The dynamic performance of 4-SPS/CU (spherical joint, prismatic joint, cylindrical joint, and universal joint) parallel mechanism considering spherical joint with clearance is developed, and the three-dimensional (3D) wear property of the socket is based on the Archard's wear model. First, the kinematics model of spherical joint with clearance is established, and the updated procedure pertaining to the contact mechanics and wear state is explained via a flowchart. An improved contact force model was proposed by Flores et al. contact force model through a revised contact stiffness coefficient. The normal and tangential contact forces between ball and socket are calculated using the improved contact force model and a modified Coulomb friction model. Second, the dynamic model of the parallel mechanism considering spherical joint with clearance is formulated based on the multibody equations of motion. In order to obtain the 3D wear property of spherical joint with clearance, the contact force is decomposed into three components in the global coordinate system. The three components of sliding distance are computed based on the 3D revolute property of the parallel mechanism. Finally, the contact pressures in three different directions are calculated by the corresponding contact force and approximate contact area components for the sake of predicting the 3D wear depth of socket based on the Archard's wear model. The simulation results show that the wear depth in different directions along the socket surface is nonuniform, which affects the performance of 4-SPS/CU parallel mechanism.
Issue Section:
Friction and Wear
References
1.
Tian
, Y.
, Shirinzadeh
, B.
, and Zhang
, D.
, 2010
, “Design and Dynamics of a 3DOF Flexure-Based Parallel Mechanism for Micro/Nano Manipulation
,” Microelectron. Eng.
, 87
(2
), pp. 230
–241
.2.
Yang
, C.
, Huang
, Q.
, Jiang
, H.
, Peter
, O. O.
, and Han
, J.
, 2010
, “PD Control With Gravity Compensation for Hydraulic 6-DOF Parallel Manipulator
,” Mech. Mach. Theory
, 45
(4
), pp. 666
–677
.3.
Zhang
, J. Z.
, Xie
, X. P.
, Li
, C. J.
, Xin
, Y. Y.
, and He
, Z. M.
, 2013
, “FEM Based Numerical Simulation of Delta Parallel Mechanism
,” Adv. Mater. Res.
, 690
, pp. 2978
–2981
.4.
Ottoboni
, A.
, Parenti-Castelli
, V.
, Sancisi
, N.
, Belvedere
, C.
, and Leardini
, A.
, 2010
, “Articular Surface Approximation in Equivalent Spatial Parallel Mechanism Models of the Human Knee Joint: An Experiment-Based Assessment
,” Proc. Inst. Mech. Eng. H.
, 224
(9
), pp. 1121
–1132
.5.
Bu
, W.
, Liu
, Z.
, Tan
, J.
, and Gao
, S.
, 2010
, “Detachment Avoidance of Joint Elements of a Robotic Manipulator With Clearances Based on Trajectory Planning
,” Mech. Mach. Theory
, 45
(6
), pp. 925
–940
.6.
Wu
, J. F.
, Zhang
, R.
, Wang
, R. H.
, and Yao
, Y. X.
, 2014
, “A Systematic Optimization Approach for the Calibration of Parallel Kinematics Machine Tools by a Laser Tracker
,” Int. J. Mach. Tool Manuf.
, 86
, pp. 1
–11
.7.
Tsai
, M. S.
, and Yuan
, W. H.
, 2010
, “Inverse Dynamics Analysis for a 3-PRS Parallel Mechanism Based on a Special Decomposition of the Reaction Forces
,” Mech. Mach. Theory
, 45
(11
), pp. 1491
–1508
.8.
Klimchik
, A.
, Chablat
, D.
, and Pashkevich
, A.
, 2014
, “Stiffness Modeling for Perfect and Non-Perfect Parallel Manipulators Under Internal and External Loadings
,” Mech. Mach. Theory
, 79
, pp. 1
–28
.9.
Dong
, X.
, Ye
, J.
, and Xiao-Feng
, H.
, 2010
, “Kinetic Uncertainty Analysis of the Reheat-Stop-Valve Mechanism With Multiple Factors
,” Mech. Mach. Theory
, 45
(11
), pp. 1745
–1765
.10.
Parenti-Castelli
, V.
, and Venanzi
, S.
, 2005
, “Clearance Influence Analysis on Mechanisms
,” Mech. Mach. Theory
, 40
(12
), pp. 1316
–1329
.11.
Chebbi
, A. H.
, Affi
, Z.
, and Romdhane
, L.
, 2009
, “Prediction of the Pose Errors Produced by Joints Clearance for a 3-UPU Parallel Robot
,” Mech. Mach. Theory
, 44
(9
), pp. 1768
–1783
.12.
Tannous
, M.
, Caro
, S.
, and Goldsztejn
, A.
, 2014
, “Sensitivity Analysis of Parallel Manipulators Using an Interval Linearization Method
,” Mech. Mach. Theory
, 71
, pp. 93
–114
.13.
Chaker
, A.
, Mlika
, A.
, Laribi
, M. A.
, Romdhane
, L.
, and Zeghloul
, S.
, 2013
, “Clearance and Manufacturing Errors' Effects on the Accuracy of the 3-RCC Spherical Parallel Manipulator
,” Eur. J. Mech-A/Solids
, 37
, pp. 86
–95
.14.
Lee
, S. J.
, Gilmore
, B. J.
, and Ogot
, M. M.
, 1993
, “Dimensional Tolerance Allocation of Stochastic Dynamic Mechanical Systems Through Performance and Sensitivity Analysis
,” ASME J. Mech. Des.
, 115
(3
), pp. 392
–402
.15.
Hassanzadeh
, H. R.
, Akbarzadeh-T
, M. R.
, Akbarzadeh
, A.
, and Rezaei
, A.
, 2014
, “An Interval-Valued Fuzzy Controller for Complex Dynamical Systems With Application to a 3-PSP Parallel Robot
,” Fuzzy Set. Syst.
, 235
, pp. 83
–100
.16.
Wu
, W.
, and Rao
, S. S.
, 2004
, “Interval Approach for the Modeling of Tolerances and Clearances in Mechanism Analysis
,” ASME J. Mech. Des.
, 126
(4
), pp. 581
–592
.17.
Frisoli
, A.
, Solazzi
, M.
, Pellegrinetti
, D.
, and Bergamasco
, M.
, 2011
, “A New Screw Theory Method for the Estimation of Position Accuracy in Spatial Parallel Manipulators With Revolute Joint Clearances
,” Mech. Mach. Theory
, 46
(12
), pp. 1929
–1949
.18.
Shiau
, T. N.
, Tsai
, Y. J.
, and Tsai
, M. S.
, 2008
, “Nonlinear Dynamic Analysis of a Parallel Mechanism With Consideration of Joint Effects
,” Mech. Mach. Theory
, 43
(4
), pp. 491
–505
.19.
Zhang
, X.
, Zhang
, X.
, and Chen
, Z.
, 2014
, “Dynamic Analysis of a 3-RRR Parallel Mechanism With Multiple Clearance Joints
,” Mech. Mach. Theory
, 78
, pp. 105
–115
.20.
Xu
, L.
, and Li
, Y.
, 2014
, “Investigation of Joint Clearance Effects on the Dynamic Performance of a Planar 2-DOF Pick-and-Place Parallel Manipulator
,” Rob. Comput. Int. Manuf.
, 30
(1
), pp. 62
–73
.21.
Flores
, P.
, Ambrósio
, J.
, Claro
, J. C.
, and Lankarani
, H. M.
, 2006
, “Dynamics of Multibody Systems With Spherical Clearance Joints
,” ASME J. Comput. Nonlinear Dyn.
, 1
(3
), pp. 240
–247
.22.
Flores
, P.
, and Lankarani
, H. M.
, 2010
, “Spatial Rigid-Multibody Systems With Lubricated Spherical Clearance Joints: Modeling and Simulation
,” Nonlinear Dyn.
, 60
(1–2
), pp. 99
–114
.23.
Askari
, E.
, Flores
, P.
, Dabirrahmani
, D.
, and Appleyard
, R.
, 2014
, “Study of the Friction-Induced Vibration and Contact Mechanics of Artificial Hip Joints
,” Tribol. Int.
, 70
, pp. 1
–10
.24.
Askari
, E.
, Flores
, P.
, Dabirrahmani
, D.
, and Appleyard
, R.
, 2015
, “Dynamic Modeling and Analysis of Wear in Spatial Hard-on-Hard Couple Hip Replacements Using Multibody Systems Methodologies
,” Nonlinear Dyn.
, 82
(1–2
), pp. 1039
–1058
.25.
Costa
, J.
, Peixoto
, J.
, Moreira
, P.
, Souto
, A. P.
, Flores
, P.
, and Lankarani
, H. M.
, 2016
, “Influence of the Hip Joint Modeling Approaches on the Kinematics of Human Gait
,” ASME J. Tribol.
, 138
(3
), p. 031201
.26.
Tian
, Q.
, Zhang
, Y.
, Chen
, L.
, and Flores
, P.
, 2009
, “Dynamics of Spatial Flexible Multibody Systems With Clearance and Lubricated Spherical Joints
,” Comput. Struct.
, 87
(13
), pp. 913
–929
.27.
Wang
, G. X.
, Liu
, H. Z.
, and Deng
, P. S.
, 2015
, “Dynamics Analysis of Spatial Multibody System With Spherical Joint Wear
,” ASME J. Tribol.
, 137
(2
), p. 021605
.28.
Mukras
, S.
, Kim
, N. H.
, Mauntler
, N. A.
, Schmitz
, T. L.
, and Sawyer
, W. G.
, 2010
, “Analysis of Planar Multibody Systems With Revolute Joint Wear
,” Wear
, 268
(5
), pp. 643
–652
.29.
Mukras
, S.
, Kim
, N. H.
, Mauntler
, N. A.
, Schmitz
, T.
, and Sawyer
, W. G.
, 2010
, “Comparison Between Elastic Foundation and Contact Force Models in Wear Analysis of Planar Multibody System
,” ASME J. Tribol.
, 132
(3
), pp. 1
–11
.30.
Flores
, P.
, 2009
, “Modeling and Simulation of Wear in Revolute Clearance Joints in Multibody Systems
,” Mech. Mach. Theory
, 44
(6
), pp. 1211
–1222
.31.
Bai
, Z. F.
, Zhao
, Y.
, and Chen
, J.
, 2013
, “Dynamics Analysis of Planar Mechanical System Considering Revolute Clearance Joint Wear
,” Tribol. Int.
, 64
, pp. 85
–95
.32.
Lopes
, D. S.
, Silva
, M. T.
, Ambrósio
, J. A.
, and Flores
, P.
, 2010
, “A Mathematical Framework for Rigid Contact Detection Between Quadric and Superquadric Surfaces
,” Multibody Syst. Dyn.
, 24
(3
), pp. 255
–280
.33.
Flores
, P.
, and Ambrósio
, J.
, 2010
, “On the Contact Detection for Contact-Impact Analysis in Multibody Systems
,” Multibody Syst. Dyn.
, 24
(1
), pp. 103
–122
.34.
Machado
, M.
, Moreira
, P.
, Flores
, P.
, and Lankarani
, H. M.
, 2012
, “Compliant Contact Force Models in Multibody Dynamics: Evolution of the Hertz Contact Theory
,” Mech. Mach. Theory
, 53
, pp. 99
–121
.35.
Alves
, J.
, Peixinho
, N.
, da Silva
, M. T.
, Flores
, P.
, and Lankarani
, H. M.
, 2015
, “A Comparative Study of the Viscoelastic Constitutive Models for Frictionless Contact Interfaces in Solids
,” Mech. Mach. Theory
, 85
, pp. 172
–188
.36.
Flores
, P.
, Machado
, M.
, Silva
, M. T.
, and Martins
, J. M.
, 2011
, “On the Continuous Contact Force Models for Soft Materials in Multibody Dynamics
,” Multibody Syst. Dyn.
, 25
(3
), pp. 357
–375
.37.
Flores
, P.
, Ambrósio
, J.
, Claro
, J. P.
, and Lankarani
, H. M.
, 2006
, “Influence of the Contact—Impact Force Model on the Dynamic Response of Multi-Body Systems
,” Proc. Inst. Mech. Eng. K.
, 220
(1
), pp. 21
–34
.38.
Ma
, J.
, Qian
, L.
, Chen
, G.
, and Li
, M.
, 2015
, “Dynamic Analysis of Mechanical Systems With Planar Revolute Joints With Clearance
,” Mech. Mach. Theory
, 94
, pp. 148
–164
.39.
Bai
, Z. F.
, and Zhao
, Y.
, 2013
, “A Hybrid Contact Force Model of Revolute Joint With Clearance for Planar Mechanical Systems
,” Int. J. Nonlinear Mech.
, 48
, pp. 15
–36
.40.
Ambrósio
, J. A. C.
, 2002
, “Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Models
,” Virtual Nonlinear Multibody System
, 2
, pp. 15
–33
.41.
Piatkowski
, T.
, 2014
, “GMS Friction Model Approximation
,” Mech. Mach. Theory
, 75
, pp. 1
–11
.42.
Liu
, L.
, Liu
, H.
, Wu
, Z.
, and Yuan
, D.
, 2009
, “A New Method for the Determination of the Zero Velocity Region of the Karnopp Model Based on the Statistics Theory
,” Mech. Syst. Signal Process.
, 23
(5
), pp. 1696
–1703
.43.
Piatkowski
, T.
, 2011
, “Analysis of Translational Positioning of Unit Loads by Directionally-Oriented Friction Force Fields
,” Mech. Mach. Theory
, 46
(2
), pp. 201
–217
.44.
Flores
, P.
, Machado
, M.
, Seabra
, E.
, and da Silva
, M. T.
, 2011
, “A Parametric Study on the Baumgarte Stabilization Method for Forward Dynamics of Constrained Multibody Systems
,” ASME J. Comput. Nonlinear Dyn.
, 6
(1
), pp. 1
–10
.45.
Archard
, J.
, 1953
, “Contact and Rubbing of Flat Surfaces
,” J. Appl. Phys.
, 24
(8
), pp. 981
–988
.46.
Janakiraman
, V.
, Li
, S.
, and Kahraman
, A.
, 2014
, “An Investigation of the Impacts of Contact Parameters on Wear Coefficient
,” ASME J. Tribol.
, 136
(3
), p. 031602
.47.
Yang
, L. J.
, 2005
, “A Test Methodology for the Determination of Wear Coefficient
,” Wear
, 259
(7
), pp. 1453
–1461
.48.
Sfantos
, G. K.
, and Aliabadi
, M. H.
, 2006
, “Wear Simulation Using an Incremental Sliding Boundary Element Method
,” Wear
, 260
(9
), pp. 1119
–1128
.49.
Páczelt
, I.
, Kucharski
, S.
, and Mróz
, Z.
, 2012
, “The Experimental and Numerical Analysis of Quasi-Steady Wear Processes for a Sliding Spherical Indenter
,” Wear
, 274
, pp. 127
–148
.50.
Põdra
, P.
, and Andersson
, S.
, 1997
, “Wear Simulation With the Winkler Surface Model
,” Wear
, 207
(1
), pp. 79
–85
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