# Performances Analysis of a Novel Electromagnetic-Frictional Integrated Brake Based on Multi-Physical Fields Coupling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure and Working Modes

## 3. Mathematical Models of Multi-Field Coupling

#### 3.1. Multi-Field Coupling Mechanism of the Integrated Brake

#### 3.2. Multi-Field Coupling Mathematical Models of the Integrated Brake

_{m}is the density of materials (kg/m

^{3}); c is the specific heat capacity of materials (J/(kg·K)); t is the time (s); k

_{x}, k

_{y}, and k

_{z}are the convective heat transfer coefficients of materials in the direction of x, y, and z, respectively (W/(m·K)); n

_{x}, n

_{y}, and n

_{z}are the cosines of the corresponding boundaries in the normal direction; q is the flux density of friction heat (W/m

^{2}); and q

_{v}is the intensity of internal heat source (W/m

^{3}).

#### 3.3. Multi-Field Coupling Boundary Conditions for the Integrated Brake

^{2}), η is the efficiency of converting friction power into heat energy, μ is the friction factor, p is the brake specific pressure (N·m

^{2}), ω

_{0}is the initial angular velocity, t

_{s}is the braking time (s), and r is the friction radius (mm).

^{2}).

_{1}and T

_{2}are the surface temperature and ambient temperature of integrated brake disc, respectively (°C), R

_{e}is the Reynolds number, P

_{r}is the Prandtl number, μ is the viscosity coefficient of air, D is the diameter of integrated brake disc, ρ is the air density, C

_{p}is the specific heat capacity of air, and k is the thermal conductivity of air.

^{−8}W/(m

^{2}·°C

^{4}).

_{z2max}of the rear axle is as follows:

_{p}is the peak value of the adhesion coefficient, which is taken as 0.8 in this paper.

_{max}of a single rear wheel is as follows:

_{max}of the integrated brake is limited to:

_{b}is the radius of tire.

_{R}(t) is the maximum friction moment (N·m), β is a parameter related to the structure of the integrated brake, and t is the braking time (s).

^{2}), and r is the radius of brake pad (mm).

## 4. Establishing the Finite Element Model

#### 4.1. Three-Dimensional Modeling of the Integrated Brake

#### 4.2. Material Properties of Integrated Brake

#### 4.3. Adding the Required Physical Fields

^{7}s/m, the diameter of coil wire was set to 1.5 mm, and the coils’ excitation current was set to 15 A. The physical field of solid heat transfer was selected in the heat transfer module, where some parameters, such as the velocity of translation motion, the initial value of temperature, the heat flux, the thermal contact, and the diffuse radiation coefficient, were set. The physical field of solid mechanics was added in the structural mechanics module, where the parameters of linear elastic material, freedom and initial value were set. In the mathematical module, the global ordinary differential equations and the differential-algebraic system of equations were selected, where the global equations for angular velocity were set. When calculating multi-physical fields, the four physical fields were simultaneously used as coupling interfaces to calculate the corresponding variables.

#### 4.4. Computational Domain and Mesh Generation

## 5. Numerical Simulation and Analysis

#### 5.1. Temperature Field Analysis for the Integrated Brake

#### 5.1.1. Emergency Braking Condition

^{2}. According to the integrated brake’s working modes, in the emergency braking condition, the electromagnetic brake works independently at the initial stage of braking, then the electromagnetic brake and the friction brake work simultaneously, and finally the friction brake works independently. When the integrated brake works, a moving heat source is applied to the friction surfaces of the integrated brake disc, and the current is applied to the coils of the electromagnetic brake. The cloud charts of temperature distribution of the integrated brake disc at different times are shown in Figure 5.

#### 5.1.2. Downhill Braking at a Constant Speed

#### 5.2. Comparative Analysis of the Integrated Brake and Traditional Friction Brake

#### 5.2.1. Emergency Braking Condition

#### 5.2.2. Downhill Braking at a Constant Speed

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Structural diagram of electromagnetic-frictional integrated brake. 1, brake fluid; 2, brake piston; 3, brake pad; 4, caliper body; 5, integrated brake disc; 6, copper layer; 7, friction brake surface; 8, electromagnetic brake surface; 9, coil; and 10, iron core.

**Figure 5.**Cloud charts of temperature distribution of integrated brake disc. (

**a**) Electromagnetic brake surface at 0.7 s; (

**b**) Friction brake surface at 0.7 s; (

**c**) Electromagnetic brake surface at 2.8 s; (

**d**) Friction brake surface at 2.8 s; (

**e**) Electromagnetic brake surface at 4.0 s; (

**f**) Friction brake surface at 4.0 s.

**Figure 11.**Cloud charts of temperature distribution of the integrated brake disc. (

**a**) Electromagnetic brake surface; (

**b**) Friction brake surface.

Name | Value |
---|---|

Total mass (m) | 2095 kg |

Wheelbase (L) | 2670 mm |

Front axle load (F_{f}) | 1119 kg |

Rear axle load (F_{r}) | 976 kg |

Wheel radius (R_{b}) | 318 mm |

Materials | Relative Permeability μ_{r} | Conductivity γ (s/m) | Relative Dielectric Constant |
---|---|---|---|

Air | 1 | 10 | 1 |

Brake disc | 200 | 10^{6} | 1 |

Copper layer | 1 | 5.998 × 10^{7} | 1 |

Iron core | 4000 | 1.03 × 10^{7} | 1 |

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**MDPI and ACS Style**

Wang, K.; He, R.; Tang, J.; Liu, R.
Performances Analysis of a Novel Electromagnetic-Frictional Integrated Brake Based on Multi-Physical Fields Coupling. *World Electr. Veh. J.* **2019**, *10*, 9.
https://doi.org/10.3390/wevj10010009

**AMA Style**

Wang K, He R, Tang J, Liu R.
Performances Analysis of a Novel Electromagnetic-Frictional Integrated Brake Based on Multi-Physical Fields Coupling. *World Electric Vehicle Journal*. 2019; 10(1):9.
https://doi.org/10.3390/wevj10010009

**Chicago/Turabian Style**

Wang, Kuiyang, Ren He, Jinhua Tang, and Ruochen Liu.
2019. "Performances Analysis of a Novel Electromagnetic-Frictional Integrated Brake Based on Multi-Physical Fields Coupling" *World Electric Vehicle Journal* 10, no. 1: 9.
https://doi.org/10.3390/wevj10010009