# Structural Optimization of Vented Brake Rotors with a Fully Parameterized Model
###### Abstract
In another research, a validated model of a disc brake was used as the basis for parametrically studying and evaluating a set of design guidelines that were intended to minimize the possibility of squeal noise production in the brake system [18]. [PERSON] et al. [19] described a fully coupled transient thermomechanical model of a disc brake that took into account the so-called rotating-heat-source effect. The experimental results from a sequence of dynamometer tests replicating a family of drag braking events, based on the SAE J2521 drag braking schedule [20], were established to validate the model. A recent study reported by [PERSON] et al. [21] studied the mechanism of high-frequency brake squeal through vibration energy. Structural optimization is a natural extension to the analysis and design of brake rotors. In the literature, due to their geometrical complexity, structural optimization of brake rotors usually involves commercial software for optimization and repeated analyses, which either employ the finite element method to solve static, dynamic, or modal problems, or employ the finite volume method to solve CFD problems. [PERSON] and [PERSON] [22] aimed to maximize the convective heat transfer of brake discs mounted on railway vehicles and proposed the specific power dissipation, the product of the average convective heat transfer coefficient and the disc wetted area, to measure the effectiveness in convective cooling for various brake disc designs. The authors adopted fluid dynamic software ANSYS CFX to evaluate the performance of disc models and were able to generate a new disc design with an increase in convective cooling power of over 10% when compared with the existing disc. [PERSON] and [PERSON] [23] employed five geometric parameters of a ventilated brake disc to minimize the maximum total deformation and equivalent stress of the model using the ANSYS software and the response surface methodology and achieved approximately 10% reduction in both deformation and stress. [PERSON] and [PERSON] [24] performed shape optimization to minimize the maximum principal stresses on finger structures of a cast-iron brake disc and then topology optimization to reduce the mass of the disc. Finite element analysis and optimization packages, Abaqus and OptiStruct, were used in their research. In another recent research, the shape and pattern of through-holes and slits on the friction surface of a brake rotor were optimized to minimize the maximum stress and temperature in the rotor model [25]. In this paper, a fully parameterized model for ventilated brake rotors is created using the ANSYS Parametric Design Language (APDL), with 22 parameters uniquely defining the rotor geometry. Then, an advanced, zero-order optimization procedure is applied iteratively on the model to maximize or minimize a predefined objective function with some constraints imposed. Two structural optimization cases are studied in this paper. The first one is a maximization problem for frequency separation between certain eigenmodes of the rotor structure. The second case minimizes the thermal deformation on both sides of the friction surfaces of the rotor with a thermal loading of heat flux generated during the braking process. A conceptual flowchart for this research is shown in Figure 1.