Dynamic modelling and properties analysis of 3RSR parallel mechanism considering spherical joint clearance and wear

Abstract

The collision and wear caused by inevitable clearance in kinematic pair have an effect on the dynamic characteristics of the mechanism. Therefore, we established the dynamic model of a 3RSR (R is the revolute joint and S is the spherical joint) parallel mechanism with spherical joint clearance based on the modified Flores contact force model and the modified Coulomb friction model using Newton-Euler method. The standard quaternion was introduced in the constraint equation, and the four-order Runge-Kutta method was adopted to solve the 3RSR dynamic model. The simulation results were compared and analyzed with the numerical results. The geometrical parameters of the worn ball socket were solved based on the Archard wear model, and the geometrical reconstruction of the worn surface was carried out. The geometric reconstruction parameters were substituted into the dynamic model, which was to analyze the dynamic response of the 3RSR parallel mechanism with wear and spherical joint clearance. The simulation results show that the irregular wear occurs in the spherical joint with clearance under the presence of the impact and friction force. The long-term wear will increase the fluctuation of the contact force, thereby decreasing the movement stability of the mechanism.

Keywords

parallel mechanism / dynamics / spherical joint clearance / wear / Newton-Euler method

References

[1] FarajtabarM, DanialiH M, VarediS M. Pick and place trajectory planning of planar 3-RRR parallel manipulator in the presence of joint clearance [J]. Robotica, 2017, 35(2): 241-253

[2] TianQ, FloresP, LankaraniH M. A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints [J]. Mechanism and Machine Theory, 2018, 122: 1-57

[3] BaiZ-f, ZhaoYang. A hybrid contact force model of revolute joint with clearance for planar mechanical systems [J]. International Journal of Non-linear Mechanics, 2013, 48: 15-36

[4] ZhangX-c, ZhangX-m, ChenZhong. Dynamic analysis of a 3-RRR parallel mechanism with multiple clearance joints [J]. Mechanism and Machine Theory, 2014, 78: 105-115

[5] WangG-x, LiuH-zhao. Dynamics analysis of 4-SPS/CU parallel mechanism with spherical joint clearance [J]. Journal of Mechanical Engineering, 2015, 51(1): 43-51 in Chinese)

[6] WangG-x, LiuH-z, DengP-s, YinK-m, ZhangG-gang. Dynamic analysis of 4-SPS/CU parallel mechanism considering three-dimensional wear of spherical joint with clearance [J]. Journal of Tribology, 2017, 139(2): 021608

[7] WangG-x, LiuH-zhao. Three-dimensional wear prediction of four-degrees-of-freedom parallel mechanism with clearance spherical joint and flexible moving platform [J]. Journal of Tribology, 2018, 1403031611

[8] WangG-x, WangLiang. Dynamics investigation of spatial parallel mechanism considering rod flexibility and spherical joint clearance [J]. Mechanism and Machine Theory, 2019, 137: 83-107

[9] WangG-x, LiuH-z, DengP-sheng. Dynamics analysis of spatial multibody system with spherical joint wear [J]. Journal of Tribology, 2015, 137(2): 021605

[10] Varedi-KoulaeiS M, DanialiH M, FarajtabarM. The effects of joint clearance on the dynamics of the 3RRR planar parallel manipulator [J]. Robotica, 2017, 3561223-1242

[11] SkrinjarL, SlaviċJ, BoltežarM. A review of continuous contact-force models in multibody dynamics [J]. International Journal of Mechanical Sciences, 2018, 145171-187

[12] FloresP, KoshyC S, LankaraniH M, AmbrósioJ, ClaroJ C P. Numerical and experimental investigation on multibody systems with revolute clearance joints [J]. Nonlinear Dynamics, 2011, 65(4): 383-398

[13] ErkayaS. Experimental investigation of flexible connection and clearance joint effects on the vibration responses of mechanisms [J]. Mechanism and Machine Theory, 2018, 121: 515-529

[14] MarquesF, IsaacF, DouradoN, SoutoA P, FloresP, LankaraniH M. A study on the dynamics of spatial mechanisms with frictional spherical clearance joints [J]. Journal of Computational and Nonlinear Dynamics, 2017, 12(5): 1-10

[15] AmbrósioJ, PomboJ. A unified formulation for mechanical joints with and without clearances/bushings and/or stops in the framework of multibody systems [J]. Multibody System Dynamics, 2018, 42(3): 317-345

[16] MukrasS, KimN H, MauntlerN A, SchmitzT L, SawyerW G. Analysis of planar multibody systems with revolute joint wear [J]. Wear, 2010, 268(5–6): 643-652

[17] FloresP. Modeling and simulation of wear in revolute clearance joints in multibody systems [J]. Mechanism and Machine Theory, 2009, 44(6): 1211-1222

[18] JiangQ-y, YiF, LiY-g, LiB-liang. Numerical simulation on mild wear of hinge configurations [J]. China Mechanical Engineering, 2005, 16: 100-103(in Chinese)

[19] AskariE, FloresP, DabirrahmaniD, AppleyardR. Dynamic modeling and analysis of wear in spatial hard-on-hard couple hip replacements using multibody systems methodologies [J]. Nonlinear Dynamics, 2015, 82(1–2): 1039-1058

[20] MarquesF, FloresP, ClaroJ C P, LankaraniH M. Modeling and analysis of friction including rolling effects in multibody dynamics: A review [J]. Multibody System Dynamics, 2019, 45: 223-244

[21] NikraveshP EComputer-aided analysis of mechanical systems [D], 1988, New Jersey, Prentice-Hall International, Inc.

[22] FLORES P, MACHADO M, SEABRA E, TAVARES DA SILVA M. A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems [C]//Proceedings of ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. San Diego, California, USA. 2010: 73–82. DOI: https://doi.org/10.1115/DETC2009-86362.

[23] LankaraniH M, NikraveshP E. Continuous contact force models for impact analysis in multibody systems [J]. Nonlinear Dynamics, 1994, 5: 193-207

[24] MachadoM, MoreiraP, FloresP, LankaraniH M. Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory [J]. Mechanism and Machine Theory, 2012, 53: 99-121

[25] AmbrosioJ A CVirtual nonlinear multibody systems [M], 2003, Dordrecht, Springer

[26] WangG-x, LiuH-zhao. Research progress of joint effects model in multibody system dynamics [J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 31-50(in Chinese)

[27] ChenX-l, WuL-k, DengY, WangQing. Dynamic response analysis and chaos identification of 4-UPS-UPU flexible spatial parallel mechanism [J]. Nonlinear Dynamics, 2017, 87(4): 2311-2324

[28] FloresP, AmbrósioJ. Revolute joints with clearance in multibody systems [J]. Computers & Structures, 2004, 82(17–19): 1359-1369