General Motors and LMS team up to develop a new prediction methodology for solving brake squeal problems

30 September 2004

General Motors, together with LMS, developed a new process that effectively combines advanced testing with systematically correlated static and dynamic simulations to identify and help fix brake squeal early in the design process. GM, one of the world’s largest vehicle manufacturers, validated this method by characterizing a 13kHz intermittent squeal, and has since used it on several current development programs. The ability to measure and model brake squeal dynamics is a dramatic step forward in our noise and vibration reduction efforts. This has generated substantial savings in engineering cost and development lead-time.

Figure 1:  An LMS Virtual.LAB analysis of the finite component models of individual brake system components developed in CATIA.

The Challenge of Modeling Brake Squeal
Brake squeal, generated by brake systems under operation, is an extremely complex phenomenon that’s difficult to model. The characteristics of the different brake system components, the way these parts are put together, the grease that is used to lubricate parts and connections, the temperature at the brake pads, and the friction between brake pads and rotors all affect the tendency of the brake to squeal. The resonances of the individual components interact heavily with each other, making the phenomenon even more difficult to control. Brake squeal has traditionally been addressed with an iterative design-build-test process because regular FE (finite element) analyses are not accurate enough. With this time-consuming approach, problems are extremely expensive to fix since they are usually not identified until relatively late in the design process.
The three of us successfully developed a systematic and rigorous correlation and updating process to reproduce and predict high-frequency brake squeal dynamics. Our process begins with the creation of an initial FE model of the complete brake corner. This model helps us determine an optimal set of measurement locations on the brake corner assembly. Experimental modal analyses performed on the main individual components of the brake system are used to update their respective FE component models by means of manual tuning and automatic optimization routines (see Figure 1, above). Then, a similar sequence of modal testing and model updating is executed on the entire brake assembly (see Figure 2, below right).

Figure 2:  This LMS Virtual.LAB screen shot shows the finite element model of the assembled brake system modeled in CATIA.

As a final step, an Operating Deflection Shape (ODS) of the brake assembly is measured while the brake is squealing. This ODS is compared to the stability results from a complex eigenvalue FE analysis. Once these results match, we can be virtually certain that the unstable modes gained from the analysis depict the same squeal mechanisms as those  on the ODS (see Figure 3, below right).

Validating the Methodology

Figure 3:  The simulated Operational Deflection Shape (ODS) of a squealing brake system as executed by LMS Virtual.LAB.

We used a brake corner exhibiting a 13 kHz squeal to validate this new prediction methodology. In this particular case, a short squeal occurred once or twice per revolution of the brake rotor.
The first step consisted of creating the FE model, selecting measurement locations, and generating the test geometry using LMS Gateway. The modes of the original FE model were used to determine whether the mesh was sufficiently detailed to support accurate modal simulations. They also helped us determine the appropriate number of degrees of freedom for the test geometry and their spatial distribution. Additionally, the software generated Modal Assurance Criteria (MAC), a measure of resemblance or colinearity, for each pair of modes.
The goal of selecting the correct measurement points is to minimize the value of the off-diagonal MAC terms in the resulting matrix. Achieving this assures that the data acquired from the selected measurement points will actually provide complete and accurate modal results. For each cheek of the brake rotor, we selected two concentric circles with 36 measurement points. Other measurement points were located on the brake pads, caliper, brackets, and axle.

Dynamic ODS
For convenience reasons, we performed the ODS next, instead of at the end of the process. The Running Modes module of LMS CADA-X was used to execute the ODS assessments. A brake noise dynamometer enabled the engineers to manually replicate the operating conditions required to produce the squeal. A laser Doppler vibrometer (LDV) captured the out-of-plane rotor deflections, while small lightweight accelerometers tracked in-plane rotor deflections and deflections on nonrotating components. The axle and associated fixture were attached to a large stationary mass, and brake pressure was applied at three different levels, corresponding to the pressure range under which squeal occurred.
The conditions of the system, particularly the rotational wheel speed and brake pressure, were kept constant throughout the tests. Measuring all points on the complete brake assembly required different measurement runs with one common reference channel, corresponding to one point on the caliper.
We split the analysis into three parts: the outboard and inboard cheeks of the disk (both out-of-plane) and the in-plane measurements. This split was needed because the front and rear cheeks could not be measured simultaneously by the LDV. A 48-channel LMS data acquisition system, including LMS CADA-X T-MON and S-MON postprocessing, a microphone trigger, accelerometers, and the LDV, were used to acquire the data for the ODS.
We saved the measured data as cross-powers of the responses with respect to the reference signal and auto-power of the reference signal. The amplitude-corrected cross-powers were animated to create the ODS. While acquiring in-plane data, the data acquisition setup was also needed to track the position of the disk with respect to the timing of squeal events. This enabled accurate positioning of the measurements in space.

Static Modal Analyses
The same locations used for the ODS measurements were also used for the individual experimental component assessments. LMS CADA-X Modal Analysis handled this series of assessments. Modifying the geometry and material properties of an individual component model made it possible to tune the model so as to have it nicely correlated with the measured modal responses.
Once all component models were validated and updated, we analyzed the modal characteristics of the entire assembly, using similar operating and boundary conditions that generated the squeal during the ODS measurements. The correlation of the complete assembly was performed starting with the lower frequencies where the interactions of the components with each other tended to dominate. We tuned the stiffness of all the connections using the LinkSolver routine in LMS Gateway. Again, complex eigenvalue analysis was performed to identify the unstable modes, which were subsequently compared to the previously measured ODS.
The FE model of the considered brake corner showed three unstable modes with a nearly identical shape and all within 150Hz of the frequency range of the experimental ODS. Both the test and the analysis shapes were similar, exhibiting a relative walking motion between the two rotor cheeks.

Brake Squeal Fixed
These results demonstrate that, with proper validation, analysis can serve as a predictive and diagnostic tool to help address brake squeal problems as high as 15kHz relatively early in the design process. The key to the success of the process is the systematic and rigorous correlation between physical tests and virtual FE modeling, at both the component and system level, and under static and dynamic conditions. Once we thoroughly verified the analytical model, we can use their information to identify and fix brake squeal problems much earlier in the design cycle. After validating this method, we have moved it into GM’s mainstream development process and used it on several actual programs.

Tinghui Steven Shi is an engineer at GM’s Pontiac, Michigan, Truck Center; Mark Riefe works as an engineer at GM’s Milford, Michigan, Proving Ground; and Steven Dom is an engineer for LMS International, Engineering Services. Send us your feedback on this article through e-mail c/o de-feedback@helmers.com.

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