Keywords: contact mechanics, conformal contact, internal cylindrical contact, finite element models, cylindrical contact force models, multibody dynamics.

The continuous contact force method has been widely used to handle the contact phenomena in multibody dynamics [1]. Being straightforward to implement in a computational code, the Hertz spherical contact model has been extensively used for modelling contact forces in multibody systems, even in the case of cylindrical contact. However, for cylindrical contact geometries the shape and the size of the bodies and the way in which they are supported must be also taken into account. Most of the cylindrical contact models available in the literature were derived based on the Hertz pressure distribution, which means that they have a validity domain of application, which depends on clearances and material properties [2]. To discuss the applicability of the Johnson model to describe the conformal contact of internal cylinders, and for very low clearance values, a numerical study was conducted using the finite element code MARCR and the results compared with those obtained using the analytical model proposed by Johnson [3]. To perform this numerical study the contact geometry of an internal cylinder inside an external cylinder was selected.

As first approach, a rigid-deformable contact was considered, with the internal cylinder corresponding to a rigid body and the external to a deformable body. The results show that modelling the contact between bodies as a rigid-deformable geometry is not the most appropriate approach, particularly for very low clearances, since differences between models are unacceptable. In fact, modelling an internal cylinder as a rigid body leads to a very rough approximation, firstly because real bodies are not absolutely rigid, and secondly, since the rigid body does not suffer any type of deformation, the stiffness of the contact is overestimated. In order to clarify this issue, the internal cylinder was modelled as a deformable body. A good agreement between the numerical results and those obtained by the Johnson analytical model was found, for a suitably refined mesh, even for extremely low clearance values, since maximum error values lower than 10% were achieved. Thus, it can be concluded that even for very small clearance-external radii ratios, the analytical solution proposed by Johnson, based on the Hertz theory, remains appropriate to describe the conformal contact between cylindrical geometries. Additionally, it proves to be the model that best describes contact between cylindrical bodies, when compared with other models provided in the literature [2].

1

P. Flores, J. Ambrósio, J.C.P. Claro, H. Lankarani, "Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies", Springer, Dordrecht, The Netherlands, 2008.

2

C.M. Pereira, A.L. Ramalho, J.A. Ambrósio, "A Critical Overview of Internal and External Cylinder Contact Force Models", Nonlinear Dynamics, 63(4), 681-697, 2011. doi:10.1007/s11071-010-9830-3

3

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

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £130 +P&P)