Optimizing Friction Block Location on Brake Pads for High-Speed Railway Vehicles Using Artificial Neural Networks

Abstract

Brake discs play a crucial role in braking railway vehicles, but the frictional heat generated during the braking process can lead to high temperatures on the disc. Changes in the friction block location on the brake pad result in variations in the temperature distribution across the brake disc. This study aims to optimize the positioning of friction blocks on the brake pad using artificial neural networks (ANN) and the Design of Experiments (DOE) approach based on the Taguchi methodology. The primary objective of this study is to mitigate temperature discrepancies in the frictional heating rate among distinct sectors along a radius from the center of the brake disc. To analyze the temperature variations caused by frictional heat, finite element analysis (FEA) is executed to account for the thermomechanical characteristics of the brake disc. The optimized brake pad, obtained through the ANN, is evaluated based on the temperature and thermal stress applied to the brake disc. The optimized model displays a larger hot band on the brake disc compared to the original model, leading to a more even distribution of thermal stress across the brake disc. In conclusion, the use of optimized pads offers significant performance benefits, resulting in a reduced maximum temperature and thermal stress, thus improving the overall braking performance of railway vehicles.

1. Introduction

Brake discs, one of the key components in a brake system, play a pivotal role in converting the kinetic energy of railway vehicles into frictional energy, thus ensuring an effective braking mechanism. A significant phenomenon that arises during the braking process is the marked rise in the temperature of the brake disc, primarily attributed to the frictional heat generated. In this way, the frictional heat from braking increases the temperature of the discs and pads, greatly affecting the life and performance of the brake [1,2]. Hence, achieving a uniform temperature distribution throughout the brake disc is of paramount importance. Deviation from this uniformity, leading to hot spots, can drastically diminish the disc’s life, amplifying the thermal stress. Therefore, to improve the braking performance, it is necessary to design the brake pad so that the uniform heat distribution of the brake disc can be achieved [3,4].

The era of high-speed railway vehicles has brought a strong need to refine and optimize braking systems in trains. Numerous studies have been undertaken to improve the braking performance by identifying the optimal design for brake discs and pads. Park [5] introduced a method to reduce the uneven wear of the brake pad. This involved analyzing the pressure distribution on the disc’s contact surface using finite element analysis and determining the optimal brake pad shape through robust design using the Taguchi method. Goo [6] proposed a new approach to the thermoelastic behavior of brake disc pads. The new approach was to determine the relations between the temperature profiles and heat flux input profiles in the radial direction on the disc surface. Ghazaly [7] investigated the optimal brake pad design to reduce squeal noise through various design factors using the response surface methodology. A finite element model at the disc brake was used to investigate brake squeal. Kuncy [8] employed an artificial neural network (ANN) to predict the wear rate and friction coefficient of brake pads. The predicted wear rate and friction coefficient obtained through the ANN models were compared to the measured values using various statistical indicators. The results showed that the ANN accurately predicted the wear rate and friction coefficient of the developed automotive brake pads. Han [9] proposed the shape optimization of the brake pad, which is performed to reduce uneven wear. The nonuniform contact pressure distribution on the pad surface that occurs during single braking was confirmed using a coupled thermomechanical analysis. The wear amount in the brake pad was measured using a brake dynamometer test to confirm the correlation between the nonuniform contact pressure distribution and uneven wear. Ikpambese [10] conducted a comparative analysis of multiple linear regression and ANNs to predict the wear rate and coefficient of friction of brake pads. The results demonstrated that the ANN model was equally effective in predicting both the wear rate and coefficient of friction for the brake pads. Harlapur [11] presented a relationship between the stopping distance of a vehicle and its brake pad thickness using simple machine learning algorithms. Saurabh [12] investigated the load-dependent wear behavior of copper-free semimetallic brake material. Through Taguchi’s method and ANOVA, the impact of the normal load on the wear process was found to be maximum. The optimum condition for the minimum wear rate was proposed. Stender [13] presented a new method for the handling of data-intensive vibration tests to gain better insights into friction brake system vibrations and noise generation mechanisms. A recurrent neural network was employed to learn the parametric patterns that determined the dynamic stability of an operating brake system. This model can predict the occurrence and onset of brake squeal with high accuracy.

The current literature on braking performance and brake disc and pad optimization mainly emphasizes reducing brake squeal and predicting the wear rate. However, there is a noticeable research gap in optimizing the brake pads to mitigate thermal stress and limit the peak temperature experienced by the brake disc. Addressing this oversight, our study employs an ANN to pinpoint the best arrangement for circular friction blocks on brake pads, aiming to boost the braking performance while diminishing thermal stresses, as illustrated in Figure 1. To train the ANN model, we sourced our dataset using the Design of Experiments (DOE) technique. The strength of the DOE lies in its ability to yield comprehensive system data from a minimal set of experiments. This ensured our ANN model’s high accuracy, even when the dataset size was constrained. The FE model, developed and validated in a previous paper, was used to analyze the thermomechanical characteristics during the braking process [14,15]. The original model and the optimized model using the ANN were compared to the maximum temperature and thermal stress.

2. Materials and Methods

The analysis of a braking mechanism through the test requires various environmental conditions, such as the configurations of the equipment and the time cost. An analytical review is needed to analyze the characteristics (thermal stress, disc temperature, etc.) that cannot be demonstrated in the test. The results of FEA for the brake disc were compared to the test results, and the validity of the FE model was verified [14,15]. Then, the FE model considering the thermomechanical characteristics during the braking process was utilized. The material properties and boundary conditions, including the heat transfer coefficient, thermal distribution, friction coefficient, velocity, etc., required for FEA were specified.

2.1. Mechanical Properties of the Brake Disc and Brake Pad

For high-speed railway vehicles reaching a maximum speed of 300 km/h, each axle is equipped with four alloy forging steel discs, as shown in Figure 2 [16].

Table 1. Mechanical properties of the brake disc and brake pad [17].

Description	Unit	Notation	Brake Disc	Brake Pad
Density	kg/m3	${\rho }_d$, ${\rho }_p$	7850	5120
Poisson’s ratio	-	$\nu$	0.3	0.25
Elastic modulus	GPa	E	202	102
Thermal conductivity	W/(m·K)	$k_d$, $k_p$	45	24
Specific heat	J/(kg·K)	$c_d$, $c_p$	460	500
Thermal expansion coefficient	1/K	$\alpha$	$1.05\times {10}^{-5}$	$1.67\times {10}^{-5}$

lists the mechanical properties of the brake disc and brake pad. The brake disc is crafted from a forged steel alloy, while the brake pad is composed of a metallic sintered friction material. Moreover,

Table 2. Specifications of the railway vehicle.

Item	Unit	Notation	Spec.
Weight of the railway vehicle	kg	M	49,060
Max. velocity	km/h	V	300
Wheel diameter	mm	$D_w$	920
Outer diameter of the disc	mm	$D_d$	640
Inner diameter of the disc	mm	$D_i$	350
Thickness of disc	mm	$t_d$	45
Diameter of the friction block on pad	mm	$D_p$	40
Thickness of the friction block on pad	mm	$t_p$	20

outlines the specifications of the railway vehicle, which are critical in ensuring efficient and secure braking system performance in high-speed railway applications.

2.2. Key Thermal Parameters: Convection Heat Transfer Coefficient and Heat Distribution Rate

For solid discs, the convection heat transfer coefficient (h) in both turbulent and laminar flow can be determined using an empirical equation. Flow characteristics are turbulent and laminar based on the Reynolds number (Re) [14,15,18,19,20,21]:

$$\begin{array}{cc}\hfill h=0.04\left(\frac{k_a}{D_d}\right){\mathrm{Re}}^{0.8}& \left(\mathrm{Re}\ge 2.4\times {10}^5\right)\hfill \\ \hfill h=0.70\left(\frac{k_a}{D_d}\right){\mathrm{Re}}^{0.55}& \left(\mathrm{Re}<2.4\times {10}^5\right)\hfill \end{array}$$

(1)

$$\mathrm{Re}=\frac{{\rho }_{a}V{D}_d}{{\mu }_a}.$$

(2)

$k_a$ represents the air’s heat transfer coefficient, $D_d$ represents the outer diameter of the brake disc, ${\rho }_a$ signifies the air density, V corresponds to the speed of the railway vehicle, and ${\mu }_a$ represents the air’s coefficient of viscosity.

For temperature analysis, precisely assessing the allocation of brake energy between the brake disc and brake pad is crucial. The heat distribution rate ($\gamma$) can be estimated using the following equation [14,15,18,19,20,21]:

$$\gamma =\frac{1}{1+\sqrt{{\rho }_p{c}_p{k}_p/\phantom{{\rho }_p{c}_p{k}_p{\rho }_d{c}_d{k}_d}{\rho }_d{c}_d{k}_d}}$$

(3)

where ${\rho }_d$ and ${\rho }_p$ are the densities of the disc and pad, $c_d$ and $c_p$ are the specific heats of the disc and pad, and $k_d$ and $k_p$ are the thermal conductivities of the disc and pad, respectively.

2.3. Finite Element Analysis Conditions

The braking system of a railway vehicle comprises a brake disc, brake pad, caliper, and additional components. To streamline the analysis and save time, the finite element (FE) model was limited to the brake disc and brake pad alone. The FE models for the brake disc and pad are depicted in Figure 3. Detailed specifications of the brake disc and friction block, including the outer/inner diameter and thickness, are outlined in Table 2. These FE models consisted of 9592 nodes and 5832 elements, utilizing hexahedron solid elements (C3D8T) for the thermomechanical analysis.

The analysis adhered to the international standard UIC 541-3 [22]. The initial velocity was set at 300 km/h, accompanied by a temperature of 60 °C. The braking process consisted of two stages: an initial deceleration from 300 km/h to 215 km/h, followed by a subsequent phase decelerating from 215 km/h to a complete halt at 0 km/h. Both commercial and emergency braking forces were accounted for and analyzed within the context of the finite element analysis (FEA). Figure 4 illustrates the progressive variation in the convective heat transfer coefficient during braking, showcasing a linear decline under constant deceleration for both laminar and turbulent flows. At the velocity of 300 km/h, the coefficient was measured at 273 W/(m²·K). Utilizing Equation (3), the heat distribution rates were computed as 0.61 for the disc and 0.39 for the pad, respectively. Deceleration and friction coefficient values were derived based on the guidelines provided in UIC 541-3.

To conduct the FEA, the ABAQUS/Explicit software was utilized, employing a coupled temperature–displacement analysis. Figure 3 visually represents the boundary conditions utilized for the braking analysis, encompassing definitions for contact, pressure, convection, velocity, and initial temperature.

3. Optimizing Friction Block Location on Brake Pads

Variations in the friction block location on the brake pad induce temperature distribution changes across the brake disc. To tackle this challenge, an artificial neural network (ANN) was employed to optimize the friction block arrangement. While conventional structural optimization methods demand theoretical knowledge, experience, and time, a well-trained ANN can approach the objective function even without such prerequisites. Utilizing the Design of Experiments (DOE), a dataset was created for ANN learning. Through finite element analysis (FEA), the optimized brake pad’s performance was evaluated in terms of the maximum disc temperature and thermal stress. Subsequently, a comparison was made between these findings and the outcomes associated with the original brake pad.

3.1. Optimal Design Approach

The interaction of friction between the brake disc and pad generates distinct hot bands and spots on the disc’s frictional surface, impeding smooth braking performance and causing uneven wear, vibrations, and noise. This can lead to elevated temperatures and thermal cracking, reducing the disc lifespan. Achieving even friction distribution is essential to prevent uneven wear, necessitating research into optimizing the braking performance [17]. Figure 5 shows the brake pad’s bilateral symmetry and numbered friction blocks. The brake disc is divided into 11 radial sections.

Table 3. Initial position of the friction blocks on the brake pad.

Friction Block #	x (mm)	y (mm)
1	27.0	199.5
2	70.0	213.5
3	112.0	191.0
4	160.0	190.5
5	34.0	246.5
6	31.0	293.0
7	80.0	272.5
8	116.0	243.5
9	162.0	236.5

presents the current friction block arrangement on the KTX high-speed railway vehicle’s brake pad. Subsequently, the problem statement for optimal brake pad design is introduced.

$$\begin{array}{cc}\hfill \mathbf{Find}& x_i,y_i\mathrm{where}i=1,2,\cdots ,9\hfill \\ \hfill \mathbf{Minimize}& F\left(f_i\right)=\frac{1}{n}\sum _{i=1}^n{\left(f_i-u\right)}^2\mathrm{where}{f}_i=\frac{1}{{\sum }_{i=1}^n{s}_i}\mathrm{and}u=\frac{1}{n}\sum _{i=1}^n{f}_i\hfill \\ \hfill \mathbf{Subject}\mathbf{to}& 4r^2-{\left(x_i-x_j\right)}^2-{\left(y_i-y_j\right)}^2\le 0\mathrm{where}j=1,2,\cdots ,9\hfill \\ \hfill & r-x_i\le 0\hfill \\ \hfill & x_i+r-190\le 0\hfill \\ \hfill & y_i+r-318.5\le 0\hfill \\ \hfill & 166.5+r-y_i\le 0\hfill \\ \hfill & y_i+0.44x_i-334.6+\frac{r}{0.92}\le 0\hfill \\ \hfill & 176.5+\frac{r}{0.99}-0.13x_i-y_i\le 0\hfill \end{array}$$

(4)

In the optimization procedure, we address 18 design variables, designated as $x_i$ and $y_i$. The objective of the optimization is to minimize the temperature deviation (frictional heat) across the brake disc, which is divided radially into 11 distinct sections. A uniform temperature distribution results in reduced temperature deviation.

Considering the size limitations of the back plate housing the circular friction block, further enlargement of the circular friction block is not practical. Moreover, enlarging the circular friction block compromises effective pad cooling and degrades the braking performance. Consequently, the dimensions of the circular friction blocks are not treated as design variables.

To maintain a uniform braking force, the pad’s cross-sectional area is adjusted to match that of the original pad. The parameter r represents the radius of the circular friction blocks, while n signifies the number of divisions along the radial direction of the brake disc. The constraints for this problem involve placing nine circular friction blocks on the back plate of the pad and preventing any instances of overlapping.

3.2. Establishing a Training Dataset for the ANN Using DOE

The Design of Experiments (DOE) is extensively used in statistical analysis to assess the influential factors (design variables) affecting outcomes. This method employs orthogonal arrays to derive results efficiently, enabling the collection of substantial data with minimal effort [23,24,25]. The Average Analysis of Means (ANOM) evaluates how input variables impact changes in the output response.

The DOE encompasses various types, with the full factorial experiment being the most precise but impractical due to the rapid increase in required experiments for our problem [26]. Fractional factorial designs are adopted to significantly reduce calculation efforts while effectively exploring the design space and determining factor importance [27]. The DOE process involves defining design variables, identifying those influencing the objective function, specifying their factors and levels, conducting experiments via orthogonal arrays, and analyzing the results to estimate optimized values [28]. However, in our study, the DOE was used to establish a training dataset for the ANN.

Table 4. Design factors and levels of the brake pad.

Friction Block #	Design Factor	Level 1 (mm)	Level 2 (mm)
1	$x_1$	21.0	27.0
	$y_1$	196.5	202.5
2	$x_2$	67.5	72.5
	$y_2$	210.5	216.5
3	$x_3$	109.0	216.5
	$y_3$	188.0	194.0
4	$x_4$	157.0	163.0
	$y_4$	187.5	193.5
5	$x_5$	31.0	37.0
	$y_5$	243.5	249.5
6	$x_6$	28.0	34.0
	$y_6$	290.0	296.0
7	$x_7$	77.0	83.0
	$y_7$	269.5	275.5
8	$x_8$	113.0	119.0
	$y_8$	240.5	246.5
9	$x_9$	159.0	165.0
	$y_9$	233.5	239.5

outlines the brake pad design factors and levels. Based on this, FEA was used to assess the disc’s thermomechanical properties for each scenario defined in

Table 5. Orthogonal array generated in MINITAB software (version 14.1).

#	Friction Block Location on the Brake Pad																		Max. Temp.	Temp.
	${\mathit{x}}_{\mathbf{1}}$	${\mathit{y}}_{\mathbf{1}}$	${\mathit{x}}_{\mathbf{2}}$	${\mathit{y}}_{\mathbf{2}}$	${\mathit{x}}_{\mathbf{3}}$	${\mathit{y}}_{\mathbf{3}}$	${\mathit{x}}_{\mathbf{4}}$	${\mathit{y}}_{\mathbf{4}}$	${\mathit{x}}_{\mathbf{5}}$	${\mathit{y}}_{\mathbf{5}}$	${\mathit{x}}_{\mathbf{6}}$	${\mathit{y}}_{\mathbf{6}}$	${\mathit{x}}_{\mathbf{7}}$	${\mathit{y}}_{\mathbf{7}}$	${\mathit{x}}_{\mathbf{8}}$	${\mathit{y}}_{\mathbf{8}}$	${\mathit{x}}_{\mathbf{9}}$	${\mathit{y}}_{\mathbf{9}}$	(°C)	Deviation
1	1 *	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	137.9	5.876
2	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	2	2	2	138.0	5.022
3	1	1	1	1	1	1	1	2	2	2	2	2	2	2	2	1	1	1	144.0	4.602
4	1	1	1	1	1	1	1	2	2	2	2	2	2	2	2	2	2	2	138.6	4.099
5	1	1	1	2	2	2	2	1	1	1	1	2	2	2	2	1	1	1	141.4	5.122
6	1	1	1	2	2	2	2	1	1	1	1	2	2	2	2	2	2	2	138.0	5.333
7	1	1	1	2	2	2	2	2	2	2	2	1	1	1	1	1	1	1	154.5	6.897
8	1	1	1	2	2	2	2	2	2	2	2	1	1	1	1	2	2	2	150.3	5.977
9	1	2	2	1	1	2	2	1	1	2	2	1	1	2	2	1	1	2	151.8	7.399
10	1	2	2	1	1	2	2	1	1	2	2	1	1	2	2	2	2	1	146.8	6.917
11	1	2	2	1	1	2	2	2	2	1	1	2	2	1	1	1	1	2	134.0	5.689
12	1	2	2	1	1	2	2	2	2	1	1	2	2	1	1	2	2	1	146.0	5.996
13	1	2	2	2	2	1	1	1	1	2	2	2	2	1	1	1	1	2	141.5	6.141
14	1	2	2	2	2	1	1	1	1	2	2	2	2	1	1	2	2	1	138.3	5.744
15	1	2	2	2	2	1	1	2	2	1	1	1	1	2	2	1	1	2	143.5	6.602
16	1	2	2	2	2	1	1	2	2	1	1	1	1	2	2	2	2	1	139.9	6.644
17	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	1	139.5	5.708
18	2	1	2	1	2	1	2	1	2	1	2	1	2	1	2	2	1	2	142.3	5.187
19	2	1	2	1	2	1	2	2	1	2	1	2	1	2	1	1	2	1	147.1	5.428
20	2	1	2	1	2	1	2	2	1	2	1	2	1	2	1	2	1	2	141.9	5.025
21	2	1	2	2	1	2	1	1	2	1	2	2	1	2	1	1	2	1	142.8	5.600
22	2	1	2	2	1	2	1	1	2	1	2	2	1	2	1	2	1	2	137.6	5.180
23	2	1	2	2	1	2	1	2	1	2	1	1	2	1	2	1	2	1	154.1	6.687
24	2	1	2	2	1	2	1	2	1	2	1	1	2	1	2	2	1	2	149.3	6.900
25	2	2	1	1	2	2	1	1	2	2	1	1	2	2	1	1	2	2	141.4	6.074
26	2	2	1	1	2	2	1	1	2	2	1	1	2	2	1	2	1	1	147.4	7.357
27	2	2	1	1	2	2	1	2	1	1	2	2	1	1	2	1	2	2	134.9	5.822
28	2	2	1	1	2	2	1	2	1	1	2	2	1	1	2	2	1	1	143.1	6.467
29	2	2	1	2	1	1	2	1	2	2	1	2	1	1	2	1	2	2	141.3	6.522
30	2	2	1	2	1	1	2	1	2	2	1	2	1	1	2	2	1	1	151.5	6.067
31	2	2	1	2	1	1	2	2	1	1	2	1	2	2	1	1	2	2	142.4	5.843
32	2	2	1	2	1	1	2	2	1	1	2	1	2	2	1	2	1	1	149.4	6.389

* 1 and 2 denote Level 1 and Level 2, described in Table 4.

. Table 5 depicts an orthogonal array table. The MINITAB software generated the orthogonal array table.

3.3. Artificial Neural Network Model

ANNs have been increasingly utilized as a tool for various applications in engineering analysis and prediction. These models are based on the principles of biological neural networks and are able to learn and adapt to different patterns in data. ANNs have been successfully applied to a wide range of fields, including estimation and control systems. One of the key advantages of ANNs is their ability to handle many data and to learn from them in an unsupervised manner. This makes them well suited for applications where traditional methods may struggle, such as in dealing with nonlinear systems or in situations where data are scarce or noisy [29]. Additionally, ANNs are able to learn from historical data. A neural network is a model made up of interconnected nodes, also known as artificial neurons, that process and transmit information. These artificial neurons are organized into layers, with the input layer receiving raw input data, the hidden layers performing the majority of the computation, and the output layer producing the final prediction or decision. During the training process, the neural network is presented with input—output examples, also referred to as training data, which it uses to adjust the weights of the nodes and learn underlying patterns in the data via the process of backpropagation, utilizing an algorithm known as gradient descent to minimize the difference between the network’s predictions and the actual output. Once the training is completed, the neural network can be utilized to make predictions on new unseen data, passing the input through the network and performing computations at each layer before passing it on to the next, with the final prediction or decision being produced by the output layer [30,31].

In our research, we employed MATLAB as our primary tool in predicting the resulting data. Neural networks are essentially composed of individual neurons. Within each neuron, the input data are adjusted by specific weight coefficients and then combined with a bias. The processed data are then passed through an activation function to obtain the final output from that neuron. The neuron’s output is determined using the following equation [31,32,33].

$$y=f\left(\sum _{i=1}^n{x}_n·w_n+b\right)$$

(5)

where f is the activation function, x is the input units, w is the weight factor, and b is the bias. The choice of the activation function is determined based on the neural network’s ability to predict. The most popular activation functions are the sigmoid function and the hyperbolic tangent function. The sigmoid activation function is differentiable; thus, either is typically used. In this study, the sigmoid function is used and can be defined by the following equation [31].

$$f\left(x\right)=\frac{1}{1+e^{-x}}.$$

(6)

Figure 6 presents a schematic illustration of the ANN architecture used in the study. After experimentation, a three-layered network with an input layer, an output layer, and hidden layers was found to provide the best performance. The inputs to the network are the x and y positions of each pad, while the outputs consist of the maximum temperature and temperature deviation. The number of nodes in the hidden layer was determined based on prior experience to achieve optimal results.

For the design, implementation, and simulation of the networks, the MATLAB software was utilized. Each hidden layer and output layer comprises artificial neurons interconnected through adaptive weights. Figure 7 illustrates the ANN process implemented in MATLAB. The selected training algorithm is “trainlm”, a network training function in MATLAB that updates weight and bias values using the Levenberg—Marquardt algorithm [34].

4. Results and Discussion

For the 32 sample points in Table 5, the analysis examined the temperature distribution on the disc’s friction surface, with deviations quantified across 11 radial regions. Table 5 presents the FEA results for the maximum temperature and temperature deviation. Figure 8 illustrates the temperature distribution analysis based on the design variable locations. Deviation values ranged from 4.099 to 7.399, corresponding to maximum temperatures of 137.9 °C to 154.5 °C. Notably, Case 9 exhibited a 7.399 deviation and a maximum temperature of 151.8 °C. Figure 9 further highlights the correlation between the deviation and maximum temperatures.

During ANN training, the Levenberg–Marquardt algorithm iteratively updated the weight and bias values, with performance assessed by the mean square error. Training, validation, and testing continued until we achieved the minimal mean square error [34]. Figure 10 compares the experimental and predicted datasets for training, validation, testing, and combined sets, confirming the ANN’s accuracy [34].

The ANN predicted the optimal brake pad positions, with

Table 6. Final position of the friction blocks on the brake pad.

Friction Block #	x (mm)	y (mm)
1	24.0	196.5
2	67.5	188.0
3	112.0	188.0
4	160.0	190.5
5	34.0	246.5
6	28.0	296.0
7	77.0	275.5
8	116.0	246.5
9	165.0	239.5

detailing the final design variable positions. Figure 11 shows a comparison of the locations of the nine circular friction blocks between the original pad and the ANN-predicted pad. Using the ANN, the friction block positions were optimized for reduced temperature deviation. Table 6 compares the analysis results between the original and optimized brake pad locations using the ANN. As shown in

Table 7. Comparative analysis of the original pad and ANN pad.

	Original Pad	Optimized Pad	Reduction Ratio
Max. temp.	480.6 °C	394.7 °C	17.9%
Temp. deviation	8.128	3.627	55.4%
Max. thermal stress	721.4 MPa	637.8 MPa	11.6%

, the original pad’s maximum temperature of 480.6 °C was reduced to 394.7 °C with the ANN (17.9% reduction). The original pad’s temperature deviation was improved from 8.128 to 3.333 with the ANN (55.4% reduction). The original pad experienced the maximum thermal stress of 721.4 MPa, lowered to 637.8 MPa with the ANN (11.6 % reduction).

Figure 12 illustrates the temperature distribution during the braking process. The optimized pad with the ANN reveals a larger hot band, yielding a more uniform temperature distribution and reduced maximum temperature. Figure 13 shows the thermal stress distribution, highlighting the optimized ANN model’s reduced thermal stress on the disc due to the expanded hot band, compared to the original model.

5. Conclusions

In this study, the temperature distribution and thermal stress of the brake disc were analyzed concerning the positioning of the friction blocks on the brake pad. An optimization process was conducted on the brake pad, composed of circular friction blocks, utilizing the Design of Experiments (DOE) and artificial neural network (ANN) techniques. The optimized brake pad, consisting of nine circular friction blocks, was compared to a conventional brake pad. The following conclusions were drawn.

• Smaller temperature deviations lead to lower maximum temperatures on the disc surface, while larger temperature deviations result in higher maximum temperatures. The optimized pad ensures a more even temperature distribution across the disc, which reduces the maximum temperature compared to the original pad.
• DOE was employed to generate a dataset for the training of the ANN. The ANN model, utilizing the Levenberg—Marquardt backward propagation algorithm, was used to predict the temperature and temperature deviation. The optimization aimed to minimize the temperature deviation of the disc during the braking process, thereby reducing the thermal stress.
• The optimized pad demonstrated improved performance over the original pad, achieving a significant 17.9% reduction in the maximum temperature and an 11.6% reduction in thermal stress.

In summary, the use of the DOE and ANN techniques allowed for the development of an optimized brake pad design, leading to enhanced braking performance and reduced thermal stresses on the brake disc.