Keywords: cylindrical contact force models, friction model, lubrication model, revolute clearance joints, contact mechanics, multibody dynamics.

In this work a slider-crank mechanism with a revolute clearance joint is used to analyze the suitability of spherical and cylindrical contact force models to describe the dry frictionless contact between cylindrical bodies. It is verified that that the use of purely elastic models, which do not account for the system components' flexibility present in real mechanisms, are not appropriate for modelling the contact between bodies resulting from the large contact forces obtained. In addition, it is demonstrated the contact force increases with the axial length of the contact cylinders, which cannot be predicted by the Lankarani and Nikravesh spherical model [1]. Furthermore, when compared with cylindrical models [2], including a new enhanced model proposed by the authors [3], the spherical model leads to a poor approximation in particular if low clearance values are involved, since contact forces are underestimated.

With regard to the performance of cylindrical models, it can be drawn that the new enhanced contact model is a good alternative to the Johnson model for modelling the contact between cylindrical geometries given that no numerical iterative technique is required to calculate the contact force, which represents an advantage to implement it in a computational program for impact simulation. However, it is observed that the trajectories of the journal inside the bearing are characterized by many free-flight modes instead of contact modes, which does not help the smoothness of the dynamic response of the system. It is demonstrated that when the friction forces [4] are included in the slider-crank model, the trajectories of the journal with respect to the bearing become mostly in the contact mode. This means that the frequency contents of the dynamic response of the system decrease and the time steps done by the numerical integrator becomes larger, adding to the numerical efficiency, of the new enhanced cylindrical model.

When the joint clearance is modelled as a lubricated journal-bearing [5], the reaction force and the crank moment variations are very smooth, resembling those obtained for models with ideal joints only. The lubricant damping effect absorbs part of the kinetic energy and produces smoother and periodic system responses.

1

H.M. Lankarani, P.E. Nikravesh, "A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems", Journal of Mechanical Design, 112, 369-376, 1990. doi:10.1115/1.2912617

2

K.L. Johnson, "Contact Mechanics", Cambridge University Press, Cambridge, England, 1994.

3

C. Pereira, A. Ramalho, J. Ambrósio, "An Enhanced Cylinder Contact Force Model", submitted to Journal of Mechanical Design, 2009.

4

P. Flores, J. Ambrósio, J.C.P. Claro, H.M. Lankarani, C.S. Koshy, "A study on Dynamics of mechanical systems including joints with clearance and lubrication", Mechanism and Machine theory, 41, 247-261, 2006. doi:10.1016/j.mechmachtheory.2005.10.002

5

P. Flores, J. Ambrósio, J.C.P. Claro, "Lubricated revolute joints in rigid multibody systems", Nonlinear Dynamics, 56, 277-295, 2009. doi:10.1007/s11071-008-9399-2

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