Research on the Influence of Biomimetic Patterns Surface on the Surface Temperature of Drum Brake Lining

Vehicles need to brake frequently on long downhill sections. In this case, the surface of the friction lining is prone to accumulating a large amount of heat, which will reduce the performance of the braking material and lead to braking failure. This article analyzes the heat generation and dissipation mechanism during the braking process of drum brakes based on the law of energy conservation, and establishes a thermal conductivity differential equation. Subsequently, with the honeycomb texture as the biomimetic target, circular, square, and honeycomb patterns with different parameters were designed on the surface of the friction lining, and a finite element model was established using Ansys Workbench. Thermodynamic coupling analysis shows that patterned friction lining can reduce the maximum temperature of the braking surface. Honeycomb patterns have better heat dissipation effects than circular and square patterns. Compared with non patterned brake pads, honeycomb patterns can reduce the maximum surface temperature of brake pads by 14.6%. When the surface area ratio of the honeycomb is 56.8%, its heat dissipation effect is the best.


Introduction
When driving on long downhill roads, vehicles need to brake frequently, and a large amount of frictional heat causes the temperature on the surface of the brake drum and friction lining to continuously rise [1][2][3].Excessive temperature may cause the decomposition of organic materials in the friction lining, reducing the strength and braking performance of the friction lining, and even causing traffic accidents due to brake failure [4][5].It is necessary to seek effective ways to reduce the surface temperature of the friction lining.
In the field of mechanical design, nature is the best teacher for humanity.For example, the honeycomb constructed by bees has a hexagonal structure, which not only saves materials but also improves the strength of the honeycomb, but also maximizes its surface area and enhances its heat dissipation performance [6][7].The insulation tiles at the head of Musk's starship adopt a honeycomb structure, with small gaps between them, which is also to improve the heat soaking and heat dissipation of the insulation tiles.
For drum brake linings, heat dissipation and strength are two important performance factors.The honeycomb structure can accurately meet the requirements of strength and heat dissipation performance.In the following work, we used honeycomb as a biomimetic object to prepare circular, square, and honeycomb shaped convex bodies with the same area arranged according to the honeycomb structure on the surface of the brake linings.Subsequently, simulation analysis was conducted on the surface temperature of friction linings with different patterns.

Description of thermal stress coupling
Based on the characteristics of each component when the drum brake is applied, the following assumptions are made.1) There is no heat source inside each component and it will not enter the plastic deformation stage.2) Ignore the heat exchange process between thermal radiation and the outside world.3) The convective heat transfer coefficient is only related to the heat flux density, the initial temperature of the solid surface, and the temperature of the surrounding fluid.4) Compared to the heat generated during the braking process of the brake drum, the heat carried away by the wear debris is very small and negligible.The braking process is a transient heat transfer process, and the entire braking process is completed in a short time.Therefore, the braking system meets the following control differential equation for heat conduction: Where, T -Temperature, K; t -Time, s;  -Density of material,kg/m 3 ; C -Specific heat, J/kg•°C;  -Thermal conductivity, W/m•°C.

Calculation of heat flux density
According to the law of conservation of energy, braking kinetic energy is converted into braking heat.
Where: Q -thermal energy generated during braking; m -mass of the vehicle; 1 v -initial braking speed; 2 v -final braking speed.
The heat flux density of a single brake drum during braking can be calculated using the following formula.
Where: A -braking area of a single brake drum. -Heat flow distribution density (0.95).

Determination of Mechanical Parameters of Friction Pair Materials
The brake drum is made of gray cast iron of HT250 with density of 7.33*10 3 kg / m 3 , while the brake lining is asbestos free material with density of 2.25*10 3 kg / m 3 .Based on data obtained from the manufacturer's design department, the following mechanical parameters of brake lining materials have been determined ( Tables 1).

Surface Pattern Design of Brake Linings
Three types of brake linings with different surface patterns (honeycomb, rectangular, and circular) were designed as experimental groups.Shorten the area of the no pattern sample to serve as the comparison group (No pattern).The depth of various patterns is 2.5 mm, which is half of the depth of the brake linings.The convex bodies in each pattern were arranged in a honeycomb hexagonal structure, and the simulation results were compared with those no patttern brake linings.Convex on brake lining with different patterns have the same surface area (such as samples 1, 4, 7 and 10) .The parameter design and schematic diagram of bionic pattern are shown in Table 2 and Fig. 1.The mesh generation model of the brake drum and brake linings is shown in Fig. 2.

Load and Boundary Conditions
The finite element method is used for thermal mechanical coupling analysis, and the simulation experiments are divided into two groups: 1) Emergency braking: Apply a braking force of 100N to the brake linings, and brake the brake drum from an initial speed of 60 km/h to 0 km/h for 3.4 seconds; 2) Repeated braking: After accelerating from 0 km/h to 60 km/h, a braking force of 60 N is applied to the brake linings.After 2.8 seconds, the brake drum speed drops to 30 km/h.Remove the braking force, and the electric motor drives the brake drum to accelerate to 60 km/h within 8.5 seconds.The single braking and acceleration process is a braking cycle.This simulation was repeated 12 times for a total of 135.84s to analyze the temperature changes of different surface bionic pattern brake linings under continuous braking conditions.

Emergency Braking
At an initial speed of 60 km/h, apply emergency braking to the brake drum using circular, square, honeycomb shaped brake linings, and no pattern brake linings.Select the temperature field of the brake drum when braking stops for analysis.Table .3shows the maximum surface temperature of the brake linings in 10 sets of tests at 0 s, 10 s, and 20 s after the end of the emergency braking test.It can be seen that at the end of braking, the surface temperature of no pattern brake linings is the highest, while the surface temperature of other patterned brake linings is higher.The reason should be that the contact surface of patterned brake

Conclusion
Using the thermo mechanical coupling method, the temperature distribution on the surface of the friction lining under emergency and repeated braking conditions was analyzed.The results showed that constructing different patterns on the lining surface can effectively reduce the maximum surface temperature of the brake lining, thereby effectively avoiding the phenomenon of thermal degradation during the braking process.
Compared with the commonly used curved friction lining, circular and honeycomb patterns are easy to dissipate heat from convex sidewalls due to their large side surface area.The honeycomb pattern can reduce the maximum surface temperature of the brake lining by 14.6%.When the surface area ratio of the honeycomb is 56.8%, its heat dissipation effect is the best.

Figure 2 .
Figure 2. Mesh model of brake drums and brake linings.

Fig. 3
shows the temperature distribution of No.1 to No.12 brake lining samples during emergency braking.The maximum temperature values are shown in Table. 6.

Figure 3 .
Figure 3. Temperature distribution of brake linings with different surface patterns.

Figure 4 .
Figure 4. Comparison of the highest temperature change curve and average temperature of each sample under repeated braking.

Table 1 .
Material properties of brake lining.

Table 2 .
Design parameters of bionic pattern of brake linings.