Modeling Multibody Systems Subjected to Impact with Friction
DOI:
https://doi.org/10.31181/rme445Keywords:
Rough Collision, Impact with Friction, Multibody System, Routh’s MethodAbstract
Impact phenomena occur in a wide range of multibody systems, either accidentally or as part of their functional operations. Regardless of its serious degrading effects, it is challenging to model, especially when friction is considered, since the discontinuity due to friction is added to the discontinuity of the velocity due to impact. In this paper, an effective scheme applicable to multibody systems with motion constraints subjected to impacts with friction is developed. The main contribution of this study is the development of a numerical strategy to solve the nonlinear differential equations of motion for three-dimensional multibody systems experiencing impact with friction, as well as the analytical solution of these equations for planar multibody systems. Routh’s incremental method is used to differentiate between the three possible modes during the contact period: continuous sliding, sticking and discontinuous sliding. A critical coefficient of friction is specified, which depends only on the system configuration, and it is used to determine whether the mode of contact is sliding or sticking. Three definitions for the coefficient of restitution are introduced to denote the end of impact. The proposed method is applied to a case study, and the dynamical behaviours are illustrated, with an emphasis on the effect of using each of the three coefficients of restitution. The results demonstrate that the present methodology is a powerful tool for modeling and simulating such practical problems and for assessing the use of different coefficients of restitution.
References
Batlle, J. (1996). The Sliding Velocity Flow of Rough Collisions in Multibody Systems. Journal of applied mechanics, 63(3), 804-809. https://doi.org/10.1115/1.2823366
Batlle, J., & Cardona, S. (1998). The Jamb (Self-Locking) Process in Three-Dimensional Collisions. Journal of applied mechanics, 65(2), 417-423. https://doi.org/10.1115/1.2789070
Bhatt, V., & Koechling, J. (1995). Partitioning the Parameter Space According to Different Behaviors During Three-Dimensional Impacts. Journal of applied mechanics, 62(3), 740-746. https://doi.org/10.1115/1.2897009
Bhatt, V., & Koechling, J. (1995). Three-Dimensional Frictional Rigid-Body Impact. Journal of applied mechanics, 62(4), 893-898. https://doi.org/10.1115/1.2896017
Chatterjee, A., & Bowling, A. (2018). Resolving the unique invariant slip-direction in rigid three-dimensional multi-point impacts at stick-slip transitions (Vol. 51838). American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2018-86126
Elkaranshawy, H. (2007). Rough collision in three-dimensional rigid multi-body systems. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 221(4), 541-550. https://doi.org/10.1243/14644193JMBD99
Elkaranshawy, H. A. (2011). Spatial robotic systems subjected to impact with friction. In Proceedings of the IASTED International Conference on Robotics, Pittsburgh (pp. 269-277). https://doi.org/10.2316/P.2011.752-047
Elkaranshawy, H. A. (2021). The Possible Algebraic Solutions for Rough Collision in Three Dimensional Multibody Systems. MEJ-Mansoura Engineering Journal, 27(3), 1-13. https://doi.org/10.21608/bfemu.2021.142984
Elkaranshawy, H. A., Abdelrazek, A. M., & Ezzat, H. M. (2015). Power series solution to sliding velocity in three-dimensional multibody systems with impact and friction. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 9(10), 585-588. https://www.researchgate.net/publication/335961796_Power_series_solution_to_sliding_velocity_in_three-dimensional_multibody_systems_with_impact_and_friction
Elkaranshawy, H. A., Abdelrazek, A. M., & Ezzat, H. M. (2017). Tangential velocity during impact with friction in three-dimensional rigid multibody systems. Nonlinear Dynamics, 90, 1443-1459. https://doi.org/10.1007/s11071-017-3737-1
Elkaranshawy, H. A., & Bajaba, N. S. (2024). Algebraic solutions and computational strategy for planar multibody systems subjected to impact with friction. Latin American Journal of Solids and Structures, 21(11), e570. https://doi.org/10.1590/1679-78258384
Elkaranshawy, H. A., Mohamed, K. T., Ashour, A. S., & Alkomy, H. M. (2017). Solving Painlevé paradox:(P–R) sliding robot case. Nonlinear Dynamics, 88, 1691-1705. https://doi.org/10.1007/s11071-017-3339-y
Flores, P. (2022). Contact mechanics for dynamical systems: a comprehensive review. Multibody System Dynamics, 1-51. https://doi.org/10.1007/s11044-021-09803-y
Goldsmith, W. (2001). Impact. Courier Corporation. https://doi.org/10.1115/1.3641808
Jia, Y.-B., & Wang, F. (2017). Analysis and computation of two body impact in three dimensions. Journal of Computational and Nonlinear Dynamics, 12(4), 041012. https://doi.org/10.1115/1.4035411
Kane, T. R., & Levinson, D. A. (1985). Dynamics, theory and applications. McGraw Hill. https://ecommons.cornell.edu/items/1f0e5629-0caa-4be2-8384-8869eb9e4fac
KELLER, J. (1986). Impact with friction. Journal of applied mechanics, 53(1), 1-5. https://doi.org/10.1115/1.3171712
Pandrea, N., & Stănescu, N.-D. (2019). A new approach in the study of the collisions with friction using inertances. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(3), 817-834. https://doi.org/10.1177/0954406218763699
Passas, P., & Natsiavas, S. (2022). A time-stepping method for multibody systems involving frictional impacts and phases with persistent contact. Mechanism and Machine Theory, 169, 104591. https://doi.org/10.1016/j.mechmachtheory.2021.104591
Routh, E. J. (1897). The elementary part of A treatise on the dynamics of a system of rigid bodies. (6th ed.). Macmillan and Co., limited, The Macmillan Company. https://openlibrary.org/books/OL7202414M/The_elementary_part_of_A_treatise_on_the_dynamics_of_a_system_of_rigid_bodies.
Stronge, W. (1994). Swerve During Three-Dimensional Impact of Rough Rigid Bodies. Journal of applied mechanics, 61(3), 605-611. https://doi.org/10.1115/1.2901502
Stronge, W. J. (1990). Rigid body collisions with friction. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 431(1881), 169-181. https://doi.org/10.1098/rspa.1990.0125
Uchida, T. K., Sherman, M. A., & Delp, S. L. (2015). Making a meaningful impact: modelling simultaneous frictional collisions in spatial multibody systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2177), 20140859. https://doi.org/10.1098/rspa.2014.0859
Whittaker, E. T. (1964). A treatise on the analytical dynamics of particles and rigid bodies. CUP Archive. https://books.google.com.pk/books?hl=en&lr=&id=qkY4AAAAIAAJ&oi=fnd&pg=PA1&dq=A+Treatise+on+the+Analytical+Dynamics+of+Particles+and+Rigid+Bodies,+Cambridge&ots=xiu3w5Z6zc&sig=GKcpCyDV5OGFyPCu5O7ptpquqRs&redir_esc=y#v=onepage&q=A%20Treatise%20on%20the%20Analytical%20Dynamics%20of%20Particles%20and%20Rigid%20Bodies%2C%20Cambridge&f=false
ZHANG, Y., & SHARF, I. (2007). Rigid body impact modeling using integral formulation. Journal of Computational and Nonlinear Dynamics, 2(1), 98-102. https://doi.org/10.1115/1.2389232
Zhen, Z., & Liu, C. (2007). The analysis and simulation for three-dimensional impact with friction. Multibody System Dynamics, 18, 511-530. https://doi.org/10.1007/s11044-007-9071-5
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