Abstract
This paper presents an analytical formula to characterize the damping coefficient as a function of system's parameters in a continuous force model of impact. The contact force element consists of a linear damper which is in a parallel connection to a spring with Hertz force-deformation characteristic. Unlike the existing models in which the separation condition is assumed to be at the time at which both zero penetration (deformation) and zero force occur, in this study, only zero contact force is considered as the separation condition. To ensure that the continuous contact model obtains the desired restitution, an optimization process is performed to find the equivalent damping coefficient. The analytical and numerical investigations show that the resulting damping coefficient can be expressed as a function of system's parameters such as the effective mass, penetration speed at the start of the impact, Hertz spring constant, and the coefficient of restitution.
Issue Section:
Research Papers
References
1.
Vereshchagin
,
A. F.
, 1974
, “
Computer Simulation of the Dynamics of Complicated Mechanisms of Robot-Manipulators
,” Eng. Cybern.
,
12
(6
), pp. 65
–70
.2.
Poursina
,
M.
, and
Anderson
,
K. S.
, 2013
, “
Canonical Ensemble Simulation of Biopolymers Using a Coarse-Grained Articulated Generalized Divide-and-Conquer Scheme
,” Comput. Phys. Commun.
,
184
(3
), pp. 652
–660
.10.1016/j.cpc.2012.10.0293.
Guess
,
T. M.
, 2012
, “
Forward Dynamics Simulation Using a Natural Knee With Menisci in the Multibody Framework
,” Multibody Syst. Dyn.
,
28
(1–2
), pp. 37
–53
.10.1007/s11044-011-9293-44.
Ehsani
,
H.
,
Poursina
,
M.
,
Rostami
,
M.
,
Mousavi
,
A.
,
Parnianpour
,
M.
, and
Khalaf
,
K.
, 2019
, “
Efficient Embedding of Empirically-Derived Constraints in the ODE Formulation of Multibody Systems: Application to the Human Body Musculoskeletal System
,” Mech. Mach. Theory
,
133
, pp. 673
–690
.10.1016/j.mechmachtheory.2018.11.0165.
Ehsani
,
H.
,
Rostami
,
M.
, and
Parnianpour
,
M.
, 2016
, “
A Closed-Form Formula for the Moment Arm Matrix of a General Musculoskeletal Model With Considering Joint Constraint and Motion Rhythm
,” Multibody Syst. Dyn.
,
36
(4
), pp. 377
–403
.10.1007/s11044-015-9469-46.
Dopico
,
D.
,
Luaces
,
A.
,
Gonzalez
,
M.
, and
Cuadrado
,
J.
, 2011
, “
Dealing With Multiple Contacts in a Human-in-the-Loop Application
,” Multibody Syst. Dyn.
,
25
(2
), pp. 167
–183
.10.1007/s11044-010-9230-y7.
Machado
,
M.
,
Flores
,
P.
,
Ambrósio
,
J.
, and
Completo
,
A.
, 2011
, “
Influence of the Contact Model on the Dynamic Response of the Human Knee Joint
,” Proc. Inst. Mech. Eng., Part K
,
225
(4
), pp. 344
–358
.10.1177/14644193114139888.
Khulief
,
Y. A.
, and
Shabana
,
A. A.
, 1986
, “
Dynamic Analysis of Constrained Systems of Rigid and Flexible Bodies With Intermittent Motion
,” ASME J. Mech., Trans. Autom. Des.
,
108
(1
), pp. 38
–45
.10.1115/1.32607819.
Flores
,
P.
, and
Ambrósio
,
J.
, 2004
, “
Revolute Joints With Clearance in Multibody Systems
,” Comput. Struct.
,
82
(17–19
), pp. 1359
–1369
.10.1016/j.compstruc.2004.03.03110.
Erkaya
,
S.
, 2018
, “
Experimental Investigation of Flexible Connection and Clearance Joint Effects on the Vibration Responses of Mechanisms
,” Mech. Mach. Theory
,
121
, pp. 515
–529
.10.1016/j.mechmachtheory.2017.11.01411.
Poursina
,
M.
,
Bhalerao
,
K. D.
,
Flores
,
S.
,
Anderson
,
K. S.
, and
Laederach
,
A.
, 2011
, “
Strategies for Articulated Multibody-Based Adaptive Coarse Grain Simulation of RNA
,” Methods in Enzymology, Computer Methods Part C
, Vol.
487
,
M. L.
Johnson
, and
L.
Brand
, eds.,
ScienceDirect
, pp. 73
–98
.12.
Poursina
,
M.
, and
Anderson
,
K. S.
, 2013
, “
Efficient Coarse-Grained Molecular Simulations in the Multibody Dynamics Scheme
,” Multibody Dynamics
,
Springer
, Dordrecht, The Netherlands, pp. 147
–172
.13.
Gilardi
,
G.
, and
Sharf
,
I.
, 2002
, “
Literature Survey of Contact Dynamics Modelling
,” Mech. Mach. Theory
,
37
(10
), pp. 1213
–1239
.10.1016/S0094-114X(02)00045-914.
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
.10.1016/j.mechmachtheory.2012.02.01015.
Nikravesh
,
P. E.
, 2018
, Planar Multibody Dynamics: Formulation, Programming With MATLAB®, and Applications
, 2nd ed.,
CRC Press
, Boca Raton, FL.16.
Mukherjee
,
R. M.
, and
Anderson
,
K. S.
, 2007
, “
Efficient Methodology for Multibody Simulations With Discontinuous Changes in System Definition
,” Multibody Syst. Dyn.
,
18
(2
), pp. 145
–168
.10.1007/s11044-007-9075-117.
Goldsmith
,
W.
, 1960
, Impact: The Theory and Physical Behaviour of Colliding Solids
,
E. Arnold
,
London
.18.
Butcher
,
E.
, and
Segalman
,
D.
, 2000
, “
Characterizing Damping and Restitution in Compliant Impacts Via Modified KV and Higher-Order Linear Viscoelastic Models
,” ASME J. Appl. Mech.
,
67
(4
), pp. 831
–834
.10.1115/1.130857819.
Hertz
,
H.
, 1895
, Gesammelte Werke
, Vol.
1
,
Leipzig
,
Germany
.20.
Hunt
,
K.
, and
Crossley
,
F. R. E.
, 1975
, “
Coefficient of Restitution Interpreted as Damping in Vibroimpact
,” ASME J. Appl. Mech.
,
42
(2
), pp. 440
–445
.10.1115/1.342359621.
Lankarani
,
H. M.
, and
Nikravesh
,
P. E.
, 1994
, “
Continuous Contact Force Models for Impact Analysis in Multibody Systems
,” Nonlinear Dyn.
,
5
(2
), pp. 193
–207
.10.1007/BF0004567622.
Lankarani
,
H. M.
, 1988
, “
Canonical Equations of Motion and Estimation of Parameters in the Analysis of Impact Problems
,” Ph.D. thesis,
The University of Arizona, Tucson, AZ
.23.
Hu
,
S.
, and
Guo
,
X.
, 2015
, “
A Dissipative Contact Force Model for Impact Analysis in Multibody Dynamics
,” Multibody Syst. Dyn.
,
35
(2
), pp. 131
–151
.10.1007/s11044-015-9453-z24.
Ye
,
K.
,
Li
,
L.
, and
Zhu
,
H.
, 2009
, “
A Note on the Hertz Contact Model With Nonlinear Damping for Pounding Simulation
,” Earthquake Eng. Struct. Dyn.
,
38
(9
), pp. 1135
–1142
.10.1002/eqe.88325.
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
.10.1007/s11044-010-9237-426.
Lankarani
,
H. M.
, and
Nikravesh
,
P. E.
, 1992
, “
Hertz Contact Force Model With Permanent Indentation in Impact Analysis of Solids
,” 18th Annual ASME Design Automation Conference, pp. 391–395.
27.
Shen
,
Y.
,
Xiang
,
D.
,
Wang
,
X.
,
Jiang
,
L.
, and
Wei
,
Y.
, 2018
, “
A Contact Force Model Considering Constant External Forces for Impact Analysis in Multibody Dynamics
,” Multibody Syst. Dyn.
,
44
(4
), pp. 397
–419
.10.1007/s11044-018-09638-028.
Lankarani
,
H..
, and
Nikravesh
,
P.
, 1990
, “
A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems
,” ASME J. Mech. Des.
,
112
(3
), pp. 369
–376
.10.1115/1.2912617Copyright © 2020 by ASME
You do not currently have access to this content.
