Investigating the Impact of Circular Sector Pole Head Structure on the Performance of a Multipole Magnetorheological Brake

: The magnetorheological brake (MRB) epitomized a revolutionary modification in the braking systems because of its extremely efficient and well-controlled performance. To increase the safety and controllability of automotive braking system, researchers have developed a different MRB structures. Although much research on magnetorheological brakes has shown positive results in terms of brake torque, braking time, thermal efficiency, etc., the ability to increase braking force by expanding the disc surface, through which the magnetic field operates in a compact structure, is restricted. To address this issue, a new multipole MRB configuration with a unique pole head design that maintains compactness. Initially, the conceptual design was achieved by leveraging the combined impact of the twin disc-type structure and multipole concept. The model was used in a dynamic simulation to show how the braking torque of a magnetorheological braking system varies with coil current. The effects of circular sector pole head shape on braking performance were investigated using COMSOL Multiphysics software (version 5.5). A three-dimensional electromagnetic model of the proposed MRB was developed to examine the magnetic flux intensity and the impact of magnetic field dispersion on the proposed pole head structure of a magnetorheological brake. Based on simulation results, the circular sector pole head configuration is capable of increasing the active chaining regions for the MR fluid on the rotor surface, allowing for a more effective use of magnetic flux throughout the whole surface of a rotating brake disc, thereby increasing the magnetic field usage rate. The acquired simulation results show an increase in braking torque while keeping a compact and practical design structure.


Introduction
Magnetorheological brakes are a sort of intelligent or controllable braking system that uses a unique type of fluid containing suspended, micron-sized magnetic particles, often made of iron or iron-based compounds.When the electromagnet is energized, it generates a magnetic field that affects the magnetic particles inside the magnetorheological fluid, and so the active zone on the surface operates to control the braking force.
Researchers have developed multiple magnetic resistance brakes with various structures to maximize their braking torque.There are several typical methods to enhance the braking torque, such as improving the properties of the magnetorheological fluid (MRF), expanding its working area, or altering the structure of the MRB, which directly impacts the strength of the magnetic field.Shiao et al. [1] introduced the concept of multipole design with a multilayer structure to address the limitations of magnetic field strength.This innovative design incorporates electromagnetic poles surrounded by multiple coils, thereby increasing the brake torque.Subsequently, Shiao et al. [2,3] proposed a unique design for a multipole multi-layer magnetorheological brake, aiming to enhance the torque density.Such high torque density designs may be more suitable for various industrial and automotive applications.Jie Wu et al. [4,5] put forward a compact magnetorheological brake that employs multiple layers of MRF.The results indicate that the magnetic flux generated in the MRB can be controlled to achieve the desired transmission torque.B K Song et al. [6] developed an MRB to improve compactness, with optimal performance depending on magnetic circuit design.This structured brake focuses on the magnetic field strength of the effective area, which is influenced by the coil current.Jie Wu et al. [7] conducted research on improving braking torque by utilizing radial dimensions in a multipole multi-layer MRB and discovered that this unique design concept enhances the strength of the magnetic field.Daoming et al. [8] proposed a hybrid magnetic circuit concept for output braking torque and found a linear relationship between ampere-turns (AT) and braking torque.The magnetic field strength is often limited by saturation.Still, Guoliang Hu et al. [9] overcame this limitation by incorporating a non-magnetic sleeve into the structural design of the magnetorheological brake's coils.Consequently, their results demonstrate an increased utilization rate of the magnetic field.
When the electromagnet is activated, the magnetic particles align along the field lines, which is crucial for magnetic flux flow in an MRB.Nguyen et al. [10] researched a zigzag flux path between the disc and housing, and the results proved that the flux line is forced to cross the MRF duct.Magnetic flux flow is critical for the operation of a magnetorheological brake, so Shiao et al. [11,12] developed a new MRB that effectively utilizes magnetic flux on the surface of a rotating brake disc, resulting in increased braking torque and a compact design.A multipole bilayer magnetorheological brake design with cylindrical separator rings results in reduced flux leakage and improved braking performance.The pole head radius and magnetic core shape play a crucial role in increasing the working area in a compact MRB.Nguyen et al. [13] suggested a hybrid magnetic circuit configuration to increase the magnetorheological brake's internal magnetic flux density.Later, Nguyen et al. [14] investigated different shapes for the MRB envelope and found that rectangular, polygonal, or spline shapes resulted in higher torque with reduced mass.Polat M. et al. [15] investigated radial forces by giving different geometric shapes to the pole heads and investigating the effect of these pole shapes on performance, achieving reasonable results when compared to the previous design.Shiao et al. [16] investigated the effect of pole head geometry in a multipole dual disc and discovered that hexagonal pole heads had a larger magnetic field area and an increase of 3.88% for braking torque performance.
Sheth et al. [17] developed a rotor design that protrudes the poles slightly outward on one side, resulting in a decrease in stator pole heights, and this configuration increases the average torque.The analysis also showed that noncircular stator pole faces increase average torque.Ren Liu yi et al. [18] conducted a study on different shapes of magnetic medium sections and found that toothed plate section shape improves magnetic force at 2.5 A magnetizing current compared to cylindrical sections.Assadsangabi et al. [19] examined the potential of a magnetic-resistance brake with geometric constraints to achieve the desired design objective and flexible structure, and results showed that the initial dynamic behavior of the magnetic field yields a significant braking torque while maintaining a compact and solid design.Similarly, Shrikant Kumbhar et al. [20] explored the use of MRB in automotive applications and demonstrated that increasing the number of discs enhances the torque, thereby confirming its viability in real-world braking applications.
The primary purpose of the geometrical designing of pole head structure into circular sector-shaped multiple poles that can be radially arranged is to understand the flux distribution in its axial outward direction of a rotating brake disc's overall surface, which can maximize MRF active working areas.Changing the shape of the pole head can impact the distribution and intensity of the magnetic flux, which affects the performance characteristics like output braking torque and overall efficiency.The proposed pole head design leads to a consistent and uniform magnetic field to achieve specific torque characteristics.This allows for precise control over the braking force exerted by the MR brake.By enhanced magnetic efficiency, it may be possible to achieve a better braking force in a compact design structure.This paper indicates that proper design considerations can significantly influence magnetic flux density and increased braking torque capacity that impact the brake's performance.

Working Principle and Structural Design
Magnetorheological brakes have received a lot of attention because of the viscoplastic behavior that achieves braking through the shearing effect of MRF, describing the critical influence on magnetic field intensity.The structural and thermal properties of the Lord MRF-140CG, as shown in Table 1, are ideal for fluid braking and meet a variety of requirements, including viscosity without a magnetic field, operating temperature, shear stress gradient for the applied magnetic field strength, thermal conductivity, and coefficient of thermal expansion.The new structural design aims to significantly increase the active MR fluid chaining area and the corresponding shear stress on rotor surfaces, thereby increasing braking torque.The Lord MRF-140CG fluid was selected for this MRB due to its high-yield stress gradient and accessibility.In the presence of a magnetic field, the rheology of MRF-140CG fluid changes reversibly and instantly from a free-flowing liquid to a semi-solid with controllable yield strength.[21].

MRF-140 CG Properties Units Value
Viscosity at 40 Operating temperature The proposed brake adopts a common double brake disc structure that has four magnetic layers and six magnetic poles, which is suitable for more complicated occasions with limited axial installation space.Figure 1 depicts the brake's major components, which include stator cases, rotor discs, magnetic poles, magnetorheological fluid layers, stator caps, and covers.Because of the magnetic properties, the shaft and MRB covers were made of non-ferromagnetic material.Stator cases were made of an aluminum alloy.Nonmagnetic materials connect two adjacent stators, allowing the produced magnetic flux to pass through MRF gaps.These case holes in the inner disc surface are intended for the insertion of magnetic poles that form a circular array, as shown in Figure 2. Magnetic poles with magnetically permeable cylindrical cores have heads and shanks inserted into those holes, and the core region has copper coil windings encircling it.Magnetically permeable rotor discs were positioned parallel to the surface of the stator cases and pole heads.MRF was used to fill the gaps between the outer cap and disc surfaces.The rotor rotates almost freely within the stator casing.
Shiao et al. [3] achieved a multipole compact dual disc magnetorheological brake with a simple and light weight mechanical construction and optimized the structural dimensions of the brake through electromagnetic simulations.In this study, we use some of the fixed dimensions of an earlier designed brake, as shown in Table 2, because it achieves a higher torque density and a fairly quick response.
When a copper coil is electrified, the brake is activated, the core heads become magnetic poles, and an induced magnetic field is generated in the working area of MR fluid.MRF particles form a chain structure at the top and bottom rotor surfaces, due to the MRF rheological effect that allows the magnetic flux to penetrate orthogonally.The multipole effect of the even number of coil-winded magnetic cores was arranged in such a way that the magnetic flux path in one pole was reversed to that of its two adjacent magnetic poles.The flux flow begins from one pole to the adjacent pole via the inner MR layer, rotor disc, and outer MR layer, as shown in Figure 3, and then returns on the opposite side of the brake.This configuration created a closed flux loop cycle between two adjacent cores.Some of the flux, however, can bypass the next pole via the rotor.The shearing effect of MR fluid in the magnetic field is influenced by this innovative pole head design and the flexible geometric configuration of the brake, which can be enhanced by adjusting the pole head configuration.Shiao et al. [3] achieved a multipole compact dual disc magnetorheological brake with a simple and light weight mechanical construction and optimized the structural dimensions of the brake through electromagnetic simulations.In this study, we use some of the fixed dimensions of an earlier designed brake, as shown in Table 2, because it achieves a higher torque density and a fairly quick response.When a copper coil is electrified, the brake is activated, the core heads become magnetic poles, and an induced magnetic field is generated in the working area of MR fluid.MRF particles form a chain structure at the top and bottom rotor surfaces, due to the MRF rheological effect that allows the magnetic flux to penetrate orthogonally.The multipole effect of the even number of coil-winded magnetic cores was arranged in such a way that the magnetic flux path in one pole was reversed to that of its two adjacent magnetic poles.The flux flow begins from one pole to the adjacent pole via the inner MR layer, rotor disc, and outer MR layer, as shown in Figure 3, and then returns on the opposite side of the brake.This configuration created a closed flux loop cycle between two adjacent cores.Shiao et al. [3] achieved a multipole compact dual disc magnetorheological brake with a simple and light weight mechanical construction and optimized the structural dimensions of the brake through electromagnetic simulations.In this study, we use some of the fixed dimensions of an earlier designed brake, as shown in Table 2, because it achieves a higher torque density and a fairly quick response.When a copper coil is electrified, the brake is activated, the core heads become magnetic poles, and an induced magnetic field is generated in the working area of MR fluid.MRF particles form a chain structure at the top and bottom rotor surfaces, due to the MRF rheological effect that allows the magnetic flux to penetrate orthogonally.The multipole effect of the even number of coil-winded magnetic cores was arranged in such a way that the magnetic flux path in one pole was reversed to that of its two adjacent magnetic poles.The flux flow begins from one pole to the adjacent pole via the inner MR layer, rotor disc, and outer MR layer, as shown in Figure 3, and then returns on the opposite side of the brake.This configuration created a closed flux loop cycle between two adjacent cores.Some of the flux, however, can bypass the next pole via the rotor.The shearing effect of MR fluid in the magnetic field is influenced by this innovative pole head design and the flexible geometric configuration of the brake, which can be enhanced by adjusting the pole head configuration.

Magnetic Field Distribution
The magnetic circuit of the MRB is one of the main design factors, it distributes the magnetic field according to Ampere's and Gauss's laws.The magnetic field analysis of the brake is a sophisticated three-dimensional magnetic field-mapped meshing technique that assesses the braking torque of the MRB.A three-dimensional finite element model for the

Magnetic Field Distribution
The magnetic circuit of the MRB is one of the main design factors, it distributes the magnetic field according to Ampere's and Gauss's laws.The magnetic field analysis of the brake is a sophisticated three-dimensional magnetic field-mapped meshing technique that assesses the braking torque of the MRB.A three-dimensional finite element model for the suggested magnetorheological brake was created using the structural dimensions.The geometry of the pole head and the magnetic circuit of the brake (effective core area) is made up of a coil, a magnetic casing, non-magnetic parts, a disk, surrounding air, and a MRF gap to determine the field distribution.The ultimate goal in magnetic circuit design is to increase the magnetic flux in the MRF gap as much as possible.The structure of the multipole MRB is symmetrical, and allows these poles to initially have the same magnetic field polarization.Larger pole heads can provide a more uniform magnetic field across the MRF, leading to more consistent and predictable braking performance.The magnetic force lines depict the magnetic potential when a higher input current is applied to each coil.The magnitudes of the input current may readily regulate the braking torque.

Formation of Magnetic Flux Density
Magnetic flux density is a crucial concept in MRB, since it represents the strength of the magnetic field.The size and shape of the pole head play a crucial role in determining the distribution and density of the magnetic field within the MRF.By increasing the pole head, more magnetic field lines pass through the MRF, thus intensifying the magnetic flux density.When the rotor surface is subjected to a uniform and higher magnetic field, the magnetic flux density created at a high input current demonstrates that the magnetic circuit of the MR brake is feasible and efficient.The magneto motive forces produce a magnetic field of intensity H and magnetic flux density B, with the majority of the magnetic flux orthogonally penetrating through the MR fluid layers in a closed loop.The torque generated by increasing the axial length of MR fluid surfaces is due to the constant magnetic flux density on the cylindrical surfaces along the axial direction.Maintaining a pole width gap to replicate the structure and raise the flux flow at the pole heads' center region is another way to boost torque.

Evaluating Braking Torque for the Proposed Pole Head Design
A magnetorheological brake functions based on the magnetic flux interactions between the moving and immovable elements.The pole head is the part of the brake through which the magnetic flux exits from the core material and enters the MRF.The distribution and density of the magnetic flux are influenced by the size and shape of the pole head.In reaction to the magnetic flux generated, the moving rotor generates braking action.While smaller pole heads lower the surface area available for magnetic interaction, they can result in a decrease in brake torque; larger pole heads increase the surface area through which magnetic flux interacts with the rotor disc.The distribution of magnetic flux is also influenced by the shape of the pole head.So, an ideal distinct shape (i.e., circular sector shape) is chosen to maximize the flux flow in the contact region for a stronger magnetic field.
In a magnetorheological brake, braking torque can be calculated by considering several factors, such as magnetic flux density, the geometry of the brake, the properties of the magnetorheological fluid, and the applied voltage/current.The strength of the magnetic field applied to the MR brake defines the flux density that passes through the pole head.Considering a circular sector pole head with trapezoidal dimensions, as shown in Figure 4, 'r' measures the radius of center of the pole head through which flux flows in a axial direction.
eral factors, such as magnetic flux density, the geometry of the brake, the properties of the magnetorheological fluid, and the applied voltage/current.The strength of the magnetic field applied to the MR brake defines the flux density that passes through the pole head.Considering a circular sector pole head with trapezoidal dimensions, as shown in Figure 4, `r' measures the radius of center of the pole head through which flux flows in a axial direction.Braking Torque Calculation for a Specified Pole Head Geometry The shear force (F) acting on the MR fluid is directly proportional to the effective area (A) exposed to the magnetic field and the magnetic flux density (B).It can be expressed as: To determine the effective area for the sector pole head geometry exposed to the magnetic field.
Firstly, calculate the area of the sector pole head geometry (Asector): where The angle subtended by the sector is θ (in degrees), the radius of the circle is r and  value = 3.14.
Calculate the area of the trapezoidal pole head (Atrapezoid): where Two lengths of the parallel sides of the trapezoid are denoted by b1 and b2, and the height of the trapezoid is denoted by h.Braking Torque Calculation for a Specified Pole Head Geometry The shear force (F) acting on the MR fluid is directly proportional to the effective area (A) exposed to the magnetic field and the magnetic flux density (B).It can be expressed as: To determine the effective area for the sector pole head geometry exposed to the magnetic field.
Firstly, calculate the area of the sector pole head geometry (A sector ): where The angle subtended by the sector is θ (in degrees), the radius of the circle is r and π value = 3.14.
Calculate the area of the trapezoidal pole head (A trapezoid ): where Two lengths of the parallel sides of the trapezoid are denoted by b 1 and b 2 , and the height of the trapezoid is denoted by h.
Therefore, the effective area 'A' of the circular sector pole head can be obtained from Equations ( 3) and (4) From Equations ( 1) and ( 2), the torque exerted on the MR fluid due to the shear force can be calculated by multiplying the shear force by the radial distance (r) from the center of rotation.It can be denoted by the following expression:

Design Optimization
Accordingly, the proposed brake was designed with four MR fluid layers and a 6-pole arrangement with a rotor and stator.The objective of the study's design was to enhance the recommended MR brake to maximize brake torque capability while preserving the brake structure's compactness, or lowest volume.The variables most likely to affect the output torque of a braking system are the coil ampere-turns, fluid working area, magnetic pole diameter, and magnetic channel thickness.An MR brake's braking force is directly correlated with the MR fluid's yield stress.The channel rapidly reaches magnetic saturation if the MR fluid layers are excessively thin.Large pole head widths affect the coil winding's space, which is directly correlated with a decrease in input ampere turn.This leads to insufficient magnetic field transmission, which lowers efficiency.To improve field dispersal, the MRF layer's working area, which is situated between the rotor and stator plates, needs to be enlarged.An increased total torque is produced by a broader working surface.Software for magnetic analysis was used to optimize the suggested brake's design.For the optimization procedure, three primary design factors, namely the gap between the pole heads, and the current applied, were examined.

Finite Element Simulation of the Proposed Magnetorheological Brake
A steady-state analysis of the brake's magnetic field, using the guiding effect of the magnetic and non-magnetic materials on the magnetic flux lines, influences the flux lines distributed perpendicular to the liquid flow, which improves the utilization rate of the limited magnetic field strength.After the structural characteristics of the brake have been determined, the magnetic flux density, due to the effective working area, has been analyzed to test the braking performance of the MRB.
The electromagnetic field inside the MRB was subjected to a finite element analysis using COMSOL Multiphysics software.The system of equations is solved by this software using three-dimensional magneto static simulation.The modeling of several coupled physics in a single example is the most significant feature of this software.To build the mutual interactions between each physical field, the relevant physics module must be chosen and added to the COMSOL software.To parameterize, for example, the geometry size, the fundamental material, and the associated operating parameters of the designed magnetorheological fluid brake, first select the global definitions node in the model wizard and enter values in the parameters table to define the parameters used throughout the model.The modeling domain is divided into a mesh of triangular components that completely split into many smaller units (i.e., extremely fine element size).Over these elements, polynomial form functions reflect the dependent variables.The model was solved using a nonlinear solver once the mesh was created, in order to obtain the magnetic field distribution onto the MRF (i.e., magnetic flux density).It is therefore expressed as a set of algebraic equations that describe the magnetic and flow fields for the variables that make up the elements.The results generated by the simulations, which made use of FEM to characterize the interaction between the various fields, were independent of the number of elements.

Simulation Results
A simulation study was performed to analyze the proposed pole head design for an effective active zone.The results showed that the output torque was proportional to the pole head design, which enhanced the flux density and also increased the overall braking torque.At most positions of the MRB structure, the magnetic flux lines are more evenly distributed when the ideal current flows through the coil that also enhances magnetic field strength.The entire working surface area is determined by the pole head structure, the number of poles, the pole head gap and the specific pole radius.It was discovered that a bigger pole area results in a higher output torque and that the magnetic core influences magnetic efficiency under varied input currents.

Effective Pole Head Structure
In a magnetorheological brake, the pole head alignment plays a critical role that determines the ability of its optimal performance.Correct pole head alignment facilitates a clear and direct path for the efficient magnetic flux between the pole heads, maximizing the strength of the magnetic field within the working area of the brake.In this study, the distance between the pole heads and coil current was changed in order to optimize the intensity of the magnetic field.The brake torque relation with the pole head structure is shown in Figure 5, and to assess improved output for circular sector design, the distance Appl.Sci.2024, 14, 5344 8 of 14 between the pole heads was changed.Increasing the gap between the pole heads from 8 mm to 10 mm and adjusting the input coil currents from 1 Ampere to 2 Ampere, the braking torque increases to its maximum and then slightly decreased due to the impact of coil saturation in the core region.The effective magnetic core area is the cross-sectional region, where a path for the magnetic field lines appears, indicating the passage of magnetic flux.If the gap between the pole heads is high and the current is high, the uniformity in the distribution of the magnetic field across the braking surface is not consistent.If the pole head gap is too close there may be chances of magnetic flux leakage or dispersion, resulting in the reduced efficiency of the brake.According to the findings, the torque value increases from 8 mm to 8.5 mm as the current in Amperes increases, and later on the braking torque reduces as the gap increases.Thus, for the proposed sector pole head shape at an optimal distance of 8.5 mm pole head gap and at a maximum of 2 amps of current, the efficient torque is obtained without current carrying coil becoming saturated.

Effective Pole Head Structure
In a magnetorheological brake, the pole head alignment plays a critical role that determines the ability of its optimal performance.Correct pole head alignment facilitates a clear and direct path for the efficient magnetic flux between the pole heads, maximizing the strength of the magnetic field within the working area of the brake.In this study, the distance between the pole heads and coil current was changed in order to optimize the intensity of the magnetic field.The brake torque relation with the pole head structure is shown in Figure 5, and to assess improved output for circular sector design, the distance between the pole heads was changed.Increasing the gap between the pole heads from 8 mm to 10 mm and adjusting the input coil currents from 1 Ampere to 2 Ampere, the braking torque increases to its maximum and then slightly decreased due to the impact of coil saturation in the core region.The effective magnetic core area is the cross-sectional region, where a path for the magnetic field lines appears, indicating the passage of magnetic flux.If the gap between the pole heads is high and the current is high, the uniformity in the distribution of the magnetic field across the braking surface is not consistent.If the pole head gap is too close there may be chances of magnetic flux leakage or dispersion, resulting in the reduced efficiency of the brake.According to the findings, the torque value increases from 8 mm to 8.5 mm as the current in Amperes increases, and later on the braking torque reduces as the gap increases.Thus, for the proposed sector pole head shape at an optimal distance of 8.5 mm pole head gap and at a maximum of 2 amps of current, the efficient torque is obtained without current carrying coil becoming saturated.

Distribution of Magnetic Field
The appropriate distribution of magnetic field strength determines the field torque generated on the rotor's top surface.The higher magnetic field intensity verifies the practicality and accuracy of the suggested magnetorheological brake with a sector pole head arrangement with a maximum of 240 turns, based on the input NI that depends on varied

Distribution of Magnetic Field
The appropriate distribution of magnetic field strength determines the field torque generated on the rotor's top surface.The higher magnetic field intensity verifies the practicality and accuracy of the suggested magnetorheological brake with a sector pole head arrangement with a maximum of 240 turns, based on the input NI that depends on varied input coil currents.According to the simulation findings, Figure 6 depicts the magnetic field intensity displayed for various input currents.The intensity of the magnetic field increases as the coil current increases from 0 Amp to 2 Amp at a set interval of 0.2 Amp.Uniformity index is observed from 0-1.2 Amp, and then a variation of low to peak intensity is observed between 1.6-2 Amp.A sector pole head shape in an MRB with a high input current of 2 Amp results in uniform magnetic field intensity, resulting in torque increase.
Appl.Sci.2024, 14, x FOR PEER REVIEW 9 of 15 input coil currents.According to the simulation findings, Figure 6 depicts the magnetic field intensity displayed for various input currents.The intensity of the magnetic field increases as the coil current increases from 0 Amp to 2 Amp at a set interval of 0.2 Amp.Uniformity index is observed from 0-1.2 Amp, and then a variation of low to peak intensity is observed between 1.6-2 Amp.A sector pole head shape in an MRB with a high input current of 2 Amp results in uniform magnetic field intensity, resulting in torque increase.Figure 7 depicts the magnetic field intensity recorded on the rotor surface at a current input of 2 A to the core.The configuration demonstrates that the majority of the flux will proceed orthogonally to the rotor surface after passing through the MR fluid.The color variation describes the intensity of the magnetic field on the rotor surface.The blue hue represents a more severely impacted region, while the yellow color represents the sur- Figure 7 depicts the magnetic field intensity recorded on the rotor surface at a current input of 2 A to the core.The configuration demonstrates that the majority of the flux will proceed orthogonally to the rotor surface after passing through the MR fluid.The color variation describes the intensity of the magnetic field on the rotor surface.The blue hue represents a more severely impacted region, while the yellow color represents the surrounding area of the most severely afflicted area, where the strength is slightly reduced.When the magnetizing current is 2 A, the magnetic density around the coil achieves saturation, but the pole head experiences the typical magnetic field intensity depicted in orange due to the larger working area and the region's distance from the core.From Figure 8, we can determine that the magnetic field lines illustration indicates the pole head active zone of the working surface, where the magnetic field intensity is greater.It demonstrates that the highest magnetic field is created through the center of the pole head with no losses.This finding demonstrates that magnetic saturation is avoided throughout the construction.

Impact of Pole Head Radius on Magnetic Flux Flow
The magnetic flux flow is considerably controlled by the pole head radius, which can impact the working area of an MRF triggered by shear stress.To achieve higher flux distribution, a greater core radius or a higher pole head radius must be built.A large core radius lowers the available space for coil winding, which affects the magnetic field.So, a large pole radius efficiently covers a wider area and the flux concentration will be uniform across the surface within a specific region.From the results, we can observe that the proposed sector pole head design can ensure better control over the magnetic field distribu-

Impact of Pole Head Radius on Magnetic Flux Flow
The magnetic flux flow is considerably controlled by the pole head radius, which can impact the working area of an MRF triggered by shear stress.To achieve higher flux distribution, a greater core radius or a higher pole head radius must be built.A large core radius lowers the available space for coil winding, which affects the magnetic field.So, a large pole radius efficiently covers a wider area and the flux concentration will be uniform across the surface within a specific region.From the results, we can observe that the proposed sector pole head design can ensure better control over the magnetic field distribution, as illustrated in Figure 9.A wider pole head radius shows more concentrated mag-

Impact of Pole Head Radius on Magnetic Flux Flow
The magnetic flux flow is considerably controlled by the pole head radius, which can impact the working area of an MRF triggered by shear stress.To achieve higher flux distribution, a greater core radius or a higher pole head radius must be built.A large core radius lowers the available space for coil winding, which affects the magnetic field.So, a large pole radius efficiently covers a wider area and the flux concentration will be uniform across the surface within a specific region.From the results, we can observe that the proposed sector pole head design can ensure better control over the magnetic field distribution, as illustrated in Figure 9.A wider pole head radius shows more concentrated magnetic field lines around the immediate surrounding area of the pole head, as well as across a broader space.It is obvious that there is a larger magnetic flux density near the pole head, and that the flux flow diminishes as far as the region from the center of the MRB.The magnetic field analysis shows that the magnetic flux is penetrating orthogonally through the MRF and forming a closed loop with the adjacent pole head, as shown in Figure 10.It can be seen that the magnetic flux lines are uniformly distributed throughout the configuration, which is essentially the same as the magnetic circuit design.

Optimized Design Variables for Sector Pole Head
The conceptual idea is to design a novel pole head for the MR brake to improve its effective working surface area.Lord MRF-140CG fluid's high-yield stress gradient led to its selection for this design.Since a thinner layer produces a higher magnetic field, the MR fluid layer thickness was fixed at 0.5 mm.The brake's axial width measured 28 mm, the rotor's radius fixed at 38 mm, and the magnetic core radius fixed at 8 mm.The SS-400 steel was used for the core blocks, rotor shaft, rotor disc, and stator caps because of its strength.The Nelder and Mead optimization strategy [22] is reasonably easy to implement to obtain the optimal design of MR brakes.It is utilized to choose the most efficient value from a range of choices.One of the most time-efficient methods is to use the Heuristic methodology to obtain an approximate solution to a problem.In this context, the optimum value (maximum or lowest) of the aim is obtained by searching in a space.
The design variables of pole head gap and coil current were shown to be important

Optimized Design Variables for Sector Pole Head
The conceptual idea is to design a novel pole head for the MR brake to improve its effective working surface area.Lord MRF-140CG fluid's high-yield stress gradient led to its selection for this design.Since a thinner layer produces a higher magnetic field, the MR fluid layer thickness was fixed at 0.5 mm.The brake's axial width measured 28 mm, the rotor's radius fixed at 38 mm, and the magnetic core radius fixed at 8 mm.The SS-400 steel was used for the core blocks, rotor shaft, rotor disc, and stator caps because of its strength.The Nelder and Mead optimization strategy [22] is reasonably easy to implement to obtain the optimal design of MR brakes.It is utilized to choose the most efficient value from a range of choices.One of the most time-efficient methods is to use the Heuristic methodology to obtain an approximate solution to a problem.In this context, the optimum value (maximum or lowest) of the aim is obtained by searching in a space.
The design variables of pole head gap and coil current were shown to be important in enhancing the magnetic field strength and efficiency of the MRB.With 0.1 Amp incre-

Optimized Design Variables for Sector Pole Head
The conceptual idea is to design a novel pole head for the MR brake to improve its effective working surface area.Lord MRF-140CG fluid's high-yield stress gradient led to its selection for this design.Since a thinner layer produces a higher magnetic field, the MR fluid layer thickness was fixed at 0.5 mm.The brake's axial width measured 28 mm, the rotor's radius fixed at 38 mm, and the magnetic core radius fixed at 8 mm.The SS-400 steel was used for the core blocks, rotor shaft, rotor disc, and stator caps because of its strength.The Nelder and Mead optimization strategy [22] is reasonably easy to implement to obtain the optimal design of MR brakes.It is utilized to choose the most efficient value from a range of choices.One of the most time-efficient methods is to use the Heuristic methodology to obtain an approximate solution to a problem.In this context, the optimum value (maximum or lowest) of the aim is obtained by searching in a space.
The design variables of pole head gap and coil current were shown to be important in enhancing the magnetic field strength and efficiency of the MRB.With 0.1 Amp increments, the input current is adjusted between 1.6 Amps and 2.0 Amps.Another factor that affects torque is the pole head gap, which was shown to be between 8 and 10 mm. Figure 11 illustrates how, up to several iterations, the brake torque value increased appropriately with the design factors.Thus, for the suggested design, values at iteration 63 were deemed to represent the best feasible pole head gap of 8.67 mm, with an ideal coil current of 1.8 Amp.

Analysis of Braking Torque Performance
The well-designed magnetic field distribution determines the magnitude of the produced field torque.The variance in field strength throughout the MRB is caused by the homogeneity of yield stress on the surface, which influences field torque.However, the higher the input currents, the stronger the field strength generated, which simultaneously increases the braking torque.First, the current is steadily increased from 0 A to 2.0 A at 0.2 Amp intervals.The change in field strength is modest, with an input current of 0.4 A, as illustrated in Figure 12.On the surface of MR, a minor quantity of flux flow may be visible.The fluid, yellow area depicts the low field that occurs in the core region.As the applied current increases, so does the braking torque in an almost linear fashion.The applied current is 1.2 Amp, the flux flow on the MRF surface is modest, and the orangecolored core area has a somewhat greater field strength, as illustrated in the figure.When the current is changed from 1.2 to 1.6 A, the growing rate is pretty fast, as shown in Figure 12b, and the change pattern is clear.However, when the current is increased within 1.6 -2.0 A, the output torque tends to be flat because the internal magnetic field of the brake is practically saturated, making the applied current less effective.Observations from the simulation show that a slight difference in magnetic flux density has the edge effects of a magnetic field.The torque in the proposed multipole MRB is linear for input current and may be precisely adjusted.We conclude that the multipole MRB can provide a high braking torque while maintaining a compact design with a low input current.

Analysis of Braking Torque Performance
The well-designed magnetic field distribution determines the magnitude of the produced field torque.The variance in field strength throughout the MRB is caused by the homogeneity of yield stress on the surface, which influences field torque.However, the higher the input currents, the stronger the field strength generated, which simultaneously increases the braking torque.First, the current is steadily increased from 0 A to 2.0 A at 0.2 Amp intervals.The change in field strength is modest, with an input current of 0.4 A, as illustrated in Figure 12.On the surface of MR, a minor quantity of flux flow may be visible.The fluid, yellow area depicts the low field that occurs in the core region.As the applied current increases, so does the braking torque in an almost linear fashion.The applied current is 1.2 Amp, the flux flow on the MRF surface is modest, and the orange-colored core area has a somewhat greater field strength, as illustrated in the figure.When the current is changed from 1.2 to 1.6 A, the growing rate is pretty fast, as shown in Figure 12b, and the change pattern is clear.However, when the current is increased within 1.6-2.0A, the output torque tends to be flat because the internal magnetic field of the brake is practically saturated, making the applied current less effective.Observations from the simulation show that a slight difference in magnetic flux density has the edge effects of a magnetic field.The torque in the proposed multipole MRB is linear for input current and may be precisely adjusted.We conclude that the multipole MRB can provide a high braking torque while maintaining a compact design with a low input current.
2.0 A, the output torque tends to be flat because the internal magnetic field of the brake is practically saturated, making the applied current less effective.Observations from the simulation show that a slight difference in magnetic flux density has the edge effects of a magnetic field.The torque in the proposed multipole MRB is linear for input current and may be precisely adjusted.We conclude that the multipole MRB can provide a high braking torque while maintaining a compact design with a low input current.The pole head structure of the MRB is symmetrical along the central axis, and the dispersion of magnetic flux lines is rather dense and progressively rises with the applied current.Figure 13 shows the average increase in braking torque with increasing coil current.When the current approaches 2 A, the braking performance rarely improves because the shear stress of the MRF practically hits saturation, such that the observed maximum braking torque is estimated to be 18.64 N-m.This finding demonstrates that the sector pole head improves the torque of the MR brake.The pole head structure of the MRB is symmetrical along the central axis, and the dispersion of magnetic flux lines is rather dense and progressively rises with the applied current.Figure 13 shows the average increase in braking torque with increasing coil current.When the current approaches 2 A, the braking performance rarely improves because the shear stress of the MRF practically hits saturation, such that the observed maximum braking torque is estimated to be 18.64 N-m.This finding demonstrates that the sector pole head improves the torque of the MR brake.

Comparison with Circular Pole Head
The results of the enhanced MRB, previously reported by Shiao et al. [3], were utilized to validate the proposed multipole magnetorheological brake with sector pole head configuration.Appropriately adjusting the magnetorheological brake's ideal settings and size for comparison, the two curves in Figure 14 represent the present circular sector pole head with the circular pole head in terms of effective increase in the brake torque.The MRF shear stress increases when the electric current travels through the coil wires, and it is acquired in the form of flux flow on the disk surface.These distributions show strong agreement with the conclusions made by Shiao et al. [3].The number of turns rises with a steady increase in brake torque.When the applied current is 2.0 A, the recommended analysis value is nearly identical to the prior research value of 18.64 N-m, with an increase of 2.69%.The observed simulation curve agrees with the overall trend of the Shiao study's simulation curve, showing that the established brake torque and magnetic field simulation may better depict actual braking performance.As a consequence, the findings show that the suggested sector pole head shape is important for multipole MRB, and outper-

Comparison with Circular Pole Head
The results of the enhanced MRB, previously reported by Shiao et al. [3], were utilized to validate the proposed multipole magnetorheological brake with sector pole head configuration.Appropriately adjusting the magnetorheological brake's ideal settings and size for comparison, the two curves in Figure 14 represent the present circular sector pole head with the circular pole head in terms of effective increase in the brake torque.The MRF shear stress increases when the electric current travels through the coil wires, and it is acquired in the form of flux flow on the disk surface.These distributions show strong agreement with the conclusions made by Shiao et al. [3].The number of turns rises with a steady increase in brake torque.When the applied current is 2.0 A, the recommended analysis value is nearly identical to the prior research value of 18.64 N-m, with an increase of 2.69%.The observed simulation curve agrees with the overall trend of the Shiao study's simulation curve, showing that the established brake torque and magnetic field simulation may better depict actual braking performance.As a consequence, the findings show that the suggested sector pole head shape is important for multipole MRB, and outperforms the present circular pole head arrangement.

Conclusions
A simulation analysis of a MRB with sector pole head configuration was conducted to determine its influence on the performance and efficiency.Though it is difficult to manufacture the circular sector pole head shape when compared to the circular pole head, it has its advantages, as it effectively increases the radial dimension of the active chaining area to maximize magnetic field strength across the magnetorheological fluid working region.Despite being more challenging to manufacture, the circular sector pole head form has advantages over the circular pole head shape.It also effectively increases the active chaining area throughout the MRF working zone to maximize the intensity of the magnetic field.Almost the whole MRF is efficiently activated, and it can be visualized that the flux flow is higher than the circular pole head design and also evenly distributed in all directions till the edges of the pole head.The acquired simulation results show an increase of 2.69% in braking torque while keeping a compact and practical design structure.These findings suggest that the suggested pole head design is both novel and viable and the improvement achieves the essential flux to provide the maximum braking torque.

Conclusions
A simulation analysis of a MRB with sector pole head configuration was conducted to determine its influence on the performance and efficiency.Though it is difficult to manufacture the circular sector pole head shape when compared to the circular pole head, it has its advantages, as it effectively increases the radial dimension of the active chaining area to maximize magnetic field strength across the magnetorheological fluid working region.Despite being more challenging to manufacture, the circular sector pole head form has advantages over the circular pole head shape.It also effectively increases the active chaining area throughout the MRF working zone to maximize the intensity of the magnetic field.Almost the whole MRF is efficiently activated, and it can be visualized that the flux flow is higher than the circular pole head design and also evenly distributed in all directions till the edges of the pole head.The acquired simulation results show an increase of 2.69% in braking torque while keeping a compact and practical design structure.These findings suggest that the suggested pole head design is both novel and viable and the improvement achieves the essential flux to provide the maximum braking torque.

Figure 3 .
Figure 3. Two-dimensional view of a magnetic flux flow in a closed loop from one pole to an adjacent pole.

Figure 3 .
Figure 3. Two-dimensional view of a magnetic flux flow in a closed loop from one pole to an adjacent pole.

Figure 4 .
Figure 4. Sector pole head structure through which magnetic flux flows.

Figure 4 .
Figure 4. Sector pole head structure through which magnetic flux flows.

Figure 5 .
Figure 5. Braking torque for variation of pole head gap.

Figure 5 .
Figure 5. Braking torque for variation of pole head gap.

Figure 6 .
Figure 6.Magnetic field intensity for varied coil current.

Figure 6 .
Figure 6.Magnetic field intensity for varied coil current.

Figure 8 .
Figure 8. Magnetic field lines on a pole head.

Figure 8 .
Figure 8. Magnetic field lines on a pole head.

Figure 8 .
Figure 8. Magnetic field lines on a pole head.

15 Figure 9 .
Figure 9. Two-dimensional view of Flux flowlines in a MRB.

Figure 12 .
Figure 12.Simulation analysis of a MRB (a) Minimum flux flow (b) Intermediate flux flow (c) Maximum flux flow.

15 Figure 12 .
Figure 12.Simulation analysis of a MRB (a) Minimum flux flow (b) Intermediate flux flow (c) Maximum flux flow.

Figure 13 .
Figure 13.Output braking torque at different input coil current.

Figure 13 .
Figure 13.Output braking torque at different input coil current.

15 Figure 14 .
Figure 14.Braking torque comparison for circular sector pole head to circular pole head.

Figure 14 .
Figure 14.Braking torque comparison for circular sector pole head to circular pole head.