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Reducing undesirable effects of clearances on dynamic and wear of planar multi-link mechanism

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Abstract

Due to influence of manufacturing accuracy, friction and wear in the working process, the clearance error of the kinematic pair is inevitable. The clearances will lead to impact of response and vibration of mechanism, which not only accelerate wear of clearance joint, but also affect normal operation and precise control of mechanism. Nine-bar mechanism with two revolute pair clearances has been taken as a research object. Aiming at problems of reduced stability, increased noise, aggravated wear, and so on, multi-objective optimization design of multi-link mechanism containing multiple clearances is studied with the help of genetic algorithm. Minimum contact force at clearance joint has been taken as optimization objective function. Influence of clearance on mechanism is reduced by optimizing mass, position of centroid and moment of inertia for key components. The influences of LuGre model and modified Coulomb friction model on dynamical responses of mechanism with clearances are analyzed in detail. Influences of optimization on dynamics responses and nonlinear characteristics of mechanism considering clearances are studied, and nonlinear characteristics are researched by phase diagrams, Poincare maps and bifurcation diagrams. Based on optimized data, ADAMS model is established to verify correctness for dynamics model. At the same time, influences of optimization on dynamics behavior of mechanism considering clearance wear are also analyzed, including wear characteristics, dynamic responses and nonlinear characteristics. The results show that optimization improves dynamics performance of mechanism to a great extent, reduces wear phenomenon and increases stability for mechanism.

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References

  1. 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 

  2. Li, Y.Y., Wang, C., Huang, W.H.: Rigid-flexible-thermal analysis of planar composite solar array with clearance joint considering torsional spring, latch mechanism and attitude controller. Nonlinear Dyn. 96(3), 2031–2053 (2019)

    Google Scholar 

  3. Megahed, S.M., Haroun, A.F.: Analysis of the dynamic behavioral performance of mechanical systems with multi-clearance joints. J. Comput. Nonlinear Dyn. 7, 011002 (2012)

    Google Scholar 

  4. Askari, E., Flores, P., Dabirrahmani, D., Appleyard, R.: Nonlinear vibration and dynamics of ceramic on ceramic artificial hip joints: a spatial multibody modeling. Nonlinear Dyn. 76(2), 1365–1377 (2014)

    Google Scholar 

  5. Akhadkar, N., Acary, V., Brogliato, B.: Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation. Multibody Syst. Dyn. 42(3), 249–282 (2018)

    MATH  Google Scholar 

  6. Isaac, F., Marques, F., Dourado, N., Flores, P.: A finite element model of a 3D dry revolute joint incorporated in a multibody dynamic analysis. Multibody Syst. Dyn. 45(3), 293–313 (2019)

    MathSciNet  Google Scholar 

  7. Guo, J., He, P., Liu, Z., Huang, H.: Investigation of an improved planar revolute clearance joint contact model with rough surface. Tribol. Int. 134, 385–393 (2019)

    Google Scholar 

  8. Erkaya, Selçuk: Experimental investigation of flexible connection and clearance joint effects on the vibration responses of mechanisms. Mech. Mach. Theory 121, 515–529 (2018)

    Google Scholar 

  9. 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 (2016)

    MathSciNet  MATH  Google Scholar 

  10. Xiang, W., Yan, S., Wu, J.: Dynamic analysis of planar mechanical systems considering stick–slip and Stribeck effect in revolute clearance joints. Nonlinear Dyn. 95(1), 321–341 (2018)

    Google Scholar 

  11. Wan, Q., Liu, G., Zhou, Y., Ma, S.J., Tong, R.T.: Numerical and experimental investigation on electromechanical aileron actuation system with joint clearance. J. Mech. Sci. Technol. 33(2), 525–535 (2019)

    Google Scholar 

  12. 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)

    MATH  Google Scholar 

  13. Mukras, S., Kim, N.H., Mauntler, N.A., et al.: Analysis of planar multibody systems with revolute joint wear. Wear 268(5), 643–652 (2010)

    Google Scholar 

  14. Zhu, A.B., He, S.L., Zhao, J.W., Luo, W.C.: A nonlinear contact pressure distribution model for wear calculation of planar revolute joint with clearance. Nonlinear Dyn. 88(1), 315–328 (2017)

    Google Scholar 

  15. Li, Y.Y., Wang, C., Huang, W.H.: Dynamics analysis of planar rigid-flexible coupling deployable solar array system with multiple revolute clearance joints. Mech. Syst. Signal Process. 117, 188–209 (2019)

    Google Scholar 

  16. Tan, H.Y., Hu, Y.J., Li, L.: Effect of friction on the dynamic analysis of slider-crank mechanism with clearance joint. Int. J. Non Linear Mech. 115, 20–40 (2019)

    Google Scholar 

  17. Ma, J., Qian, L., Chen, G., Li, M.: Dynamic analysis of mechanical systems with planar revolute joints with clearance. Mech. Mach. Theory 94, 148–164 (2015)

    Google Scholar 

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

    Google Scholar 

  19. Chen, X.L., Jiang, S., Deng, Y., Wang, Q.: Dynamic modeling and response analysis of a planar rigid-body mechanism with clearance. J. Comput. Nonlinear Dyn. 14, 051004 (2019)

    Google Scholar 

  20. Chen, Y., Sun, Y., Chen, C.: Dynamic analysis of a planar slider–crank mechanism with clearance for a high speed and heavy load press system. Mech. Mach. Theory 98, 81–100 (2016)

    Google Scholar 

  21. Skrinjar, L., Slavič, J., Boltežar, M.: A validated model for a pin-slot clearance joint. Nonlinear Dyn. 88(1), 131–143 (2017)

    Google Scholar 

  22. 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. 28(4), 369–393 (2012)

    MathSciNet  Google Scholar 

  23. Flores, P., Leine, R., Glocker, C.: Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Syst. Dyn. 23(2), 165–190 (2010)

    MathSciNet  MATH  Google Scholar 

  24. Zhang, J., Wang, Q.: Modeling and simulation of a frictional translational joint with a flexible slider and clearance. Multibody Syst. Dyn. 38(4), 367–389 (2016)

    MathSciNet  MATH  Google Scholar 

  25. Chen, X.L., Jiang, S., Deng, Y., Wang, Q.: Dynamics analysis of 2-DOF complex planar mechanical system with joint clearance and flexible links. Nonlinear Dyn. 93(3), 1009–1034 (2018)

    Google Scholar 

  26. Wu, J., Luo, L., Zhu, B., Zhang, N., Xie, M.: Dynamic computation for rigid-flexible multibody systems with hybrid uncertainty of randomness and interval. Multibody Syst. Dyn. (2019). https://doi.org/10.1007/s11044-019-09677-1

    Article  MathSciNet  MATH  Google Scholar 

  27. Ben Abdallah, M.A., Khemili, I., Aifaoui, N.: Numerical investigation of a flexible slider–crank mechanism with multijoints with clearance. Multibody Syst. Dyn. 38(2), 173–199 (2016)

    Google Scholar 

  28. Erkaya, S., Doğan, S., Ulus, Ş.: Effects of joint clearance on the dynamics of a partly compliant mechanism: numerical and experimental studies. Mech. Mach. Theory 88, 125–140 (2015)

    Google Scholar 

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

    Google Scholar 

  30. Rahmanian, S., Ghazavi, M.R.: Bifurcation in planar slider–crank mechanism with revolute clearance joint. Mech. Mach. Theory 91, 86–101 (2015)

    Google Scholar 

  31. Farahan, S.B., Ghazavi, M.R., Rahmanian, S.: Bifurcation in a planar four-bar mechanism with revolute clearance joint. Nonlinear Dyn. 87(2), 955–973 (2016)

    Google Scholar 

  32. Wang, J.: Modified models for revolute joints coupling flexibility of links in multibody systems. Multibody Syst. Dyn. 45(1), 37–55 (2019)

    MathSciNet  Google Scholar 

  33. 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 

  34. Zheng, X., Li, J., Wang, Q., Liao, Q.: A methodology for modeling and simulating frictional translational clearance joint in multibody systems including a flexible slider part. Mech. Mach. Theory 142, 103603 (2019)

    Google Scholar 

  35. Cavalieri, F.J., Cardona, A.: Non-smooth model of a frictionless and dry three-dimensional revolute joint with clearance for multibody system dynamics. Mech. Mach. Theory 121, 335–354 (2018)

    Google Scholar 

  36. Marques, F., Isaac, F., Dourado, N., Flores, P.: An enhanced formulation to model spatial revolute joints with radial and axial clearances. Mech. Mach. Theory 116, 123–144 (2017)

    Google Scholar 

  37. Chen, X., Li, Y., Jia, Y.: Dynamic response and nonlinear characteristics of spatial parallel mechanism with spherical clearance joint. J. Comput. Nonlinear Dyn. 14(4), 041010 (2019)

    Google Scholar 

  38. Bai, Z.F., Jiang, X., Li, F., Zhao, J.J., Zhao, Y.: Reducing undesirable vibrations of planar linkage mechanism with joint clearance. J. Mech. Sci. Technol. 32(2), 559–565 (2018)

    Google Scholar 

  39. Erkaya, S., Uzmay, İ.: A neural–genetic (NN–GA) approach for optimising mechanisms having joints with clearance. Multibody Syst. Dyn. 20(1), 69–83 (2008)

    MathSciNet  MATH  Google Scholar 

  40. Erkaya, S., Uzmay, İ.: Determining link parameters using genetic algorithm in mechanisms with joint clearance. Mech. Mach. Theory 44(1), 222–234 (2009)

    MATH  Google Scholar 

  41. Bai, Z.F., Zhao, J.J., Chen, J., Zhao, Y.: Design optimization of dual-axis driving mechanism for satellite antenna with two planar revolute clearance joints. Acta Astron. 144, 80–89 (2018)

    Google Scholar 

  42. Erkaya, S.: Trajectory optimization of a walking mechanism having revolute joints with clearance using ANFIS approach. Nonlinear Dyn. 71(1–2), 75–91 (2013)

    MathSciNet  Google Scholar 

  43. Sardashti, A., Daniali, H.M., Varedi, S.M.: Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm. Meccanica 48(1), 1681–1693 (2013)

    MATH  Google Scholar 

  44. Varedi, S.M., Daniali, H.M., Dardel, M., Fathi, A.: Optimal dynamic design of a planar slider–crank mechanism with a joint clearance. Mech. Mach. Theory 86, 191–200 (2015)

    Google Scholar 

  45. Sun, D.Y., Shi, Y., Zhang, B.Q.: Robust optimization of constrained mechanical system with joint clearance and random parameters using multi-objective particle swarm optimization. Struct. Multidiscip. Optim. 58(5), 2073–2084 (2018)

    MathSciNet  Google Scholar 

  46. Varedi, S.M., Daniali, H.M., Dardel, M.: Dynamic synthesis of a planar slider–crank mechanism with clearances. Nonlinear Dyn. 79(2), 1587–1600 (2015)

    Google Scholar 

  47. Varedi, S.M., Daniali, H.M., Farajtabar, M., et al.: 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 

  48. Zhao, B., Dai, X.D., Zhang, Z.N., Xie, Y.B.: Numerical study of the effects on clearance joint wear in flexible multibody mechanical systems. Tribol. Trans. 58(3), 385–396 (2015)

    Google Scholar 

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

    MATH  Google Scholar 

  50. Bai, Z.F., Zhang, H.B., Sun, Y.: Wear prediction for dry revolute joint with clearance in multibody system by integrating dynamics model and wear model. Latin Am. J. Solids Struct. 11(14), 2624–2647 (2014)

    Google Scholar 

  51. Li, P., Chen, W., Li, D.S., Yu, R.F., Zhang, W.J.: Wear analysis of two revolute joints with clearance in multibody systems. J. Comput. Nonlinear Dyn. 11, 011099 (2016)

    Google Scholar 

  52. Xiang, W., Yan, S.: Dynamic analysis of space robot manipulator considering clearance joint and parameter uncertainty: modeling, analysis and quantification. Acta Astron. 169, 158–169 (2020)

    Google Scholar 

  53. Alves, J., Peixinho, N., Da Silva, M.T., Flores, P., Lankarani, H.M.: A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids. Mech. Mach. Theory 85, 172–188 (2015)

    Google Scholar 

  54. Chen, X., Gao, W., Deng, Y., Wang, Q.: Chaotic characteristic analysis of spatial parallel mechanism with clearance in spherical joint. Nonlinear Dyn. 94(4), 2625–2642 (2018)

    Google Scholar 

  55. Wang, G., Wang, L.: Dynamics investigation of spatial parallel mechanism considering rod flexibility and spherical joint clearance. Mech. Mach. Theory 137, 83–107 (2019)

    Google Scholar 

  56. Marques, F., Flores, P., Pimenta Claro, J.C., et al.: A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dyn. 86(3), 1407–1443 (2016)

    MathSciNet  Google Scholar 

  57. Marques, F., Isaac, F., Dourado, N., Souto, A.P., Flores, P., Lankarani, H.M.: A study on the dynamics of spatial mechanisms with frictional spherical clearance joints. J. Comput. Nonlinear Dyn. 12(5), 051013 (2017)

    Google Scholar 

  58. Marques, F., Flores, P., Claro, J.C.P., Lankarani, H.M.: Modeling and analysis of friction including rolling effects in multibody dynamics: a review. Multibody Syst. Dyn. 45(2), 223–244 (2019)

    MathSciNet  Google Scholar 

  59. Ambrósio, J., Pombo, J.: A unified formulation for mechanical joints with and without clearances/bushings and/or stops in the framework of multibody systems. Multibody Syst. Dyn. 42(3), 317–345 (2018)

    MathSciNet  MATH  Google Scholar 

  60. Marques, F., Souto, A.P., Flores, P.: On the constraints violation in forward dynamics of multibody systems. Multibody Syst. Dyn. 39(4), 385–419 (2017)

    MathSciNet  MATH  Google Scholar 

  61. Flores, P., Machado, M., Seabra, E., et al.: A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. J. Comput. Nonlinear Dyn. 6(1), 011019 (2011)

    Google Scholar 

  62. Askari, E., Flores, P., Dabirrahmani, D., Appleyard, R.: Dynamic modeling and analysis of wear in spatial hard-on-hard couple hip replacements using multibody systems methodologies. Nonlinear Dyn. 82(1–2), 1039–1058 (2015)

    MathSciNet  Google Scholar 

  63. Lai, X., He, H., Lai, Q., et al.: Computational prediction and experimental validation of revolute joint clearance wear in the low-velocity planar mechanism. Mech. Syst. Signal Process. 85, 963–976 (2017)

    Google Scholar 

  64. Luo, A.C.J., Gegg, B.C.: An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems. Nonlinear Dyn. 49(3), 401–424 (2007)

    MathSciNet  MATH  Google Scholar 

  65. Luo, A.C.J., Xing, S.Y.: Bifurcation trees of period-3 motions to chaos in a time-delayed Duffing oscillator. Nonlinear Dyn. 88(4), 2831–2862 (2017)

    MathSciNet  MATH  Google Scholar 

  66. Luo, A.C.J., Gegg, B.C.: Dynamics of a harmonically excited oscillator with dry-friction on a sinusoidally time-varying, traveling surface. Int. J. Bifurc. Chaos 16(12), 3539–3566 (2006)

    MathSciNet  MATH  Google Scholar 

  67. Gegg, B.C., Luo, A.C.J., Suh, S.C.: Grazing bifurcations of a harmonically excited oscillator moving on a time-varying translation belt. Nonlinear Anal. Real World Appl. 9(5), 2156–2174 (2008)

    MathSciNet  MATH  Google Scholar 

  68. Guo, Y., Luo, A.C.J.: On complex periodic motions and bifurcations in a periodically forced, damped, hardening Duffing oscillator. Chaos Solitons Fractals 81, 378–399 (2015)

    MathSciNet  MATH  Google Scholar 

  69. Guo, Y., Luo, A.C.J.: Parametric analysis of bifurcation and chaos in a periodically driven horizontal impact pair. Int. J. Bifurc. Chaos 22(11), 1250268 (2012)

    MathSciNet  MATH  Google Scholar 

  70. Luo, A.C.J., O’Connor, D.: Periodic and chaotic motions in a gear-pair transmission system with impacts. Nonlinear Sci. Complex. 13–24, (2011). https://doi.org/10.1007/978-90-481-9884-9_2

  71. Guo, Y., Luo, A.C.J.: Periodic motions in a double-well Duffing oscillator under periodic excitation through discrete implicit mappings. Int. J. Dyn. Control 5(2), 223–238 (2015)

    MathSciNet  Google Scholar 

  72. Luo, A.C.J., Gegg, B.C.: Periodic motions in a periodically forced oscillator moving on an oscillating belt with dry friction. J. Comput. Nonlinear Dyn. 1(3), 212–220 (2006)

    Google Scholar 

  73. Guo, Y., Luo, A.C.J.: Routes of periodic motions to chaos in a periodically forced pendulum. Int. J. Dyn. Control 5(3), 551–569 (2016)

    MathSciNet  Google Scholar 

  74. Luo, A.C.J., O’Connor D.: Stable and unstable periodic solutions to the Mathieu–Duffing oscillator. In: 2012 IEEE 4th International Conference on Nonlinear Science and Complexity (NSC). IEEE (2012)

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Acknowledgements

This work was supported by Shandong Key Research and Development Public Welfare Program (2019GGX104011), Natural Science Foundation of Shandong Province (Grant No. ZR2017MEE066).

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

    Shuai Jiang & Xiulong Chen

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

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