Figure 4 - uploaded by Guillaume Martin
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Complex modes frequency (left) and damping (right) for variable friction coefficient. Reduction on two real modes (dashed lines) and on all real modes (full lines).
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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 var...
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... comparison between the system reduced on the two real modes on the one hand and on all real modes on the other hand is provided by Figure 4. The accuracy of frequencies is not as good with only two shapes, but the coupling still occurs and the damping computation is almost unchanged. ...
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Citations
... When squeal occurs, the 3D-SLDV sequentially scans all points. Using reference accelerometers placed on the brake system, the sequential measurements are then combined using the procedure developed in [1] which deals with the variation of the limit cycle in frequency, amplitude and shape due to the wheel spin. A complex shape is obtained, which contains the two main real shapes that interact throughout the limit cycle. ...
... More details on the implementation, norm definitions and examples can be found in [1], [11]. One just reminds here that model reduction is mandatory to solve the expansion in an acceptable time. ...
... Display of the spatial repartition of modeling and test errors is helpful to go deeper in the analysis of sources of bad correlation as can be seen in [1], [11], [12] which is helpful if model updating must be performed. This is not the main topic for this paper so it will not be developed here. ...
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 [3], the Minimum Dynamic Residual Expansion (MDRE) [4,5], was first proposed to improve the interpretation of experimental shapes measured with low sensor density, typically with accelerometers. In presence of higher number of sensors, this expansion technique can also be used to highlight areas where model error exists [6,3]. It is proposed in this paper to go further with two steps: first with a model parameterization of the areas pointed out by the MDRE result and secondly by updating the parameters. ...
... Two main techniques are available to perform the ODS measurements: using accelerometers which can be measured synchronously but have a low spatial resolution or using 3D Scanning Laser Doppler Vibrometer (3DSLDV) measurements which allow a higher spatial density but lead to sequential measurements. Using sequential measurements is a difficulty previously addressed in [3,6] because the squealing system cannot be considered as time invariant. Results from previous papers, with experiments on both drum and disc brakes, showed that the shapes associated with squeal instabilities are expected and actually found to be dominated by the combination of two real modes. ...
... To extract the two main shapes; three reference mono-axial accelerometers were used: one on the caliper, one on the anchor bracket and one on the arm. From sequential time measurements, the procedure presented in [3,6] was used to extract two main real shapes around 4250Hz, where squeal occurs. The two main shapes are shown in Figure 2. The first shape shows mainly a deformation of the bracket. ...
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.
