# Optimization of Brake Calipers Using Topology Optimization for Additive Manufacturing
## 1 Introduction  
The reduction of car weight is a topic of high importance in the automotive industry. A lighter car has an increased acceleration, and thus an improved performance. Moreover, this weight reduction reduces material cost, improves fuel efficiency, as well as reduces vehicle exhaust emissions. According to [PERSON], et al. [1], for every 100 kg weight reduction of light transport vehicles (LTV), their fuel consumption will be decreased on average by approximately 0.4 L/100 km, and thus their CO\({}_{2}\) emissions will be mitigated by 8-11 g/km. There are several ways to reduce car weight, such as the use of lighter materials in manufacturing, the downsizing of the car, and the removal of unwanted material from car components [2]. One of the most implemented material-removal methods is topology optimization (TO). TO is a popular optimization procedure that is applied for both research and manufacturing purposes. It is a mathematical method that optimizes the distribution of the material spatially in a design domain under the given objective functions, boundary conditions, and constraints. This can result in significant material savings of the structures while their mechanical strength is either maintained or enhanced. The TO, together with the size and shape optimization, constitute the three categories of the so-called structural optimization (SO) [3]. The most common approaches for solving the TO-problem are the Solid Isotropic Material with Penalization (SIMP), the Bidirectional Evolutionary Structural Optimization (BESO), and the level-set based optimization [4]. A description of the TO problem along with the SIMP approach that was applied in this research work is presented thoroughly in Section 2. In general, TO finds many applications in the automotive industry and in mechanics, where the weight savings can be remarkable. The car doors, the suspension systems, and the brake systems are some of the most common topologically optimized components in literature. One of the first publications on TO applications in the automotive industry is the work of [PERSON] and [PERSON] [5]. In their research paper, they optimized three models, including a truck frame, a deck lid, and a space frame structure, by using the traditional compliance TO method with an in-house TO software in Ford Motor Company. Another worth mentioning example is the optimization of the automotive tailor-welded blank door either by [PERSON], et al. [6] or by [PERSON], et al. [7]. [PERSON], et al. [6] applied compliance TO in the first place, followed by a size/shape optimization, while [PERSON], et al. [7] utilized the benefits from the BESO. [PERSON], et al. [8] optimized a spring lower seat from a suspension system by using a topology and topography optimization approach. [PERSON] and [PERSON] [9] conducted multi-material compliance TO with SIMP as an interpolation method of an engine cradle and a cross-member of a chassis frame. [PERSON], et al. [10], in their study, optimized a Ferrari F458 chassis with the SIMP method. A conceptual design of an engine cradle was developed by [PERSON], et al. [1] using a combined size, shape, and compliance TO. [PERSON], et al. [2] applied the SIMP method to optimize the mass of a brake pedal. Concerning the optimization of brake calipers, only a few works are found in the literature. [PERSON] [11] optimized both the brake caliper and the upright of a racecar with compliance TO. [PERSON], et al. [12] developed a lightweight design of brake caliper implementing the SIMP approach. [PERSON], et al. [13] optimized a brake caliper in order to reduce both its weight and its heat transfer. On the other hand, [PERSON] and [PERSON] [14] optimized the shape of a brake caliper for squeal noise reduction. Finally, [PERSON], et al. [15] optimized the mass of an opposed piston brake. The optimized structures in all these examples are characterized by their considerable weight savings or/and their performance improvements compared to their initials designs.