Figure 7: Von Mises Stress distribution in the contact area 7. Conclusion It has been shown, that the POD based approach can be used for the computation of joint interface modes. Even the convergence characteristic is similar to the already existing method the POD based method has four important practical advantages: x The POD based JIM have a clear physical meaning. POD with weighted inner product approximates a given subspace in terms of energy. x Using a POD based method instead of an approach which is based on a generalized eigenvalue problem delivers a useful a-priory estimation of the number of necessary JIM. x The proposed method gives an indication whether the number of subareas for the computation of the mechanical joint characteristics is high enough. x Finally it is worth to mention that the POD based approach does not need any system matrixes at all. This is a very important fact when it comes to the commercial realisation of the proposed method which has been done by MAGNA Powertrain. The developed software code is called MAMBA [16]. 8. Acknowledgement Most of the content of this publication is a result of research activities during the first author’s employment at the Linz Center of Mechatronics GmbH (LCM). The investigations have been completed by the author’s follower DI Markus Breitfuss. Support of the authors by the LCM, the Engineering Center Steyr (MAGNA Powertrain) and the K2 Austria Center of Competence in Mechatronics (ACCM) is gratefully acknowledged. 9. Bibliography [1] Gaul L., Nitsche R., The role of friction in mechanical joints, Appl. Mech. Rev.; Vol. 54; No. 2; pp. 93 – 105, March 2001 [2] Ungar E.E., The status of engineering knowledge concerning the damping of built-up structures, Journal of Sound and Vibration, Vol 26(1), pp 141-154, 1973 [3] Craig R. J., A Review of Time-Domain and Frequency-Domain Component Mode Synthesis Methods, Int. J. Anal. and Exp. Modal Analysis, Vol. 2, No. 2, 1987, pp. 59-72 [4] Noor A. K., Recent advances and applications of reduction methods, Appl. Mech. Rev., Vol. 47, No. 5, 1994, pp. 125 – 146. [5] Zu Q. Q., Model order reduction techniques, Springer Verlag London, 2004 [6] W. Witteveen, Irschik H., Riener H., Engelbrechtsmüller M., Plank A., An efficient mode based approach for the dynamic analysis of jointed and local damped structures: Joint Interface Modes, Proceedings of ISMA 2008, Leuven, Belgium, pp. 1815-1824 27
RkJQdWJsaXNoZXIy MTMzNzEzMQ==