Article citation information:
Hoang, Q.T., Vu, H.Q. Parametric
study on the magnetic circuit of MR mounts utilizing magnetic shielding. Scientific Journal of Silesian University of
Technology. Series Transport. 2026, 132,
129-144. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2026.132.7
Quang Tuan HOANG[1], Hai Quan VU[2]
PARAMETRIC
STUDY ON THE MAGNETIC CIRCUIT OF MR MOUNTS UTILIZING MAGNETIC SHIELDING
Summary. This study
proposes a novel Magnetorheological (MR) Mount incorporating an aluminum non-magnetic shield to mitigate magnetic flux
leakage. Using 3D magnetostatic FEM simulations under 0-2 A excitation, results
demonstrate that the shield successfully eliminates short-circuit paths,
forcing magnetic flux through the working fluid gap. Consequently, the magnetic
field intensity at the gap increases 12-fold (from 20.27 to 244 kA/m),
amplifying the overall damping force by over 8 times (from 22 N to
approximately 180 N). Quantitative parametric analysis identifies the optimal
configuration: MRF-140CG fluid (yielding ~275 N), a 4 mm oil gap (increasing
force 2.7-fold), a 25 mm disc radius, and a 4.5–5 mm shield thickness. The
study identifies local magnetic saturation at the journal neck (2.2 Tesla) as a
performance bottleneck, establishing a critical foundation for future axial
dimension optimization.
Keywords: magnetorheological
mount, magnetic shield, finite element method, damping force
1.
INTRODUCTION
Magnetorheological (MR) mounts have garnered significant attention due
to their potential applications in automotive suspension and vibration
isolation systems, offering effective semi-active vibration damping
characterized by low latency and a wide dynamic force range [1, 2]. In MR mount designs, the magnetic field generated by the
electromagnetic coil plays a decisive role in altering the apparent viscosity
(yield stress) of the MR fluid, which consequently regulates the damping force
of the entire system [3, 4].
However, conventional magnetic circuit designs frequently suffer from
significant performance limitations caused by uneven magnetic field
distribution and magnetic flux leakage [5, 6]. Both simulations and experimental observations indicate that magnetic
field intensity is predominantly localized at the edge regions adjacent to the
coil, whereas the majority of the active working area experiences a
substantially lower magnetic field [7, 8]. The root cause of this phenomenon is the tendency of magnetic flux to
follow the path of least magnetic reluctance – typically short-circuiting
through magnetically permeable components such as the base plate or housing,
rather than penetrating the MR fluid gap, which inherently possesses a higher
reluctance [9, 10].
To comprehensively address this issue, this study proposes a novel
structural solution that integrates a magnetic shield. This paper details the
development of a 3D model for the mount and conducts a series of parametric
studies on its physical and structural variables using the Finite Element
Method (FEM). These simulations aim to comprehensively evaluate and optimize
the force-generating performance of the MR mount.
2. METHODOLOGY
Figure 1 illustrates the primary structural configuration of the
proposed magneto-rheological (MR) bearing. The prototype utilizes an
axisymmetric design to ensure mechanical stability and optimize the magnetic
field distribution [11]. The 3D model consists of five main components: a disk, a housing, an
electromagnetic coil, a rubber element, and an MR fluid gap. Concentric and
surface-to-surface geometric constraints were rigorously established to
maintain a uniform thickness of the working fluid gap along the disk profile.
|
|
|
Fig. 1. Main structural
components of the proposed MR mount
To formulate and analyze the damping force
generated by the device, the analytical model is established based on the
following core assumptions [12]:
-
The
magneto-rheological (MR) fluid is incompressible.
-
The variation of the
magnetic field in the axial direction (across the fluid gap thickness, z-axis)
is neglected. This assumption is justified by the fact that the gap thickness
is exceptionally small compared to other geometric dimensions, allowing the magnetic
field to be treated as uniform at any given radial coordinate.
-
The disk is
restricted to purely vertical translational motion.
The total damping force of the MR mount is
illustrated in Figure 2 and can be expressed by the following equation [12]:
where:
Fig. 2.
Force components acting within the MR mount system
According to Hooke's law, the elastic force of an object is directly
proportional to its deformation within the elastic limit, which is expressed by
the following equation [13]:
The viscous damping force is a resistance that occurs when the fluid
undergoes shear deformation caused by the relative motion between the boundary
surfaces, which is given by [12]:
where:
For the field-dependent force component, the MR fluid is assumed to
exhibit Bingham plastic behavior when subjected to an
external magnetic field. Within this model, the fluid's shear stress comprises
a yield stress component (
where
Although the magnetic
field is assumed to be uniform in the axial direction (across the gap
thickness), in reality, the magnetic field intensity is non-uniformly
distributed in the radial direction (along the r-axis) due to the
configuration of the magnetic circuit. This non-uniformity causes the yield
stress (
|
(a) 1: Disc; 2: MR Fluid; 3: Housing; 4: Coil
; 5: Rubber |
(b) 1: Disc; 2: MR Fluid; 3: Housing; 4: Coil; 5: Rubber;
6: Magnetic shield |
Fig. 3. Geometric
models: (a) Conventional MR mount; (b) Enhanced MR mount with an integrated
magnetic shield
In this study, the
relationship between the yield stress and the magnetic field intensity is
represented by the characteristic curves of the 132DG fluid grade provided by
Lord Corporation [15]. By applying the curve-fitting method in MATLAB software, a polynomial
expressing the relationship between the yield stress and the magnetic field
intensity was derived. The equation and the corresponding coefficients are presented below
where:
Within each annular zone, under the assumption of a constant yield
stress
The total magnetic field-induced force exerted across the entire disc
can be expressed as follows:
Taking into account the axial translational dynamics and the working
mechanism of the magnetorheological fluid, only the gap subjected to
compression produces a magnetic field-induced force [12]. Therefore, the resulting force is contingent upon the velocity
direction.
The proposed design incorporates two distinct metallic materials with
contrasting magnetic properties to effectively guide the magnetic flux [3]. Specifically, AISI 1010 steel is utilized for the disk and housing due
to its high magnetic permeability and high saturation magnetization,
facilitating an efficient magnetic circuit [14]. Conversely, aluminum is selected for the
magnetic shield; as a non-magnetic and low-density material, it effectively
prevents undesired magnetic flux leakage [14]. Furthermore, this study employs the magnetization properties (B-H
curves) of three commercial MR fluids manufactured by Lord Corporation:
MRF-140CG, MRF-132DG, and MRF-122EG [15-17]. These fluids differ significantly in their iron particle volume
fractions, a parameter that directly governs their base viscosity and dynamic
yield stress.
Tab. 1
Magnetic and rheological properties of the selected MR fluids
|
|
MRF-122EG
[17] |
MRF-132DG [15] |
MRF-140CG [16] |
|
Density
ρ ( |
2280¸
2480 |
2950¸
3150 |
3054¸
3074 |
|
Viscosity |
0.042
± 0.020 |
0.112
± 0.02 |
0.280
± 0.070 |
|
Operating Temperature ( |
-40
to 130 |
-40
to 130 |
-40 to 130 |
2.2.2. Finite Element Model Setup
The 3D magnetostatic analysis was performed using the Altair Flux 3D
finite element software to fully capture the effects of magnetic flux leakage
in three-dimensional space [18]. Figure 4 illustrates the mesh model of the mount, which utilizes a
uniform tetrahedral mesh with a total element count of approximately 1,426,737,
a mesh growth rate of 0.15, and a minimum mesh size of 0.15 mm within the MR
fluid gap region.
Fig. 4. Finite element mesh of the MR mount model
An infinite
box domain was established surrounding the model to account for the magnetic
field propagation at the boundaries. The excitation current supplied to the
electromagnetic coil was varied from 0 A to 2 A during the investigation.
Tab. 2
Mesh quality parameters and convergence criteria for
the FEM model
|
Mesh Quality Metric |
Percentage (%) |
|
Unevaluated elements |
0% |
|
Excellent quality elements |
74.36% |
|
Good quality
elements |
24.09% |
|
Fair quality elements |
1.55% |
|
Poor quality elements |
0% |
Furthermore,
Table 2 indicates that the mesh quality was strictly controlled, with 74.36% of
the elements achieving 'Excellent' quality and a complete absence (0%) of
'Poor' quality elements. This high-quality mesh structure enables the model to
accurately capture complex physical phenomena, particularly in regions
characterized by high magnetic field gradients and localized saturation.
Three-dimensional 3D magnetostatic analysis of the MR mount was
performed using the Finite Element Method (FEM) within the Flux software
environment to solve Maxwell’s equations. The physical model-comprising
magnetically permeable materials (AISI 1010 steel for the disc and housing),
non-magnetic components (aluminum shield and rubber),
and the magnetorheological fluid-was investigated under excitation currents
ranging from 0 to 2 A with an increment of 0.25 A. The simulation applies
Dirichlet boundary conditions (magnetic potential = 0) at the outer domain and
Neumann boundary conditions at the symmetry planes to appropriately constrain
the magnetic flux [19].
Figure 5 illustrates the magnetic field intensity distribution within
the MR fluid gap of the original MR mount configuration (without a magnetic
shield) at an excitation current of 2 A. The simulation results reveal a
significant non-uniformity in the magnetic distribution. Specifically, the
magnetic field is locally concentrated at the outer periphery of the disk
(near-coil region), reaching a peak value of approximately 20.27 kA/m.
Conversely, the central region (far-coil region) remains largely unmagnetized,
as evidenced by the dark blue contours. This phenomenon is primarily attributed
to the magnetic flux preferentially bypassing the fluid gap through the disk
base-constructed from high-permeability steel-to complete the magnetic circuit
via the path of least reluctance. This magnetic short-circuiting and flux
leakage result in substantial energy inefficiency, as the yield stress of the
MR fluid in the central zone is not activated, thereby significantly degrading
the damping force controllability of the mount.
Fig. 5. Magnetic field intensity distribution within the MR fluid gap at
2 A
In the initial configuration, a substantial portion of the magnetic flux
tends to bypass the working gap by traveling through the steel shaft
(high-permeability material), thereby significantly diminishing the damping
efficiency of the MR mount. To mitigate this magnetic short-circuiting, an aluminum magnetic shield is incorporated into the design
(Fig 3b). This modification reconfigures the magnetic circuit by forcing the
flux lines to penetrate the MR fluid gap to complete the loop.
Figure 6 illustrates the magnetic field intensity distribution of the
enhanced MR mount featuring the magnetic shield at an excitation current of 2
A. In contrast to the original design, where the magnetic field is concentrated
only at the outer periphery, the enhanced design achieves a more uniform
distribution across the entire effective radius. Notably, the peak magnetic
field intensity within the fluid gap surges to 244 kA/m, representing a more
than 12-fold increase compared to the initial model.
Fig. 6. Magnetic field intensity of the shielded MR mount at an
excitation current of 2 A
This breakthrough improvement is attributed to the non-magnetic aluminum layer, which functions as a high-reluctance
barrier that effectively eliminates the magnetic short-circuit path through the
disk base. Under the forcing effect of this shield, the magnetic flux vectors
are compelled to penetrate directly through the MR fluid gap. Consequently, the
design establishes a closed magnetic circuit traversing the active fluid zone,
thereby maximizing the activation of the yield stress and substantially
enhancing the damping performance of the MR mount.
|
|
b |
Fig. 7. Magnetic circuit analysis at 2 A: (a) Magnetic flux paths;
(b) Magnetic flux density distribution
However,
magnetic flux density analysis (Figures 7a and 7b) reveals a significant
magnetization imbalance. While the large disk safely operates within the linear
region (B < 0.5 T) , the narrow shaft neck experiences localized
magnetic saturation. At this location, flux density reaches approximately 2.2
T, substantially exceeding the 1.9–2.0 T limit of AISI 1010 steel. To eliminate
this critical performance bottleneck in future prototypes, it is essential to
increase the shaft neck radius to expand its magnetic cross-section.
The
breakthrough improvement in flux density across the gap ensures the maximum
activation of the MR fluid's yield stress. The correlation between these
microscopic electromagnetic changes and the macroscopic performance of the
mount is further evidenced by the increased damping force shown in Figure 8.
Fig.8. Damping force as a function of excitation current for the enhanced
MR mount
The characteristic plots demonstrate that the magnetic
shield significantly enhances the performance of the MR mount. Quantitatively,
as the excitation current increases from 0 A to 2.0 A, the damping force rises
near-linearly from a baseline resistance of 22 N to a peak value of
approximately 180 N, achieving an amplification factor of over 8 times. These
results confirm that the non-magnetic shield effectively eliminates flux
leakage, forcing the magnetic circuit to concentrate through the active fluid
gap. Consequently, the device maximizes the MR fluid's yield stress, thereby
extending the force control range and ensuring high reliability for semi-active
vibration control applications.
Figure 9 illustrates the distinct dependence of the damping force on the
type of magneto-rheological (MR) fluid employed. Among the evaluated fluids,
MRF-140CG generates the highest damping force, significantly outperforming the
MRF-132DG and MRF-122EG grades. Quantitatively, at the peak excitation current
of 2.0 A, MRF-140CG produces a resistance force of approximately 275 N, which
is substantially higher than the 180 N and 135 N recorded for MRF-132DG and
MRF-122EG, respectively. Even in the off-state (0 A), MRF-140CG maintains a
slightly higher baseline force of approximately 30 N, which is attributed to
its inherently higher zero-field viscosity.
Fig. 9. Influence of different MR fluid grades on damping force versus
excitation current
The underlying physical mechanism for this superiority is attributed to
the high magnetic particle volume fraction of MRF-140CG. When the magnetic flux
is constrained by the shield to concentrate through the working gap, this dense
particle population forms robust chain-like structures, leading to a
significantly higher field-dependent yield stress. Consequently, the synergy
between the magnetic shielding solution and the high-grade MR fluid is
demonstrated as an optimal strategy for maximizing the overall damping
performance of the system.
Figure 10 illustrates the influence of the MR fluid gap width (varying
from 4 mm to 8 mm) on the damping force magnitude. The results indicate that
this parameter plays a pivotal role in the device's performance. Specifically,
at a peak excitation current of 2.0 A, reducing the gap from 8 mm to 4 mm leads
to a significant surge in the damping force, increasing from 105 N to
approximately 270 N-a 2.7-fold enhancement.
Fig. 10. Impact of MR fluid gap width (4 mm - 8 mm) on the generated
damping force
This
improvement is attributed to the synergistic interaction between hydraulic and
magnetic mechanisms within the active zone. Hydraulically, since the system
operates in compression mode, a narrower gap substantially increases flow
resistance and fluid constraint, resulting in elevated back-pressure and higher
baseline viscous forces. Magnetically, a smaller gap reduces the total
reluctance of the magnetic circuit, thereby increasing the flux density across
the fluid layer and maximizing the activation of the field-dependent yield
stress. Consequently, the small-gap configuration not only yields superior
force generation but also expands the dynamic force ratio, enhancing the
control sensitivity of the overall system.
In addition to axial parameters, the disk radius significantly
influences the force-generation performance of the MR mount. Figure 11
investigates the outer disk radius ranging from 25 mm to 32 mm, revealing a
clear inverse relationship: an increase in the radius leads to a reduction in
the generated damping force.
Fig. 11. Relationship between damping force and outer disk radius (25 mm
- 32 mm)
Specifically,
at an excitation current of 2 A, the 25 mm disk configuration yields a peak
force of approximately 160 N, whereas the 32 mm configuration exhibits a
decline to around 135 N. This phenomenon is attributed to the variation in
magnetic flux density within the working gap. Expanding the disk radius
increases the contact surface area of the fluid gap. Since the total magnetic
flux supplied by the coil and the core cross-section remain constant, the flux
is forced to distribute over a larger area. Consequently, the average flux
density penetrating the MR fluid layer decreases. Given that the yield stress
of the MR fluid is directly dependent on flux density, this reduction
inevitably results in a diminished damping force.
The investigation into the magnetic shield thickness (ranging from 4.0
to 6.0 mm with 0.25 mm increments) demonstrates that this parameter exerts
a direct influence on the flux guidance capability and the resulting damping
force of the MR mount. As illustrated in Figure 12, the damping force exhibits
a near-linear increase across all configurations as the excitation current
rises from 0 to 2 A. Notably, thinner shield configurations (4.0-4.75 mm) yield
superior damping forces, reaching a peak of approximately 175 N, compared to
the thicker variants (5.5-6.0 mm), which achieve approximately 155 N.
Fig. 12. Effect of magnetic shield thickness on the damping force
performance
This discrepancy arises because an excessively thick shield increases
the overall magnetic reluctance, thereby hindering flux transmission to the
active zone and reducing the effective magnetic field intensity. Conversely, a
shield that is too thin lacks the necessary barrier effect to optimally direct
the magnetic flux. Consequently, to balance system performance, a thickness
range of 4.5-5.0 mm is identified as the optimal configuration, ensuring
efficient magnetic transmission and robust damping force generation.
The
investigation into the disk thickness (varying from 2 mm to 5 mm) reveals that
this parameter has a negligible impact on the force-generation performance of
the MR mount. As illustrated in Figure 13, despite a 2.5-fold increase in
thickness, the damping force curves relative to the excitation current (0-2 A)
remain nearly coincident.
Fig. 13. Sensitivity of damping force to disk thickness variations (2 mm
- 5 mm)
At the peak current of 2 A, the damping force across all configurations
consistently maintains a value of approximately 160 N, with statistically
insignificant deviations. This phenomenon is elucidated by the magnetic
saturation characteristics of the structure. Fundamentally, the disk thickness
determines the cross-sectional area available for radial magnetic flux
transmission.
However, since the disk in the current design operates within the
low-field (linear) region of the magnetization curve, the material remains far
from its saturation limit. Consequently, the existing cross-section provides
sufficient capacity for flux conduction, and further increasing the thickness
does not enhance the magnetic circuit efficiency. These findings provide a
solid foundation for selecting the minimum disk thickness (2 mm), thereby
optimizing both the system mass and spatial requirements without compromising
performance.
This study successfully implemented a 3D Finite Element Method (FEM)
simulation to comprehensively address the issue of magnetic flux leakage in
magnetorheological (MR) mounts through the integration of a magnetic shield.
Based on the quantitative analyses, the following key conclusions can be drawn:
-
The aluminum magnetic barrier effectively eliminates the
magnetic short-circuit path through the disk base, redirecting the magnetic
flux to concentrate within the active fluid zone. This structural enhancement
results in a 12-fold increase in the peak magnetic field intensity within the
MR gap, reaching 244 kA/m. Consequently, the damping force is amplified by more
than 8 times, rising from a baseline of 22 N to approximately 180 N at an
excitation current of 2 A.
-
The force-generation
capacity of the MR mount is highly sensitive to both physical properties and
geometric parameters, specifically:
-
Magnetorheological
(MR) Fluid Properties: MRF-140CG, with its high iron particle volume fraction,
produces the highest yield stress, resulting in a superior damping force of
approximately 275 N, compared to 180 N and 135 N for MRF-132DG and MRF-122EG,
respectively.
-
Working Zone
Geometry: A narrow fluid gap of 4 mm yields a 2.7-fold increase in damping
force compared to an 8 mm gap, attributed to the synergistic effect of
increased hydraulic resistance and reduced magnetic reluctance. Additionally, a
compact disk radius of 25 mm achieves the highest average flux density and
force output (~160 N).
-
Magnetic Circuit
Configuration: The magnetic shield thickness achieves optimal flux guidance
efficiency within the 4.5–5.0 mm range. Conversely, variations in disk
thickness (2–5 mm) have a negligible impact on force generation (~160 N), as
this region operates within the unsaturated low-field region.
Although the magnetic shield significantly enhances overall performance,
localized magnetic saturation (up to 2.2 T) at the shaft neck-due to its
limited cross-section-remains a critical bottleneck. Future research will focus
on optimizing the shaft neck geometry to fully exploit the potential of the
magnetic circuit.
Furthermore, a current limitation of this study is the lack of
experimental validation. The primary objective of this paper is to provide a
proof of concept and a detailed parametric study for a novel structural
solution featuring an integrated aluminum
non-magnetic shield. Given that prototype fabrication requires high-precision
manufacturing and specialized sealing solutions for aluminum-steel
assemblies, experimental verification is scheduled for the next research phase.
Future work will focus on optimizing the shaft neck geometry to fully exploit
the potential of the magnetic circuit while conducting prototype testing to
comprehensively validate these simulation results.
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Received 20.04.2026; accepted in
revised form 08.06.2026
Scientific
Journal of Silesian University of Technology. Series Transport is licensed
under a Creative Commons Attribution 4.0 International License
[1] Faculty of Automotive
Technology, School of Mechanical and Automotive Engineering, Hanoi University
of Industry, 298 Cau Dien Street, Bac Tu Liem District, Hanoi, Vietnam. Email:
tuanhq@haui.edu.vn. ORCID: https://orcid.org/0000-0002-0362-0921
[2] Faculty of Automotive
Technology, School of Mechanical and Automotive Engineering, Hanoi University
of Industry, 298 Cau Dien Street, Bac Tu Liem District, Hanoi, Vietnam. Email:
quanvh@haui.edu.vn (corresponding author). ORCID: https://orcid.org/0000-0002-9560-8662