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Experimental research and dynamics analysis of multi-link rigid–flexible coupling mechanism with multiple lubrication clearances

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Abstract

Clearance joint and component flexibility are the key factors affecting the dynamic performance of mechanisms. Lubrication clearance joint can effectively improve dynamic responses and slow down collision and wear of the clearance joint. There are few researches on dynamic of planar complex multi-link mechanism considering the coupling action of clearance, lubrication, and elasticity of member. In this paper, the 2-DOF nine-bar mechanism which can be used as the main transmission mechanism of hybrid-driven multi-link press was taken as the research object. Considering the coupling action of lubrication clearance and element flexibility, a dynamic model of rigid–flexible coupling multi-link mechanism (RFC-MLM) with multiple lubrication clearances was established. Influences of lubrication clearances on dynamic of rigid/rigid–flexible coupling mechanisms were investigated. Effects of dry friction/lubrication clearances on the dynamics of the RFC-MLM were also studied. The influences of dynamic viscosity, clearance value, driving velocity, and cross-sectional dimension on the dynamics of the RFC-MLM were comprehensively analyzed. A 2-DOF nine-bar mechanism test platform containing multiple lubrication clearances was constructed to verify the correctness of theoretical model.

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Data used to support the findings of this study are included within the article.

References

  1. Zheng, E., Wang, T., Guo, J., Zhu, Y., Lin, X., Wang, Y., Kang, M.: Dynamic modeling and error analysis of planar flexible multilink mechanism with clearance and spindle-bearing structure. Mech Mach Theory. 131, 234–260 (2019). https://doi.org/10.1016/j.mechmachtheory.2018.09.023

    Article  Google Scholar 

  2. Etesami, G., Felezi, M.E., Nariman-Zadeh, N.: Optimal transmission angle and dynamic balancing of slider-crank mechanism with joint clearance using Pareto Bi-objective Genetic Algorithm. J Braz Soc Mech Sci. 43(4), 185 (2021). https://doi.org/10.1007/S40430-021-02834-8

    Article  Google Scholar 

  3. Xiang, W., Yan, S., Wu, J., Niu, W.: Dynamic response and sensitivity analysis for mechanical systems with clearance joints and parameter uncertainties using Chebyshev polynomials method. Mech Syst Signal Pr. 138, 106596 (2020). https://doi.org/10.1016/j.ymssp.2019.106596

    Article  Google Scholar 

  4. Zheng, Y., Yang, C., Wan, H., Luo, Y., Yu, Y.: Dynamics analysis of spatial mechanisms with dry spherical joints with clearance using finite particle method. Int J Struct Stab Dy 20(3), 2050035 (2020). https://doi.org/10.1142/S0219455420500352

    Article  MathSciNet  Google Scholar 

  5. Qian, M., Qin, Z., Yan, S., Zhang, L.: A comprehensive method for the contact detection of a translational clearance joint and dynamic response after its application in a crank-slider mechanism. Mech Mach Theory. 145, 103717 (2020). https://doi.org/10.1016/j.mechmachtheory.2019.103717

    Article  Google Scholar 

  6. Wang, J.: Modified models for revolute joints coupling flexibility of links in multibody systems. Multibody Syst Dyn. 45(1), 37–55 (2019). https://doi.org/10.1007/s11044-018-9616-9

    Article  MathSciNet  Google Scholar 

  7. Tan, X., Chen, G., Shao, H.: Modeling and analysis of spatial flexible mechanical systems with a spherical clearance joint based on the LuGre friction model. J Comput Nonlin Dyn. 15(1), 011005 (2020). https://doi.org/10.1115/1.4045240

    Article  Google Scholar 

  8. Li, Y., Wang, C., Huang, W.: Rigid-flexible-thermal analysis of planar composite solar array with clearance joint considering torsional spring, latch mechanism and attitude controller. Nonlinear Dynam. 96(3), 2031–2053 (2019). https://doi.org/10.1007/s11071-019-04903-z

    Article  Google Scholar 

  9. Miao, H., Li, B., Liu, J., He, A., Zhu, S.: Effects of revolute clearance joint on the dynamic behavior of a planar space arm system. Proc Inst Mech Eng Part G: J Aerosp Eng 233(5), 1629–1644 (2019). https://doi.org/10.1177/0954410018760024

    Article  Google Scholar 

  10. Reis, V.L., Daniel, G.B., Ca Valca, K.L.: Dynamic analysis of a lubricated planar slider-crank mechanism considering friction and Hertz contact effects. Mech Mach Theory 74(6), 257–273 (2014). https://doi.org/10.1016/j.mechmachtheory.2013.11.009

    Article  Google Scholar 

  11. 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 Dynam. 64(1–2), 25–47 (2011). https://doi.org/10.1007/s11071-010-9843-y

    Article  MATH  Google Scholar 

  12. Tan, H., Hu, Y., Li, L.: A continuous analysis method of planar rigid-body mechanical systems with two revolute clearance joints. Multibody Syst Dyn. 40(4), 347–373 (2017). https://doi.org/10.1007/s11044-016-9562-3

    Article  MathSciNet  MATH  Google Scholar 

  13. Xiang, W., Yan, S., Wu, J.: Dynamic analysis of planar mechanical systems considering stick-slip and Stribeck effect in revolute clearance joints. Nonlinear Dynam. 95(1), 321–341 (2018). https://doi.org/10.1007/s11071-018-4566-6

    Article  Google Scholar 

  14. Chen, K., Zhang, G., Wu, R., Wang, L., Zheng, H., Chen, S.: Dynamic analysis of a planar hydraulic rock-breaker mechanism with multiple clearance joints. Shock Vib. 2019, 4718456 (2019). https://doi.org/10.1155/2019/4718456

    Article  Google Scholar 

  15. Salahshoor, E., Ebrahimi, S., Zhang, Y.: Frequency analysis of a typical planar flexible multibody system with joint clearances. Mech Mach Theory. 126, 429–456 (2018). https://doi.org/10.1016/j.mechmachtheory.2018.04.027

    Article  Google Scholar 

  16. Erkaya, S., Dogan, S.: A comparative analysis of joint clearance effects on articulated and partly compliant mechanisms. Nonlinear Dynam. 81(1–2), 323–341 (2015). https://doi.org/10.1007/s11071-015-1994-4

    Article  Google Scholar 

  17. Zhang, T., Liu, G., Wang, X., Ma, S.: Dynamic analysis of planar multibody system with a lubricated revolute clearance joint using an improved transition force model. Adv Mech Eng 9(12), 168781401774408 (2017). https://doi.org/10.1177/1687814017744086

    Article  Google Scholar 

  18. Fang, C., Meng, X., Lu, Z., Wu, G., Tang, D., Zhao, B.: Modeling a lubricated full-floating pin bearing in planar multibody systems. Tribol Int. 113, 222–237 (2019). https://doi.org/10.1016/j.triboint.2018.10.045

    Article  Google Scholar 

  19. Flores, P., Lankarani, H.M.: Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dynam. 60(1), 99–114 (2010). https://doi.org/10.1007/s11071-009-9583-z

    Article  MATH  Google Scholar 

  20. Krinner, A., Rixen, D.: Interface reduction methods for mechanical systems with elastohydrodynamic lubricated revolute joints. Multibody Syst Dyn. 42, 79–96 (2018). https://doi.org/10.1007/s11044-017-9575-6

    Article  MathSciNet  MATH  Google Scholar 

  21. Sun, D.: Tracking accuracy analysis of a planar flexible manipulator with lubricated joint and interval uncertainty. J Comput Nonlin Dyn. 11(5), 051024 (2016). https://doi.org/10.1115/1.4033609

    Article  Google Scholar 

  22. 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 Dynam. 83(1–2), 137–159 (2016). https://doi.org/10.1007/s11071-015-2315-7

    Article  MathSciNet  Google Scholar 

  23. Li, Y., Yang, Y., Li, M., Huang, Y.: Dynamics analysis and wear prediction of rigid-flexible coupling deployable solar array system with clearance joints considering solid lubrication. Mech Syst Signal Pr. 162(7–8), 108059 (2022). https://doi.org/10.1016/j.ymssp.2021.108059

    Article  Google Scholar 

  24. Zheng, E., Chu, L., Jiang, S., Zhu, S., Kang, M., Shi, J.: Multi-body dynamic modeling and error analysis of planar flexible multi-link mechanism with lubricated revolute clearance joints and crankshaft-bearing structure. J Mech Eng-En. 56(3), 106–120 (2020). https://doi.org/10.3901/JME.2020.03.106

    Article  Google Scholar 

  25. Zhang, H., Zhang, X., Zhan, Z., Yang, L.: Dynamic modeling and comparative analysis of a 3-PRR parallel robot with multiple lubricated joints. Int J Mech Mater Des. 16(3), 541–555 (2020). https://doi.org/10.1007/s10999-019-09479-5

    Article  Google Scholar 

  26. Ahmedalbashir, M., Romdhane, L., Lee, J.: Dynamics of a four-bar mechanism with clearance and springs—modeling and experimental analysis. J Mech Sci Technol. 31(3), 1023–1033 (2017). https://doi.org/10.1007/s12206-017-0201-6

    Article  Google Scholar 

  27. Li, X., Zhao, D., Xie, F., Wu, S., Li, X.: Experimental investigations of the dynamic responses of a multi-link mechanism with revolute clearance joints. Adv Mech Eng. 13(4), 1–10 (2021). https://doi.org/10.1177/16878140211012541

    Article  Google Scholar 

  28. Chen, Y., Feng, J., He, Q., Wang, Y., Yu, C.: A methodology for dynamic behavior analysis of the slider-crank mechanism considering clearance joint. Int J Nonlin Sci Num. 22(3–4), 373–390 (2021). https://doi.org/10.1515/ijnsns-2018-0307

    Article  MathSciNet  MATH  Google Scholar 

  29. Li, H., Xie, J., Wei, W.: Numerical and dynamic errors analysis of planar multibody mechanical systems with adjustable clearance joints based on Lagrange equations and experiment. J Comput Nonlin Dyn. 15, 081001 (2020). https://doi.org/10.1115/1.4047135

    Article  Google Scholar 

  30. Zhu, C., Katupitiya, J., Wang, J.: Effect of links deformation on motion precision of parallel manipulator based on flexible dynamics. Ind Robot. 44(6), 776–787 (2017). https://doi.org/10.1108/IR-12-2016-0368

    Article  Google Scholar 

  31. Zhuang, X., Afshari, S., Yu, Y., Liang, X.: A hybrid model for wear prediction of a single revolute joint considering a time-varying lubrication condition. Wear (2020). https://doi.org/10.1016/j.wear.2019.203124

    Article  Google Scholar 

  32. Wang, X., Liu, G., Ma, S., Tong, R.: Study on dynamic responses of planar multibody systems with dry revolute clearance joint: Numerical and experimental approaches-ScienceDirect. J Sound Vib 438, 116–138 (2019). https://doi.org/10.1016/j.jsv.2018.08.052

    Article  Google Scholar 

  33. 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[J]. Mech Mach Theory. 122, 1–57 (2018). https://doi.org/10.1016/j.mechmachtheory.2017.12.002

    Article  Google Scholar 

  34. Chen, X., Jiang, S., Wang, S., Deng, Y.: Dynamics analysis of planar multi-DOF mechanism with multiple revolute clearances and chaos identification of revolute clearance joints. Multibody Syst Dyn. 47, 317–345 (2019). https://doi.org/10.1007/s11044-018-09654-0

    Article  MathSciNet  MATH  Google Scholar 

  35. 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). https://doi.org/10.1023/B:MUBO.0000042901.74498.3a

    Article  MATH  Google Scholar 

  36. Jiang, S., Chen, X.: Reducing undesirable effects of clearances on dynamic and wear of planar multi-link mechanism. Nonlinear Dynam. 100, 1173–1201 (2020). https://doi.org/10.1007/s11071-020-05591-w

    Article  Google Scholar 

  37. Zhao, B., Cui, Y., Xie, Y., Zhou, K.: Dynamics and lubrication analyses of a planar multibody system with multiple lubricated joints[J]. P I Mech Eng J-J Eng. 232(3), 326–346 (2018). https://doi.org/10.1177/1350650117713891

    Article  Google Scholar 

  38. 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. Nonlin Dyn. 69(1–2), 635–654 (2012). https://doi.org/10.1007/s11071-011-0293-y

    Article  Google Scholar 

  39. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S.: Lubricated revolute joints in rigid multibody systems. Nonlinear Dynam. 56(3), 277–295 (2009). https://doi.org/10.1007/s11071-008-9399-2

    Article  MATH  Google Scholar 

  40. Pinkus, O., Sternlicht, S.A.: Theory of hydrodynamic lubrication. McGraw-Hill, New York (1961)

    MATH  Google Scholar 

  41. Jiang, S. Dynamic modeling and analysis of planar multi-link mechanism considering lubrication clearance and flexible components, Shandong University of Science and Technology, Qing Dao (2021)

  42. Tian, Q., Zhang, Y., Chen, L.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dynam. 60(4), 489–511 (2010). https://doi.org/10.1007/s11071-009-9610-0

    Article  MATH  Google Scholar 

  43. Berzeri, M., Shabana, A.: Development of simple models for the elastic force in the absolute nodal coordinate formulation. J Sound Vib 235(4), 539–565 (2000). https://doi.org/10.1006/jsvi.1999.2935

    Article  Google Scholar 

  44. Li, Y., Wang, C., Huang, W.: Dynamics analysis of planar rigid-flexible coupling deployable solar array system with multiple revolute clearance joints[J]. Mech Syst Signal Pr. 117, 188–209 (2019). https://doi.org/10.1016/j.ymssp.2018.07.037

    Article  Google Scholar 

  45. Li, Y. Study of rigid flexible coupling multibody dynamics of solar array considering joint clearance, Harbin Institute of Technology, Harbin, (2019)

  46. Li, Y., Chen, G., Sun, D., Gao, Y., Wang, K.: Dynamic analysis and optimization design of a planar slider-crank mechanism with flexible components and two clearance joints. Mech Mach Theory. 99, 37–57 (2016). https://doi.org/10.1016/j.mechmachtheory.2015.11.018

    Article  Google Scholar 

  47. Jiang, S., Chen, X.: Test study and nonlinear dynamic analysis of planar multi-link mechanism with compound clearances. Eur J Mech A-Solid 88, 104260 (2021). https://doi.org/10.1016/j.euromechsol.2021.104260

    Article  MathSciNet  MATH  Google Scholar 

  48. Song, H. Mechanical analysis of a novel and multi-link mechanical press mechanism, Shandong University of Science and Technology, Qing Dao (2018)

  49. Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput Method Appl M. 1(1), 1–16 (1972). https://doi.org/10.1016/0045-7825(72)90018-7

    Article  MathSciNet  MATH  Google Scholar 

  50. Cui, M. Study on dynamic characteristics of spatial parallel mechanism considering spherical joint clearance and component flexibility effect, Shandong University of Science and Technology, Qing Dao (2021)

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Acknowledgements

This paper is supported by the Natural Science Foundation of Shandong Province ZR2022QE022.

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Authors and Affiliations

  1. Department of Electrical and Information, Shandong University of Science and Technology, Jinan, 250031, Shandong, China

    Shuai Jiang

  2. Swinburne College, Shandong University of Science and Technology, Jinan, 250031, Shandong, China

    Jianan Liu, Yuanpeng Lin & Maoran Zhao

  3. College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Yang Yang

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Correspondence to Yang Yang.

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Appendix

Appendix

When lubrication clearances A and B are both considered, the constraint equation of the entire system is as follows:

$${\varvec{\varPhi}}\left( {{\varvec{q}},t} \right) = \left( \begin{gathered} q_{1(1)} - L_{s1} \cos (q_{1(3)} ) \hfill \\ q_{1(2)} - L_{s1} \sin (q_{1(3)} ) \hfill \\ q_{{2(5)}}^{{1}} - q_{{2(1)}}^{{2}} \hfill \\ q_{{2(6)}}^{{1}} - q_{{2(2)}}^{{2}} \hfill \\ \vdots \hfill \\ q_{{2(5)}}^{{n_{2} - 1}} - q_{{2(1)}}^{{n_{2} }} \hfill \\ q_{{2(6)}}^{{n_{2} - 1}} - q_{{2(2)}}^{{n_{2} }} \hfill \\ q_{7(1)} - L_{s72} \cos (q_{7(3)} - \beta_{1} - \pi ) - q_{{2(5)}}^{{n_{2} }} \hfill \\ q_{7(2)} - L_{s72} \sin (q_{7(3)} - \beta_{1} - \pi ) - q_{{2(6)}}^{{n_{2} }} \hfill \\ q_{7(1)} - L_{s72} \cos (q_{7(3)} - \beta_{1} - \pi ) - q_{{3(5)}}^{{n_{3} }} \hfill \\ q_{7(2)} - L_{s72} \sin (q_{7(3)} - \beta_{1} - \pi ) - q_{{3(6)}}^{{n_{3} }} \hfill \\ q_{4(1)} - L_{{s{4}}} \cos (q_{4(3)} ) \hfill \\ q_{4(2)} - L_{{s{4}}} \sin (q_{4(3)} ) + L_{5} \hfill \\ q_{{3(5)}}^{{1}} - q_{{3(1)}}^{{2}} \hfill \\ q_{{3(6)}}^{{1}} - q_{{3(2)}}^{{2}} \hfill \\ \vdots \hfill \\ q_{{3(5)}}^{{n_{{3}} - 1}} - q_{{3(1)}}^{{n_{{3}} }} \hfill \\ q_{{3(6)}}^{{n_{{3}} - 1}} - q_{{3(2)}}^{{n_{{3}} }} \hfill \\ q_{6(1)} - L_{{s{6}}} \cos (q_{6(3)} ) - H_{x} \hfill \\ q_{6(2)} - L_{{s{6}}} \sin (q_{6(3)} ) - H_{y} \hfill \\ q_{6(1)} { + }L_{s6} \cos (q_{6(3)} ) - q_{7(1)} + L_{s71} \cos (q_{7(3)} + \beta ) \hfill \\ q_{6(2)} { + }L_{s6} \sin (q_{6(3)} ) - q_{7(2)} + L_{s71} \sin (q_{7(3)} + \beta ) \hfill \\ q_{7(1)} + L_{s73} \cos (q_{7(3)} + \beta_{12} + \omega_{12} ) - q_{{8(1)}}^{{n_{{8}} }} \hfill \\ q_{7(2)} + L_{s73} \sin (q_{7(3)} + \beta_{12} + \omega_{12} ) - q_{{8(2)}}^{{n_{{8}} }} \hfill \\ q_{9(1)} - q_{{8(5)}}^{{n_{{8}} }} \hfill \\ q_{9(2)} - q_{{8(6)}}^{{n_{{8}} }} \hfill \\ q_{{8(5)}}^{{1}} - q_{{8(1)}}^{{2}} \hfill \\ q_{{8(6)}}^{{1}} - q_{{8(2)}}^{{2}} \hfill \\ \vdots \hfill \\ q_{{8(5)}}^{{n_{{8}} - 1}} - q_{{8(1)}}^{{n_{{8}} }} \hfill \\ q_{{8(6)}}^{{n_{{8}} - 1}} - q_{{8(2)}}^{{n_{{8}} }} \hfill \\ q_{{1(3)}} - \omega_{1} t - 5.7645 \hfill \\ q_{{4(3)}} - \omega_{4} t + 2.4934 \hfill \\ \end{gathered} \right) = {\mathbf{0}}$$
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Jiang, S., Liu, J., Yang, Y. et al. Experimental research and dynamics analysis of multi-link rigid–flexible coupling mechanism with multiple lubrication clearances. Arch Appl Mech 93, 2749–2780 (2023). https://doi.org/10.1007/s00419-023-02405-4

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