• Damping in guides This includes energy dissipation in longitudinal guides (e.g. slides) and circular guides (e.g. journal bearings). • Electromechanical damping Electromechanical damping can be caused by piezoelectric, magnetostrictive, or electromagnetic effects. • Energy release to the surrounding medium This includes: – air damping – fluid damping – bedding damping Notes on modern, computer-based analytical and measurement programs Whereas the mass and stiffness matrices of relatively complex structures can be readily determined nowadays using three-dimensional CAD drawings, automatic grid generation, and subsequent FEM analysis, an appropriate calculation model cannot usually be established which sufficiently precise information on damping. More precise damping parameters contains can be determined experimentally. “Experimental Modal Analysis” (EMA) has become established as the suitable tool worldwide. It uses measured frequency-response curves between appropriately chosen excitation points and measuring points, and modern curve-fitting techniques for identifying the modal parameters: natural frequencies, eigenmodes, and modal damping ratios. In the case of simple structures, the system can be excited by means of a hammer inpact. In the case of complex components and considerable damping, excitation using one or several exciters has proven convenient, allowing to control exciter amplitudes and energy distribution for selected frequency ranges. The system response is often measured by means of piezoelectric accelerometers or laseroptical sensors. Modern measurement and analytical systems offer the possibility to identify discrete damping couplings provided that the substructures have been separately investigated beforehand. Link modules allow to establish the connection between the results of experimental modal analysis and the calculated FEM analysis (e.g. matching of nodal points and coordinate axes through interpolation). Quality criteria such as MAC (Modal Assurance Criterion) compare the relations (such as orthogonality) between the eigenmodes found in terms of the scalar product of the eigenvectors. Additional normalisation using the mass or stiffness matrix allows a quantitative assessment. After model updating on the modal level, including damping ratios determined by experiment, operation vibrations can be calculated for any load function. The 22
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