An optimal design method for brake squeal noise based on complex eigenvalue and sensitivity analyses and response surface methodology.

摘要

Brake squeal noise is caused by the dynamic instability originating from the rotational friction in the brake system. An asymmetric stiffness matrix is the end result of the dynamic friction in a finite element model of a brake system.; Complex eigenvalue analysis has been used to assess the brake squeal frequencies and their corresponding instabilities of an asymmetric eigenvalue problem (AEVP). The double shift QR or the QZ algorithms should be applied to solve a real AEVP. Other algorithms produce a number of fictitious complex eigenvalues.; The optimization problem for the brake squeal noise consists of a complex-valued objective function (COF) and physical design variables (PDV). A direct solution has been hampered by many unknowns between the COF and PDV. Nonetheless, an optimal solution is possible if the problem is separated into two steps.; In the first step, sensitivity analysis is used to calculate the optimal components' eigenvalues capable of eliminating all unstable eigenvalues. If only the sensitive components' eigenvalues for each unstable eigenvalue are chosen as design variables, finding an optimal solution is virtually guaranteed.; It was first discovered that one of the rotor in-plane doublet modes has the opposite sign to the other in the real parts of the sensitivity, and this precludes eliminating the unstable eigenvalues, which are dominated by rotor in-plane modes. However, it was also found that the corresponding unstable eigenvalues can be eliminated if we use the frequency separation of these modes, which is obtainable by including the rotational effect into the FE model.; Once the optimal components' eigenvalues are found in the first step, the second step of the optimization involves the real-valued objective function. Resolving complex eigenvalues in essence allowed us to resume the conventional optimization with response surface methodology. The optimal physical dimensions are thus obtained in this step.; Using this approach, the double-piston-floating-type-caliper disk brake system is successfully optimized.