Effects of wear and member flexibility on the dynamic performance of a planar five-bar mechanism with joint-clearance are investigated. The equation of motion of the mechanism is derived based on the absolute nodal coordinate formulation (ANCF). In order to enhance the accuracy of the contact force, the slope of the load–displacement curve of the cylindrical joint with clearance is used. The contact deformation couples the joint wear to the contact state. The contact force model of Flores and coworkers is improved, by the introduction of the stiffness coefficient. The wear depth is predicted by using the Archard's wear model. Simulations show that the multiclearance joints can generate stronger contact forces relative to single clearance joint case. This leads to more severe wear in the joint. However, the mechanism with multiple flexible links can absorb more of the energy arising from the clearance joint, and this improves the wear phenomenon.

References

1.
Flores
,
P.
,
Ambrósio
,
J.
,
Claro
,
J. P.
, and
Lankarani
,
H. M.
,
2007
, “
Dynamic Behaviour of Planar Rigid Multi-Body Systems Including Revolute Joints With Clearance
,”
Proc. Inst. Mech. Eng., Part K
,
221
(
2
), pp.
161
174
.
2.
Flores
,
P.
,
Leine
,
R.
, and
Glocker
,
C.
,
2010
, “
Modeling and Analysis of Planar Rigid Multibody Systems With Translational Clearance Joints Based on the Non-Smooth Dynamics Approach
,”
Multibody Syst. Dyn.
,
23
(
2
), pp.
165
190
.
3.
Flores
,
P.
,
Koshy
,
C. S.
,
Lankarani
,
H. M.
,
Ambrósio
,
J.
, and
Claro
,
J. C. P.
,
2011
, “
Numerical and Experimental Investigation on Multibody Systems With Revolute Clearance Joints
,”
Nonlinear Dyn.
,
65
(
4
), pp.
383
398
.
4.
Koshy
,
C. S.
,
Flores
,
P.
, and
Lankarani
,
H. M.
,
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
(
1–2
), pp.
325
338
.
5.
Flores
,
P.
,
2009
, “
Modeling and Simulation of Wear in Revolute Clearance Joints in Multibody Systems
,”
Mech. Mach. Theory
,
44
(
6
), pp.
1211
1222
.
6.
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
.
7.
Mukras
,
S.
,
Kim
,
N. H.
,
Sawyer
,
W. G.
,
Jackson
,
D. B.
, and
Bergquist
,
L. W.
,
2009
, “
Numerical Integration Schemes and Parallel Computation for Wear Prediction Using Finite Element Method
,”
Wear
,
266
(
7
), pp.
822
831
.
8.
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
), p. 031604 .
9.
Su
,
Y.
,
Chen
,
W.
,
Tong
,
Y.
, and
Xie
,
Y.
,
2010
, “
Wear Prediction of Clearance Joint by Integrating Multi-Body Kinematics With Finite-Element Method
,”
Proc. Inst. Mech. Eng., Part J
,
224
(
8
), pp.
815
823
.
10.
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
.
11.
Khemili
,
I.
, and
Romdhane
,
L.
,
2008
, “
Dynamic Analysis of a Flexible Slider–Crank Mechanism With Clearance
,”
Eur. J. Mech. A: Solids
,
27
(
5
), pp.
882
898
.
12.
Dupac
,
M.
, and
Beale
,
D. G.
,
2010
, “
Dynamic Analysis of a Flexible Linkage Mechanism With Cracks and Clearance
,”
Mech. Mach. Theory
,
45
(
12
), pp.
1909
1923
.
13.
Erkaya
,
S.
, and
Uzmay
,
İ.
,
2014
, “
Modeling and Simulation of Joint Clearance Effects on Mechanisms Having Rigid and Flexible Links
,”
J. Mech. Sci. Technol.
,
28
(
8
), pp.
2979
2986
.
14.
Li
,
Y.
,
Wang
,
Z.
,
Wang
,
C.
, and
Huang
,
W.
,
2016
, “
Dynamic Responses of Space Solar Arrays Considering Joint Clearance and Structural Flexibility
,”
Adv. Mech. Eng.
,
8
(
7
), pp.
1
11
.
15.
Zhao
,
B.
,
Zhang
,
Z. N.
, and
Dai
,
X. D.
,
2014
, “
Modeling and Prediction of Wear at Revolute Clearance Joints in Flexible Multibody Systems
,”
Proc. Inst. Mech. Eng., Part C
,
228
(
2
), pp.
317
329
.
16.
Flores
,
P.
,
Ambrósio
,
J.
,
Claro
,
J. C. P.
,
Lankarani
,
H. M.
, and
Koshy
,
C. S.
,
2006
, “
A Study on Dynamics of Mechanical Systems Including Joints With Clearance and Lubrication
,”
Mech. Mach. Theory
,
41
(
3
), pp.
247
261
.
17.
Machado
,
M.
,
Costa
,
J.
,
Seabra
,
E.
, and
Flores
,
P.
,
2012
, “
The Effect of the Lubricated Revolute Joint Parameters and Hydrodynamic Force Models on the Dynamic Response of Planar Multibody Systems
,”
Nonlinear Dyn.
,
69
(
1–2
), pp.
635
654
.
18.
Tian
,
Q.
,
Sun
,
Y.
,
Liu
,
C.
,
Hu
,
H.
, and
Flores
,
P.
,
2013
, “
Elastohydrodynamic Lubricated Cylindrical Joints for Rigid-Flexible Multibody Dynamics
,”
Comput. Struct.
,
114–115
, pp.
106
120
.
19.
Tian
,
Q.
,
Xiao
,
Q.
,
Sun
,
Y.
,
Hu
,
H.
,
Liu
,
H.
, and
Flores
,
P.
,
2015
, “
Coupling Dynamics of a Geared Multibody System Supported by Elastohydrodynamic Lubricated Cylindrical Joints
,”
Multibody Syst. Dyn.
,
33
(
3
), pp.
259
284
.
20.
Zhao
,
B.
,
Zhou
,
K.
, and
Xie
,
Y. B.
,
2016
, “
A New Numerical Method for Planar Multibody System With Mixed Lubricated Revolute Joint
,”
Int. J. Mech. Sci.
,
113
, pp.
105
119
.
21.
Zheng
,
E.
,
Zhu
,
R.
,
Zhu
,
S.
, and
Lu
,
X.
,
2016
, “
A Study on Dynamics of Flexible Multi-Link Mechanism Including Joints With Clearance and Lubrication for Ultra-Precision Presses
,”
Nonlinear Dyn.
,
83
(
1–2
), pp.
137
159
.
22.
Flores
,
P.
,
2010
, “
A Parametric Study on the Dynamic Response of Planar Multibody Systems With Multiple Clearance Joints
,”
Nonlinear Dyn.
,
61
(
4
), pp.
633
653
.
23.
Flores
,
P.
, and
Lankarani
,
H. M.
,
2012
, “
Dynamic Response of Multibody Systems With Multiple Clearance Joints
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
3
), p. 031003.
24.
Salahshoor
,
E.
,
Ebrahimi
,
S.
, and
Maasoomi
,
M.
,
2016
, “
Nonlinear Vibration Analysis of Mechanical Systems With Multiple Joint Clearances Using the Method of Multiple Scales
,”
Mech. Mach. Theory
,
105
, pp.
495
509
.
25.
Yaqubi
,
S.
,
Dardel
,
M.
,
Daniali
,
H. M.
, and
Ghasemi
,
M. H.
,
2016
, “
Modeling and Control of Crank–Slider Mechanism With Multiple Clearance Joints
,”
Multibody Syst. Dyn.
,
36
(
2
), pp.
143
167
.
26.
Yang
,
Y.
,
Cheng
,
J. R.
, and
Zhang
,
T.
,
2016
, “
Vector Form Intrinsic Finite Element Method for Planar Multibody Systems With Multiple Clearance Joints
,”
Nonlinear Dyn.
,
86
(
1
), pp.
421
440
.
27.
Erkaya
,
S.
,
Doğan
,
S.
, and
Ulus
,
Ş.
,
2015
, “
Effects of Joint Clearance on the Dynamics of a Partly Compliant Mechanism: Numerical and Experimental Studies
,”
Mech. Mach. Theory
,
88
, pp.
125
140
.
28.
Zheng
,
E.
, and
Zhou
,
X.
,
2014
, “
Modeling and Simulation of Flexible Slider-Crank Mechanism With Clearance for a Closed High Speed Press System
,”
Mech. Mach. Theory
,
74
, pp.
10
30
.
29.
Li
,
Y.
,
Chen
,
G.
,
Sun
,
D.
,
Gao
,
Y.
, and
Wang
,
K.
,
2016
, “
Dynamic Analysis and Optimization Design of a Planar Slider–Crank Mechanism With Flexible Components and Two Clearance Joints
,”
Mech. Mach. Theory
,
99
, pp.
37
57
.
30.
Abdallah
,
M. A. B.
,
Khemili
,
I.
, and
Aifaoui
,
N.
,
2016
, “
Numerical Investigation of a Flexible Slider–Crank Mechanism With Multijoints With Clearance
,”
Multibody Syst. Dyn.
,
38
(
2
), pp.
173
199
.
31.
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
.
32.
Omar
,
M. A.
, and
Shabana
,
A. A.
,
2001
, “
A Two-Dimensional Shear Deformable Beam for Large Rotation and Deformation Problems
,”
J. Sound Vib.
,
243
(
3
), pp.
565
576
.
33.
Shabana
,
A. A.
,
2015
, “
Definition of ANCF Finite Elements
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
5
), p. 054506.
34.
Shabana
,
A. A.
,
2011
,
Computational Continuum Mechanics
,
Cambridge University Press
,
New York
.
35.
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
.
36.
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
.
37.
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
.
38.
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
.
39.
Lankarani
,
H. M.
, and
Nikravesh
,
P. E.
,
1990
, “
A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems
,”
ASME J. Mech. Des.
,
112
(
3
), pp.
369
376
.
40.
Zhiying
,
Q.
, and
Qishao
,
L.
,
2006
, “
Analysis of Impact Process Based on Restitution Coefficient
,”
J. Dyn. Control
,
4
, pp.
294
298
.
41.
Shivaswamy
,
S.
,
1997
, “
Modeling Contact Forces and Energy Dissipation During Impact in Mechanical Systems
,” Doctoral dissertation, Department of Mechanical Engineering, Wichita State University, Wichita, KS.
42.
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., Part K
,
220
(
1
), pp.
21
34
.
43.
Brutti
,
C.
,
Coglitore
,
G.
, and
Valentini
,
P. P.
,
2011
, “
Modeling 3D Revolute Joint With Clearance and Contact Stiffness
,”
Nonlinear Dyn.
,
66
(
4
), pp.
531
548
.
44.
Sawyer
,
W. G.
,
2001
, “
Wear Predictions for a Simple-Cam Including the Coupled Evolution of Wear and Load
,”
Tribol. Lubr. Technol.
,
57
(
9
), pp.
31
36
.
45.
Gummer
,
A.
, and
Sauer
,
B.
,
2012
, “
Influence of Contact Geometry on Local Friction Energy and Stiffness of Revolute Joints
,”
ASME J. Tribol.
,
134
(
2
), p. 021402.
46.
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
.
47.
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
.
48.
Wang
,
X.
,
Liu
,
G.
, and
Ma
,
S.
,
2016
, “
Dynamic Analysis of Planar Mechanical Systems With Clearance Joints Using a New Nonlinear Contact Force Model
,”
Mech. Mach. Theory
,
30
(
4
), pp.
1537
1545
.
49.
Liu
,
C. S.
,
Zhang
,
K.
, and
Yang
,
R.
,
2007
, “
The FEM Analysis and Approximate Model for Cylindrical Joints With Clearances
,”
Mech. Mach. Theory
,
42
(
2
), pp.
183
197
.
50.
Wang
,
G.
,
Liu
,
H.
, and
Deng
,
P.
,
2015
, “
Dynamics Analysis of Spatial Multibody System With Spherical Joint Wear
,”
ASME J. Tribol.
,
137
(
2
), p. 021605.
51.
Marques
,
F.
,
Flores
,
P.
,
Claro
,
J. P.
, and
Lankarani
,
H. M.
,
2016
, “
A Survey and Comparison of Several Friction Force Models for Dynamic Analysis of Multibody Mechanical Systems
,”
Nonlinear Dyn.
,
86
(
3
), pp.
1407
1443
.
52.
Piatkowski
,
T.
,
2014
, “
GMS Friction Model Approximation
,”
Mech. Mach. Theory
,
75
, pp.
1
11
.
53.
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
.
54.
Piatkowski
,
T.
,
2011
, “
Analysis of Translational Positioning of Unit Loads by Directionally-Oriented Friction Force Fields
,”
Mech. Mach. Theory
,
46
(
2
), pp.
201
217
.
55.
Archard
,
J.
,
1953
, “
Contact and Rubbing of Flat Surfaces
,”
J. Appl. Phys.
,
24
(
8
), pp.
981
988
.
56.
Yang
,
L. J.
,
2005
, “
A Test Methodology for the Determination of Wear Coefficient
,”
Wear
,
259
(
7
), pp.
1453
1461
.
You do not currently have access to this content.