دانلود رایگان مقاله تحلیل ثبات دامنه نوسان مودال و کاربرد آن در جیغ ترمز

Abstract

In the present study, a new approach is proposed to predict the occurrence of squeal in brake systems. This strategy, called Modal Amplitude Stability Analysis (MASA), is based on the calculation of the first harmonic state-space system of nonlinear original equations using a specific linearization of the nonlinear contact forces at the frictional interfaces. An estimation of the occurrence and generation of increasing self-excited vibration is proposed on the basis of monitoring and the evolution of the real parts of the dynamic system considered as a function of modal amplitudes. The application of the proposed MASA methodology to a real industrial brake system is presented. The occurrence of unstable modes and the generation of increasing self-excited vibrations strongly depends on the initial predefined modal amplitudes. The occurrence of new unstable modes (not predicted by classical stability analysis) can be detected. Therefore the MASA methodology appears to be a good compromise in terms of computing time and ease of implementation between the classical Complex Eigenvalue Analysis (CEA) and more complex nonlinear methods (such as the Generalized Constrained Harmonic Balance Method used to predict periodic and quasi-periodic motion).

5. Conclusion

This paper proposed a new method called Modal Amplitude Stability Analysis based on the transformation of the first harmonic approximation of equations of motion (using Harmonic Balance Method) into a state-space system compatible with a stability analysis. This approach and the evolution of the real parts of the dynamic system versus modal amplitudes were used to detect the occurrence and generation of increasing self-excited vibrations. For the global strategy, a new linearization was proposed for nonlinear forces at the frictional interface in order to linearize each contact element independently. This linearization introduced terms in both stiffness and damping matrices and should allow reduction on relative displacements [37] for future developments based on CHBM [29] which could probably be used to reassess the mode shape and frequency according to modal amplitudes. An application for an industrial finite element automotive brake system was presented. The numerical results obtained and the scientific approach proposed demonstrated that the Modal Amplitude Stability Analysis is very interesting for several reasons, despite the assumption on the mode shape and the frequency of the unstable modes. Firstly, there was no convergence problem since no optimization was used. Secondly, the calculation times were compatible with industrial use, as illustrated in this present work.