scholar
  9. Flores, P., Lankarani, H.M.: Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. 60(1–2), 99–114 (2010)zbMATHGoogle Scholar
  10. Flores, P., Ambrósio, J., Claro, J.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12(1), 47–74 (2004)zbMATHGoogle Scholar
  11. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H., Koshy, C.: A study on dynamics of mechanical systems including joints with clearance and lubrication. Mech. Mach. Theory 41(3), 247–261 (2006)zbMATHGoogle Scholar
  12. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H., Koshy, C.: Lubricated revolute joints in rigid multibody systems. Nonlinear Dyn. 56(3), 277–295 (2009)zbMATHGoogle Scholar
  13. Flores, P., Machado, M., Silva, M.T., Martins, J.M.: On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst. Dyn. 25(3), 357–375 (2011)zbMATHGoogle Scholar
  14. Frêne, J., Nicolas, D., Degueurce, B., Berthe, D., Godet, M.: Hydrodynamic Lubrication: Bearings and Thrust Bearings. Elsevier, Amsterdam (1997)zbMATHGoogle Scholar
  15. Gao, X., Niu, J., Liu, Z., Tian, J.: Semi-active control of ambulance stretcher system based on parallel mechanism with mr dampers and perturbation analysis. Int. J. Mech. Mater. Design (2019).  https://doi.org/10.1007/s10999-019-09444-2 Google Scholar
  16. Jawale, H., Thorat, H.: Investigation of positional error in two degree of freedom mechanism with joint clearance. J. Mech. Robot. 4(1), 011002 (2012)Google Scholar
  17. Li, P., Chen, W., Li, D., Yu, R.: A novel transition model for lubricated revolute joints in planar multibody systems. Multibody Syst. Dyn. 36(3), 279–294 (2016)MathSciNetzbMATHGoogle Scholar
  18. Machado, M., Costa, J., Seabra, E., 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)Google Scholar
  19. Pinkus, O., Sternlicht, S.: Theory of Hydrodynamic Lubrication. McGraw-Hill, New York (1961)zbMATHGoogle Scholar
  20. Reis, V.L., Daniel, G.B., Cavalca, K.L.: Dynamic analysis of a lubricated planar slider-crank mechanism considering friction and hertz contact effects. Mech. Mach. Theory 74, 257–273 (2014)Google Scholar
  21. Song, Z., Yang, X., Li, B., Xu, W., Hu, H.: Modular dynamic modeling and analysis of planar closed-loop mechanisms with clearance joints and flexible links. Proc. Inst. Mech. Eng C: J. Mech. Eng. Sci. 231(3), 522–540 (2017)Google Scholar
  22. Sun, D.: Tracking accuracy analysis of a planar flexible manipulator with lubricated joint and interval uncertainty. J. Comput. Nonlinear Dyn. 11(5), 051024 (2016)Google Scholar
  23. Sun, D., Shi, Y., Zhang, B.: Dynamic analysis of planar mechanisms with fuzzy joint clearance and random geometry. J. Mech. Des. 141(4), 042301 (2019)Google Scholar
  24. Tian, Q., Zhang, Y., Chen, L., Yang, J.J.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60(4), 489–511 (2010)zbMATHGoogle Scholar
  25. Tian, Q., Xiao, Q., Sun, Y., Hu, H., Liu, H., Flores, P.: Coupling dynamics of a geared multibody system supported by elastohydrodynamic lubricated cylindrical joints. Multibody Syst. Dyn. 33(3), 259–284 (2015)MathSciNetGoogle Scholar
  26. Tian, Q., Lou, J., Mikkola, A.: A new elastohydrodynamic lubricated spherical joint model for rigid-flexible multibody dynamics. Mech. Mach. Theory 107, 210–228 (2017)Google Scholar
  27. Tian, Q., Flores, P., Lankarani, H.M.: A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints. Mech. Mach. Theory 122, 1–57 (2018)Google Scholar
  28. Varedi-Koulaei, S., Daniali, H., Farajtabar, M., Fathi, B., Shafiee-Ashtiani, M.: Reducing the undesirable effects of joints clearance on the behavior of the planar 3-RRR parallel manipulators. Nonlinear Dyn. 86(2), 1007–1022 (2016)Google Scholar
  29. Xu, L., Li, Y.: Investigation of joint clearance effects on the dynamic performance of a planar 2-dof pick-and-place parallel manipulator. Robot. Comput. Integr. Manuf. 30(1), 62–73 (2014)MathSciNetGoogle Scholar
  30. Yang, L., Zhang, X., Huang, Y.: Dynamic analysis of open-loop mechanisms with multiple spatial revolute clearance joints. Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 233(2), 593–610 (2019)Google Scholar
  31. Zhang, X., Zhang, X.: A comparative study of planar 3-RRR and 4-RRR mechanisms with joint clearances. Robot. Comput. Integr. Manuf. 40, 24–33 (2016)Google Scholar
  32. Zhang, X., Zhang, X.: Minimizing the influence of revolute joint clearance using the planar redundantly actuated mechanism. Robot. Comput. Integr. Manuf. 46, 104–113 (2017)Google Scholar
  33. Zhang, X., Zhang, X., Chen, Z.: Dynamic analysis of a 3-RRR parallel mechanism with multiple clearance joints. Mech. Mach. Theory 78, 105–115 (2014)Google Scholar
  34. Zhan, Z., Zhang, X., Jian, Z., Zhang, H.: Error modelling and motion reliability analysis of a planar parallel manipulator with multiple uncertainties. Mech. Mach. Theory 124, 55–72 (2018)Google Scholar
  35. Zhan, Z., Zhang, X., Zhang, H., Chen, G.: Unified motion reliability analysis and comparison study of planar parallel manipulators with interval joint clearance variables. Mech. Mach. Theory 138, 58–75 (2019)Google Scholar
  36. Zhang, H., Zhang, X., Zhang, X., Mo, J.: Dynamic analysis of a 3-PRR parallel mechanism by considering joint clearances. Nonlinear Dyn. 90(1), 405–423 (2017)Google Scholar
  37. Zhang, H., Zhang, X., Zhang, X., Zhan, Z.: Dynamic comparison of a 3-degrees-of-freedom parallel manipulator with multiple dry clearance joints and with lubricated joints. In: ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, pp. V04BT06A010–V04BT06A010 (2018)Google Scholar
  38. Zhao, B., Cui, Y., Xie, Y., Zhou, K.: Dynamics and lubrication analyses of a planar multibody system with multiple lubricated joints. Proc. Inst. Mech. Eng. J: J. Eng. Tribol. 232(3), 326–346 (2018)Google Scholar
  39. Zheng, E., Zhu, R., Zhu, S., Lu, X.: A study on dynamics of flexible multi-link mechanism including joints with clearance and lubrication for ultra-precision presses. Nonlinear Dyn. 83(1–2), 137–159 (2016)MathSciNetGoogle Scholar
  40. Zhou, W., Qiu, N., Wang, L., Gao, B., Liu, D.: Dynamic analysis of a planar multi-stage centrifugal pump rotor system based on a novel coupled model. J. Sound Vib. 434, 237–260 (2018)Google Scholar
  41. Zhu, B., Zhang, X., Zhang, H., Liang, J., Zang, H., Li, H., Wang, R.: Design of compliant mechanisms using continuum topology optimization: A review. Mech. Mach. Theory 143, 103622 (2020)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Guangdong Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive EngineeringSouth China University of TechnologyTianhe DistrictPeople’s Republic of China

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