# Structural Topology Optimization of Brake Disc Using the Equivalent Moving Load Method

## Authors

• Shengfang Zhang School of Mechanical Engineering, Dalian Jiaotong University, No. 794 Huanghe Road, Shahekou, Dalian 116028,
• Jian Yin School of Mechanical Engineering, Dalian Jiaotong University, No. 794 Huanghe Road, Shahekou, Dalian 116028,
• Yu Liu School of Mechanical Engineering, Dalian Jiaotong University, No. 794 Huanghe Road, Shahekou, Dalian 116028,
• Fujian Ma School of Mechanical Engineering, Dalian Jiaotong University, No. 794 Huanghe Road, Shahekou, Dalian 116028,
• Zhihua Sha School of Mechanical Engineering, Dalian Jiaotong University, No. 794 Huanghe Road, Shahekou, Dalian 116028,
• Dapeng Yang School of Mechanical Engineering, Dalian Jiaotong University, No. 794 Huanghe Road, Shahekou, Dalian 116028,

## Keywords:

brake pad, brake disc, disc brake, equivalent moving load method, topology optimization

## Abstract

During the braking process, the brake disc is subjected to the moving load. The process-point of the moving load moves along a certain trajectory, which makes it difficult to design the brake disc structure by using a traditional topology optimization method. The novel Equivalent Moving Load (EML) method proposed in this paper aims to solve this problem. According to the principle of continuous photographing technology, a mathematical model was established by using the round inward polygonal approximation algorithm. The EML method equalizes the continuous dynamic load action to many finite working conditions by geometric approximation. These working conditions are placed along the trajectory. The structure of the brake disc is then optimized by the EML method. Additionally, the influence of the layout style of the brake pads and the total number of working conditions on the optimization result are discussed in this paper. The optimization results showed that the new structure is a three-annulus structure. The weight of the new structure is reduced by 57.95% compared to the initial structure by structural topology optimization using the EML method. It was proved that structural topology optimization using the EML method is efficient in optimizing a structure subjected to dynamic load.

## References

Bendsoe, M.P. & Kikuchi, N., Generating Optimal Topologies in Structural Design Using a Homogenization Method, Computer Methods in Applied Mechanics & Engineering, 72(2), pp. 197-224, 1988.

Gao, J., Li, H., Gao, L. & Xiao, M., Topological Shape Optimization of 3D Micro-Structured Materials Using Energy-Based Homogenization Method, Advances in Engineering Software, 116, pp. 89-102, 2018.

Noguchi, Y., Yamada, T., Izui, K. & Nishiwaki, S., Topology Optimization for Hyperbolic Acoustic Metamaterials Using a high-Frequency Homogenization Method, Computer Methods in Applied Mechanics & Engineering, 335(2), pp. 419-471, 2018.

Fernandes, W.S., Greco, M. & Almeida, V.S., Application of the Smooth Evolutionary Structural Optimization Method Combined with a Multi-Criteria Decision Procedure, Engineering Structures, 143(2), pp. 40-51, 2017.

Sigmund, O., A 99 Line Topology Optimization Code Written in Matlab, Structural and Multidisciplinary Optimization, 21(2), pp. 120-127, 2001.

Min, S., Nishiwaki, S. & Kikuchi, N., Unified Topology Design of Static and Vibrating Structures Using Multiobjective Optimization, Computers & Structures, 75(1), pp. 93-116, 2000.

Kunakote, T. & Bureerat, S., Multi-objective Topology Optimization Using Evolutionary Algorithms, Engineering Optimization, 43(5), pp. 541-557, 2011.

Qu, J. & Su, H.F., Optimization Design on Ventilated Disc Brake Based on surrogarte Model Technology, Engineering Mechanics, 30(2), pp. 332-339, 2013.

Meng, G.Q., Zhang, Z.L. & Dai, R.Q., Disc Brake Optimization Design and Finite Element Analysis, Advanced Materials Research, 811, pp. 325-330, 2013.

Zhang, X. & Kang, Z., Dynamic Topology Optimization of Piezoelectric Structures with Active Control for Reducing Transient Response, Computer Methods in Applied Mechanics & Engineering, 281(11), pp. 200-219, 2014.

Ivarsson, N., Wallin, M. & Dan, T., Topology Optimization of Finite Strain Viscoplastic Systems under Transient Loads. International Journal for Numerical Methods in Engineering, 2018.

Liu, J., Wen, G. & Xie, Y.M., Layout Optimization of Continuum Structures considering the Probabilistic and Fuzzy Directional Uncertainty of Applied Loads Based on the Cloud Model, Structural & Multidisciplinary Optimization, 53(9), pp. 1-20, 2015.

Liu, J., Wen, G. & Huang, X., To Avoid Unpractical Optimal Design without Support, Structural & Multidisciplinary Optimization, 56(6), pp. 1589-1595, 2017.

Jeong, S.H., Lee, J.W., Yoon, G.H. & Choi, D.H., Topology Optimization Considering the Fatigue Constraint of Variable Amplitude Load Based on the Equivalent Static Load Approach. Applied Mathematical Modeling, 56, pp. 626-647, 2018.

2019-12-31

## How to Cite

Zhang, S., Yin, J., Liu, Y., Ma, F., Sha, Z., & Yang, D. (2019). Structural Topology Optimization of Brake Disc Using the Equivalent Moving Load Method. Journal of Engineering and Technological Sciences, 51(6), 791-804. https://doi.org/10.5614/j.eng.technol.sci.2019.51.6.4

Articles