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Research Papers

A Comparative Study of the Dissipative Contact Force Models for Collision Under External Spring Forces

[+] Author and Article Information
Dong Xiang

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: xd@mail.tsinghua.edu.cn

Yinhua Shen

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: syhua_2001@163.com

Yaozhong Wei

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: weiyz12@163.com

Mengxing You

Department of Mechanical Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: ymx2016qy@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 19, 2018; final manuscript received July 20, 2018; published online August 22, 2018. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 13(10), 101009 (Aug 22, 2018) (13 pages) Paper No: CND-18-1177; doi: 10.1115/1.4041031 History: Received April 19, 2018; Revised July 20, 2018

The dissipative contact force model plays a key role in predicting the response of multibody mechanical systems. Contact-impact event can frequently take place in multibody systems and the impact pair is often affected by supporting forces which are treated as external spring forces. However, the external spring forces are ignored during the derivation process of existing dissipative contact force models. Considering the influences of external spring forces, the fact is discussed that the crucial issues, including relative velocity and energy loss, in modeling dissipative contact force are different compared to the same issues analyzed in existing literatures. These differences can result in obvious errors in describing the collision response in multibody systems. Thus, a comparative study is carried out for examining the performances of several popular dissipative contact force models in multibody dynamics. For this comparison, a method associated with Newton's method is proposed to calculate the contact force that meets the Strong's law of energy loss and this force is used as reference. The comparative results show that the models suitable for both hard and soft contact exhibit good accuracy when contact equivalent stiffness is far larger than external spring stiffness by two orders of magnitude. Conversely, these models can cause varying degree and obvious errors in contact force, number of collisions, etc., especially when the difference in stiffness is close to or less than one order of magnitude.

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References

Chau-Chin Changt, R. L. , and Huston , 1995, “ Computational Methods for Studying Impact in Multibody Systems,” Comput. Struct., 57(3), pp. 421–425. [CrossRef]
Flores, P. , Ambrósio, J. , Claro, J. C. P. , and Lankarani, H. M. , 2008, Kinematics and Dynamics of Multibody Systems With Imperfect Joints: Models and Case Studies, Lecture Notes in Applied and Computational Mechanics, Vol. 34, Springer, Berlin, Heidelberg.
Pereira, C. M. , Ramalho, A. L. , and Ambrósio, J. A. , 2011, “ A Critical Overview of Internal and External Cylinder Contact Force Models,” Nonlinear Dyn., 63(4), pp. 681–697. [CrossRef]
Alves, J. , Peixinho, N. , Silva, M. T. D. , 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. [CrossRef]
Ravn, P. , 1998, “ A Continuous Analysis Method for Planar Multibody Systems With Joint Clearance,” Multibody Syst. Dyn., 2, pp. 1–24. [CrossRef]
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(13–14), pp. 913–929. [CrossRef]
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. [CrossRef]
Khulief, Y. A. , 2013, “ Modeling of Impact in Multibody Systems: An Overview,” ASME J. Comput. Nonlinear Dyn., 8(2), p. 021012. [CrossRef]
Shabana, A. A , 1997, “ Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody Syst. Dyn., 1(2), pp. 189–222. [CrossRef]
Zhao, Y. , and Bai, Z. , 2011, “ Dynamics Analysis of Space Robot Manipulator With Joint Clearance,” Acta Astronaut., 68(7–8), pp. 1147–1155. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Vuquoc, L. , Zhang, X. , and Lesburg, L. , 2000, “ A Normal Force-Displacement Model for Contacting Spheres Accounting for Plastic Deformation: Force-Driven Formulation,” ASME J. Appl. Mech., 67(2), pp. 363–371. [CrossRef]
Tian, Q. , Flores, P. , and Lankarani, H. M. , 2018, “ A Comprehensive Survey of the Analytical, Numerical and Experimental Methodologies for Dynamics of Multibody Mechanical Systems With Clearance or Imperfect Joints,” Mech. Mach. Theory, 122, pp. 1–57. [CrossRef]
Pereira, C. , Ramalho, A. , and Ambrosio, J. , 2014, “ Applicability Domain of Internal Cylindrical Contact Force Models,” Mech. Mach. Theory, 78, pp. 141–157. [CrossRef]
Uchida, T. K. , Sherman, M. A. , and Delp, S. L. , 2015, “ Making a Meaningful Impact: Modelling Simultaneous Frictional Collisions in Spatial Multibody Systems,” Proc. R. Soc. A, 471(2177), p. 20140859. [CrossRef]
Masoudi, R. , and McPhee, J. , 2016, “ A Novel Micromechanical Model of Nonlinear Compression Hysteresis in Compliant Interfaces of Multibody Systems,” Multibody Syst. Dyn., 37(3), pp. 325–343. [CrossRef]
Marques, F. , Isaac, F. , Dourado, N. , and Flores, P. , 2017, “ An Enhanced Formulation to Model Spatial Revolute Joints With Radial and Axial Clearances,” Mech. Mach. Theory, 116, pp. 123–144. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Lin, Y. C. , Haftka, R. T. , Queipo, N. V. , and Fregly, B. J. , 2010, “ Surrogate Articular Contact Models for Computationally Efficient Multibody Dynamic Simulations,” Medical Eng. Phys., 32(6), pp. 584–594. [CrossRef]
Malla, R. B. , and Vila, L. J. , 2017, “ Dynamic Impact Force in an Axial Member With Coupled Effects of Structural Vibration and Various Support Conditions,” Eng. Struct., 144, pp. 210–224. [CrossRef]
Khulief, Y. A. , and Shabana, A. A. , 1987, “ A Continuous Force Model for the Impact Analysis of Flexible Multibody Systems,” Mech. Mach. Theory, 22(3), pp. 213–224. [CrossRef]
Hunt, K. H. , and Crossley, F. R. E. , 1975, “ Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42(2), pp. 440–445. [CrossRef]
Lee, T. W. , and Wang, A. C. , 1983, “ On the Dynamics of Intermittent-Motion Mechanisms—Part 1: Dynamic Model and Response,” ASME J. Mech. Des., 105(3), pp. 534–540.
Lankarani, H. M. , and Nikravesh, P. E. , 1990, “ A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems,” ASME J. Appl. Mech., 112(3), pp. 369–376. [CrossRef]
Gonthier, Y. , Mcphee, J. , Lange, C. , and Piedboeuf, J. C. , 2004, “ A Regularized Contact Model With Asymmetric Damping and Dwell-Time Dependent Friction,” Multibody Syst. Dyn., 11(3), pp. 209–233. [CrossRef]
Zhang, Y. , and Sharf, I. , 2004, “ Compliant Force Modeling for Impact Analysis,” ASME Paper No. DETC2004-57220.
Zhiying, Q. , and Qishao, L. , 2006, “ Analysis of Impact Process Based on Restitution Coefficient,” J. Dyn. Control, 4, pp. 294–298. http://dlxykzxb.cnjournals.net/ch/reader/view_abstract.aspx?file_no=20060402&flag=1
Gharib, M. , and Hurmuzlu, Y. , 2012, “ A New Contact Force Model for Low Coefficient of Restitution Impact,” ASME J. Appl. Mech, 79(6), p. 064506. [CrossRef]
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. [CrossRef]
Guo, Y. , and Parker, R. G. , 2010, “ Dynamic Modeling and Analysis of a Spur Planetary Gear Involving Tooth Wedging and Bearing Clearance Nonlinearity,” Eur. J. Mech. A/Solids, 29(6), pp. 1022–1033. [CrossRef]
Erkaya, S. , 2012, “ Investigation of Joint Clearance Effects on Welding Robot Manipulators,” Rob. Comput.-Integr. Manuf., 28(4), pp. 449–457. [CrossRef]
Meng, Q. , Liu, F. , Fisher, J. , and Jin, Z. , 2013, “ Contact Mechanics and Lubrication Analyses of Ceramic-on-Metal Total Hip Replacements,” Tribol. Int., 63, pp. 51–60. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Varedi, S. M. , Daniali, H. M. , Dardel, M. , and Fathi, A. , 2015, “ Optimal Dynamic Design of a Planar Slider-Crank Mechanism With a Joint Clearance,” Mech. Mach. Theory, 86, pp. 191–200. [CrossRef]
Rahmanian, S. , and Ghazavi, M. R. , 2015, “ Bifurcation in Planar Slider–Crank Mechanism With Revolute Clearance Joint,” Mech. Mach. Theory, 91, pp. 86–101. [CrossRef]
Li, Y. Y. , Chen, G. P. , Sun, D. Y. , 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. [CrossRef]
Lai, X. , He, H. , Lai, Q. , Wang, C. , Yang, J. , Zhang, Y. , Fang, H. , and Liao, S. , 2017, “ Computational Prediction and Experimental Validation of Revolute Joint Clearance Wear in the Low-Velocity Planar Mechanism,” Mech. Syst. Signal Process., 85, pp. 963–976. [CrossRef]
Eritenel, T. , and Parker, R. G. , 2012, “ Three-Dimensional Nonlinear Vibration of Gear Pairs,” J. Sound Vib., 331(15), pp. 3628–3648. [CrossRef]
Jiang, H. , and Liu, F. , 2016, “ Dynamic Features of Three-Dimensional Helical Gears Under Sliding Friction With Tooth Breakage,” Eng. Failure Anal., 70, pp. 305–322. [CrossRef]
Wu, C.-Y. , Li, L.-Y. , and Thornton, C. , 2005, “ Energy Dissipation During Normal Impact of Elastic and Elastic–Plastic Spheres,” Int. J. Impact Eng., 32(1–4), pp. 593–604. [CrossRef]
Stronge, W. J. , 1990, “ Rigid Body Collisions With Friction,” Proc. R. Soc. London, Ser. A: Math. Phys. Sci., 431(1881), pp. 169–181. [CrossRef]
Gilardi, G. , and Sharf, I. , 2002, “ Literature Survey of Contact Dynamics Modelling,” Mech. Mach., 37(10), pp. 1213–1239. [CrossRef]
Pereira, C. , Ramalho, A. , and Ambrosio, J. , 2015, “ An Enhanced Cylindrical Contact Force Model,” Multibody Syst Dyn, 35(3), pp. 277–298. [CrossRef]

Figures

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Fig. 1

One-dimensional direct central collision process between two solid spheres

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Fig. 2

Relation between εpost and εpre for different contact models

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Fig. 3

Example of single steel ball supported by spring impacts on wall

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Fig. 4

Dynamic response of the ball when k = 1.4 × 106 N/m and ε = 0.9

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Fig. 5

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.3

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Fig. 6

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.5

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Fig. 7

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.7

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Fig. 8

Comparison of hysteresis loop when k = 1.4 × 104 N/m and ε = 0.9

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Fig. 9

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.3

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Fig. 10

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.5

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Fig. 11

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.7

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Fig. 12

Comparison of hysteresis loop when k = 1.4 × 106 N/m and ε = 0.9

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Fig. 13

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.3

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Fig. 14

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.5

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Fig. 15

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.7

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Fig. 16

Comparison of hysteresis loop when k = 1.4 × 107 N/m and ε = 0.9

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