A new shape optimization with robustness and its application for brake squeal phenomena

Abstract

This paper proposes a new shape optimization with robustness, and its application for disc brake squeal phenomena is shown. The disc brake squeal is known as self-excited vibration; the real and imaginary parts of the complex eigenvalue indicate the damping coefficient and natural angular frequency, respectively. The modes that have a negative damping coefficient cause disc brake squeal. For reducing brake squeal, non-parametric shape optimization has been applied for the modes that have a negative damping coefficient. However, in the non-parametric shape optimization, shape uncertainties of the brake system components are neglected. The uncertainties influence the robustness of the brake system for brake squeal. Therefore it is necessary to take into account the uncertainties on the non-parametric shape optimization to improve the performance of brake system with robustness. In this paper, component's natural frequencies are adopted as noise factor to express the influence of shape uncertainties. Since the shape uncertainties are non-parametric, it is difficult to measure and quantify the shape uncertainties in the actual design process. On the other hand, the component's natural frequencies are parametric and it is easier to measure and quantify the uncertainties than shape uncertainties. In this paper, a new non-parametric shape optimization with robustness which takes the component's shape as design variables (control factors) and the component's natural frequencies as noise factors is proposed. For a verification of the proposing robust shape optimization, a numerical example by using a simplified disc brake model is presented. For the result, it is shown that the standard derivation of damping coefficient monotonously decreases, satisfying the constraint for the mass of the brake pad at each iteration.