Mr. Hayuru Inoue, Hitachi Astemo, JAPAN

Brake squeal caused by friction induced vibration is still one of the most important issues in conventional automotive disc brakes development. Today, Complex Eigenvalue Analysis (CEA) is widely utilized as a brake squeal simulation. It is an effective implement that can predict several types of self-excited vibrations. On the other hand, It is difficult to quantitatively predict eigenvalues that change and bifurcate by updating the parameters of an equation of motion. Therefore, for example, the degree of eigenvalues transition due to the friction coefficient is clarified only after CEA calculation. Attributed to the cause, the initial design stage of brake caliper has no guidelines for squealing.

Widely known, when the friction coefficient increases, Mode Coupling occurs due to the structural instability behavior of the two-degree-of-freedom system. First, the eigenvalues approach each other in the imaginary direction, and then repel in the real direction. Even in stable two-degree-of-freedom vibrations, a phenomenon called Curve Veering occurs and the eigenvalues approach each other in the imaginary direction, and then repel in the eigenvalue imaginary part direction. Mode Coupling and Curve Veering are known to show similar behavior; however, the correlation between the two is not clear. The purpose of this study is to explain the mechanism of the transition of eigenvalues when coupled.

This study focuses on the eigen polynomial, which is the left side of the eigen equation, and assumes that the eigenvalues exist at the intersections of the curved surface representing the real part of the eigen polynomial and the zero plane. The curved surface is composed of a complex quartic function, and the solution of CEA appears at the intersection, so that the solution can be derived geometrically. The curved surface has the same saddle shape for both unstable and stable vibration. Whether it is stable or unstable depends on how the saddle and the zero plane intersect. Therefore, the geometrical evaluation using the curved surface explains that Mode Coupling and Curve Veering are equivalent, except that their transition directions are different. This assessment prior to the multi-degree-of-freedom CEA is believed to be helpful in obtaining guidance on brake squeal reduction.