Improved Modal Assurance Criterion using a quantification of identification errors per mode/sensor

Scanning laser vibrometer measurements generate detailed maps of modal characteristics in normal or 3D directions. Since many points are measured, individual validation of cannot be performed manually in a reasonable time frame and a notable fraction of measurements is expected to be fairly noisy. The key new notion of the paper is a quantification of identification error and level of contribution for each mode and each sensor based on the comparison of measured and synthesized transfers around each resonance. These criteria are shown to allow efficient analysis of the validity of large measurement sets to provide an automated procedure to select sensors that should be kept for each mode. This quantification, being performed before correlation, provides a priori estimates of sources of poor correlation associated with the identification process. It thus becomes possible to provide improved Modal Assurance Criterion estimations where, for each modeshape, sensors known to be incorrectly identified can be discarded. The 3D vibrometer scan of a brake component is used to illustrate the proposed strategies

On the influence of geometry updating on modal correlation of brake components.

In most industries dealing with vibration, test/analysis correlation of modal properties is considered a key aspect of the design process. The success of test/analysis methods however often show mixed results. The aim of this paper is to assess and answer some classical correlation problems in structural dynamics. First an investigation of correlation problems from tests is proposed. Tools based on the modal assurance criterion are presented to provide a deeper analysis of correlation and results improvement. In a second part, the need of FEM topology correlation and update is demonstrated, using an efficient morphing technique. Tolerances in the manufacturing process that are well accepted in design and production stages are shown to lead to significant degradation of the test/analysis correlation. An application to an industrial brake part is eventually presented, in an approach of correlation procedure automatization for recurrent use

Review of model updating processes used for brake components

To be confident in the prediction capability of a model, verification and validation steps are classically performed. Verification checks that the model is properly solved. Since the model used are fairly standard, this is not issue for brake components. Validation checks the relation between model and experiments on actual structures. Here geometry measurements and vibration tests are considered. The study seeks to perform a systematic review of how test quality is evaluated, and models are correlated and then updated. This will give a solid basis to define clear and easily used validations protocols for brake components where prediction of modes and their stability in the manufacturing process is often deemed critical. Updating the geometry before updating the material properties is shown to be very important: the residual error on frequencies is smaller and no bias is introduced in the estimated material properties. Proper pairing of modeshapes is important for broadband comparisons and the MAC criterion is used. Intermediate steps: experimental topology correlation using easy tools with accuracy evaluation, estimation of errors on test shapes, handling of mode crossing, are sources of errors that are analyzed. For the updating of contact properties, where many parameters may need update, the use of model reduction is shown to allow a major speed-up of parametric studies

The Component Mode Tuning (CMT) method. A strategy adapted to the design of assemblies applied to industrial brake squeal

Numerical prototyping is widely used in industrial design processes, allowing optimization and limiting validation costs through experimental testing. Industrial applications nowadays focus on the simulation of complex component assemblies that are generally mass produced. Coupling properties thus have to be modelled, updated and accounted for variability. For squeal applications, simulations still fail at robustly producing exploitable results due to the systems complexity, while experimentations are limited for diagnostic and design improvement. This paper presents a new application of the Component Mode Tuning, an efficient model reduction method adapted to quick system level reanalysis as function of component free modes, to study the effect of coupling. The impact of component coupling stiffness and coupling surface topology is thus assessed on a drum brake subassembly which design is sensitive to squeal. It is shown that significant system differences can come from coupling surface variations with patterns close to experimental observations. This emphases the need for refined analyses to control coupling in the perspective of robust modelling

Characterization of identification errors and uses in localization of poor modal correlation

While modal identification is a mature subject, very few studies address the characterization of errors associated with components of a mode shape. This is particularly important in test/analysis correlation procedures, where the Modal Assurance Criterion is used to pair modes and to localize at which sensors discrepancies occur. Poor correlation is usually attributed to modeling errors, but clearly identification errors also occur. In particular with 3D Scanning Laser Doppler Vibrometer measurement, many transfer functions are measured. As a result individual validation of each measurement cannot be performed manually in a reasonable time frame and a notable fraction of measurements is expected to be fairly noisy leading to poor identification of the associated mode shape components. The paper first addresses measurements and introduces multiple criteria. The error measures the difference between test and synthesized transfer functions around each resonance and can be used to localize poorly identified modal components. For intermediate error values, diagnostic of the origin of the error is needed. The level evaluates the transfer function amplitude in the vicinity of a given mode and can be used to eliminate sensors with low responses. A Noise Over Signal indicator, product of error and level, is then shown to be relevant to detect poorly excited modes and errors due to modal property shifts between test batches. Finally, a contribution is introduced to evaluate the visibility of a mode in each transfer. Using tests on a drum brake component, these indicators are shown to provide relevant insight into the quality of measurements. In a second part, test/analysis correlation is addressed with a focus on the localization of sources of poor mode shape correlation. The MACCo algorithm, which sorts sensors by the impact of their removal on a MAC computation, is shown to be particularly relevant. Combined with the error it avoids keeping erroneous modal components. Applied after removal of poor modal components, it provides spatial maps of poor correlation, which help localizing mode shape correlation errors and thus prepare the selection of model changes in updating procedures

On the influence of geometry updating on modal correlation of brake components.

In most industries dealing with vibration, test/analysis correlation of modal properties is considered a key aspect of the design process. The success of test/analysis methods however often show mixed results. The aim of this paper is to assess and answer some classical correlation problems in structural dynamics. First an investigation of correlation problems from tests is proposed. Tools based on the modal assurance criterion are presented to provide a deeper analysis of correlation and results improvement. In a second part, the need of FEM topology correlation and update is demonstrated, using an efficient morphing technique. Tolerances in the manufacturing process that are well accepted in design and production stages are shown to lead to significant degradation of the test/analysis correlation. An application to an industrial brake part is eventually presented, in an approach of correlation procedure automatization for recurrent use

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

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

Squeal measurement using operational deflection shape. Quality assessment and analysis improvement using FEM expansion.

In presence of squeal, Operational Deflection Shapes (ODS) are classically measured to gain understanding of brake behavior. A simple numeric example is analyzed to justify the use of time-frequency analysis and shows that two real shapes should probably dominate the response. Using measurements on a real brake, this expectation is shown to hold even in the presence of variations with wheel position as well as for reproducibility tests. For a proper relation with the model, it is desirable to also extract modes. The test campaign is used to illustrate how this can be quite difficult due to reproducibility problems. Finally, shapes characterizing the squeal event are fundamentally limited by measurable quantities. Minimum Dynamic Residual Expansion (MDRE), which estimates test motion at all FE degrees of freedom, is shown to be applicable for industrial models and gives insight of test and model imperfections

Review of model updating processes used for brake components

To be confident in the prediction capability of a model, verification and validation steps are classically performed. Verification checks that the model is properly solved. Since the model used are fairly standard, this is not issue for brake components. Validation checks the relation between model and experiments on actual structures. Here geometry measurements and vibration tests are considered. The study seeks to perform a systematic review of how test quality is evaluated, and models are correlated and then updated. This will give a solid basis to define clear and easily used validations protocols for brake components where prediction of modes and their stability in the manufacturing process is often deemed critical. Updating the geometry before updating the material properties is shown to be very important: the residual error on frequencies is smaller and no bias is introduced in the estimated material properties. Proper pairing of modeshapes is important for broadband comparisons and the MAC criterion is used. Intermediate steps: experimental topology correlation using easy tools with accuracy evaluation, estimation of errors on test shapes, handling of mode crossing, are sources of errors that are analyzed. For the updating of contact properties, where many parameters may need update, the use of model reduction is shown to allow a major speed-up of parametric studies

The Component Mode Tuning (CMT) method. A strategy adapted to the design of assemblies applied to industrial brake squeal

Numerical prototyping is widely used in industrial design processes, allowing optimization and limiting validation costs through experimental testing. Industrial applications nowadays focus on the simulation of complex component assemblies that are generally mass produced. Coupling properties thus have to be modelled, updated and accounted for variability. For squeal applications, simulations still fail at robustly producing exploitable results due to the systems complexity, while experimentations are limited for diagnostic and design improvement. This paper presents a new application of the Component Mode Tuning, an efficient model reduction method adapted to quick system level reanalysis as function of component free modes, to study the effect of coupling. The impact of component coupling stiffness and coupling surface topology is thus assessed on a drum brake subassembly which design is sensitive to squeal. It is shown that significant system differences can come from coupling surface variations with patterns close to experimental observations. This emphases the need for refined analyses to control coupling in the perspective of robust modelling