Robustness of Residual Stresses in Brake Discs by Metamodeling

Abstract

During casting residual stresses are developed due to the solidification and cooling. In this work the robustness of residual stresses in casted brake discs with respect to variations in four parameters is evaluated. The parameters are Young’s modulus, yield strength and hardening, time of breaking the mould and the thickness of the brake disc. The robustness analysis is performed by Monte Carlo simulations of metamodels which are surrogates to a finite element model. Quadratic response surfaces and Kriging approximations are considered. Those are based on finite element analyses defined by a Latin hypercube sampled design of experiments. In the finite element analyses an un-coupled approach is utilized where a thermal analysis generates a temperature history of the solidification and cooling. Then follows a structural analysis which is driven by the temperature history. After casting the machining of the brake disc is analyzed by gradually removing elements in the finite element model. The results show that the variation in the studied parameters yield large variation in residual stresses. The thickness of the brake disc is the parameter that has largest influence to the variation in residual stresses. Furthermore, the level of the residual stresses are in general high and might influence the fatigue life of the brake disc.

Overview of disc brakes and related phenomena - a review

“…Shin et al [90] also showed that a non heat-treated disc when exposed to a high temperature experiences run out which is more than twice the run out experienced by a heat-treated disc. In another study, Hofwing [91] showed with numerical simulations that residual stresses exist after casting and machining of the disc.…”

Temperature Uncertainty Analysis of Injection Mechanism Based on Kriging Modeling

“…It outperforms other surrogate modeling techniques due to its unique characteristics of spatiotemporal modeling. In particular, regarding materials forming, a lot of research based on kriging model technique has been conducted (e.g., [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 ]). Tuo et al [ 24 ] proposed a kriging model based on a nonstationary Gaussian process that integrates the outputs of different mesh densities in finite element analysis and provides approximation to the exact solution, and then applied the model in casting simulation.…”

“…Tuo et al [ 24 ] proposed a kriging model based on a nonstationary Gaussian process that integrates the outputs of different mesh densities in finite element analysis and provides approximation to the exact solution, and then applied the model in casting simulation. Hofwing et al [ 25 ] performed the robustness analysis of residual stresses in the brake discs casting by Monte Carlo simulations of metamodels, considering quadratic response surfaces and kriging approximations. Li et al [ 26 ] presented a hybrid inverse identification approach by combining the finite element method, kriging model, Latin hypercube sampling and multi-island genetic algorithm to deal with material parameters of aluminum alloy.…”