Multipole Multi-Layered Magnetorheological Brake with Intermediate Slots

Abstract

Magnetorheological (MR) brakes are flourishing in low-torque applications due to their dynamic controllability nature. Researchers have introduced multi-layer and multipole concepts to increase the torque–volume ratio (TVR) of the MR brake. However, the combination of these two ideas did not exist due to the design limitations. Therefore, this study aims to design a brake that combines the multipole magnetic field and multi-layered structure concepts. The axial slots were introduced on the brake rotor and the stator drum axial surfaces to achieve a high TVR. These slots stop the flux bypass in the inner layers; therefore, the magnetic flux can also reach the brake’s outer layers. This brake was designed with multiple stator and rotor drums and MR fluid layers. The number of poles was placed so that the magnetic field from these poles traveled in a closed loop via the stator, rotor, and MR layers. A 3D model of the brake was prepared for the virtual study. Electromagnetic simulations were conducted to analyze the effect of axial slots’ and other design parameters of the brake. According to those simulation results, the axial slots’ width and position significantly affect the brake output torque. The maximum torque obtained from the brake is 38 Nm, and the TVR value of the brake is 41 Nm/dm³. Additionally, multiphysics simulations were performed to understand the Joule-heating effect of the magnetic coil and the frictional heating in MR fluid. Results showed that the maximum possible temperature in the brake is under the MR fluid temperature limits. Therefore, this multipole multi-layered (MPML) MR brake with axial slots idea is very useful for high-torque MR brake growth.

1. Introduction

Magnetorheological (MR) fluid is a composite material consisting of ferromagnetic particles suspended in a carrier medium, typically silicon oil. The rheological properties of this fluid, such as its viscosity and yield strength, can be precisely controlled by varying the strength of an applied magnetic field. This reversible, rapid, and continuously controllable response enables the creation of versatile MR devices. Lord Corporation produces different types of MR fluids and MR devices [1].

Table 1. Properties of commercially available MR fluids.

	MRF-140CG	MRF-132G	MRF-122EG
Viscosity at 400c, Pa-s	0.280	0.112	0.042
Density, g/cm3	3.64	3.09	2.28
Flashpoint, 0c	>150	>150	>150
Thermal conductivity at 250c, W/m0c	0.28–1.28	0.25–1.06	0.21–0.81
Operating Temperature, K	233 to 400	233 to 400	233 to 400
Solids Content by Weight, %	85.44	80.98	72
Yield Strength at 200 kA/m, kPa	57	42	32

shows the properties, such as viscosity, density, conductivity, operating temperatures, and yield strength, of three types of MR fluids. Research by Osial has extensively explored the MR properties of these fluids, including their flow characteristics, yield strength, and viscoelastic behavior under shearing flows [2]. Building upon these findings, various MR actuators have been developed, operating in three primary resistance modes: shear mode, flow mode, and squeeze mode. Among these, shear and flow mode-based actuators have proven to be the most feasible and practical, offering a wide range of applications.

Numerous flow mode devices, including dampers, shock absorbers, grippers, and magnetorheological valves, have already been developed and implemented [3]. MR dampers, in particular, have been effectively utilized to mitigate earthquake vibrations in civil structures and absorb road shocks in vehicle structures [4,5,6]. Furthermore, MR valves offer a reliable alternative to mechanical valves in hydraulic actuation systems, boasting benefits such as reduced weight, simplified control, and the absence of moving parts. Researchers have made significant strides in optimizing the design and performance of MR valves. For instance, Yoo and Wereley [7] designed a high-efficiency MR valve, analyzing its performance through simulations and experiments. Building upon the reliable dynamic behavior of MR fluids, innovative applications such as engine valve trains have been explored. Shiao [8] introduced a groundbreaking magnetorheological valve device, enabling the achievement of variable valve actuation (VVA) in engine systems.

The shear mode resistance principle is useful for MR clutches and brakes. These devices are emerging in the places of traditional low-torque clutches and brakes to achieve reasonable active control of torque transmission and braking force. Singh developed a hybrid-mode MR brake for two-wheeler applications [9]. MR brakes are getting very popular in haptic, rehabilitation, and prosthetic applications [10,11,12]. This paper mainly focused on the MR brake. It is generally constructed with the stator, rotor, MR fluid, and magnetic field coil. MR fluid is filled in the space between the rotor and stator. When the current is supplied to the field coil, it generates a magnetic flux. This flux travels from the stator to the rotor via MR fluid. Therefore, the ferromagnetic particles in the fluid align in the field direction, and then the shear resistance in the MR fluid increases. That resistance acts as a braking force on the rotor. This force can be controlled with the magnitude of the coil current. Using this concept, there are several design models available, like single-layer drum type and disc type, hybrid T-shaped drum type, multiple layers of MR fluid type, multipole coil type, and multipole and bilayer MR brake type.

Basic disc-type and drum-type MR brakes are the original designs for this technology. The significant difference between these two types is the geometry of the rotor. The disc-type brake can be used for applications where the accessible space is thin. In contrast, the drum-type brake is suitable for applications where the space is long and cylindrical. Huang et al. [13] developed a mathematical model for drum-type MR brakes. LORD Corporation designed and manufactured a simple single-disc brake [14] with a maximum resistance of 4 Nm. Attia investigated the performance of this brake theoretically and experimentally. Li and Du introduced a disc-shaped MR brake design with a simple disc construction [15]. Nguyen designed a new configuration, i.e., a T-shaped drum-type brake, to combine drum and disc-type models with individual advantages [16,17]. From these papers, it is understood that the brake torque increases with the increase in the magnetic field. However, once the saturation limit is touched, torque no longer increases. Therefore, multi-layered brakes were introduced to increase the maximum torque of the brake. Huanhuan [18] used multi-drum architecture to achieve higher torque at a lower volume. Shiao [19] developed a multi-layered magnetorheological brake for knee orthosis applications. In all these types of brakes, the magnetic flux flow area is limited; therefore, these brakes are low-braking-torque generators, and their torque–volume ratios (TVR) are lower.

On the other hand, using multipole magnetic coil construction, the torque of the brake can be enhanced without increasing its size; therefore, the TVR significantly increases. In this multiple-pole brake, even though one of the coils fails, the brake does not fail. Therefore, it is safer than conventional MR brakes. Shiao [20] introduced a higher TVR brake with a multipole drum brake. In that design, the generated magnetic flux will orthogonally travel all over the MR fluid, which gives the maximum possible performance. Figure 1 shows the six-pole arrangement, flux travel direction, and the MR fluid with a magnetic field. Later, Shiao [21] attempted to combine multi-layer and multipole concepts with his multipole bilayer MR brake. However, that design is limited to two layers only. The biggest challenge to developing multi-layers in a multipole concept brake is the magnetic flux flow to the outer layers. Flux always tries to flow to the neighbor pole via the nearest inner rotor plates (flux bypassing) in the multipole concept. Therefore, the outside MR layers receive very little magnetic flux. Eventually, a multi-layer concept cannot be applied to multipole brakes.

Recently, Wu et al. [22] proposed a radial multipole multi-layered (MPML) magnetorheological (MR) brake, achieving high torque density. Their design employed inner and outer poles to realize the multiple poles concept. However, this arrangement differs from Shiao’s multipole concept, as it follows a multi-directional pattern rather than a true multipole configuration. Moreover, the placement of inner and outer poles occupies additional volume, ultimately reducing the overall torque–volume ratio. Furthermore, the outer poles limit the mechanical advantage, as the perpendicular distance from the MR layers to the brake’s center is decreased. To address these limitations, this study aims to design an MPML drum-type MR brake with an enhanced torque–volume ratio and mechanical advantage. To achieve this, the MR layers are positioned on the outer side of the brake, maximizing the mechanical advantage. Additionally, axial slots are introduced on the rotor and stator drums’ axial surfaces to mitigate the flux bypass issue. These slots are filled with a non-magnetic, permeable material. Through computer simulations, the effects of slot dimensions and position on the brake’s performance are thoroughly analyzed.

MR brake devices are still in the conceptual stages, necessitating detailed and realistic analyses to accurately predict their performance. A critical aspect of MR brake design is the heat generated during braking, which requires comprehensive magnetic, thermal, and coupled effects simulations to understand the device’s behavior under realistic conditions. Previous studies have highlighted the importance of multiphysics analysis in MR brake design. Patil [23] employed the Joule heating concept to estimate the temperature rise in MR brakes, establishing a connection between magnetic and thermal conditions. Meng [24] developed magneto-fluid and fluid-thermal coupled models to investigate heat generation due to shear during braking. Wang [25] outlined a methodology for coupled analysis, while the Wojciech model [26] integrated transient fluid dynamics, electromagnetic and thermal fields, and mechanical equilibrium equations to capture the complex interactions within MR brakes. These studies emphasize the need for multiphysics analysis in MR brake design. Furthermore, Zhang [27] focused on designing a cooling system to dissipate heat generated during braking. In line with these recommendations, this study employed multiphysics analysis to investigate the thermal conditions of the MR brake and optimize its design.

2. Design of MR Brake

Following an exhaustive literature review, which facilitated a comprehensive understanding of the existing challenges and technological advancements in the field, the conceptual design phase of the MR brake was initiated. Three distinct conceptual designs were proposed for this device, namely: (1) a multipole MR brake with outer multi-layers, (2) a multipole MR brake with inner multi-layers, and (3) a multipole MR brake with both-side multi-layers. Figure 2 illustrates the design concepts for these three configurations.

Each of these designs possesses unique advantages and limitations. The outer multi-layer design, for instance, offers a uniform stress distribution and a mechanical leverage advantage, which can enhance the overall braking performance. However, this design also presents a challenge in terms of heat dissipation, as the heat liberated by the coil may not be effectively dissipated. In contrast, the inner multi-layer design is relatively straightforward to manufacture and exhibits a high heat transfer rate. Nevertheless, this design also has a limitation, as the magnetic flux strength is not uniformly distributed across all MR layers.

The both-side multi-layer’ design, on the other hand, achieves a uniform distribution of the magnetic field, thereby overcoming the heat transfer issue. However, this design is more complex to manufacture, and the percentage of torque generated by the inner layers is relatively low compared to the outer layers.

After carefully evaluating the pros and cons of each design, the multipole MR brake with outer multi-layers was selected as the preferred design. This decision was based on the design’s simple construction and high mechanical advantage, which are critical factors in achieving optimal braking performance. The outer multi-layer design also provides a uniform stress distribution and mechanical leverage advantage, making it an attractive choice. The proposed MPML MR brake design is presented in detail in Figure 3. This design builds upon Shiao’s earlier model of a multipole MR brake [20], incorporating key enhancements to achieve improved performance and efficiency.

As shown in Figure 3, this design contains a stator, rotor, and MR fluid. The rotor holds two rotor plates. The stator includes an inner stator plate, an outer stator plate, six magnetic cores, and a stator casing. The MR fluid fills the gap located between the stator and rotor plates. The wires are coiled around every pole with the same turns but in opposite directions. Three oil seal bearings were used to hold the rotor and restrict the oil leakages.

When applying the current input to the coils, the cores will become the electric magnetos, and the magnetic field will start from one pole and move to two adjacent poles and back to the original pole like a circle line. The magnetic field that is perpendicular to the surface of the MR fluid generates the yield stress. Additionally, stress restricts the movement between the rotor and the stator. This brake is an improved design of Shiao’s early design concept of a multipole single-layer MRB. The Shiao concept is not effective for the multiple layers option due to the lesser flux density in the outer layers. Therefore, axial slots on the rotor and stator plates were introduced for this multi-layer brake. As shown in Figure 4, small non-permeable pads were designed to tightly insert into those axial slots. Due to these axial slots, the flux bypass in the inner plates can be arrested, and more flux travels to the stator outer plate, as shown in Figure 5. This way, the flux density in the outer layers can be enhanced.

3. Mathematical Models

3.1. Electromagnetic Model

This is the initial step for the optimization of design parameters. Because of the symmetrical advantages of the design, one-sixth of the brake is considered for this study. Hence, this magnetic model considered the one complete loop of magnetic flux between the two adjacent poles. Both poles have equal winding coil turns and input current; however, the coil winding is in the opposite direction. Flux leakages in windings and between gaps are negligible. Every component in this design is assumed to be homogeneous in material properties.

Moreover, the complex 3-D model was simplified as a magnetic circuit of lumped reluctances. By using Ampere’s law and Gauss’s law analogies, a mathematical model was generated for the magnetic circuit related to the designed MPML MR brake. This model is to understand the magnetic field strength within the MR fluid ($H_{MR}$). $H_{MR}$ depends on the magnetic reluctance (R) of the different sections of the design, as shown in Figure 6. Reluctance is a function of length and cross-section area, as given in the equation.

Magnetomotive force from the coil with number of turns N and current i amperes can be expressed as Equation (1).

$$F=F1=F2=Ni$$

(1)

According to Kirchhoff’s voltage law analogy for magnetic analysis, the magneto-motive force is as follows:

$$F=R\Phi$$

(2)

According to Gauss’s flux theorem, magnetic flux $\Phi$ over the cross-section area A in the permeability material is as in Equation (3).

$$\Phi =BA=\mu HA$$

(3)

To model the entire MR brake, additional magnetic flux was added to each node in the circuit, which represents one-sixth of the brake. ${\Phi }_{d16}$, ${\Phi }_{d12}$, and ${\Phi }_{d32}$ are the magnetic flux on the stator-ring area from pole 1 to 6, pole 1 to 2, and pole 3 to 2, respectively. ${\Phi }_{d61}$, ${\Phi }_{d21}$, and ${\Phi }_{d23}$ are the magnetic flux on the rotor-ring area from pole 6 to 1, pole 2 to 1, and pole 2 to 3, respectively

With the same structural configuration and current input, the magnitude of the magnetic flux and magnetomotive forces in both coils are identical.

$${\Phi }_1={\Phi }_2={\Phi }_c$$

(4)

Applying Gauss’s law to nodes a1 and a2

$$-{\Phi }_1+{\Phi }_{a16}+{\Phi }_{12}=0$$

(5)

$${\Phi }_2-{\Phi }_{a32}-{\Phi }_{12}=0$$

(6)

A negative signal in Equations (5) and (6) indicates that the magnetic flux is directed towards the node. From the above two equations,

$${\Phi }_{a32}={\Phi }_{a16}$$

(7)

Owing to the symmetrical nature of the MR brake’s structural design, at node a1:

$${\Phi }_{a12}={\Phi }_{a16}={\displaystyle \frac{{\Phi }_c}{2}}$$

(8)

Similarly, at d1 and d2:

$${\Phi }_{d23}={\Phi }_{d61}$$

(9)

$${\Phi }_{d21}={\Phi }_{d61}=-{\displaystyle \frac{{\Phi }_c}{2}}$$

(10)

Applying Ampere’s circuit law to the loop

$${R\Phi }_1-F1+{\Phi }_{a12}{R}_{so}-F2+{R\Phi }_2+{\Phi }_{d21}{R}_{si}=0$$

(11)

Substituting Equations (7)–(10) in Equation (11)

$$2{R\Phi }_c-2Ni+{\displaystyle \frac{{\Phi }_c}{2}}(R_{so}-R_{si})=0$$

(12)

$${\Phi }_c=4Ni/(4R+R_{so}-R_{si})$$

(13)

$$R_{so}={\displaystyle \frac{l_{so}}{{\mathrm{\mu }}_{so}\ast A_{so}}}$$

(14)

$$R_{si}={\displaystyle \frac{l_{si}}{{\mathrm{\mu }}_{si}\ast A_{si}}}$$

(15)

$$R={R_c+2R}_{sp}+2R_{rp}+4R_{mr}$$

(16)

where $R_{so}$ is reluctance in stator outer case, $R_{si}$ is reluctance in stator inner case, $R_{sp}$ is reluctance in stator plate, $R_{rp}$ is reluctance in rotor plate, $R_{MR}$ is reluctance in the MR fluid layer, $R_c$ is reluctance in coil, $A$ is cross-section area, and $l$ is the thickness of the plates or MR fluid.

$$R={\displaystyle \frac{t_c}{{\mathrm{\mu }}_c\ast A_c}}+2{\displaystyle \frac{t_{sp}}{{\mathrm{\mu }}_{sp}\ast A_{sp}}}+2{\displaystyle \frac{t_{rp}}{{\mathrm{\mu }}_{rp}\ast A_{rp}}}+4{\displaystyle \frac{g}{{\mathrm{\mu }}_{mr}\ast A_{mr}}}$$

(17)

Note that the cross-sectional area at MR fluid, stator plate, core, and rotor plate is the same, i.e., $A_{mr}$ ≈ $A_{sp}$ ≈ $A_c$ ≈ $A_{rp}$. Moreover, ${\mathrm{\mu }}_c$ or ${\mathrm{\mu }}_{sp}$ or ${\mathrm{\mu }}_{rp}$ ≈ 1000 or ${\mathrm{\mu }}_{mr}$; and $t_c,t_{sp},t_{rp}$ are not too large.

Therefore, after simplifications, the required equations were achieved, as shown in Equation (18).

$$H_{MR}=4Ni/(16g+{\displaystyle \frac{{\mathrm{\mu }}_{MR}\ast A_{MR}\ast lso}{{\mathrm{\mu }}_{so}\ast A_{so}}}-{\displaystyle \frac{{\mathrm{\mu }}_{MR}\ast A_{MR}\ast lsi}{{\mathrm{\mu }}_{si}\ast A_{si}}})$$

(18)

where $Ni$ is input power in ampere-turns, A is the cross-section area of the respective member in mm², l is the length in mm, t is the thickness in mm, and µ is the permeability of component material. Where MR fluid length is nothing but a g is the MR fluid layer gap (g). The equation purely depends on the brake’s design parameters, and it can be adapted to the new model.

3.2. Magneto-Stress Model

The next step is creating an analytical model of the MR brake to find the total torque generated by the brake. The total torque generated by the MR brake contains field torque, viscous torque, and friction torque. Field torque depends on the magnetic field strength, which can be estimated by the curve fitting method. Viscous torque depends on speed and brake structure, and frictional torque is a fixed value. This mathematical model is prepared based on the Bingham-plastic model as given in Equation (19).

$$\tau ={\tau }_{yd}+\eta {\displaystyle \frac{\omega r}{g}}$$

(19)

where $r$ is the radius of the rotor disc, ${\tau }_{yd}$ is yield shear stress due to the magnetic field, $\eta$ is the viscosity of MR fluid, $\omega$ is the angular velocity, and $g$ is MR layer thickness.

The torque generated by the designed multi-layer MR brake can be calculated through area integration (Equation (20)). Specifically, this involves summing the contributions from each layer and integrating the area of the MR fluid.

$$T={\sum }_{n=1}^4{{\mathrm{r}}_{mrn}}^2\ast \left({\int }_0^z{\int }_0^{2\pi }{\tau }_n\mathrm{d}\theta \mathrm{d}\mathrm{Z}\right)$$

(20)

Substituting Equation (19) in (20):

$$T_{mrn}={\sum }_{n=1}^4{{\mathrm{r}}_{mrn}}^2\ast \left({\int }_0^z{\int }_0^{2\pi }{\tau }_n\mathrm{d}\theta \mathrm{d}\mathrm{Z}\right)+{\displaystyle \frac{2\pi \eta \mathrm{w}\mathrm{Z}}{g}}{\sum }_{n=1}^4\left({{\mathrm{r}}_{mrn}}^3\right)$$

(21)

where ${\mathrm{T}}_{mrn}$ is active torque in MR layers, $r_{mr}$ is the radius of the MR layer, n is the layer number, Z is the axial width, and w is the speed. The Lord MRF-140CG magnetorheological fluid was utilized in this investigation.

Equation (23) gives the total torque generated by the MPML MR brake.

$$T=T_{mrn}+Frictionaltorque$$

(22)

$$T={\sum }_{n=1}^4{{\mathrm{r}}_{mrn}}^2\ast \left({\int }_0^z{\int }_0^{2\pi }{\tau }_{yn}\mathrm{d}\theta \mathrm{d}\mathrm{Z}\right)+{\displaystyle \frac{2\pi \eta \mathrm{w}\mathrm{Z}}{g}}{\sum }_{n=1}^4\left({{\mathrm{r}}_{mrn}}^3\right)+{\mathrm{T}}_{fr}$$

(23)

where $T_{fr}$ is the frictional torque. Yield stress $\left({\tau }_y\right)$ of the MR fluid can be found by using a curve-fitting method from experimental studies [21],

$$\left({\tau }_y\right)=k5{{\ast \mathrm{H}}_{MR}}^5+k4{{\ast \mathrm{H}}_{MR}}^4+k3{{\ast \mathrm{H}}_{MR}}^3+k2{{\ast \mathrm{H}}_{MR}}^2+k1{{\ast \mathrm{H}}_{MR}}^1+k0$$

The values of k1–k5 are the experimental curve-fitting constants, and those are as follows:

[−2 × 10⁻¹⁰    9 × 10⁻⁸    −2 × 10⁻⁰⁵    0.0002    0.5324    1.0303]

3.3. Multiphysics Analysis

The required resistance force of MR fluid depends on the current in the magnetic coil. Due to the electrical resistivity in this magnetic coil, some amount of energy is liberated in the form of heat. Also, during the brake activation condition, the kinetic energy in the rotating disc converts into heat. This dissipated heat increases the device’s temperature, and then this temperature affects the resistance of the coil and the properties of MR fluid. Therefore, electromagnetic analysis and heat transfer analysis are needed to understand the performance of this MR brake, and these two physics must be interlinked. Thus, in this study, the MR brake was analyzed with multiphysics analysis in which magnetic and thermal concepts were coupled.

3.3.1. Determination of Joule Heating

It is the heat formed in the coil due to the flow of electric current through it. One of the earliest concepts in physics that relates the electrical and thermal fields with a simple equation is the Joule-heating effect.

$$Q_g=i^2Ŕ\mathrm{ŧ}$$

(24)

From Equation (24), the amount of heat generated by the coil can be determined, where $Ŕ$ is electric resistance in the coil and $\mathrm{ŧ}$ denotes time.

3.3.2. Determination of Frictional Heating

It is crucial to determine the amount of heat generated due to the relative motion between the rotor’s surfaces and the stator in contact with MR fluid during braking. Heat flux for the proposed analysis can be calculated using the first law of thermodynamics, i.e., conservation of energy. It is assumed that the vehicle’s whole kinetic energy is converted into thermal energy when the brake is applied. The following assumptions are made for the same.

Average angular acceleration in brake can be written as Equation (25).

$$\alpha =\mathrm{T}/{\mathrm{J}}_{\mathrm{p}}$$

(25)

where $\alpha$ is the average angular acceleration in brake and $J_p$ is the moment of inertia for the calculated part (kg·m²).

The produced heat per unit of the contact area in time t can be calculated as Equation (26).

$$Q_f=\tau \ast r\ast ({\omega }_0+\alpha \ast \mathrm{ŧ}).$$

(26)

The total heat generated during braking time is given as Equation (27)

$$Q_e=Q_g+Q_f$$

(27)

Then, the energy balance equation gives the temperatures in the system as Equation (28).

$$\rho C_p\nabla T=\nabla ·\left(k\nabla T\right)+Q_e$$

(28)

Then, linear resistivity in the concept of the metal gives the relation between temperature and resistance of the coil. According to this principle, the resistivity of the conductor depends on temperature with the following relation (Equation (29)).

$$\sigma ={\rho }_0(1+\delta \left(T-T_{ref}\right)),$$

(29)

where $\left({\rho }_0\right)\mathrm{i}\mathrm{s}\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}\left[\mathrm{n}\Omega .\mathrm{m}\right],$

$$\begin{gathered} {(T}_{ref})\mathrm{i}\mathrm{s}\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{s}\left[\mathrm{K}\right], \\ \mathrm{a}\mathrm{n}\mathrm{d}\left(\delta \right)\mathrm{i}\mathrm{s}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{o}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{i}\mathrm{c}\mathrm{e}\mathrm{i}\mathrm{n}\mathrm{t}\left[{\displaystyle \frac{1}{\mathrm{K}}}\right]. \end{gathered}$$

Using the above three equations, this two-way coupled analysis is performed. COMSOL Multiphysics, version 5.6 software was used to do the two-way coupled magnetic field and thermal analysis. A 3D model of the MR brake was built, governing equations were incorporated, and simulations were conducted.

4. Design Parameters Optimization

According to the theoretical idea and application requirements, an MPML drum brake was designed. Optimization of the design has been conducted to maximize the torque. As mentioned in

Table 2. Fixed parameters of brake.

Parameter	Initial Values in mm
rotor radius	56 to 57.5
stator radius	58
axial width	70

. Parameters like rotor radius, stator radius, and maximum axial width of the brake were fixed due to application constraints. The total shear force in the MR fluid consists of two components: yield force and viscous force. While the viscous force component is influenced by the fluid’s default viscosity and speed, the yield force is solely dependent on the magnetic flux. Notably, the viscous force is relatively insensitive to variations in brake design. Therefore, for the purposes of this study, we have maintained a constant rotor speed of 300 rpm. As illustrated in Figure 7, rotor and stator plate thickness (t_p), MR fluid thickness (t_mr), axial slot width (t_s), number of layers, and the stator material are the design variables in this optimization. By using local optimization, the final values of these parameters were found. This optimization has proceeded in several steps: the effect of the plate and MR fluid thickness, the impact of slot width, the selection of the number of MR layers, and choosing the best material for stator and rotor parts.

In this design, the possible number of turns for a given design space is 200 T. The maximum current for the chosen winding wire is 3.25 A. Therefore, after considering coil safety aspects, the maximum input supply is 600 AT. The axial slots were placed on the rotor and stator plates to overcome the flux bypassing and bring the maximum possible flux to the outer layers. A 12 mm axial slot width was considered for the initial steps, and then the best probable width was identified in the further steps. In the same way, initially, AISI 1010 material was used for magnetic permeable parts. Then, the design was updated with better material. A three-dimensional (3D) model of the MR brake was created to simulate its behavior under various operating conditions. The 3D model was then imported into COMSOL Multiphysics, a graphical interface platform that enables the simulation of complex physical phenomena.

Using COMSOL’s intuitive interface, the electromagnetic, magneto-stress, and thermal relations were assigned to the 3D model. This involved defining the material properties, boundary conditions, and physical laws that govern the behavior of the MR brake. Then, the simulations were conducted for the optimization procedure.

Firstly, the effect of MR fluid, stator plates, and rotor plate thicknesses on output torque was analyzed. From Figure 8, it is clear that the lesser MR fluid layer thickness gives higher torque. This is due to the lower magnetic permeability of the MR fluid. However, the thinning of the MR layer increases the risk of direct contact with plates. The analysis of the MR fluid layer thickness takes into account the constructional constraints and their interrelationship with the thickness of the rotor and stator plates. Therefore, the least possible thickness, i.e., 0.5, was considered.

Figure 9 illustrates that reducing the plate thickness leads to an increase in output torque. This is because magnetic reluctance is directly proportional to the flow length. Consequently, thinner plates are desirable for optimal performance. However, structural constraints dictate that the stator and rotor plates cannot be thinner than 1.5 mm. Therefore, we selected 1.5 mm thick rotor and stator plates, accompanied by a 0.5 mm thick MR fluid layer, for further analysis.

Secondly, the effect of axial slot width on the final torque was considered. The biggest problem in MPML brake design is magnetic flux propagation to the outermost layers. Flux travels from one pole to another pole in the top rotor plate until it gets saturated. Therefore, flux density on the outer side is much lower. This flux flow to the outer plates can be increased using axial slots on the rotor and stator plates. The width of these axial slots affects the magnetic field density and, eventually, output torque. Therefore, higher torque is achieved at higher axial slot widths. This trend is similar for different input currents and different stator and rotor plate thicknesses. Figure 10 shows those trends. However, after the slot width of 21, the curves started declining. This is due to the consequence of the overall working area reduction. Hence, 21 mm is the best possible slot width for this brake design.

Next is the selection of the MR layer number. Simulations were conducted for starting from a single layer to multiple layers. Figure 11 shows the overall output torque from the brake with the number of MR layers. The torque increases with an increasing number of layers. This is obvious due to the overall shear area increment. However, the effect of the number of layers is not significant after four layers. This is due to the flux flow length, though MR fluid is increasing; consequently, there is a zero flux in the outer layers, as shown in the Figure 12. Also, it is noticeable from the figure that this trend is similar at different currents. The slope of this trend is increasing with currents due to the flux availability.

The last step is the selection of material. AISI 1008, 1010, 1018, and 1020 are highly permeable materials. Electromagnetic simulations were conducted on the designed brake by assigning the above materials. Figure 13 shows the torque generated by the MR brake with different materials for the stator and rotor. From the results, it is clear that AISI 1020 was considered the ideal material due to its favorable properties. However, taking into account manufacturing considerations, availability, and durability factors, AISI 1018 was ultimately selected as a suitable alternative.

Table 3. Final values of brake.

Parameter	Final Values
Rotor and stator plate thickness (mm)	1.5
MR fluid thickness (mm)	0.5
Axial slot width (mm)	21
Material	AISI 1018
Input current (AT)	600
Flux effected axial width w (mm)	35
Outer radius of the brake (mm)	65

presents the optimized and feasible parametric values that have been determined for the proposed MPML MR brake design, following a thorough analysis and simulation-based optimization process.

5. Results

Following the optimization of key parameters, the final model underwent comprehensive magnetic and thermal analyses. The simulations were performed using the optimized parameters listed in Table 3, in conjunction with the following additional settings: a rotor speed of 300 rpm and the utilization of Lord’s MRF-140 as the MR fluid. Figure 14a shows the direction of the magnetic flux in the cross-section of the MR brake. Its flow direction is noticeable as a loop from one pole through the MR fluid layer to the rotor plates, then back through the MR fluid layer again to the adjacent poles via the stator outer casing. Figure 14b displays the torque results at different input currents from the simulations. The maximum simulated torque is 38 Nm, which is at the input of 600 AT. The relation between torque and input is linear. Therefore, brake torque can be controlled precisely with the input current.

5.1. Magnetic Simulations

Figure 15a shows the magnetic flux density and its maximum possible magnitude in the brake part. Since the occurrence of magnetic saturation for AISI 1018 steel becomes saturated at around 2.2 T, these brake parts are just near saturation. In Figure 15b, the magnitude of the magnetic field strength in the MR fluid layers of the MR brake is shown. The maximum magnetic field strength occurs across the MR fluid gap under the pole-head area. These areas are the sources of high-yield stress, which helps to slow the motion of the rotor.

5.2. Slot Position Study

The axial slots on the stator and rotor plates are not always aligned due to the rotational motion of the rotor during operation. As a result, the alignment difference between the rotor and stator positions varies cyclically from 0 to 60 degrees. This study investigated the impact of this positional difference on the output torque.

Figure 16 illustrates the significant effect of this alignment difference on torque. Notably, the torque is higher when the difference is 25 degrees and 35 degrees. This is attributed to the maximum percentage of available flux flowing in the direction normal to the MR layers, resulting in a concentrated flux in one area (Figure 17). Consequently, more flux flows into the outer layers, leading to increased torque.

Although this torque fluctuation may be negligible in standard braking systems, where the primary objective is to stop the rotor, it becomes a critical consideration in applications requiring uniform torque. To mitigate this fluctuation, a sophisticated input control system must be designed to provide precise control over the braking torque. One of the notable drawbacks of MR brakes is the presence of minimum off-field torque. To address this limitation, innovative designs have been proposed. For instance, Shamieh [28] introduced a novel MR brake design featuring a neighboring gap that effectively traps the MR fluid during the off-state, thereby minimizing the off-field torque.

Various types of MR brakes were stated in

Table 4. Comparison of designed brakes with existing brakes.

	Lord Co. MRB [14]	Multipole MR Brake [19]	Multipole Bilayer MR Brake [20]	Multipole Multi-Layer without Slots [21]	Designed MR Brake
Radius (cm)	4.83	7.0	5.0	130	6.5
Volume (dm3)	1.508	1.068	0.430	0.995	0.928
Width (cm)	5.87	9.8	13.6	98	7.0
Torque (Nm)	5.0	19.9	27.5	133	38
TVR(Nm/dm3)	11.6	13.1	25.8	25	41

for TVR comparison. The TVR of the existing multipole brakes ranges near 25 Nm/dm³. At the same time, the TVR of the designed MPML MR brake is 41 Nm/dm^3, which is much higher than that of the existing MR brakes. This shows that the suggested axial slots on rotor plates have a significant role in future MPML MR brake designs, and this designed brake is a great promise for future use, such as in vehicles, sports, and medical devices. Note to the readers that the designed brake is intended for low-torque applications with high TVR, specifically in rehabilitation devices, prosthetic devices, and bicycles. These applications require precise control strategies and are very compact in size, which our design aims to provide.

5.3. Thermal Simulations

MR brakes generated heat during braking. Also, there is a rise in temperature in the MR brake due to the coils’ Joule heating effect. Therefore, thermal field simulations were conducted to find the maximum temperature in MR layers and brakes. Ambient air condition was given around the brake outer surface with an initial temperature of 313 K and 1 atm pressure. A full torque condition was considered for this study, i.e., the 600 AT input condition. To understand the brake’s maximum possible temperature, a simulation was conducted until the brake reached a thermally steady-state condition.

Two primary sources of heat generation are identified: coil and frictional heating. The heat generated in the coil can be calculated using Equation (24), with a total wire resistance of 6 ohms and a rated input current of 2.5 A. In contrast, the thermal power generated in the liquid at 300 rpm can be calculated using Equation (26), which considers the average shear stress (shear stress averages 60 kPa) and angular velocity of 5 rad/sec. Notably, the frictional heat generated is significantly lower than the heat produced by the coil.

As previously discussed, the coil-generated heat significantly surpasses the frictional heat. This is evident in the simulation results depicted in Figure 18a, where the maximum temperature is concentrated at the stator core that was found to be 354 K, which is about 314 K more than the initial condition. This is due to the heat liberated by the coil. Due to this reason, as shown in Figure 18b, the inner MR layer was hotter than the outer layers. However, this temperature is within the acceptable range of Lord’s MRF-140, i.e., 233 to 400 K.

6. Conclusions

This exhaustive study has successfully conceptualized and meticulously analyzed a groundbreaking multipole multi-layered (MPML) magnetorheological (MR) brake design, incorporating axial slots on the rotor and stator drum axial surfaces. By effectively addressing the inherent limitations of existing MR brake designs, this novel configuration has successfully mitigated the flux bypass phenomenon, thereby achieving a substantial increase in torque–volume ratio (TVR). The optimized design parameters have yielded a remarkable brake torque of 38 Nm and a TVR value of 41 Nm/dm³, with operating temperatures conveniently falling within the permissible limits of the MR fluid. These outstanding findings unequivocally demonstrate the immense potential of the proposed MPML MR brake design for high-torque applications, offering a promising solution for industries requiring compact, high-performance braking systems. Future research endeavors will focus on experimental validation and control of a prototype, as well as a comprehensive examination of hysteresis effects, to further refine and optimize the performance of this innovative brake design, ultimately paving the way for its successful integration into real-world applications.