A Study on the Improvement in Response Characteristics of an Electromagnetic Brake Through Electromagnetic Balance-Based Structural Design and Shim Plate Application

Abstract

This study proposes an electromagnetic balance-based structural design and shim plate application to improve the response characteristics of an electromagnetic brake. Electromagnetic brakes typically experience response delay due to inductive effects and residual magnetic flux after power-off. To address this issue, the inner and outer thicknesses of the stator were parameterized to achieve balanced magnetic flux distribution, and a non-magnetic shim plate (SUS 304) was applied to reduce residual flux within the electromagnet. Finite element analysis (FEA) was conducted to evaluate the influence of structural parameters on the magnetic flux balance and attractive force. The optimized stator geometry provided a stable electromagnetic balance, and the shim plate effectively reduced the response delay and improved the overall response performance compared with the conventional design. These findings demonstrate that the proposed electromagnetic balance design combined with shim plate application is an effective approach to enhance the reliability and control responsiveness of electromagnetic brakes, with potential applicability to robotic and industrial actuator systems.

1. Introduction

With the growing demand for automation and safety in various industrial applications, the requirement for braking systems offering fast response and high operational reliability has increased significantly. Electromagnetic brakes (EMBs) are widely utilized in military, robotic, medical, and automotive systems, as they can provide fail-safe braking in power-off conditions or dynamic braking during emergency operations, depending on their structural design. An EMB typically comprises a solenoid-type configuration consisting of an armature, spring, coil winding, and stator. Unlike conventional hydraulic brake systems that rely on fluid transmission, EMBs operate solely via magnetic actuation and are inherently free from failure modes such as fluid leakage or pressure loss, resulting in higher reliability and reduced maintenance requirements [1,2].

Solenoid-based electromagnetic brakes (EMBs) require a continuous holding current to maintain their engaged state, making it essential to generate sufficient magnetic force and establish efficient magnetic flux paths through proper electromagnetic design. However, due to the inductive characteristics of the solenoid coil, a delay in current rise occurs when voltage is applied, resulting in slower dynamic responses during both attraction (pull-in) and release operations. During the release phase, the current decay after power-off leaves residual magnetic flux trapped in the stator core, which prolongs the release delay time and adversely affects the overall response and safety of the braking system. In addition, various mechanical factors and magnetic force asymmetry can induce imbalance between the inner and outer regions, which deteriorates braking uniformity and dynamic stability [3,4,5]. To overcome these limitations, this study proposes a structural optimization approach for the electromagnetic brake. The optimization aims to enhance magnetic balance and improve mechanical symmetry while minimizing the delay caused by residual magnetism. In particular, a shim-assisted configuration is introduced between the armature and stator. The inserted shim functions as a controlled stroke gap that helps to equalize the magnetic flux distribution, suppress residual magnetic effects, and reduce the release delay time. This configuration ultimately improves both the electromagnetic responsiveness and operational reliability of the brake.

2. Principle and Design of Electromagnetic Brake

2.1. Principle of the Electromagnetic Brake

The structure of the electromagnetic brake is shown in Figure 1. The brake consists of a stator, armature, coil, bobbin, brake pad, etc. A winding is wound around the stator, and when current is applied, the stator becomes magnetized and acts as an electromagnet. The resulting magnetic attraction force pulls the armature toward the stator, enabling the braking mechanism.

The operating principle of the brake is illustrated in Figure 2a, which shows the braking mode, in which the power is not applied. In this state, the spring restoring force presses the armature toward the brake pad, generating the braking torque. In contrast, Figure 2b shows the release mode, where the power is applied. When current flows through the coil, a magnetic field is generated, and the armature is attracted toward the stator, causing the friction surfaces to separate and allowing the rotor shaft to rotate freely.

The electromagnetic brake operates through the interaction between magnetic attraction and spring restoring force depending on whether the power is applied or not.

This operating principle is mathematically formulated in Section 2.2.

2.2. Fundamental Theoretical Equations of the Electromagnetic Brake

The braking characteristics of an electromagnetic brake are determined by the interaction among electromagnetic attraction force, spring restoring force, and frictional force. To quantitatively analyze these characteristics, this section formulates the fundamental operating principles of the electromagnetic brake. The braking torque is generated by the compressive force of the spring and the friction coefficient at the contact surface, while during power-on conditions, the magnetic attraction force produced by the coil current overcomes the spring restoring force, thereby releasing the brake.

Therefore, the braking torque and magnetic attraction force are the key physical quantities that govern the brake’s performance, and their mathematical relationships are presented in this section.

2.2.1. Calculation of Braking Torque

To calculate the holding torque required for brake design, the braking torque can be determined from the effective radius of the friction surface and the coefficient of friction. Figure 3 shows the relationship between the friction surface and the spring force. $R_o$ and $R_i$ represent the outer and inner radii of the friction surface, respectively, and the effective radius $R_{\mathrm{eff}}$ is approximated as $(R_o+R_i)/2$. Although in practical electromagnetic brake designs the normal force is concentrated near the outer region due to spring placement, the uniform-wear assumption is adopted here to simplify the torque derivation. This assumption provides a reasonable approximation of the effective braking radius. The braking torque is derived from the relationship between the frictional force and the effective radius of the contact surface. Equations (1)–(3) present the step-by-step formulation of the spring force and normal pressure acting on the friction surface, and the final expression for the braking torque is obtained in Equation (4) based on these parameters. ${\mu }_s$ denotes the coefficient of friction of the brake pad, $F_{spring}$ is the spring restoring force, $k_{\mathrm{spring}}$ is the spring constant, $n_{\mathrm{spring}}$ is the number of springs, and $\Delta x$ represents the spring compression displacement [6].

$$R_{eff}={\displaystyle \frac{R_o-R_i}{2}} \left[\mathrm{m}\right]$$

(1)

$$F={\mu }_s{F}_{spring} \left[\mathrm{N}\right]$$

(2)

$$N=k_{spring}{n}_{spring}∆x \left[\mathrm{N}\right]$$

(3)

$$T_{brake}={\mu }_{s}N{R}_{eff}\left[\mathrm{N}\mathrm{m}\right]$$

(4)

2.2.2. Calculation of Electromagnetic Attraction Force

The electromagnetic brake moves the armature by using the magnetic force of the electromagnet to counteract the restoring force of the spring.

The attractive force generated in this process is derived through the Maxwell stress tensor, and the total force acting on an arbitrary surface $S$ in the magnetic field is defined in Equation (5).

$$\mathit{T}={\displaystyle \frac{1}{{\mu }_0}}\left(\mathit{B}\mathit{B}-{\displaystyle \frac{1}{2}}{B}^2\mathit{I}\right)$$

(5)

$\mathit{T}$ is the Maxwell stress tensor, $\mathit{B}$ is the magnetic flux density vector, $\mathit{I}$ is the identity matrix, and ${\mu }_0$ is the permeability of free space. The total attractive force is calculated by integrating the stress tensor over the stroke gap surface, as expressed in Equation (6).

$$\mathit{F}={\oint }_s\left(\mathit{T}·\mathit{n}\right)dS$$

(6)

$S$ is the surface area, and $n$ is the normal vector of the surface. Since the electromagnetic brake has an axisymmetric cylindrical structure, Equation (6) can be simplified in cylindrical coordinates as shown below.

$$F_z={\displaystyle \frac{1}{2{\mu }_0}}{\int }_S\left(B_z^2-B_r^2\right)\hspace{0.17em}dS$$

(7)

Assuming that the magnetic flux density in the stroke gap is uniformly distributed, Equation (7) can be simplified into an approximate expression using the average magnetic flux density, and the total attractive force is expressed as Equation (8).

$$F_{mag}={\displaystyle \frac{B^{2}A}{2{\mu }_0}}$$

(8)

where $A$ represents the effective area of the stroke gap, over which the Maxwell stress is integrated to obtain the total attractive force [7,8,9].

2.3. Workflow of the Proposed Electromagnetic Brake Design

The design procedure employed in this study is summarized in Figure 4. The sections indicated by solid lines represent the scope actually conducted in this work, which includes defining the design requirements, performing 2D transient finite element analysis, and verifying the equivalence between 2D and 3D models for the selected geometry. Through these steps, the fundamental electromagnetic characteristics of the brake were evaluated.

As shown in Figure 5, the attractive force of the brake was compared using both 2D and 3D Ansys Maxwell simulations. The resulting forces were 3.04 [kN] (2D) and 3.06 [kN] (3D), demonstrating that the two results are quantitatively very similar. In contrast, the computation time required for the 3D simulation was significantly longer than that of the 2D model under identical conditions. Considering the axisymmetric geometry of the brake and the strong numerical agreement between the 2D and 3D results, it is reasonable to adopt the 2D analysis as the primary design tool during the initial design and parameter-study stages, particularly from the perspective of computational efficiency. Meanwhile, the steps indicated by dashed lines represent extended research activities planned for future studies. These include thermal considerations—such as evaluating the effect of temperature rise on electromagnetic performance—as well as prototype fabrication and benchtop experiments for model correlation.

In the present study, the focus was placed on analyzing the fundamental structure and response characteristics of the electromagnetic brake, and the derived design results will be used as the basis for subsequent experimental validation and coupled thermal–electromagnetic analysis.

2.4. Comparison of Solenoid Structures

The solenoid geometry directly affects the magnetic flux distribution and the attractive force characteristics. As shown in Figure 6, typical solenoid configurations include flat, conical, and proportional structures. Among them, the flat and conical types are applicable to electromagnetic brake designs, and their characteristics are as follows.

The flat structure has a planar contact surface between the stator and the armature, resulting in a uniform magnetic flux distribution and a simple geometry that requires low machining precision. Since the total magnetic flux is transferred through a constant area, the magnetic saturation occurs gradually. In the conical structure, the inclined magnetic path allows the magnetic flux to be concentrated, resulting in a higher initial attraction force under the same current condition [8]. However, this effect tends to decrease as the stroke gap increases. This configuration was applied to the electromagnetic brake, as shown in Figure 7 [10,11].

To evaluate how these geometric differences influence the magnetic attraction force, a finite element analysis (FEA) was performed using Ansys Maxwell. In this study, two types of electromagnetic simulations were conducted:

(1) Magnetostatic analysis, used for parametric and sensitivity studies to examine how variations in geometry and excitation affect flux distribution and attraction force; and (2) Transient analysis, used to capture time-dependent electromagnetic behavior, including pull-in and release responses.

A current-source-based parametric study was conducted across the following ranges: excitation current from 0 to 2 A, stroke gap from 0 to 0.5 mm, and conical pole angle from 0° to 45°. The resulting attraction-force characteristics for each geometry are shown in Figure 8, which illustrates how the three models behave across varying stroke gap lengths. When the stroke gap is relatively large (0.2–0.5 mm) or the excitation current is small (below approximately 0.8 A), the conical models exhibit a slightly higher attractive force than the flat model. This occurs because the inclined magnetic path effectively reduces the local stroke gap and increases flux linkage in the low-excitation regime. However, as the current increases or the stroke gap decreases, this advantage diminishes and eventually reverses. At higher current levels, the flat model produces a slightly larger attractive force due to its more uniform flux distribution and delayed magnetic saturation. For example, at a stroke gap of 0.5 mm and an excitation of 0.4 A, the 45° conical model produces approximately 16.4% greater force than the flat model; however, at 2.0 A, the flat model exhibits approximately 9.8% greater force than the 45° conical model.

Therefore, the conical pole shape provides a small advantage in the low-current or large-gap region, whereas the flat structure becomes more efficient in the high-current or small-gap region due to its uniform flux distribution and lower susceptibility to early saturation.

3. Performance Improvement Analysis Through Electromagnetic Balance and Shim Structure Application

This section presents a stator design approach aimed at improving the performance of the electromagnetic brake. Since the brake operates based on the attractive force generated by the electromagnet, an imbalance in the stroke gap magnetic flux can degrade control stability and reduce the maximum achievable attractive force [12,13]. In addition, residual magnetic flux remaining in the stator core after power-off may cause a response delay.

To mitigate these issues, this study proposes an electromagnetic design method that ensures a balanced and symmetric stroke gap flux distribution, together with a shim-assisted structure that reduces the response delay induced by residual flux.

3.1. Design Considering Electromagnetic Balance

The analysis was performed using magnetostatic finite element analysis to investigate the electromagnetic balance between the stator and the armature. To achieve a uniform distribution of magnetic flux density, the inner length (①) and outer length (②) of the stator, as indicated in Figure 9, were selected as the primary design variables. The overall geometry and definitions of the geometric parameters are shown in Figure 9, and their corresponding numerical values are summarized in

Table 1. Geometric parameters of the electromagnetic brake model.

Number	Item	Value	Material
①	Stator inner	17.5~23.0 [mm]	Steel 1008
②	Stator outer	12.0~14.0 [mm]	Steel 1008
③	Stator bottom	12 [mm]	Steel 1008
④	Armature	13 [mm]	Steel 1008
⑤	Axial length	33 [mm]	Steel 1008
⑥	Stroke gap	0.5 [mm]	Air
⑦	Coil	500 [Turns]	Copper
⑧	Bobbin	-	Plastic
-	Current	2 [A]

. Parametric simulations were then carried out by varying the ratio between these two parameters to evaluate their effects on the magnetic flux distribution and attractive force characteristics. Figure 10 presents the B–H curve of Steel 1008, which is used as the magnetic material for both the stator and the armature. The material also exhibits an electrical conductivity of approximately 2.0 × 10⁶ S/m, reflected in the finite-element analysis. The magnetic flux density of the electromagnet is determined by this material property in combination with the applied current and number of coil turns.

In this study, the inner–outer balance of the electromagnetic attractive force is evaluated using the ratio of the inner attractive force to the total attractive force, as defined in Equation (9).

$$\mathrm{Balance} \mathrm{Ratio}={\displaystyle \frac{F_{\mathrm{inner}}}{F_{\mathrm{total}}}}$$

(9)

Here, the inner attractive force corresponds to the force generated in the region labeled as Area ① (inner region), and the outer attractive force corresponds to Area ② (outer region), as illustrated in Figure 9.

By setting the inner and outer lengths of the stator as variables, the conditions for achieving electromagnetic balance were derived through the analysis of magnetic flux distribution and attractive force variations. The magnetic flux path and attractive force characteristics for each parameter combination were compared. The degree of balance in the magnetic attraction force was evaluated by calculating the ratio of the inner attractive force to the total attractive force. A smaller ratio indicates a more uniform flux distribution and a better electromagnetic balance between the stator and armature. The results are shown in Figure 11, where the configuration with the lowest ratio and highest total attraction force was selected as the optimal model. Consequently, the most balanced magnetic performance was achieved when the inner length was 23 [mm] and the outer length was 13 [mm].

3.2. Analysis of Response Characteristic Improvement by Shim Plate Application

Residual magnetism remaining in the stator after power-off prolongs the release delay time, which not only degrades dynamic responsiveness but also limits the achievable precision of brake control. To alleviate this limitation, a shim-assisted structure is introduced to accelerate magnetic flux decay and reduce the delay induced by residual magnetism. A shim plate is a thin, non-magnetic spacer typically employed for alignment or gap adjustment. In this study, SUS 304 was selected as the shim material because its relative magnetic permeability is nearly equal to that of air (μ ≈ μ₀), allowing it to act as a controlled magnetic barrier rather than a flux carrier. The electrical conductivity of SUS 304 is approximately 1.4 × 10⁶ S/m, which is considerably lower than that of magnetic steels. To suppress eddy-current effects and isolate the geometric influence of the shim, it was modeled as an electrically non-conductive layer in the finite element analysis. This modeling approach ensures that the shim’s influence on the magnetic circuit arises solely from its geometry and magnetic permeability, excluding any induced-current interaction. When a shim of 0.1 mm thickness is inserted between the stator and the armature, a small initial magnetic separation is introduced, which prevents complete magnetic saturation and reduces the retention of residual flux. As shown in Figure 12, the shim was placed between the stator and the armature to implement this configuration. Although this modification slightly decreases the maximum attractive force due to the increased magnetic reluctance, it dramatically improves the release response. The apparent 0.4 mm armature displacement observed during release originates from the nonlinear relationship between magnetic force and stroke gap length—once the magnetic attraction drops below a critical level, the restoring spring rapidly pulls the armature back. In addition to its magnetic effect, the shim also functions as a mechanical alignment aid, ensuring a consistent and uniform stroke gap during assembly. This alignment compensation mitigates flux imbalance caused by mechanical tolerances, thereby enhancing both the magnetic and mechanical stability of the brake. Consequently, the proposed shim mechanism provides a favorable trade-off: it slightly reduces the holding force but significantly shortens the release delay, leading to faster and more stable braking performance.

The simulation results were compared with those of the conventional brake model. When the power supply is switched off, the current decay in the excitation coil follows the first-order RL differential equation, as shown in Equation (10).

$$L{\displaystyle \frac{di\left(t\right)}{dt}}+Ri\left(t\right)=0$$

(10)

where $L$ and $R$ denote the inductance and resistance of the coil, respectively. Solving Equation (9) yields the exponential decay expression given in Equation (11).

$$i\left(t\right)=I_0{e}^{-{\displaystyle \frac{t}{\tau }}}$$

(11)

This result indicates that the electrical time constant τ, defined as τ = L/R, governs the rate at which the magnetic field collapses during power-off. A larger inductance or smaller resistance increases τ, resulting in a slower decrease in magnetic flux and consequently a longer release delay. In contrast, the proposed shim-assisted structure reduces magnetic retention in the stator core, enabling the flux to dissipate more rapidly than expected from the electrical time constant alone. Figure 13 and Figure 14 show the magnetic flux density distributions of the conventional and shim-assisted models, respectively, at t = 0.71 s, corresponding to the power-off phase when the coil current begins to decay. In the conventional model, strong magnetic saturation remains concentrated in the stator core, indicating residual magnetic flux that delays the release of the armature. In contrast, the shim-assisted model exhibits a visibly reduced flux density and weaker saturation near the stator–armature interface. This confirms that the introduction of the non-magnetic shim facilitates faster demagnetization by interrupting the magnetic path, leading to shorter release delay and improved response behavior. Furthermore, transient finite element analysis was performed to validate the dynamic electromagnetic response predicted by the RL model. The transient results confirmed that the shim-assisted configuration exhibits a faster decay of coil current and magnetic flux density during the power-off phase, which corresponds to the shortened release delay observed in the simulation. As shown in Figure 15 and

Table 2. Comparison of response delay characteristics of the electromagnetic brake with and without the shim structure.

Model	Pull-In Delay Time [ms]	Release Delay Time [ms]
Conventional model	180	680
Shim model	180	210

, the conventional brake exhibited a release delay of 680 [ms] with a peak attractive force of 9.14 [kN], whereas the model incorporating the shim reduced the delay to 210 [ms] with a peak force of 7.49 [kN]. Although the introduction of the non-magnetic shim decreases the maximum attractive force due to the increased magnetic reluctance, the overall braking performance is enhanced because the faster demagnetization enables a quicker and more stable release behavior. This result demonstrates that the shim effectively trades a reduction in holding force for a substantial improvement in dynamic response speed.

4. Conclusions

In this study, a design approach based on electromagnetic balance and the application of a shim plate were proposed to improve the overall performance of an electromagnetic brake. The stator geometry was optimized to maximize the attractive force, and the validity of the design was verified through finite element analysis (FEA). The analysis results confirmed that adjusting the ratio between the inner and outer thicknesses of the stator can balance the magnetic flux distribution and minimize the variation in attractive force. Furthermore, to address the release delay caused by residual magnetic flux after power-off, a non-magnetic shim plate (SUS 304) was applied, resulting in a significant reduction in release delay time and enhanced operational responsiveness. Although the shim reduces the maximum attractive force due to increased magnetic reluctance, it does not compromise braking capability or stability. Instead, it accelerates the collapse of residual flux and enables faster and more reliable release behavior.

Overall, the combination of electromagnetic-balance-based stator design and shim application proves to be an effective method for improving both the performance and operational stability of electromagnetic brakes. Future work will incorporate thermal considerations and experimental validation to further substantiate the simulation results and evaluate temperature-dependent effects under practical operating conditions.