# Structural Optimization of Vented Brake Rotors with a Fully Parameterized Model
## 4 Conclusions  
A fully parameterized model for ventilated brake rotors was created using the ANSYS Parametric Design Language, with 22 parameters uniquely defining the rotor geometry. To ensure the credibility of the finite element model and to ease the computational burden during optimization, a convergence test was performed, resulting in an accurate finite element model with a moderate grid size. With this parameterized model, two optimization cases were investigated. In Case 1, frequency differences between the 6 ND and 1T modes and 1T and 7 ND modes were combined and maximized. Frequency separation optimization was achieved, resulting in a combined improvement of 181.4 Hz in the objective function. Care had to be taken to ensure correct modes were identified and tracked during optimization because mode orders indeed changed as the geometrical parameters of the rotor model varied in the process. In Case 2, a complete analysis involved a transient thermal analysis and a structural analysis on a sliced rotor model. A transient thermal analysis was first performed, with a heat flux loading applied on the friction surfaces, and a series of temperature distributions on the model were obtained. Then, a structural analysis was executed with the temperature variations as a multistep loading, to finally acquire the thermal deformation of the model. Minimization on the deformation was performed to accomplish a great reduction in thermal distortion, with the objective function values reduced from 0.0611 mm to 0.0037 mm. Since wear and the manufacturing process cause the geometrical values of a brake rotor to deviate from its design values, all calculations are valid only for a new braking system in an ideal condition. Some general conclusions from the present study can be summarized as follows:  
1. Structural optimization, including frequency separation maximization and thermal distortion minimization, based on a fully parameterized model for vented brake rotors can be efficient and very effective;
2. During an optimization process involving modal analysis, mode orders alter as the geometry changes. Therefore, it is of the utmost importance that the code be able to automatically identify and track correct modes, and consequently, that the modal frequencies not be misused for calculating constraints or the objective function;
3. Abrupt temperature variation near the intersection of the hub and disc caused brake rotor coning. However, uneven temperature distribution between the inboard and outboard discs could offset the coning effects to some extent. A brake rotor design with a thinner outboard disc and a thicker inboard disc provides a great choice for rotor coning reduction.  
Conceptualization, Y.-T.H. and K.-N.C.; methodology, Y.-T.H. and K.-N.C.; software, Y.-T.H. and Y.-M.L.; validation, Y.-T.H., Y.-C.L. and K.-N.C.; formal analysis, Y.-T.H. and K.-N.C.; investigation, Y.-T.H. and K.-N.C.; resources, Y.-C.L. and K.-N.C.; data curation, Y.-T.H., K.-N.C. and Y.-M.L.; writing--original draft preparation, Y.-T.H. and K.-N.C.; writing--review and editing, Y.-C.L. and K.-N.C.; visualization, Y.-T.H. and Y.-M.L.; supervision, Y.-C.L. and K.-N.C.; project administration, Y.-C.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.