A general methodology for the dynamic modelling and analysis of planar multi-body systems with a continuous friction model in joint clearance is presented. Joint clearance is the critical factor that influences the dynamic response and the performance of mechanisms for high-speed application. In light of recent developments in the joint clearance studies, the number of contact force models has been introduced with ignoring friction continuity. The selection of an appropriate continuous friction model is still challenging and essential, which requires further development. Therefore, a perfect continuous friction model, including the Stribeck effect, static, dynamic and viscous friction terms, is proposed and validated. Investigating the dynamic modelling and analysis of double rocker four-bar linkage mechanisms with frictional revolute clearance joints is presented to investigate friction models' effect when surfaces collide with a non-zero tangential velocity. Unlike the smooth crank input mechanism, a double rocker four-bar linkage mechanism is analysed as a challenging problem in the impact mode. Resolving this concern, the novel friction model avoids discontinuity at zero velocity considering the accurate static friction zone. The results reveal that the novel friction model, compared with the piecewise friction model, is more effective in reflecting the mechanical systems' dynamic behaviour. In order to grasp the nonlinear characteristics of the high-speed four-bar linkage mechanism with our model in joint clearance, the Poincaré portrait, and Fast Fourier transformation plot are employed. It is proved that chaos exists in the dynamic response with the influence of the restitution coefficients and kinetic coefficient of friction.
DubowskySFreudensteinF. Dynamic analysis of mechanical systems with clearances-part 1: formation of dynamic model. J Eng Industry1971; 93(1): 305–309.
2.
SeneviratneLDEarlesSWEFennerDN. Analysis of a four-bar mechanism with a radially compliant clearance joint. Proc Inst Mech Eng C J Mech Eng Sci1996; 210(3): 215–223.
3.
FloresPLankaraniHM. Dynamic response of multibody systems with multiple clearance joints. J Comput Nonlinear Dynam2012; 7(3): 031003.
4.
FarahanSBGhazaviMRRahmanianS. Bifurcation in a planar four-bar mechanism with revolute clearance joint. Nonlinear Dynam2017; 87(2): 955–973.
5.
StoenescuEDMarghituDB. Dynamic analysis of a planar rigid-link mechanism with rotating slider joint and clearance. J Sound Vib2003; 266(2): 394–404.
6.
LankaraniHMNikraveshPE. A contact force model with hysteresis damping for impact analysis of multibody systems. In: International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers (ASME), 1989 Sep 17.
7.
IsaacF.MarquesF.DouradoN., et al.A finite element model of a 3D dry revolute joint incorporated in a multibody dynamic analysis. Multibody Syst Dyn2019; 45(3): 293–313.
8.
PereiraCRamalhoAAmbrosioJ. An enhanced cylindrical contact force model. Multibody Syst Dyn2015; 35(3): 277–298.
9.
JohnsonKL. Contact Mechanics. Cambridge: Cambridge University Press, 1985.
10.
ZhangJLiWZhaoL, et al.A continuous contact force model for impact analysis in multibody dynamics. Mechanism Machine Theor2020; 153: 103946.
11.
LouJLiC. An improved model of contact collision investigation on multi-body systems with revolute clearance joints. Proc Inst Mech Eng D: J Automobile Eng2020; 234(7): 2103–2112.
12.
AskariEFloresPDabirrahmaniD, et al.Dynamic modeling and analysis of wear in spatial hard-on-hard couple hip replacements using multibody systems methodologies. Nonlinear Dynam2015; 82(1): 1039–58.
13.
SafaeifarHFarshidianfarA. A new model of the contact force for the collision between two solid bodies. Multibody Syst Dyn2020; 50(3): 233–257.
14.
CarvalhoASMartinsJM. Exact restitution and generalizations for the hunt-crossley contact model. Mechanism Machine Theor2019; 139: 174–194.
15.
TianQFloresPLankaraniHM. A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints. Mechanism Machine Theor2018; 122: 1–57.
16.
WangGLiuC. Further investigation on improved viscoelastic contact force model extended based on hertz's law in multibody system. Mechanism Machine Theor2020; 153: 103986.
17.
PoursinaMNikraveshPE. Optimal damping coefficient for a class of continuous contact models. Multibody Syst Dyn2020; 50: 169–188.
18.
MachadoMFloresPAmbrosioJ, et al.Influence of the contact model on the dynamic response of the human knee joint. Proc Ins Mechan Eng K J Multi Body Dynam2011; 225(4): 344–358.
19.
PiatkowskiTWolskiM. Model of positioning objects by the system of oblique friction force fields on horizontal and vertically offset planes. Mechanism Machine Theor2021; 156: 104155.
20.
PennestrìERossiVSalviniP, et al.Review and comparison of dry friction force models. Nonlinear Dynam2016; 83(4): 1785–801.
21.
MakkarCDixonWESawyerWG, et al.A new continuously differentiable friction model for control systems design. In: Proceedings, 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, IEEE, 2005 Jul 24, pp. 600–605.
22.
TustinA. The effects of backlash and of speed-dependent friction on the stability of closed-cycle control systems. J Inst Electr Eng Part A Automat Regul Servo Mech1947; 94(1): 143–151.
23.
FleischmannJSerbanRNegrutD, et al.On the importance of displacement history in soft-body contact models. J Comput Nonlinear Dynam2016; 11(4).
24.
LiangJ.FillmoreS.MaO.. An extended bristle friction force model with experimental validation. Mechanism Machine Theor2012; 56: 123–137.
25.
AmbrósioJA. Impact of rigid and flexible multibody systems: deformation description and contact models. In: Virtual Nonlinear Multibody Systems. Dordrecht: Springer, 2003, pp. 57–81.
ThrelfallDC. The inclusion of Coulomb friction in mechanisms programs with particular reference to DRAM au programme DRAM. Mechanism Machine Theor1978; 13(4): 475–483.
28.
AnderssonSSöderbergABjörklundS. Friction models for sliding dry, boundary and mixed lubricated contacts. Tribol Int2007; 40(4): 580–587.
29.
BengisuMTAkayA. Stick-slip oscillations: dynamics of friction and surface roughness. J Acoust Soc America1999; 105(1): 194–205.
30.
ZhuAHeSZhaoJ, et al.A nonlinear contact pressure distribution model for wear calculation of planar revolute joint with clearance. Nonlinear Dynam2017; 88(1): 315–328.
31.
JavanfarADanialiHMDardelM, et al.Dynamic behavior analysis of four-bar linkage mechanisms with joints' clearance. In: 2015 3rd RSI International Conference on Robotics and Mechatronics (ICROM). IEEE; 2015, pp. 383–388.
32.
YangLZhangXHuangY. Dynamic analysis of open-loop mechanisms with multiple spatial revolute clearance joints. Proc Inst Mech Eng Part C J Mech Eng Sci2019; 233(2): 593–610.
33.
LiKLTsaiYKChanKY. Identifying joint clearance via robot manipulation. Proc Inst Mech Eng Part C J Mech Eng Sci2018; 232(15): 2549–2574.
34.
Varedi-KoulaeiSMBamdadMFathiB. The effects of revolute joint clearance on the kinematic behavior of the 3RPR planar parallel manipulator. J Appl Comput Sci Mech2020; 31(1): 39–52.
35.
YaqubiSDardelMDanialiHM. Nonlinear dynamics and control of crank-slider mechanism with link flexibility and joint clearance. Proc Inst Mech Eng Part C J Mech Eng Sci2016; 230(5): 737–755.
36.
ZhengXZhangRWangQ. Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint. Appl Math Mech2018; 39(9): 1239–1258.
37.
GaoYZhangFLiY. Reliability optimization design of a planar multi-body system with two clearance joints based on reliability sensitivity analysis. Proc Inst Mech Eng Part C J Mech Eng Sci2019; 233(4): 1369–1382.
38.
MarquesFFloresPPimenta ClaroJC, et al.A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dynam2016; 86(3): 1407–1443.
39.
MarquesFIsaacFDouradoN, et al.A study on the dynamics of spatial mechanisms with frictional spherical clearance joints. J Comput Nonlinear Dynam2017; 12(5): 051013.
40.
ChenGYuanJ. Nonlinear dynamics analysis of shift manipulator for robot driver considering multiple revolute clearance joints and variable load. Mech Based Des Struct Machine2020; 49(4): 596–614.
41.
ZhengXZhangRWangQ. Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint. Appl Math Mech2018; 39(9): 1239–1258.
42.
YanSGuoP. Kinematic accuracy analysis of flexible mechanisms with uncertain link lengths and joint clearances. Proc Inst Mech Eng Part C J Mech Eng Sci2011; 225(8): 1973–1983.
43.
HuFSunYPengB. Dynamic precision analysis and experimental verification of high-speed precision punch press. Proc Inst Mech Eng Part C J Mech Eng Sci2016; 230(20): 3655–3662.
44.
WangXRuiX. Dynamics modeling and simulation of tracked armored vehicle with planar clearance trunnion-bearing revolute joint. J Mech Sci Technol2021; 35(6): 2285–2302.
45.
HertzH. Ueber die Berührung fester elastischer Körper. De Gruyter, 2021.
46.
GoldsmithW. The Theory and Physical Behaviour of Colliding Solids. Dover Publ., 1999.
47.
HuntKHCrossleyFRE. Coefficient of restitution interpreted as damping in vibroimpact. J Appl Mech1975; 42(2): 440–445.
48.
YangYChengJJRZhangT. Vector form intrinsic finite element method for planar multibody systems with multiple clearance joints. Nonlinear Dynam2016; 86(1): 421–440.
49.
FloresPAmbrósioJClaroJCP, et al.Dynamic behaviour of planar rigid multi-body systems including revolute joints with clearance. Proc Inst Mech Eng K J Multi-Body Dynam2007; 221(2): 161–174.
50.
BaiZFZhaoY. Dynamics modeling and quantitative analysis of multibody systems including revolute clearance joint. Precision Eng2012; 36(4): 554–567.
