Optimal Study for Multi-field Coupling of the Disc Brake Based on Kriging Agent Model

Abstract

In order to alleviate the problem of the temperature rise, thermal deformation and unreasonable local distribution of equivalent stress which will cause fatigue damage and reduction of the service life of the disc brake. In this study, the friction-thermal-mechanical multi-dimensional coupling analysis of the disc brake of belt conveyor is carried out, and the distribution of the transient temperature field and stress field of the disc brake under the emergency braking condition is obtained. The structural parameters of brake disc and brake shoe are taken as design variables, and the maximum temperature and maximum equivalent stress of the brake disc are taken as the optimization objectives. The Kriging response surface proxy model of the maximum temperature and maximum equivalent stress of the brake disc is constructed by using the optimal space filling to collect the data sample points. According to this, the multi-objective genetic algorithm (MOGA) is used to optimize the design, and the optimized structural parameters are obtained, such as thickness and diameter of the brake disc, thickness, length and width of the brake shoe. The maximum temperature, maximum equivalent stress and maximum deformation are reduced, and the fatigue life cycle is improved, which provides a theoretical basis and reference basis for the improvement of relevant technologies of the disc brakes.

Appendix

Thermal conductivity of air:

k_a = 0.0276 W/m K

Outer diameter of brake disc:

d₀ = 0.8 m

Density of air:

p_a = 1.13 kg/m³

Dynamic viscosity of air:

μ_a = 1.91 × 10⁻⁵ N s/m²

Material thermal conductivity:

λ (W/m K)

Material density:

ρ (kg/m³)

Material specific heat capacity:

c (J/(kg K))

Friction coefficient between brake disc and brake shoe:

μ

Angular speed of brake disc rotation:

w (rad/s)

Contact pressure:

p (kN)

Approximate values obtained from response surface model:

$\hat{y}_{i}$

Real value obtained by finite element analysis:

y _i

Average of true values:

$\overline{y}$

Design variables of disc brake:

x = (x₁, x₂, x₃, x₄, x₅)

Upper and lower limits of design variables:

$x_{i}^{\min } ,x_{i}^{\max }$

Target maximum temperature:

y₁(x)

Target maximum equivalent stress:

y₂(x)