Prediction of unstable friction-induced vibrations using an energy criterion

This thesis describes a new energy-based method to predict friction-induced vibration instabilities in a braking system using complex eigenvalue analysis. Conventional application of the eigenvalue method relies on the real part of the eigenvalue (RPE) of unstable solutions to quantify the relative severity of predicted vibration instabilities. While some correlation has been shown between the magnitude of the RPE and vibration severity, this correlation is not complete, i.e., positive RPE is necessary, but not sufficient, to predict occurrence of unstable vibrations.; The methods introduced in this thesis provide an alternative to the RPE to identify critical unstable modes in a complex eigenvalue solution. A newly developed energy-based stability criterion (EBC) is applied to the eigenvector data of the unstable solution to quantify the relative severity of the predicted vibrations. EBC is significantly better than RPE for predicting the relative severity of unstable operating conditions, when compared with test results. In addition, the newly developed EBC can be extended to predict the unstable vibration amplitude, while conventional complex eigenvalue methods can only provide relative displacements.; The method introduced in this thesis is validated using a beam-on-disk laboratory prototype, which simulates friction-induced coupled vibrations of an automotive disk brake. Three-dimensional finite-element models of the laboratory hardware are developed. The friction and sliding in the stability models are simulated with a nonsymmetric stiffness matrix. Quasi-static correlation of the baseline model is shown for normal modes, contact stiffness, and sliding coefficient of friction.; The energy criterion is developed by evaluating the sliding energy at a friction interface for sinusoidal relative motion and sinusoidally varying load. This formulation is extended to the eigenvector data of unstable complex eigenvalue solutions, providing predictions of the unstable vibration energy as a function of vibration amplitude. The predicted energies show good agreement with the measured unstable vibration propensity and vibration amplitudes. The developed method can also be used to calculate the dissipated energy during unstable vibrations, using measured data at critical points near the sliding interface. A comparison of model energy with measured energy dissipation can then be used to predict the unstable vibration amplitudes from the complex eigenvector results.; The newly developed method has been validated by comparing its results with measured unstable coupled vibrations of the beam-on-disk system. (Abstract shortened by UMI.)...