Abstract
Recently proposed joint interface modes (JIM), which have been presented at the IMAC 25th, consider Newton’s third law across a joint already at the stage of mode generation. This approach leads to significant improvements in the subsequent mode based simulation, where nonlinear contact and frictional forces are applied. This contribution is focusing on the efficient computation of forces according to dry friction. The first part covers the friction model itself. A lot of literature points out that the discontinuity of the well known Coulomb friction is a major drawback in terms of efficient time integration. Therefore alternative friction models are investigated and a comparison with the Coulomb model is performed. The second part deals with the relevance of trial functions in tangential direction of the contact surface. The latter mentioned JIM can be subdivided into Ritz vectors, which are required to approximate the joint deformation in joint normal direction where the contact forces are acting, and such, which are required to approximate the joint deformation in joint tangential direction where the friction forces are acting. Theoretical considerations and a numerical example are presented which reveal, that the number of JIM in tangential direction is significantly smaller as the one in contact direction without losing remarkable quality of the result.
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Abbreviations
- \( {{\tilde{\mathbf M}}} \) :
-
Mass matrix of FE model
- \( {{{\tilde{\mathbf M}}}_{\rm{red}}} \) :
-
Mass matrix of reduced model
- \( {{\tilde{\mathbf D}}} \) :
-
Damping matrix of FE model
- \( {{{\tilde{\mathbf D}}}_{\rm{red}}} \) :
-
Damping matrix of reduced model
- \( {{\tilde{\mathbf K}}} \) :
-
Stiffness matrix of FE model
- \( {{{\tilde{\mathbf K}}}_{\rm{red}}} \) :
-
Stiffness matrix of reduced model
- \( {{\tilde{\mathbf T}}} \) :
-
Transformation matrix
- \( {{\tilde{\bf\Phi }}} \) :
-
Mode matrix
- \( {{{ \vec{f}}}_{\rm{ext}}} \) :
-
Vector of external nodal forces of FE model
- \( {{{ \vec{f}}}_{\rm{fric}}} \) :
-
Vector of frictional nodal forces of FE model
- \( {{{ \vec{f}}}_{\rm{red}}} \) :
-
Vector of projected nodal forces
- \( {{ \vec{x}}} \) :
-
Vector of nodal DOF of FE model
- \( {{{ \vec{x}}}_{\rm{B}}} \) :
-
Boundary nodal DOF
- \( {{{ \vec{x}}}_{\rm{I}}} \) :
-
Internal nodal DOF
- \( {{{ \vec{x}}}_{\rm{IJ}}} \) :
-
Contact area nodal DOF
- \( {{\dot{\vec{\mathbf x}}}} \) :
-
First derivative of \( {{ \vec{x}}} \) with respect to time
- \( {{ \ddot{\bf\vec{x}}}} \) :
-
Second derivative of \( {{ \vec{x}}} \) with respect to time
- \( {{ \vec{q}}} \) :
-
Generalized coordinates of reduced model
- \( {{\dot{\vec{\mathbf q}}}} \) :
-
First derivative of \( {{ \vec{q}}} \) with respect to time
- \( {{ \ddot{\bf\vec{q}}}} \) :
-
Second derivative of \( {{ \vec{q}}} \) with respect to time
- n:
-
Number of degrees of freedom of FE model
- nq :
-
Number of generalized coordinates
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Acknowledgements
Support of the authors by the Engineering Center Steyr (MAGNA Powertrain) and the K2 Austria Center of Competence in Mechatronics (ACCM) is gratefully acknowledged.
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Breitfuss, M., Witteveen, W., Prechtl, G. (2012). On the Mode Based Simulation of Dry Friction inside Lap Joints. In: Mayes, R., et al. Topics in Experimental Dynamics Substructuring and Wind Turbine Dynamics, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2422-2_26
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DOI: https://doi.org/10.1007/978-1-4614-2422-2_26
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