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An approach for dynamic analysis of planar multibody systems with revolute clearance joints

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Abstract

Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic performance of mechanism, namely noise, vibration and fatigue failure. This paper presents the development of a dynamic model for planar multibody systems with clearance joints. Based on the continuous contact law, the contact force model proposed by Lankarani and Nikravesh is employed to describe the contact–impact phenomenon between pin and hole. And, the incorporation of the friction influence on revolute joint clearance is conducted by a modified friction force model. According to the geometric relationship between contact elements, the kinematics of the multibody systems is mapped into the global coordinate systems. Additionally, an experimental test platform is set up whereby a slider–crank mechanism with two clearance joints is used as an example to demonstrate the correctness and effectiveness of the proposed approach. Finally, the effects of joint clearance on the dynamic characteristics of planar multibody systems are investigated.

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References

  1. Ahmad A, Andersson K, Sellgren U (2014) A stiffness modeling methodology for simulation-driven design of haptic devices. Eng Comput 30(1):125–141

    Google Scholar 

  2. Bellary SAI, Samad A, Couckuyt I (2016) Acomparative study of kriging variants for the optimization of a turbomachinery system. Eng Comput 32(1):49–59

    Google Scholar 

  3. Wang Q, Tian Q, Hu H (2014) Dynamic simulation of frictional contacts of thin beams during large overall motions via absolute nodal coordinate formulation. Nonlinear Dyn 77:1411–1425

    MathSciNet  Google Scholar 

  4. Erkaya S, Dogan S (2015) A comparative analysis of joint clearance effects on articulated and partly compliant mechanisms. Nonlinear Dyn 81:323–341

    Google Scholar 

  5. Kortelainen J, Mikkola A (2015) Semantic restrictions and rules in applications of multibody dynamics. Eng Comput 31(1):85–97

    Google Scholar 

  6. Wang Q, Tian Q, Hu H (2016) Dynamic simulation of frictional multi-zone contacts of thin beams. Nonlinear Dyn 83:1919–1937

    Google Scholar 

  7. Zheng EL, Zhou XL (2014) Modeling and simulation of flexible slider-crank mechanism with clearance for closed high speed press system. Mech Mach Theory 74:10–30

    Google Scholar 

  8. Naeeni IP, Keshavarzi A, Fattahi I (2018) Parametric study on the geometric and kinetic aspects of the slider-crank mechanism. Iran J Sci Technol Trans Mech Eng 77:405–417

    Google Scholar 

  9. Lankarani HM, Nikravesh PE (1994) Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn 5:193–207

    Google Scholar 

  10. Bauchau OA, Rodriguez J (2002) Modeling of joints with clearance in flexible multi-body systems. Int J Solids Struct 39(1):41–63

    MATH  Google Scholar 

  11. Pérez-González A, Fenollosa-Esteve C, Sancho-Bru JL (2008) A modified elastic foundation contact model for application in 3D models of the prosthetic knee. Med Eng Phys 30(3):387–398

    Google Scholar 

  12. Flores P, Ambrósio J (2010) On the contact detection for contact-impact analysis in multibody systems. Multibody Syst Dyn 24(1):103–122

    MathSciNet  MATH  Google Scholar 

  13. Machado M, Flores P, Ambrósio J, Completo A (2011) Influence of the contact model on the dynamic response of the human knee joint. Proc Inst Mech Eng Part K J Multi-body Dyn 225(4):344–358

    Google Scholar 

  14. Muvengei O, Kihiu J, Ikua B (2012) Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints. Multibody Syst Dyn 28(4):369–393

    MathSciNet  Google Scholar 

  15. Bai ZF, Zhao Y (2012) Dynamic behaviour analysis of planar mechanical systems with clearance in revolute joints using a new hybrid contact force model. Int J Mech Sci 54(1):190–205

    Google Scholar 

  16. Bai ZF, Zhao Y (2013) A hybrid contact force model of revolute joint with clearance for planar. Int J Nonlinear Mech 48:15–36

    Google Scholar 

  17. Wang Y, Li FM (2015) Nonlinear dynamics modeling and analysis of two rods connected by a joint with clearance. Appl Math Model 39:2518–2527

    MathSciNet  MATH  Google Scholar 

  18. Qi ZH, Wang G, Zhang ZG (2015) Contact analysis of deep groove ball bearings in multibody systems. Multibody Syst Dyn 33(2):115–141

    MathSciNet  MATH  Google Scholar 

  19. Ma J, Qian LF, Chen GS (2015) Dynamic analysis of mechanical systems with planar revolute joints with clearance. Mech Mach Theory 94:148–164

    Google Scholar 

  20. Tian Q, Xiao Q, Sun Y, Hu HY, Flores P (2015) Coupling dynamics of a geared multibody system supported by elastohydrodynamic lubricated cylindrical joints. Multibody Syst Dyn 33:259–284

    MathSciNet  Google Scholar 

  21. Tian Q, Lou J, Mikkola A (2017) A new elastohydrodynamic lubricated spherical joint model for rigid-flexible multibody dynamics. Mech Mach Theory 107:210–228

    Google Scholar 

  22. Shi X, Polycarpou AA (2005) Measurement and modeling of normal contact stiffness and contact damping at the meso scale. J Vibr Acoust 127:52–60

    Google Scholar 

  23. Akhadkar N, Acary V, Brogliato B (2017) 3D revolute joint with clearance in multibody systems. In: 7th International workshop on computational kinematics. Springer, France

  24. Haines RS (1985) An experimental investigation into the dynamic behaviour of revolute joints with varying degrees of clearance. Mech Mach Theory 20(3):221–231

    Google Scholar 

  25. Bouyer J, Fillon M (2002) An experimental analysis of misalignment effects on hydrodynamic plain journal bearing performances. J Tribol 124:313–319

    Google Scholar 

  26. Xu NN, Tang WC, Chen YJ (2015) Modeling analysis and experimental study for the friction of a ball screw. Mech Mach Theory 87:57–69

    Google Scholar 

  27. Akhadkar N, Acary V, Brogliato B (2017) Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation. Multibody Syst Dyn 2:1–34

    MATH  Google Scholar 

  28. Jayaprakash G, Thilak M, Sivakumar K (2014) Optimal tolerance design for mechanical assembly considering thermal impact. Int J Adv Manuf Technol 73:859–873

    Google Scholar 

  29. Bai ZF, Zhao Y, Chen J (2013) Dynamics analysis of planar mechanical system considering revolute clearance joint wear. Tribol Int 64:85–95

    Google Scholar 

  30. Schwab AL, Meijaard JP, Meijers P (2002) A comparison of revolute joint clearance model in the dynamic analysis of rigid and elastic mechanical systems. Mech Mach Theory 37(9):895–913

    MATH  Google Scholar 

  31. Flores P, Ambrósio J (2004) Revolute joints with clearance in multibody systems. Comput Struct 82(17–19):1359–1369

    Google Scholar 

  32. Flores P, Ambrósio JAC, Claro JCP, Lankarani HM (2006) Influence of the contact-impact force model on the dynamic response of multibody systems. Proc Inst Mech Eng Part K J Multi-body Dyn 220(1):21–34

    Google Scholar 

  33. Muvengei O, Kihiu J, Ikua B (2012) 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

    Google Scholar 

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

    MathSciNet  Google Scholar 

  35. Tian Q, Sun Y, Liu C, Hu HY, Flores P (2013) Elastohydrodynamic lubricated cylindrical joints for rigid–flexible multibody dynamics. Comput Struct 114:106–120

    Google Scholar 

  36. Wang Z, Tian Q, Hu HY, Flores P (2016) Nonlinear dynamics and chaotic control of planar flexible multibody systems with interval clearance size joint. Nonlinear Dyn 86(3):1571–1597

    Google Scholar 

  37. Zhao B, Zhou K, Xie YB (2016) A new numerical method for planar multibody system with mixed lubricated revolute joint. Int J Mech Sci 113:105–119

    Google Scholar 

  38. Xu LX, Han YC (2016) A method for contact analysis of revolute joints with noncircular clearance in a planar multibody system. Proc Inst Mech Eng Part K J Multi-body Dyn 230(4):589–605

    Google Scholar 

  39. Ma J, Qian LF (2017) Modeling and simulation of planar multibody systems considering multiple revolute clearance joints. Nonlinear Dyn 90:1907–1940

    Google Scholar 

  40. Tan HY, Hu YJ, Li L (2017) A continuous analysis method of planar rigid-body mechanical systems with two revolute clearance joints. Multibody Syst Dyn 40:347–373

    MathSciNet  MATH  Google Scholar 

  41. Li YY, Wang ZL, Wang C, Huang WH (2018) Planar rigid-flexible coupling spacecraft modeling and control considering solar array deployment and joint clearance. Acta Astronaut 142:138–151

    Google Scholar 

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

    MATH  Google Scholar 

  43. Flores P, Koshy CS, Lankarani HM (2011) Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn 65(4):383–398

    Google Scholar 

  44. Crowther AR, Singh R, Zhang N, Chapman C (2007) Impulsive response of an automatic transmission system with multiple clearances: formulation, simulation and experiment. J Sound Vib 306(3):444–466

    Google Scholar 

  45. Koshy CS, Flores P, Lankarani HM (2013) Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches. Nonlinear Dyn 73:325–338

    Google Scholar 

  46. Lai X, He H, Lai Q, Wang C, Yang J, Zhang Y (2017) Computational prediction and experimental validation of revolute joint clearance wear in the low-velocity planar mechanism. Mech Syst Signal Process 85:963–976

    Google Scholar 

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

    Google Scholar 

  48. Zheng EL, Jia F, Sha HW, Shi JF (2012) Non-circular belt transmission design of mechanical press. Mech Mach Theory 57:126–138

    Google Scholar 

  49. Daniel GB, Cavalca KL (2011) Analysis of the dynamics of a slider-crank mechanism with hydrodynamic lubrication in the connecting rod-slider joint. Mech Mach Theory 46:1434–1452

    MATH  Google Scholar 

  50. Xiao MH, Geng GS, Li GH, Li H (2017) Analysis on dynamic precision reliability of high-speed precision press based on Monte Carlo method. Nonlinear Dyn 90:2979–2988

    Google Scholar 

  51. Chen GL, Wang H, Lin ZQ (2013) A unified approach to the accuracy analysis of planar parallel manipulators both with input uncertainties and joint clearance. Mech Mach Theory 64:1–17

    Google Scholar 

  52. Reis VL, Daniel GB, Cavalca KL (2014) Dynamic analysis of a lubricated planar slider-crank mechanism considering friction and Hertz contact effects. Mech Mach Theory 74:257–273

    Google Scholar 

  53. Gummer A, Sauer B (2014) Modeling planar slider-crank mechanisms with clearance joints in RecurDyn. Multibody Syst Dyn 31:127–145

    Google Scholar 

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

    Google Scholar 

  55. Flores P, Machado M, Silva MT, Martins JM (2011) On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst Dyn 25(3):357–375

    MATH  Google Scholar 

  56. Flores P, Lankarani HM (2012) Dynamic response of multibody systems with multiple clearance joints. J Comput Nonlinear Dyn 7(3):031003–031013

    Google Scholar 

  57. Zheng EL, Jia F, Zhou SH (2014) Thermal modeling and characteristics analysis of the high speed press system. Int J Mach Tool Manuf 85:87–99

    Google Scholar 

  58. Zhong GY, Wang CQ, Yang SF, Zheng EL (2015) Position geometric error modeling, identification and compensation for large 5-axis machining center prototype. Int J Mach Tool Manuf 89:142–150

    Google Scholar 

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

    Google Scholar 

  60. Zheng EL, Zhu R, Zhu SH, Lu XJ (2016) A study on dynamics of flexible multi-link mechanism including joints with clearance and lubrication for ultra-precision presses. Nonlinear Dyn 83:137–159

    MathSciNet  Google Scholar 

  61. Alves J, Peixinho N, Silva MTD, Flores P (2015) A comparative study on the viscoelastic constitutive laws for frictionless contact interfaces in multibody dynamics. Mech Mach Theory 85:172–188

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  63. Erkaya S (2012) Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network. J Mech Sci Technol 26:1419–1430

    Google Scholar 

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Acknowledgments

This work is supported by the “National Natural Science Foundation of China (Nos. 51605208 and 11902161)”, “Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 19KJB460001)” and “The Talent Introduction Foundation of Jiangsu University of Technology (No. KYY18016)”.

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Authors and Affiliations

  1. School of Mechanical Engineering, Jiangsu University of Technology, Changzhou, 213001, China

    Yu Chen & Chengtao Yu

  2. National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, 210094, China

    Jun Feng & Xu Peng

  3. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yu Chen, Jun Feng, Yu Sun & Qiang He

  4. School of Mechanical Engineering, Jiangsu University of Science and Technology, Zhenjiang, 212000, China

    Qiang He

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  1. Yu Chen
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Correspondence to Qiang He.

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Chen, Y., Feng, J., Peng, X. et al. An approach for dynamic analysis of planar multibody systems with revolute clearance joints. Engineering with Computers 37, 2159–2172 (2021). https://doi.org/10.1007/s00366-020-00935-x

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