NVH compliance issues related to brake squeal constitute nowadays a major cost in industry. Simulation remains very challenging, brake systems being complex assemblies operating in various conditions. Industrial applications rely on Complex Eigenvalue Analysis (CEA) whose recurrent correlation to squeal measurements makes it a relevant working basis. In this context, model exploitation capability for correlation, updating and mitigation design specification is at stake. Modern model order reduction techniques provides ways of controlling parametric squeal studies computation time, data volumes and naturally express modal quantities. Such tools open the path to large parametric studies handling, mode tracking and parameter regression.

Since tests only provide measurements at sensors, it is interesting to use models to estimate the response at all degree of freedom, correct measurement errors and possibly allow updating of model parameters. The paper gives an integrated perspective on methods developed by the control and structural dynamics communities and in particular methods seeking a trade-off between test and model error. The case of a measured brake squeal limit cycle is used to illustrate implementation details found to be important.

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. The methodology will be illustrated for a recent disk brake test and model.

In brake FEM, model updating is often needed to improve the model accuracy and well describe problematic phenomena such as the squeal. To avoid performing a full model updating which is often time consuming, the use of the Minimum Dynamic Residual Expansion method is proposed to help building the updating strategy. The procedure proposed in this paper is evaluated on a disc brake system, using experimental measurements and the nominal model as input data. From experimental squeal measurements, two shapes are extracted and expanded on the current model. The evaluation of the residual error of model shows areas where the model is wrong and guides through the definition of sensitive parameters which need to be updated. Once the model is parameterized, a model reduction strategy is proposed for further computations to be performed in a time compatible with industrial processes. A parametric study is then achieved: the expansion is computed for all the combinations of the chosen parameters. It is finally possible to navigate through the expansion results for all the parameters, evaluate the evolution of the model accuracy and extract the best combination which improves the model representability.

In the presence of squeal, Operational Deflection Shapes (ODS) are classically performed to analyze behavior. A simple numeric example is used to show that two real shapes should dominate the response. This justifies an ad-hoc procedure to extract main shapes from the real brake time measurements. The presence of two shapes is confirmed despite variations with wheel position and reproducibility tests. To obtain a high spatial density measurement, 3D Scanning Laser Doppler Vibrometer is interesting but leads to iterative measurements on a time-varying system. An algorithm to merge sequential measurement and extract main shapes is detailed. Even with a high-density 3D SLDV measurement, shapes characterizing the squeal event are still only known on accessible surfaces. Minimum Dynamic Residual Expansion (MDRE) is thus finally used to estimate motion on a full FE mesh which eases interpretation and highlights areas where the test and the model contain errors.