Utilizing ABAQUS finite element software, the study established the relationship between a brake pad structure and distributions of temperature and thermal stress on brake disc. By introducing radial structure factor and circular structure factor concepts, the research characterized the effect of friction block radial and circumferential arrangement on temperature field of the brake disc. A method was proposed for improving heat flow distribution of the brake disc through optimizing the position of the friction block of the brake pad. Structure optimization was conducted on brake pads composed of 5 or 7 circular friction blocks. The result shows that, with the same overall contact area of friction pair, an appropriate brake pad structure can make the friction energy distribute evenly and therefore lowers peak temperature and stress of the brake disc. Compared with a brake pad of 7 friction blocks, an optimized brake pad of 5 friction blocks lowered the peak temperature of the corresponding brake disc by 4.9% and reduced the highest stress by 10.7%.
Disc brake is widely used currently for highspeed train braking. It transforms dynamic energy into heat energy by utilizing friction between brake pad and brake disc and then dissipates the heat energy through heat exchange. This process involves heat transfer, structural features, mechanical characteristics, material properties, and other aspects and is a complex thermalmechanical coupling process. Focusing on brake pressure, brake disk, brake mode, brake pad material, and other factors, domestic and foreign scholars have conducted many studies on the brake disc temperature and stress in the braking process through test experiments and finite element analyses. Chung Kyun Kim and so forth [
The structure differences of friction blocks of a brake pad can lead directly to differences in friction contact time and friction speed at each point on the brake disc surface, result in uneven temperature distribution on the brake disc surface, consequently cause high thermal stress, and therefore exacerbate the brake disc thermal fatigue. It is an important topic to study the relationship between the structure of the friction blocks of the brake pad and the temperature field of the brake disc.
Starting from the relations between the friction block structural difference of the brake pad and the temperature and stress fields of brake disc, this paper establishes a connection between friction block structures of brake pad and temperature and stress distribution characteristics of brake disc, optimizes the structure and arrangement of the brake pad friction blocks, analyzes the variation of brake disc temperature and stress with the optimized brake pad, and finally validates the findings by sequential coupling simulations with ABAQUS6.8 finite element software.
Disc brake assembly consists of brake dick, disc braking element, brake pad, lever, and other parts. It would greatly increase the simulation difficulty and analysis time if including all the parts in the finite element model. Only the brake disc and brake pad are considered when creating the model. Furthermore, the disc (Figure
Brake disc.
Brake pads.
Brake pad and brake disc finite element model.
Friction braking is a complex process involving friction wear, deformation, vibration, and so forth. It is also a process of interactions of multiple physical, chemical, and mechanical changes. To simplify the analysis models, the following assumptions are made:
neglect the effect of the roughness and friction wear of the friction pair contact surfaces;
the contact of the friction pair is face to face contact;
the braking pressure is distributed evenly on the friction blocks;
the heat dissipation of the brake disc is mainly through convection and radiation during braking and neglect the conduction of heat between the disc and the shaft;
the physical properties of the friction blocks do not change with temperature in the braking process.
In the process of braking, the thermal energy generated from the kinetic energy can be divided into two parts: the majority of the heat is first absorbed through conduction by the brake disc and the pads and then gradually dissipated after the braking into the surrounding environment; the other part is rather emitted into the surrounding environment directly off the friction surface through convection and radiation. This paper assumes that 90% of the total kinetic energy is converted into friction thermal energy which is absorbed by the disc and the pads.
How to distribute the friction heat between the friction pair is also needed to be considered when establishing the finite element analysis model. The current approach is to set a thermal distribution ratio that artificially distributes the thermal energy to the disc and the pads. The ABAQUS software used in this study uses constant thermal energy distribution factor which has a default value of 0.5, or 50% of the thermal energy is taken by the disc and the other 50% by the pads.
Because the brake disc rotates at high speed, the convection coefficient of the brake disc changes with the disc speed during braking. For convection heat exchange based on convection heat transfer theory,
And simultaneously,
Therefore, the convection coefficient
The Reynolds number
Therefore, the convection coefficient
Substitute Newton’s cooling equation
This study applies Newton’s law of cooling and StefanBoltzmann equation to convert heat radiation to convection heat transfer coefficient. Take the brake disc emissivity
Refer to Table
Geometric parameters of brake disc and cylindrical friction blocks.
Brake disc size (mm)  Friction block size (mm)  

Inner diameter  Outer diameter  Thickness  Wheel radius  Friction block radius  Friction block height 
 
116  320  20  445  20, 21, 22.5, 23  20 
Properties of friction pair materials.
Density ( 
Elastic modulus ( 
Poisson ratio ( 
Thermal conductivity coefficient ( 
Specific thermal capacity ( 
Thermal expansion coefficient  

Brake disc  7850  202  0.29  32  477  12.3 
Brake pad  5500  180  0.3  74  436  11.1 
The calculation is done in ABAQUS by sequential coupling method. Refer to Table
Information on finite element mesh.
Number of nodes  Number of elements  Element type  Element abbreviation  

Brake disc  28917  24192  8Node thermal coupling hexahedral element with reduced integration  C3D8RT 
A1  1560  879  
A2  1872  1053  
A3  2183  1228  
Brake pads  
B1, B2  1590  987  
B3, B4  2275  1487 
Figure
Distribution of brake disc surface temperatures of different structures of brake pads.
Brake time 10 s
Brake stop
Figure
Variations of brake disc Mises stress in depth direction.
The above results show that for different structures of brake pads, the distributions of the generated friction heat are different, and, as a result, the values and distributions of the peak temperatures and stresses on the brake disc surfaces are different. For brake disc A1, the friction blocks are distributed more evenly on its surface, the overlaying of friction heat decreases, and the brake disc surface temperature and stress are the lowest. For disc A2, the surface temperature and stress fluctuate the most at the initial braking phase. Brake disc A3 has the highest temperature at the end of the braking because the friction radii of the centers of the contact areas of the multiple friction blocks are basically the same, and the friction heat is superimposed leading to high variation in temperature and stress.
Assuming that the energy produced by friction is distributed uniformly in circumferential direction of the brake disc, the heat source produced by the friction pair of the brake pad and brake disc moves relative to the brake disc in the braking process. Therefore, the heat flow density into any differential arc block of the brake disc shall be the ratio of the total heat entering the brake disc and the covered area of the brake disc by the differential arc block. Then the heat flow density [
If dividing the friction area of the disc into
From Formula (
From the point of view of energy,
The following will illustrate the process of calculating the radial structural factor through an example (Figures
Geometric parameters of the block and pad.
Disc dimension (mm)  Pad dimension (mm)  

Inner radius  Outer radius  Number of blocks  Radius of friction block 
 
147.97  268.52  3  30 
Friction ring illustration.
Areas of friction rings.
The area of each ring is as shown in Figure
The center radii of the seven friction rings are calculated based on the ring thicknesses and listed in Table
Center radius of friction rings.
Center radius of friction ring (mm)  








 
156.58  173.80  191.02  208.25  225.47  242.69  259.91 
The areas of the rings
Areas of friction rings.
Areas of friction rings (mm^{2})  








 
85.62  1155.54  1959.88  2294.09  1566.58  986.16  434.42 
The corresponding radial structural factors, as shown in Table
Radial structural factors.

1  2  3  4  5  6  7 


13406.38  200850.23  374376.28  477744.24  353198.76  239331.17  112910.10 

1771817.16  

0.76  11.34  21.13  26.96  19.93  13.51  6.37 
Table
For the impact of brake pad structure on the friction heat distribution on the brake disc in circumferential direction, we adopt the circumferential structural factor, which is defined as the ratio of clearance area
The lager the circumferential structural factor, the lager the diversion of the brake pad in the circumferential direction.
There is a corresponding relationship between the radial structural factor and the circumferential structural factor of a brake pad and the temperature field and thermal stress field of the brake disc. The fluctuation of the radial structural factor can impact the disc surface temperature and distribution of the stress field. Therefore, the temperature field and thermal stress distribution of a brake disc can be improved by reducing the fluctuation of radial structural factor, lowering the largest radial structural factor and increasing the circumferential structural factor.
A program for brake pad optimization is written in MATLAB. Firstly, program the friction block positions and limit the moving range of the blocks. Secondly, calculate all radial structural factors under the friction block arrangement on any friction ring of the brake disc at certain increment. Draw the distribution curve of radial structural factors in radial direction, calculate the difference
MATLAB program flow chart.
Table
Data of optimized pad structure.
Serial number  1  2  3  4  5  6  7 

In friction ring radius 
202  217  240  262  284  
Circumferential angle 
12.3  41.5  26.6  13.26  34.25  
In friction ring radius 
214 
228 
245 
260 
265  291  291 
Circumferential angle 
14.95  28.36  5.46  18.56  35.24  9.65  26.85 
Diagram of friction pair.
Numerical model of friction blocks arrangement (optimized: B1 and B3, nonoptimized: B2 and B4).
Figure
Nodal temperature distribution on brake disc.
Figure
Relationship between nodal temperature and friction radius.
Figure
Relationship between structure factor and friction radius.
Brake pad of 5 round friction blocks
Brake pad of 7 round friction blocks
Comparing Figures
Figure
Relationship between thermal pressure and friction radius.
With the same total contact area of friction pair, the number and arrangement of friction blocks can impact the temperature and stress on the brake disc surface. An appropriate brake pad structure can make friction energy distribution more uniform to lower peak temperature and stress.
Based on the relationship between the features of friction blocks arrangement and the heat distribution on brake disc surface, the concepts of radial structural factor and circumferential structural factor are introduced. The radial structural factor reflects the distribution pattern of friction power on brake disc in radial direction; the circumferential structural factor reflects the distribution pattern of friction power in circumferential direction. The larger the radial structural factor and the smaller the circumferential structural factor the more uniform the temperature distribution on the brake disc surface and the lower the maximum temperature on the disc surface.
Utilizing MATLAB to program brake pad structure optimization. The brake pads formed by 5 round friction blocks and 7 round friction blocks are optimized by reducing the largest radial structural factor and increasing the circumferential structural factor. The maximum temperature and stress on brake disc of the optimized brake pad of 5 friction blocks are 4.9% and 10.7% lower, respectively, than those of the optimized brake pad of 7 friction blocks.
The work was supported by the Scientific Research Project of Liaoning Provincial Education Department (Project no. L2013187).