Research and /or Engineering Questions/Objective: NVH compliance issues related to brakes constitute nowadays a major cost in industry. Numerical prototyping is a must-have to efficiently design countermeasures but brake noise applications are limited by predictability challenges. Brakes are complex assemblies operating in various conditions, but modelling quality must first be controlled through verification and validation. The latter relies on experimental squeal measurements correlation, efficiently quantified using the Minimum Dynamic Residual Expansion method. It provides a full model expansion of the experimental shape with a local error indicator that can be minimized using large scale parametric studies to produce an updated model with optimal correlation error. Methodology: Squeal modes are evaluated using the Complex Eigenvalue Analysis (CEA) applied to steady sliding conditions from which a tangent model is derived. Correlation is then performed using experimentally measured squeal Operational Deflection Shapes (ODS). Besides the Modal Assurance Criterion (MAC) that directly compares CEA to ODS shapes on sensors, the Minimum Dynamic Residual Expansion (MDRE) method generates an optimal model based shape that minimizes the dynamic strain energy while remaining compliant with the ODS at sensor locations. As a result, the ODS can be observed on the full model along with an indicator based on an error energy field. Quality is thus robustly quantified. In a second step, the MDRE method can be performed on Parametric Reduced Order Models (PROM) to find the optimal parameter set minimizing correlation error. Model updating can thus be performed using a robust metric. Results: It is an unfortunate observation that industrial brake models often fail to reproduce observed noisy phenomena. Design offices being unable to reproduce a noisy frequency or provide sensitive design evolution is a common use case. The presented methodology drives modelling quality improvement through tangible processes upon which teams can capitalize modern best practices. It also provides a quality indicator to rate modelling confidence for countermeasure designs. In the presented use case the final updated model shows a very low error, which resulted in the recovery of unstable modes very close the experimental frequency. Limitations of this study: The MDRE method requires an experimental measurement with enough sensors to provide a relevant result. Sensor numbers are fairly accessible, but should increase with the frequency of interest and should also be distributed on as many components as possible. Unmeasured components is not an issue to apply the method, but areas with coarse sensor distribution will consequently be less precisely quantified. What does the paper offer that is new in the field in comparison to other works of the author: Parametric Reduced Order Modelling for Complex Eigenvalue Analysis and Operational Deflection Shape expansion using Minimal Dynamic Residue Expansion are two methods that have already been extensively presented by the authors. The combination of both into a robust experimentally based model quality optimization process prior to countermeasure studies is new. Conclusion: Brake model quality is the foundation of simulation predictability that is currently lacking in vibration applications. Due to models complexity, quality improvement is a challenging task requiring modern tools. The presented methodology provides an efficient way of leveraging experimental data to obtain quality indicators upon which tangible updating can be performed.
Dr.-Ing. Guillaume Vermot des Roches, Research Engineer, SDTools; Dr.-Ing. Martin Zacharczuk, method development & simulation brake systems department (RD/VDB), Mercedes-Benz AG; Prof. Dr.-Ing. Etienne Balmes, CEO, SDTools