Abstract
The dynamic simulation of contact in rolling processes is very time-consuming. This is mainly based on the fine resolution of the surface domain of each roll, which, however, is essential in order to capture the effect of concentrated contact forces. Existing model order reduction techniques cannot be readily applied due to the nonlinear nature of the contact dynamics. In order to improve the speed of contact analysis, the present paper proposes a sophisticated combination of so-called characteristic static correction modes and vibration normal modes for describing the deformation of each roll. While the characteristic static correction modes are required to capture the concentrated nonlinear contact forces, the vibration normal modes describe the global deformation behavior of the rolls. For the computation of the characteristic static correction modes, first attachment modes are computed for a longitudinal sub-area of each roll. Then an eigenanalysis is performed on the component mode synthesis mass and stiffness matrices that correspond to the attachment modes. The resultant eigenvectors have been truncated and applied to the entire surface domain of the rolls. In order to obtain well-conditioned equations, all modes are finally orthonormalized. An example from the metal forming industry is used to demonstrate the results.
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- M :
-
Mass matrix of FE model
- K :
-
Stiffness matrix of FE model
- f :
-
External force vector of FE model
- u :
-
Vector of nodal DOF of FE model
- u b :
-
Boundary DOF of FE model
- u i :
-
Inner DOF of FE model
- u c :
-
Potential contact DOF of FE model
- u n :
-
DOF of set u i minus DOF of set u c
- Φ n :
-
Fixed-interface normal modes
- Ψ c :
-
Constraint modes
- Ψ a :
-
Attachment modes
- \( {\widehat{\boldsymbol{\varPsi}}}_{\mathrm{a}} \) :
-
Characteristic attachment modes
- q :
-
Generalized coordinates of reduced model
- F ESL :
-
Equivalent static load case matrix
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Acknowledgement
Support of this work in the framework of the K2-Austrian Center of Competence in Mechatronics (ACCM) and the Siemens VAI Metals Technologies GmbH is gratefully acknowledged.
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© 2014 The Society for Experimental Mechanics, Inc.
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Sherif, K., Witteveen, W. (2014). Deformation Mode Selection and Orthonormalization for an Efficient Simulation of the Rolling Contact Problem. In: Allen, M., Mayes, R., Rixen, D. (eds) Dynamics of Coupled Structures, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04501-6_11
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DOI: https://doi.org/10.1007/978-3-319-04501-6_11
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