# Optimization of Brake Calipers Using Topology Optimization for Additive Manufacturing
## 4 Methodology
Concerning the third optimization level, the housings of both front and rear calipers were topologically optimized, for weight reduction, without sacrificing their stiffness. The TO of the housings is divided into five steps; (1) Pre-processing, (2) Topology Optimization (TO), (3) Post-processing, (4) Validation, and (5) Production. The pre-processing consists of the computer-aided design (CAD) of the housings in SolidWorks and the finite element analysis (FEA) of them in ABAQUS. The initial design concepts of the calipers' housings were created in SolidWorks with respect to the ISR brake calipers. The CAD files were exported and transferred to ABAQUS for FEA. The applied load case in the FEA was for maximum brake force at 120 km/h and warm tires. On the one hand, a pressure, \(P=10\) MPa, and surface traction, \(t=7200\) N, were applied at the pistons' area of the front housing. Furthermore, the housing was fixed with two bolts to the upright. These bolts were replaced in the simulations by two fixtures to reduce the simulation time. On the other hand, the pressure and the surface traction were \(P=4\) MPa and \(t=2800\) N, respectively, at the housing of the rear caliper. The same boundary conditions were also applied in this case. The design space, as well as the used forces and boundary conditions in both housings, are presented in Figure 7. The 3D models were discretized using 1 mm tetrahedral finite elements, resulted in 2,334,921 and 1,981,349 total elements for the front and the rear housing, respectively. The assigned material was an anisotropic Ti6 Al4V with [PERSON]'s modulus \(E_{XY}=120\) GPa and \(E_{Z}=110\) GPa, [PERSON]'s ratio \(\
u=0.31\), and density \(\rho=4.41\) g/cm\({}^{3}\). The material properties were taken from the EOS data sheet, which was the used material of the 3D printed housings. Different TO software was used for the two case studies for comparison reasons. On the one hand, the housing of the front caliper was optimized with a condition-based algorithm in ABAQUS. This algorithm is based on the SIMP approach. The minimization of the model's strain energy was used as objective function while a volume fraction, equal to 7.45% of the initial design space, was used as function constraint. This volume fraction could lead to a 160 g housing. The 160 g target was set with regard to the targeted stiffness properties of the ISR caliper. Optimizing with volume constraints is a process of experimentation with different values of volume fraction until the stiffness goal is reached. Furthermore, the surfaces for the pistons and the fluid channel were the \"frozen areas\", and thus were excluded from the available design space. Finally, 300 design cycles were used as maximum limit. On the other hand, the housing of the rear caliper was optimized in ANSYS Discovery software. This software uses a sensitivity-based algorithm for the optimization and is GPU-based that promises automatically generated CAD models in less than an hour. The applied TO here was also the traditional compliance optimization where the minimization of strain energy was used again as objective function and the volume as  
Figure 7: The design space, the loads, and the boundary conditions of the housings: (**a**) Housing of the front caliper, (**b**) Housing of the rear caliper. function constraint. However, in this case, the volume was set equal to 8.55% of the initial design space, which could lead to a 75 g housing. The surfaces for the pistons and the fluid channel were defined as frozen areas also here. At the post-processing step, the optimized design solutions were imported as STL files to SolidWorks for redesign. Usually, the complex geometries of the optimized designs are making challenging their production with CPM. For this reason, a redesign procedure based on the optimized solutions takes place after the TO. However, when TO is oriented to AM, this step can be omitted. In this study work, it was decided to manufacture the housings with SLM 3D printing.