Journal of Mechanical Engineering and Technology 

*Corresponding author. Email: ddanardono@staff.uns.ac.id

ISSN 2180-1053 Vol. 14 No. 1   July – December 2022 

ANALYSIS OF ADDITION THE NUMBER OF HALF CIRCLE 

TYPE SLOT ON PERFORMANCE CHARACTERISTICS OF DISC 

CONDUCTOR EDDY CURRENT BRAKE 

Alfian Jihan Saputra1, Dominicus Danardono Dwi Prija Tjahjana1,2*, Muhammad 

Nizam2,3,4, Mufti Reza Aulia Putra1 

1 Mechanical Engineering Department, Faculty of Engineering, Universitas Sebelas 

Maret, Jl. Ir. Sutami 36A, Surakarta 57126, Indonesia 

2 National Center of Sustainable Transportation Technology (NCSTT) ITB, Bandung 

40132, Indonesia 

3 Electrical Engineering Department, Faculty of Engineering, Universitas Sebelas Maret, 

Jl. Ir. Sutami 36A, Surakarta 57126, Indonesia 

4 Lithium Battery Research and Technology Centre, Universitas Sebelas Maret, Jl. 

Slamet Riyadi 435, Surakarta 57146, Indonesia 

ABSTRACT 

Brake is a vital component of a vehicle, particularly for motor vehicles. One of the 

braking used the principle of Eddy Current Brake by utilizing electromagnetic. Eddy 

Current Brake is a braking technology without direct contact by utilizing eddy currents. 

Eddy Current Brake performance can be influenced by several factors, one of them is the 

surface shape of the disc conductor. Using finite element simulation, this research 

examines the impact of increasing the number of slot half-circles on the performance of 

the Eddy Current Brake with the number of slot changes. Variations number of slots that 

used are 6, 8, 10, and 12 slots. The result of this study obtained the best braking torque 

value in the variation with the number of 10 slots at a rotational speed of 450 rpm with a 

15,930 Nm torque value. The addition slots of the number of half-circle types have a less 

significant effect on the torque from the simulation. 

KEYWORDS: Eddy Current Brake, Finite Element Method, Half-circle slotted 

1.0 INTRODUCTION 

Vehicles currently use a lot of conventional brakes to slow down the speed and the most 

common types of brakes are drum brakes and disc brakes. In the operation of both types 

of brakes, the friction concept is applied. Friction that occur will change from kinetic 

energy to heat energy when the brake operating (Günay et al., 2020). The vehicle's speed 

will be reduced by friction until it comes to a halt. However, the friction between the two 

objects will almost definitely produce an increase in temperature surrounding the brakes 

(Gerdes & Hedrick, 1999). 

To solve the problems developed technology on braking. Using an Eddy Current Brake 

(ECB) is one of them (Mufti Reza Aulia Putra et al., 2020). Eddy current brakes are 

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mailto:ddanardono@staff.uns.ac.id


ISSN 2180-1053 Vol. 14 No. 1     July – December 2022 

intended to be used in place of konventional brakes (Cho, Liu, Lee, et al., 2017). Karakoc 

also used the FEM method to analyze the dispersion of eddy currents. In his research, it 

was found that ECB braking can be used to replace conventional brakes (Karakoc et al., 

2016). Eddy Current Braking is a sort of electric braking that relies on eddy currents for 

braking  (Lequesne, 1997). The ECB braking system is frictionless braking which has 

advantages such as not producing wear, making little noise, and having a fast response 

(Cho, Liu, Ahn, et al., 2017). ECB is now being developed for light vehicles, such as 

motorcycles, in addition to being employed in large vehicles (Sinmaz et al., 2016). 

In the development of ECB braking, Robert, et al. analyze the surface design of disk 

conductors by adding slots. The slot can be defined as a hollow shape on the surface of 

the disc that serves to improve braking performance. The addition of the number of slots 

in this study affects the resulting braking torque. The results indicated that the brake with 

a slotted disk rotor had 1.1–1.2 times the torque of the brake with a plain rotor (Robert, 

2017). The form of the conductor slot's surface is next investigated by Prayoga et al. 

Compared to other shapes, the conductor disc with a semicircular shape has a maximum 

torque value (Prayoga et al., 2019). In this study, research will be carried out with 

variations in the number of slots on a semicircular type of conductor plate. The studies in 

the research is how the number of slots on a semicircular type conductor plate impacts 

the ECB's braking torque when using a single magnet. 

2.0 METHODOLOGY 

2.1 Governing Equation 

The resulting torque can be influenced by the size of the magnetic field that arises (Cho, 

Liu, Lee, et al., 2017). The amount of torque on braking can be calculated through the 

following equation (Rodrigues et al., 2016): 

𝑇 =  
1

2
× 𝜎𝛿𝜔𝜋𝑟2𝑚2𝐵𝑧

2 [1 − {
(
𝑟

𝑎
)
2

(1−(
𝑚

𝑎
)
2
)
2}]  (1) 

Where 𝜎 is the electrical conductivity of the disc (S/m), 𝛿 = disc thickness (mm), 𝜔 = 
angular velocity (rad/s), r = electromagnetic radius (mm), m = distance between disc axis 

and magnetic axis position (mm), 𝐵𝑧
.  = magnetic flux density (T), and 𝑎 = disc radius 

(mm). In equation 2.8 it can be seen that there are several factors that affect the braking 

torque on the Eddy Current Brake. The influencing factors include the choice of material 

on the disc conductor, rotational speed, surface area of the electromagnet, magnetic flux 

density, disc thickness, and disc radius. The area of the electromagnet can also be 

interpreted as the area of the active region. The active region is the area on the conductor 

that is perpendicular to the magnetic face, while the passive region is the area that is 

affected by the magnetic field around the magnetic face. The size of the active region is 

influenced by the dimensions of the magnetic face and the surface area of the conductor 

perpendicular to the magnetic face. 

The ECB works according to Faraday's law. When a conductor cuts the magnetic force 

line, it will produce a loop whose magnitude is proportional to the magnetic field and 

velocity of the conductor (Satya et al., 2021). Faraday's law equation can be seen in 

equation (2). According to Lenz's law, the rotating loop will generate a new magnetic 

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field. As a result, the magnet will provide a drag force on the moving conductor (Satya et 

al., 2021). Lenz's law equation can be seen in equation (3). Conductivity is also important 

in ECB design because the eddy current is proportional to the eddy current conductivity 

shown in equation (4). The interaction between eddy currents and magnetic flux density 

produces a braking force as in equation (5) so that the braking torque equation can be 

obtained in equation (6). 

∇ × �⃗� = − 
𝜕�⃗� 

𝜕𝑡
 (2) 

𝑒 = (𝑣 . 𝐵). 𝑙  (3) 

𝐽 = 𝜎. �⃗�  (4) 

𝐹 = 𝐽 × �⃗�  (5) 

�⃗� = 𝐹 . 𝑟  (6) 

Where �⃗�  = magnetic field intensity (N/C), �⃗�  = magnetic induction (T), 𝑒 = induced emf 

(v), 𝑣 = velocity (m/s), 𝑙 = conductor length (m), 𝐽  = eddy current density (A/m2), 𝜎 = 

conductivity of the material (S/m), 𝐹  = braking force (N), �⃗�  = torque (Nm), and r = radius 
(m). 

2.2 Developed Model 

The finite element method (FEM) is used in this study's simulation process. Fusion 360 

software was used for modeling, and Ansys Electronics 2018 was used for simulation. 

Simulation data is displayed in the form of a curve that represents the rotational speed 

and braking torque generated for each modification. This simulation uses parameters that 

affect the performance of the ECB, namely by varying the effect of increasing the number 

of half-circle slots and comparing the data between all simulation results. Variations in 

the number of half-circle slots used in this study are 6, 8, 10, and 12 slots. As for variations 

in rotational speed include 150, 300, 450, 600, and 750 rpm. 

The speed variation is also taken from low to high speed in order to know the difference 

in its effect on braking performance. Then the variation in the number of slots of the half-

circle type is carried out in order to find out about the difference in the number of slots 

that will affect the performance of the Eddy Current Brake which will be better. The 

variation in the number of slots was chosen based on the fact that the more slots with the 

half-circle type, the better the braking process performance (Razavi & Lampérth, 2006). 

The difference in distance between slot variations with a difference of 2 slots is used to 

find out more details and specifically regarding changes in the addition of braking torque 

generated in the simulation. The speed variation used refers to the average speed of the 

vehicle in general. Figure 1 shows the design that will be used in the simulation. 

 (a)     (b) 

Figure 1. (a) 3D model of a unipolar axial ECB, (b) Eddy current design variable (Waloyo et al., 2020). 

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ISSN 2180-1053 Vol. 14 No. 1   July – December 2022 

Table 1 lists the parameters that were employed in this study's simulation design. 
Tabel 1. Design Parameter of ECB (Mufti Reza Aulia Putra et al., 2020). 

Variable Value Unit 

Current (I) 20 A 

Count of coil (N) 360 - 

Length of pole shoe (a) 30 mm 

Wide of pole shoe (b) 12.5 mm 

Total length of winding core (l) 248 mm 

Distance from center to center of pole shoe (r) 83.5 mm 

Air gap 0.5 mm 

Thick of disc (d) 5 mm 

Radius disc brake (R) 120 mm 

Relative permeability aluminium (μal) 1.26 x 10
-6 H· m-1 

Relative permeability iron (μfe) 6.3×10
-3 H· m-1 

Aluminium conductivity (σ) 36.9 × 106 S· m-1 

Disc modeling consists of 3 layers, namely disc groove layer, mid layer, and flat layer. 

Where the groove layer is a layer that is given a half-circle slot, while the flat layer is a 

layer that is not given a slot. The material used on the disc consists of 2 materials, namely 

iron material for the mid section and aluminum material for the flat disc section and disc 

groove (Ubaidillah et al., 2020). The disc parts used can be seen in Figure 2a and the 

dimensions of the half-circle slots are shown in Figure 2b, where a = thickness, b = slot 

width, and c = slot depth. 

  (a)        (b) 

Figure 2. (a) ECB disc section, (b) Aluminum disc slot dimensions. 

The meshing used in this study uses a meshing size of 5 mm and the meshing shape is 

used with a tetrahedral model (M. R.A. Putra et al., 2019). Figure 3 shows an image of 

the meshing process in the simulation. The materials used in this simulation include 

aluminum, iron, copper, and air (vacuum). The value of the material properties of these 

materials is shown in Table 2. 

Figure 3. The meshing process in the ECB simulation 

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Tabel 2. Material Properties 

Materials Relative 
Permeability (μr) 

Bulk Conductivity 

(S/m) 
Mass Density 

(kg/m
3
) 

Aluminium 1.000021 3.8 x 107 2689 
Iron 4000 1.03 x 107 7870 

Copper 0.999991 5.8 x 107 8933 
Vacuum 1 0 0 

3.0 RESULT AND DISCUSSION 

3.1 Verification 

Data validation was carried out by re-modelling in accordance with the modeling and 

simulation of previous research. The validation was carried out by comparing the data to 

the previous research conducted by Putra (M. R.A. Putra et al., 2019). The goal of this 

simulation is to determine the braking torque and initial flux. Modeling is done by 

creating a 3D design using Fusion 360 software. The modeling that will be used for data 

validation is designed as closely as possible to the design to be compared, so that it can 

produce an assessment similar to the previous design. Validation will hold the 

simulation's parameters accountability. Table 3 shows a table of data validation against 

previous studies. 
Table 3. Table of data validation against previous research 

Rotating Speed 

(rpm) 

Braking Torque (Nm) Deviation 

Putra’s Research 

(M. R.A. Putra et 

al., 2019) 

New 

Research 
(%) |%| 

150 5.086 4.847 4.7 4.7 

300 8.300 7.937 4.37 4.37 

450 9.429 9.120 3.28 3.28 

600 9.383 9.129 2.71 2.71 

750 8.828 8.542 3.24 3.24 

Average 3.66 

Table 3 shows that the average deviation in this study is 3.66%. This shows that the results 

of the comparison of data between previous studies and new studies have a deviation of 

less than 5%. It can be said that the modeling and simulation results are valid. 

3.2 Braking Torque 

The simulation results for each variation are shown in Table 4. 

Table 4. ECB simulation result data 

NO 
Rotating 

Speed (rpm) 

Braking Torque (Nm) 

6 Slots 8 Slots 10 Slots 12 Slots 

1 150 8.86 8.99 9.18 9.02 

2 300 14.09 14.27 14.51 14.26 

3 450 15.52 15.71 15.93 15.72 

4 600 14.93 15.12 15.30 15.07 

5 750 13.66 13.70 13.80 13.63 

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It can be seen that the largest braking torque in each variation of the number of slots is 

found at a rotational speed of 450 rpm and the smallest braking torque in each variation 

is found at a rotational speed of 150 rpm. The highest braking torque value produced is 

the number of slots 10 with a speed of 450 rpm of 15.93 Nm. After the speed passes 450 

rpm, the resulting data will tend to decrease as the rotational speed increases. This is in 

accordance with the nature and characteristics of the disc conductor used from non-

ferrous material, namely aluminum which causes the emergence of critical speed during 

the braking process (Kou et al., 2014). 

Figure 4 shows the relationship between braking torque and rotational speed. The graph 

shows that each variation in the number of slots has almost the same graphic pattern. 

Figure 4 shows that when the number of slots increases from 6 to 8 to 10, the brake torque 

value increases. However, when 12 slots are added to the conductor plate, the value of 

brake torque produced in 12 slots is less than the value in 10 slots. The chart tends to 

show a downward trend after crossing the 450-rpm mark. This occurs as a result of the 

skin effect (Waloyo et al., 2020). Skin effect is an alternating electric current that appears 

in the disc conductor so that the current density is formed on the surface of the conductor 

and will decrease as it gets deeper in the conductor (Taghizadeh Kakhki et al., 2016). 

With the skin effect on the disc conductor, it will greatly affect the braking torque at high 

speeds (Waloyo et al., 2020). The addition of a semicircular type conductor disc slot on 

the ECB braking system has only a small impact on the braking performance of the ECB. 

Figure 4. Graph of the relationship between braking torque and rotational speed for each variation 

Calculation of braking is done by braking force when the vehicle slows down from a 

certain speed. The calculation is only to prove the characteristics of the modeling process 

used, namely regarding the effect of adding a conductor disk slot. At the next stage the 

braking process can be analyzed with several additional parameters such as rolling 

resistance, etc. 

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3.3 Comparation of Magnetic Flux on Variation of Slots 

The spread of magnetic flux in each slot variation is shown in Figure 5 below. 

 (a)  (b) 

     (c)             (d) 

Figure 5. Distribution of magnetic flux in variations of (a) 6 slots, (b) 8 slots, (c) 10 Slots, and (d) 12 

slots. 

The magnetic flux distribution in Figure 5 in each variation has a magnetic flux 

distribution that is almost the same or uniform. This makes the addition of the number of 

half-circle type slots have a less significant effect. The value of the torque produced will 

also have almost the same value. In addition, the distribution of the magnetic flux is all 

concentrated in the conductors and cores of the ECB. This phenomenon can be seen in 

the image in red which indicates that the magnetic field strength is highest in the area 

closer to the core that carries the electric current. 

3.4 Comparation of Magnetic Flux on Rotating Speed 

The spread of magnetic flux at each rotational speed variation is shown in Figure 6 below. 

 (a)  (b) 

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 (c)  (d) 

(e) 

Figure 6. Spread of magnetic flux at variations in rotational speed (a) 150 rpm, (b) 300 rpm, (c) 450 rpm, 

(d) 600 rpm, and (e) 750 rpm.

In Figure 6 it can be seen that the higher the rotational speed, the greater the spread of the 

magnetic flux on the disc conductor. In addition, the magnetic field at low speeds is more 

concentrated to the magnetic source (core) and will spread as the speed increases. The 

magnetic field strength (red color) will disappear with increasing speed. The phenomenon 

that occurs is related to the skin effect. The skin effect has a significant impact on braking 

torque and disc rotation speed (Waloyo et al., 2020). Skin effects appear at high rotational 

speeds which will cause a decrease in the value of the resulting torque. At low speeds, it 

is seen that the spread of magnetic flux is still around the center of the magnetic field, 

while at high speeds the distribution of the magnetic field will be further away from the 

center of the magnetic field and the resulting area will be larger. 

4.0 CONCLUSION 

From the research that has been done, it can be concluded that the addition of the number 

of half-circle type slots with slot variations of 6, 8, 10, and 12 slots does not have a 

significant effect on the torque generated from the simulation. The trend of the graph of 

adding slots to the conductor has almost the same trend. The highest braking torque value 

is produced by a variation of 10 slots with a torque value of 15.93 at a speed of 450 rpm. 

The spread of magnetic flux in the variation of the number of slots has almost the same 

area shape. It is concluded that the distribution of magnetic flux with variations in the 

number of slots does not have much effect on ECB braking. In variations in rotational 

speed, the spread of magnetic flux from low to high-speed changes the shape of the area. 

The higher the rotational speed, the wider the magnetic flux distribution because the 

magnetic field strength will spread and be influenced by the skin effect that appears at 

high speeds. 

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5.0 ACKNOWLEDGMENT 

Thanks to UNS for providing funding and laboratory facilities for ECB research. Thank 

you to ICE-SEAM 2021 for accepting and presenting the results of this research work. 

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