A Structural Dynamics Modification Strategy based on Expanded Squeal Operational Deflection Shapes

Abstract

To analyze brake squeal, measurements are performed to extract Operational Deflection Shapes (ODS) characteristic of the limit cycle. The advantage of this strategy is that the real system behavior is captured, but measurements suffer from a low spatial distribution and hidden surfaces, so that interpretation is sometimes difficult. It is even more difficult to propose system modifications from test alone. Historical Structural Dynamics Modification (SDM) techniques need mass normalized shapes which is not available from an ODS measurement. Furthermore, it is very difficult to translate mass, damping or stiffness modification between sensors into physical modifications of the real system. On the model side, FEM methodology gives access to fine geometric details, continuous field over the whole system. Simple simulation of the impact of modifications is possible, one typical strategy for squeal being to avoid unstable poles. Nevertheless, to ensure accurate predictions, test/FEM correlation must be checked and model updating may be necessary despite high cost and absence of guarantee on results. To combine both strategies, expansion techniques seek to estimate the ODS on all FEM DOF using a multi-objective optimization combining test and model errors. The high number of sensors compensates for modeling errors, while allowing imperfect test. The Minimum Dynamics Residual Expansion (MDRE) method used here, ensures that the complex ODS expanded shapes are close enough to the measured motion but have smooth, physically representative, stress field, which is mandatory for further analysis. From the expanded ODS and using the model, the two underlying real shapes are mass-orthonormalized and stiffness-orthogonalized resulting in a reduced modal model with two modes defined at all model DOFs. Sensitivity analysis is then possible and the impact of thickness modifications on frequencies is estimated. This provides a novel structural modification strategy where the parameters are thickness distributions and the objective is to separate the frequencies associated with the two shapes found by expansion of the experimental ODS.