Research on the torque performance for two multi-pole bilayer magnetorheological fluid couplings

Abstract

This paper studies on the permanent magnets configuration on the transmission torque of the multi-pole bilayer magnetorheological (MR) coupling. Based on the electromagnetic field theory, the magnetic circuit models of traditional permanent magnet array (TPMA) and Halbach permanent magnet array (HPMA) are established, and the magnetic flux density within the MR fluid working gaps has been derived in order to evaluate the merits of the designed MR coupling. A 3D FE magnetic-fluid analysis has been necessary following the initial conceptual analysis, in order to study the influence of key parameters on the transmission torque. The results show that the transmission torque of the MR coupling with Halbach permanent magnet array is 33.45% higher than that of the ordinary permanent magnet array, with a same structure size. For the MR coupling with Halbach permanent magnet array, the unilateral magnetic focusing effect is better with the increase of the residual flux density of the secondary magnetic pole as well as the radial length of magnetic pole. And the single side magnetic focusing effect is the best when the main magnetic pole is 15°. The influence of the magnetic pole angle on the transmission torque has been further studied.

Keywords

Multi-pole bilayer magnetorheological (MR) coupling traditional permanent magnet array (TPMA)Halbach permanent magnet array (HPMA)permanent magnet transmission torque

1. Introduction

Magnetorheological (MR) fluid is a new type of smart material. Due to its fast, controllable, and reversible liquid-solid transformation under the applied magnetic field [1,2], it is widely used in brakes [3], clutches [4], dampers [5,6], MR valves [7], MR couplings [8], MR polishing machines [9], and others [10,11]. Compared to traditional mechanical transmission devices, MR transmission devices which utilizing the characteristics of MR fluid has the advantages of quick response, and adjustable torque output. Therefore, it has a mature application in various transmission scenarios.

At present, MR transmission devices mainly include disc type, cylindrical type, multi-pole type, multi-disc type, multi-cylinder type and other structures. Li et al. [12] established the coupling model of structure and magnetic circuit, and optimized the design method after simulation. By optimizing the design of the disc MR brake, the power density of the brake is improved. Yuan et al. [13] designed a disc MR brake with a circular groove, and its braking torque is 35% higher than that of the common disc MR brake. Zhao et al. [14] designed a cylindrical MR transmission controlled by shape memory alloy, and analyzed its braking performance. Wu et al. [15] designed a high-power multi-level and multi-layer MR brake based on the principle of magnetic field superposition. Compared with the traditional single-disc, multi-disc, or multi-stage single-layer MR brakes, it has a larger braking torque and power density. Wu et al. [16] proposed a multi-disc MR transmission device, which uses the electromagnetic force generated by the coil to squeeze the MR fluid, thereby improving the transmission torque. Qin et al. [17] designed a multi-cylinder MR brake, using the magnetic fluid sealing technology to reduce the unsteady friction, and deduced its current-torque model to predict the output torque according to the input current size.

Aiming at the problems of large power consumption, complicated structure, and coil heating of the coil-type MR transmission devices. Bucchi et al. [18] designed a MR clutch with a magnetic field provided by a permanent magnet, and changed the working state of the clutch by changing the position of the permanent magnet, and analyzed its transmission performance. Further, Rizzo et al. [19–21] proposed a new gap shape on this basis to reduce the torque loss in the separation operation, and the eddy current in the working process of the clutch was analyzed. Chen [22] proposed a MR coupling with a magnetic field provided by a permanent magnet, and analyzed the magnetic field distribution characteristics of the region where the MR fluid of the device is located, as well as the circumferential distribution of shear yield stress and viscosity in polar coordinates for two specified locations. Böse et al. [23] proposed a magnetorheological clutch with magnetic field provided by permanent magnet and coil. Based on this, the torque transmission performance of three magnetorheological clutches with different structures was designed, manufactured, and tested. Moghani et al. [24] proposed a hybrid magnetorheological clutch which adjusts the magnetic field generated by the permanent magnet through the excitation coil, and they carried out multi-objective optimization design for the transmission torque, clutch quality, and magnetic field strength. The conclusion is that the advantage of the permanent magnet MR transmission devices is that the coil type MR devices will not be unable to transmit torque due to power failure, but not limited to low power consumption and simple structure.

For the MR devices with permanent magnet arrays, the Halbach permanent magnet array can make the device more compact, and the power density of the device is higher than that of the traditional permanent magnet array. The unique arrangement of the Halbach permanent magnet array allows the magnetic field generated by it to concentrate on one side of the array, which is very suitable for applications where only one side of the magnetic field is needed. It can utilize most of the magnetic field, which improves the utilization rate of the magnetic field [25].

When the Halbach permanent magnet array is used, it avoids the loss and heat generated at the stator due to the eddy current effect, and saves more space than the traditional permanent magnet array.

To date, there are few researches focused on the performance of MR couplings with different permanent magnets configuration. In this paper, the effects of the permanent magnets’ configuration and the permanent magnets parameters on the performance of the multi-pole bilayer MR coupling is studied. Section 2 introduces the structure of the multi-pole bilayer permanent magnets MR coupling. Section 3 derives the transmission torque. Section 4 establishes the magnetic circuit modeling. Section 5 compares and analyzes the two configurations the multi-pole bilayer MR coupling by finite element simulation. Section 6 concludes the study.

2. Structural design of the multi-pole bilayer permanent magnets MR coupling

Figure 1 shows the multi-pole bilayer permanent magnets MR coupling with traditional permanent magnet array (TPMA) and Halbach permanent magnet array (HPMA). As shown in Fig. 1(a) and (b), the coupling is mainly composed of an inner stator, a MR fluid, a permanent magnet array, and a shell. An outer MR fluid gap is formed between the shell and the permanent magnet array, while an inner MR fluid gap is located between the inner stator and the permanent magnet array. The transmission torque of the coupling is generated by the shear between the MR fluid in the inner and outer gaps.

Fig. 1.

Structural diagram of the multi-pole bilayer MR coupling with: (a) TPMA; (b) HPMA.

In this design, R ₁ is the inner diameter of the inner stator, R ₂ is the outer diameter of the inner stator as well as the inner diameter of the inner MR fluid gap, R ₃ is the outer diameter of the inner MR fluid gap, R ₄ is the inner diameter of the outer MR fluid gap, and R ₅ is the outer diameter of the outer MR fluid gap, R ₆ is the outer diameter of the shell, z is the axial length of the inner and outer MR fluid gap, and c ₁ is the main pole angle.

In terms of material selection, neodymium iron boron (NdFeB) with high magnetic energy product and coercive force is selected as the permanent magnet. MRF-132DG from Lord Company is selected as the MR fluid. The inner stator and the shell are made of electric pure iron (20#) which is magnetically conductive and not easily magnetized. Material properties are in Table 1.

Table 1

Material parameters

NdFeB-33M		MRF-132DG
Remanence (T)	11.3–11.7	Density (g ⋅ cm⁻³)	3.09
Coercivity (A ⋅ m⁻¹)	836	Coefficient of thermal expansion 0–50 °C	5.5 × 10⁻⁴
Maximum magnetic energy product (kJ ⋅ cm⁻³)	247–263	Plastic viscosity (mPa s) at 40 °C, 𝛾 > 500 s⁻¹	112
Operating temperature (°C)	≤80	Operating temperature (°C)	−40∼130

The size of structural parameters is the same, except that the arrangement of permanent magnets is different. It is seen that the arrows indicate the direction of the residual magnetic flux of the permanent magnets. For the multi-pole bilayer MR coupling with TPMA, the permanent magnet array is composed of permanent magnets and aluminum blocks arranged at intervals along the circumferential direction, and the magnetic pole directions of adjacent permanent magnets are opposite. For the multipole bilayer MR coupling with HPMA, the arrangement of permanent magnets is a Halbach permanent magnet array in which the magnetic field direction of the main magnetic pole is along the radial direction while the magnetic field direction of the secondary magnetic pole is along the circumferential direction.

3. Transmission torque

The torque transmission of multi-pole bilayer MR coupling depends on the dynamic yield stress and viscosity of MR fluids. Due to the effectiveness and simplicity, the Bingham model is commonly used in designs of the MR transmission device. According to the Bingham model, the shear stress equation of MR fluids is established as [26,27]: $\begin{eqnarray}\displaystyle {\tau}={\tau}_{y}+{\eta}\dot{{\gamma}} & & \displaystyle\end{eqnarray}$ (1) where τ is the shear stress, τ_y is the dynamic yield stress of the MR fluid, 𝜂 is the plastic viscosity of the MR fluid, and $\dot{{\gamma}}$ is the shear strain rate of the MR fluid.

The dynamic shear stress τ_y can be obtained from the yield characteristics and magnetization characteristics of the MR fluid. For the MRF-132DG, the shear yield stress is fitted polynomials by the least squares’ method, and its expression is obtained [28]: $\begin{eqnarray}\displaystyle {\tau}_{y}=52.962B^{4}-176.51B^{3}+158.79B^{2}+13.708B+0.1442 & & \displaystyle\end{eqnarray}$ (2) where B is the magnetic flux density.

Shear rate $\dot{{\gamma}}$ can be expressed as: $\begin{eqnarray}\displaystyle \dot{{\gamma}}=R\frac{d{\omega}}{dR} & & \displaystyle\end{eqnarray}$ (3) where dR is the differential of the working radius of the magnetorheological fluid, and dω is the differential of the angular velocity of the clutch.

The magnetic field strength in MR fluid is evenly distributed, and the edge effect is ignored. The transmission torque generated by the inner MR fluid gap can be expressed as: $\begin{eqnarray}\displaystyle T_{1}=\int _{S}R{\tau}dS=2{\pi}R^{2}{\tau}z & & \displaystyle\end{eqnarray}$ (4) where S is the contact area between the MR fluid and the cylinder, and z is the axial effective width of the MR fluid gap.

Substituting Eqs (1) and (4) into Eq. (3): $\begin{eqnarray}\displaystyle {\eta}d{\omega}=\left(\frac{T_{1}}{2{\pi}R^{3}z}-\frac{{\tau}_{y}}{R}\right)dR. & & \displaystyle\end{eqnarray}$ (5)

For Eq. (5), integrating it on the inner MR fluid gap: $\begin{eqnarray}\displaystyle \int _{0}^{{\omega}}{\eta}d{\omega}=\int _{R_{2}}^{R_{3}}\left(\frac{T_{1}}{2{\pi}R^{3}z}-\frac{{\tau}_{y}}{R}\right)dR. & & \displaystyle\end{eqnarray}$ (6)

By simplifying it, the expression of torque generated by the inner MR fluid gap is obtained [29]: $\begin{eqnarray}\displaystyle T_{1}=\frac{4{\pi}zR_{2}^{2}R_{3}^{2}}{R_{3}^{2}-R_{2}^{2}}\left[{\tau}_{y}\ln \frac{R_{3}}{R_{2}}+{\eta}{\omega}\right]. & & \displaystyle\end{eqnarray}$ (7)

Similarly, the torque generated by the outer MR fluid gap can be expressed as: $\begin{eqnarray}\displaystyle T_{2}=\frac{4{\pi}zR_{4}^{2}R_{5}^{2}}{R_{5}^{2}-R_{4}^{2}}\left[{\tau}_{y}\ln \frac{R_{5}}{R_{4}}+{\eta}{\omega}\right]. & & \displaystyle\end{eqnarray}$ (8)

Therefore, the total torque of the multi-pole bilayer MR coupling is: $\begin{eqnarray}\displaystyle T=T_{1}+T_{2}=\frac{4{\pi}zR_{2}^{2}R_{3}^{2}}{R_{3}^{2}-R_{2}^{2}}\left[{\tau}_{y}\ln \frac{R_{3}}{R_{2}}+{\eta}{\omega}\right]+\frac{4{\pi}zR_{4}^{2}R_{5}^{2}}{R_{5}^{2}-R_{4}^{2}}\left[{\tau}_{y}\ln \frac{R_{5}}{R_{4}}+{\eta}{\omega}\right]. & & \displaystyle\end{eqnarray}$ (9)

It can be seen from Eq. (9) that the magnitude of the transmission torque is proportional to the axial width of the MR fluid gap, and is positively related to the radius of the MR fluid gap. The larger the radius of the MR fluid gap is, the bigger the transmission torque will be. In order to increase the transmission torque of the multi-pole bilayer MR coupling, the magnetic field needs to be concentrated as far as possible at the outer gap. For this reason, the influence of the arrangement of the permanent magnets on the transmission torque is analyzed.

4. Magnetic circuit modeling

In this section, the magnetic density in the MR gaps is firstly derived based on the magnetic circuit analysis. The magnetic circuit is modeled by the average magnetic circuit method without considering the magnetic leakage. The magnetic circuit model and simplified equivalent magnetic circuit of the multi-pole bilayer MR coupling with TPMA and HPMA are shown in Fig. 2 and Fig. 3, respectively.

Fig. 2.

Magnetic circuit node configuration and simplified magnetic circuit of TPMA: (a) node configuration of one-sixth of the bilayer MR coupling; (b) simplified magnetic circuit of one-sixth of the bilayer MR coupling.

Fig. 3.

Magnetic circuit model and simplified equivalent magnetic circuit of HPMA: (a) node configuration of one-sixth of the bilayer MR coupling; (b) simplified magnetic circuit of one-sixth of the bilayer MR coupling.

The components in the magnetic circuit of multi-pole bilayer MR coupling are divided into sections and connected at nodes according to the difference of crosssectional area and material of the magnetic circuit. R _ab, R _{a
^′
b
^′}, R _gh, R _{g
^′
h
^′} are the magnetic resistance of the inner gap MR fluid ab, a ^′ b ^′, gh, g ^′ h ^′, respectively. R _bc, R _{b
^′
c
^′}, R _fg, R _{f
^′
g
^′} are the magnetic resistance of the main pole bc, b ^′ c ^′, fg, f ^′ g ^′, respectively. R _cd, R _{c
^′
d
^′}, R _ef, R _{e
^′
f
^′} are the magnetic resistance of the outer MR fluid gap cd, c ^′ d ^′, ef, e ^′ f ^′, respectively. R _de, R _{d
^′
e
^′} are the magnetic resistance of the shell de, d ^′ e ^′, respectively. R _ah, R _{a
^′
h
^′} are the magnetic resistance of the inner stator ah, a ^′ h ^′, respectively. R _{i
^′
j
^′} is the magnetic resistance of the permanent magnets i ^′ j ^′.

The magnetomotive force in the permanent magnet circuit can be expressed as: $\begin{eqnarray}\displaystyle F=H_{m}L_{m} & & \displaystyle\end{eqnarray}$ (10) where H _m is the magnetic field strength of the m-th permanent magnet in the magnetic circuit, which can be obtained from the demagnetization curve of the permanent magnet. L _m is the length of the m-th permanent magnet in the direction of residual magnetic flux density.

The expression for the magnetic flux Φ obtained from Ohm’s law of the magnetic circuit: $\begin{eqnarray}\displaystyle {\rm\Phi}=\frac{F}{R_{\text{total}}}=B_{i}S_{i} & & \displaystyle\end{eqnarray}$ (11) where R _total is the total reluctance in the magnetic circuit, and it is the sum of the magnetic reluctance of each section in the magnetic circuit. F is the magnetomotive force in the magnetic circuit. B _i is the magnetic flux density of the i-th magnetic circuit. S _i is the effective flux area of the i-th magnetic circuit. The average magnetic field strength in each magnetic circuit can be obtained as followed: $\begin{eqnarray}\displaystyle B_{i}=\frac{F}{R_{\text{total}}S_{i}}. & & \displaystyle\end{eqnarray}$ (12)

Substituting the effective magnetic flux area S _i and magnetoresistance of each magnetic circuit into Eq. (12) to obtain the average magnetic flux density in each magnetic circuit. Thus, the magnetoresistance can be calculated: $\begin{eqnarray}\displaystyle R_{i}=\frac{l_{i}}{{\mu}_{i}S_{i}} & & \displaystyle\end{eqnarray}$ (13) where l _i is the effective magnetic circuit of the i-th magnetic circuit, and μ_i is the magnetic permeability of the material of the i-th magnetic circuit.

The reluctance of each section of the magnetic circuit is: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle R_{ab}=R_{a^{\prime }b^{\prime }}=\int _{R_{2}}^{R_{3}}\frac{R_{3}-R_{2}}{{\mu}_{mr}{\displaystyle \frac{c}{4{\pi}}}2{\pi}rz}∼dr=\frac{2(R_{3}-R_{2})}{cz{\mu}_{mr}}\ln \left(\frac{R_{3}}{R_{2}}\right)\end{eqnarray}$ (14) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle R_{bc}=R_{b^{\prime }c^{\prime }}=R_{fg}=R_{f^{\prime }g^{\prime }}=\int _{R_{3}}^{R_{4}}\frac{R_{4}-R_{3}}{{\mu}_{m}{\displaystyle \frac{c}{4{\pi}}}2{\pi}rz}∼dr=\frac{2(R_{4}-R_{3})}{cz{\mu}_{m}}\ln \left(\frac{R_{4}}{R_{3}}\right)\end{eqnarray}$ (15) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle R_{cd}=R_{c^{\prime }d^{\prime }}=R_{ef}=R_{e^{\prime }f^{\prime }}=\int _{R_{4}}^{R_{5}}\frac{R_{5}-R_{4}}{{\mu}_{mr}{\displaystyle \frac{c}{4{\pi}}}2{\pi}rz}∼dr=\frac{2(R_{5}-R_{4})}{cz{\mu}_{mr}}\ln \left(\frac{R_{5}}{R_{4}}\right)\end{eqnarray}$ (16) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle R_{de}=R_{d^{\prime }e^{\prime }}=\frac{2{\pi}{\displaystyle \frac{(R_{5}+R_{6})}{2}}{\displaystyle \frac{3c}{4{\pi}}}}{{\mu}_{20}(R_{6}-R_{5})z}=\frac{3c(R_{5}+R_{6})}{4z{\mu}_{20}(R_{6}-R_{5})}\end{eqnarray}$ (17) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle R_{ah}=R_{a^{\prime }h^{\prime }}=\frac{2{\pi}{\displaystyle \frac{(R_{1}+R_{2})}{2}}{\displaystyle \frac{3c}{4{\pi}}}}{{\mu}_{20}(R_{2}-R_{1})z}=\frac{3c(R_{1}+R_{2})}{4z{\mu}_{20}(R_{2}-R_{1})}\end{eqnarray}$ (18) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle R_{i^{\prime }j^{\prime }}=\frac{2{\pi}{\displaystyle \frac{(R_{4}+R_{3})}{2}}{\displaystyle \frac{3c}{4{\pi}}}}{{\mu}_{m}(R_{4}-R_{3})z}=\frac{3c(R_{3}+R_{4})}{4z{\mu}_{m}(R_{4}-R_{3})}.\end{eqnarray}$ (19)

For the multi-pole bilayer MR coupling with TPMA, the magnetomotive force can be calculated according to the first law of magnetic circuit: $\begin{eqnarray}\displaystyle F_{1}+F_{2}={\rm\Phi}(R_{ab}+R_{bc}+R_{cd}+R_{de}+R_{ef}+R_{fg}+R_{gh}+R_{ah}). & & \displaystyle\end{eqnarray}$ (20)

The magnetic flux Φ can be calculated by substituting the magnetomotive force and the reluctance of each section of the magnetic circuit. Then, the magnetic flux density of each section of the magnetic circuit can be obtained by substituting the result into the Eq. (12). The magnetic flux density within the inner and outer gaps can be expressed as: $\begin{eqnarray}\displaystyle B_{1} & = & \displaystyle \frac{H_{1}L_{1}+H_{2}L_{2}}{(R_{ab}+R_{bc}+R_{cd}+R_{de}+R_{ef}+R_{fg}+R_{gh}+R_{ah})S_{bc}}\end{eqnarray}$ (21) $\begin{eqnarray}\displaystyle B_{2} & = & \displaystyle \frac{H_{1}L_{1}+H_{2}L_{2}}{(R_{ab}+R_{bc}+R_{cd}+R_{de}+R_{ef}+R_{fg}+R_{gh}+R_{ah})S_{cd}}.\end{eqnarray}$ (22)

According to the magnetic circuit law: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle {\rm\Phi}_{1}-{\rm\Phi}_{2}-{\rm\Phi}_{3}=0\end{eqnarray}$ (23) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle F_{1}+F_{2}={\rm\Phi}_{1}(R_{b^{\prime }c^{\prime }}+R_{c^{\prime }d^{\prime }}+R_{d^{\prime }e^{\prime }}+R_{e^{\prime }f^{\prime }}+R_{f^{\prime }g^{\prime }})+{\rm\Phi}_{3}(R_{a^{\prime }b^{\prime }}+R_{g^{\prime }h^{\prime }}+R_{a^{\prime }h^{\prime }})\end{eqnarray}$ (24) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle F_{1}+F_{1}^{\prime }+F_{2}={\rm\Phi}_{1}(R_{b^{\prime }c^{\prime }}+R_{c^{\prime }d^{\prime }}+R_{d^{\prime }e^{\prime }}+R_{e^{\prime }f^{\prime }}+R_{f^{\prime }g^{\prime }})+{\rm\Phi}_{2}R_{i^{\prime }j^{\prime }}.\end{eqnarray}$ (25)

The magnetic fluxes Φ₁, Φ₂ and Φ₃ in the magnetic circuit can be calculated from Eqs ((23))–((25)). Substituting the above results into Eq. ((12)), then the magnetic flux density of each section of the magnetic circuit for the multi-pole bilayer MR coupling with HPMA can be obtained. Thus, the magnetic flux densities $B_{1}^{\prime }$ and $B_{2}^{\prime }$ within inner and outer gap can be expressed as: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle \displaystyle \hspace{-18.0pt}B_{1}^{\prime }=\frac{H_{1}L_{1}+H_{1}^{\prime }L_{1}^{\prime }+H_{2}L_{2}-{\displaystyle \frac{H_{1}L_{1}+H_{2}L_{2}}{R_{a^{\prime }b^{\prime }}+R_{g^{\prime }h^{\prime }}+R_{a^{\prime }h^{\prime }}}}}{\left((R_{a^{\prime }b^{\prime }}+R_{g^{\prime }h^{\prime }}+R_{a^{\prime }h^{\prime }})-R_{i^{\prime }j^{\prime }}\left(1+{\displaystyle \frac{1}{R_{b^{\prime }c^{\prime }}+R_{c^{\prime }d^{\prime }}+R_{d^{\prime }e^{\prime }}+R_{e^{\prime }f^{\prime }}+R_{f^{\prime }g^{\prime }}}}\right)\right)S_{a^{\prime }b^{\prime }}}\end{eqnarray}$ (26) $\begin{eqnarray} \displaystyle \text{} & \text{} & \displaystyle \displaystyle \hspace{-18.0pt}B_{2}^{\prime }=\frac{H_{1}L_{1}+H_{1}^{\prime }L_{1}^{\prime }+H_{2}L_{2}-{\displaystyle \frac{(H_{1}L_{1}+H_{2}L_{2})R_{i^{\prime }j^{\prime }}}{R_{a^{\prime }b^{\prime }}+R_{g^{\prime }h^{\prime }}+R_{a^{\prime }h^{\prime }}}}}{\left((R_{b^{\prime }c^{\prime }}+R_{c^{\prime }d^{\prime }}+R_{d^{\prime }e^{\prime }}+R_{e^{\prime }f^{\prime }}+R_{f^{\prime }g^{\prime }})\left(1-{\displaystyle \frac{R_{i^{\prime }j^{\prime }}}{R_{a^{\prime }b^{\prime }}+R_{g^{\prime }h^{\prime }}+R_{a^{\prime }h^{\prime }}}}\right)-R_{i^{\prime }j^{\prime }}\right)S_{c^{\prime }d^{\prime }}}. \end{eqnarray}$ (27)

Similarly, the magnetic flux density in other sections of the magnetic circuit can be obtained, and the magnetic field strength can be calculated by using the magnetization curve of the materials. In this design, it is necessary to ensure that there is no magnetic saturation in each part of the magnetic circuit, and the magnetic field should be concentrated in the two MR fluid gaps. The magnetic circuit model of the designed MR coupling provides a reference for the design of the key dimensional parameters of the multi-pole MR coupling.

5. Finite element simulation

5.1. Magnetic analysis of the multi-pole bilayer MR coupling

In order to evaluate transmission torque of the multi-pole bilayer MR coupling with TPMA and HPMA, finite element analysis is employed to solve the magnetic circuit. Firstly, the values of structural parameters are carried out according to the magnetic circuit modeling which is shown in Section 4, and a 3D simulation model of the multi-pole bilayer MR coupling has been built. Then, the magnitude and direction of the residual flux density of each permanent magnet are set. After the final mesh is divided, the simulation analysis is carried out under the steady state. The values of structural parameters are shown in Table 2.

Table 2
Parameters and values

Parameters (mm) Values

R ₁ 22

R ₂ 30

R ₃ 30.5

R ₄ 62

R ₅ 62.5

R ₆ 74.5

z 80

Parameters (mm)	Values
R ₁	22
R ₂	30
R ₃	30.5
R ₄	62
R ₅	62.5
R ₆	74.5
z	80

The total transmission torque of the multi-pole bilayer MR coupling with TPMA obtained from the simulation results is 47.02 N m, while that of the HPMA is 70.65 N m, when the residual magnetic flux density of the permanent magnets is set to 0.8 T. The simulation results show that the designed MR coupling with HPMA which has six poles can significantly improve the transmission torque compared to the same size of the MR coupling with TPMA.

Figure 4 shows the crosssectional magnetic flux density and flux direction of the two multi-pole bilayer MR couplings with TPMA and HPMA. From the simulation results, it is seen that the direction of the magnetic flux is the same as the equivalent magnetic circuit in the magnetic circuit analysis. This result verifies the correctness of the magnetic circuit design. For the multi-pole bilayer MR coupling with TPMA, as shown in Fig. 4(a), most of the magnetic flux passes through the adjacent permanent magnets because the magnetic permeability of the permanent magnets is high and the direction of the magnetic poles of two adjacent permanent magnets are opposite. Due to the distribution of the magnetic field, its magnetic permeability properties may not be considered when selecting the materials of the spaced block between the two adjacent permanent magnets. The block can be designed as a hollow structure to reduce the weight, thereby the weight of the coupling be reduced, and the torquemass ratio of the coupling could be also improved. For the multi-pole bilayer MR coupling with HPMA, as shown in Fig. 4(b), the magnetic flux density on the outer stator is higher than that of the MR coupling with TPMA, while the magnetic flux density on the inner stator is significantly lower than the MR coupling with TPMA. The results show that the multi-pole bilayer MR coupling with HPMA can well concentrate the magnetic field to one side.

Fig. 4.

Flow direction of the magnetic flux in the cross section of the multi-pole bilayer MR coupling with: (a) TPMA; (b) HPMA.

The magnetic flux density of the inner and outer MR fluid working gaps is shown in Fig. 5. It is seen that the average flux densities in the inner gap of the MR coupling with TPMA and HPMA are 0.99 T and 0.48 T, respectively, as shown in Fig. 5(a). The arc length is the product of radian and radius. The magnetic flux density within the inner gap of the multi-pole bilayer MR coupling with TPMA is larger than that MR coupling with HPMA. This is due to that the sum of the magnetic resistance of the magnetic circuit nodes a ^′ b ^′, g ^′ h ^′ and a ^′ h ^′ in HPMA is larger than that of the magnetic circuit node i ^′ j ^′, which results in less magnetic flux passing through the inner gap in HPMA. Figure 5(b) shows that the average flux densities in the outer gap of the MR coupling with TPMA and HPMA are 0.63 T and 0.98 T, respectively. The magnetic flux density within the outer gap of the multi-pole bilayer MR coupling with TPMA is smaller than that MR coupling with HPMA. This is due to that less magnetic flux passes through the inner gap and inner stator in the multi-pole bilayer MR coupling with HPMA, while the flux density in the outer gap of MR coupling with HPMA is greater than that of TPMA.

Fig. 5.

Magnetic flux density in the MR fluid working gaps. (a) Inner gap; (b) outer gap.

To sum up, the magnetic field strength in the outer gap of the MR coupling with HPMA is larger. It can be seen from Eq. (3) that the radius of MR fluid is positively correlated with the generated torque. Therefore, increasing the magnetic field strength of the outer gap is beneficial to increase the total torque. Its unilateral magnetic focusing effect in the outer gap is obvious, and the transmission torque of the coupling is effectively improved.

The comparison results between the calculated value and the simulation value of the gap magnetic flux density of the magnetorheological fluid of the two schemes are shown in Table 3.

Table 3

Simulation and calculation values of magnetic flux density within the MR fluid gaps

	TPMA			HPMA
	Simulation value (B)	Calculated value (B)	Difference (%)	Simulation value (B)	Calculated value (B)	Difference (%)
Magnetic flux density in the inner gap	0.99	1.20	17.5	0.48	0.41	14.6
Magnetic flux density in the outer gap	0.63	0.58	7.9	0.98	1.20	18.3

The magnetic flux density on the cylindrical surfaces of the inner and outer MR fluid gaps along the axial direction is shown in Fig. 6. The distribution of magnetic flux density along the axial direction is the same, which makes the torque evenly distributed on the circumference. Due to the aluminum block and the secondary magnetic pole, lower magnetic flux density is observed in the areas where the spacer block or the secondary magnetic pole is located (dark blue region) while higher magnetic flux density is observed in the areas near the main permanent pole (red or yellow region).

Fig. 6.

Magnetic flux density distribution in the MR fluid gaps: (a) TPMA; (b) HPMA.

Furthermore, the influence of residual magnetic flux which generated by the secondary pole of the permanent magnet is studied. As shown in Fig. 7, with the increase of the residual magnetic flux density of the secondary magnetic pole, the torque generated by the inner gap decreases. This is because that the magnetic field strength in the inner gap decreases. It is also seen that the torque generated by the outer gap increases with the increase of the residual flux density of the secondary magnetic pole. This is mainly due to that the flux passing through the outer gap increases, and the magnetomotive force in the magnetic circuit increases with the increase of the residual flux density of the secondary pole. The magnetic field in the inner gap decreases gradually, which also indicates that the magnetic field gradually accumulates in the outer gap. The magnetic focusing effect can be defined by the ratio of the torque generated by the inner gap to the torque generated by the outer gap. The smaller the ratio is, the better the magnetic focusing effect is. From the simulation results, with the increase of the residual flux density of the secondary pole, the unilateral magnetic focusing effect of the multi-pole bilayer MR coupling with HPMA is more obvious.

Fig. 7.

Effect of residual flux density on transmission torque.

5.2. Influence of the inner diameter of the inner gap on torque

Figure 8 shows the influence of the inner diameter of the permanent magnet which is also the radius of the inner gap on the transmission torque of the MR coupling. In Fig. 8(a), the torque generated by the inner gap of the MR coupling with TPM increases with the increase of the inner diameter of the permanent magnet. This is due to that the working radius of the inner gap increases when the inner diameter of the inner stator increases. It can be seen from Eq. (4) that the torque increases with the increases of the radius of the inner gap. And the inner diameter of the inner stator has little effect on the transmission torque generated by the outer gap.

Fig. 8.

Effect of inner stator diameter on transmission torque: (a) TPMA; (b) HPMA.

In Fig. 8(b), the torque generated by the inner gap of the MR coupling with HPMA gradually increases with the increase of the inner diameter of the inner stator, which is also due to the increase of the working radius of MR fluid gap. However, the torque generated by the outer gap decreases with the increase of the inner diameter of the inner stator, which is also due to the decrease of the magnetomotive force of the main pole. It results in the decrease of the magnetic field strength in the outer gap. It is found that the total torque decreases with the increase of inner diameter of the inner stator. With the increase of inner diameter of the inner stator, the ratio of the torque generated by the inner gap to the outer gap gradually increases. It indicates that the unilateral magnetic focusing effect of Halbach permanent magnet array (HPMA) becomes weaker with the decrease of radial length of permanent magnet. The results show that the longer the radial length of the permanent magnet is, the better the magnetic field will be gathered on the outer gap side is.

5.3. The influence of the main magnetic pole angle on the transmission torque

The relationship between the transmission torque and the angle of the main pole of the permanent magnet is shown in Fig. 9. From the Fig. 9(a), it is seen that the torques generated by the inner gap, the outer gaps and the total torque of the MR coupling with TPMA increase with the increase of the angle of the main magnetic pole. According to the Eqs (11) and (13), the magnetic flux in the magnetic circuit increases with the increase of the main pole angle. Therefore, both the torques generated by the inner gap and the outer gap will increase, as well as the total torque.

Fig. 9.

Transmission torque versus the main magnetic pole angle: (a) TPMA; (b) HPMA.

As can be seen from Fig. 9(b), the torque generated by the inner gap of the MR coupling with HPMA first decreases and then increases with the angle of the main magnetic pole, and it reaching the minimum value 4.63 N m at 15°. This is due to that as the angle of the secondary magnetic pole decreases with the increases of the angle of the main magnetic pole. This makes the reluctance of the magnetic circuit node i ^′ j ^′ decreases gradually, and the flux passing through the inner gap decreases. However, the magnetic flux at the main magnetic pole increases with the increase of its angle, which makes the magnetic field in the inner gap begin to increase after 15°. It is also found that the torque generated by the outer gap first increases and then decreases with the increase of the main magnetic pole angle, and it reaches the maximum value 74.56 N m at 50°. This is due to that as the angle of the main magnetic pole increases, the magnetic field passing through the inner gap decreases, and the magnetic flux in the magnetic circuit increases as the angle of the main magnetic pole increases. However, at the same time, the magnetomotive force at the secondary magnetic pole decreases when the angle of the secondary magnetic pole decreases, and the magnetic flux at the secondary magnetic pole will pass through the outer gap, which makes the torque generated by the outer gap begin to decrease after 50°. The total torque increases with the increase of the main pole angle. The ratio of the torque generated by the inner to the outer gap first decreases and then increases with the increase of the angle of the main magnetic pole. When the main magnetic pole is 15°, the ratio is the smallest, and the magnetic gathering effect is the best. In this case, a single gap MR coupling design is suitable, which can further simplify its structure, and the loss of torque is smaller than that of the bilayer gap design.

6. Conclusions

The purpose of this paper is to improve the transmission torque of the multi-pole bilayer permanent magnets MR coupling by enhancing the magnetic field strength in the MR fluid gaps. Firstly, two structures of the multi-pole bilayer MR with traditional permanent magnet array (TPMA) and Halbach permanent magnet array (HPMA) are introduced. Then, the transmission torque of the MR coupling is deduced. Based on the electromagnetic field theory, the magnetic circuit models are established, and the magnetic flux density within the MR fluid working gaps has been derived in order to evaluate the merits of the designed MR coupling. Finally, a 3D FE magnetic-fluid analysis has been conducted. The results show that the torque generated by the multi-pole bilayer MR with HPMA is 33.45% higher than that of the MR coupling with TPMA when six main magnetic poles are set.

For the multi-pole bilayer MR with TPMA, the transmission torque generated by the inner and outer gaps increases with the increase of the main magnetic pole angle, and the inner diameter of the inner stator has little effect on the transmission torque generated by the outer gap.

For the multi-pole bilayer MR with HPMA, the bigger the residual magnetic flux density of the secondary magnetic pole and the radial length of the magnetic pole are, the better the unilateral magnetic concentration effect is. In this design, the transmission torque generated by the inner gap decreases first and then increases with the angle of the main magnetic pole, while the transmission torque generated by the outer gap increases first and then decreases. The results show that the torque generated by the outer gap reaches the maximum value 74.56 N m when the main magnetic pole is 50°. When the angle of the main magnetic pole is 15°, the single side magnetic gathering effect is the best.

Footnotes

Acknowledgements

This work supported by Research Program supported by the National Natural Science Foundation of China (51805444), the Young Scholars Reserve Talents Support Program of Xihua University (DC1900007176) and Talent Introduction Project of Xihua University (Z201017).

References

Rabinow

, The magnetic fluid clutch, Transactions of the American Institute of Electrical Engineers 67 (1948), 1308–1315.

J.S.

Sohn

J.W.

and Choi

S.B.

, Applications of magnetorheological fluid actuator to multi-DOF systems: State-of-the-art from 2015 to 2021, Actuators 11 (2022), 44.

and Li

, Torque characteristics analysis of a magnetorheological brake with double brake disc, Actuators 10 (2021), 23.

Thakur

M.K.

and Sarkar

, Experimental and numerical study of magnetorheological clutch with sealing at larger radius disc, Defence Science Journal 70 (2020), 575–582.

Olivier

and Sohn

J.W.

, Design optimization and performance evaluation of hybrid type magnetorheological damper, Journal of Mechanical Science and Technology 35(8) (2021), 3549–3558.

Chen

, A novel vibration isolator for vibrating screen based on magnetorheological damper, Journal of Mechanical Science and Technology 35(10) (2021), 4343–4352.

Yang

Chen

Liu

and Zhang

, Modeling and experiments of an annular multi-channel magnetorheological valve, Actuators 11 (2022), 19, doi:10.3390/act11010019.

Sun

Fang

C.N.

Long

and Wang

G.X.

, Design and research of a novel magnetorheological fluid coupling with cycloid corrugated surface, International Journal of Applied Electromagnetics and Mechanics 60 (2019), 355–377.

Kordonski

and Golini

, Multiple application of magnetorheological effect in high precision finishing, Journal of Intelligent Material Systems and Structures 13 (2002), 401–404.

10.

Lee

and Park

, Shape design and performance evaluation of small lightweight MR brake for improvement torque, Journal of Mechanical Science and Technology 34(11) (2020), 4675–4683.

11.

Hua

D.Z.

Liu

X.H.

and Li

Z.Q.

, A review on structural configurations of magnetorheological fluid based devices reported in 2018–2020, Frontiers in Materials 24 (2021), 640102.

12.

Z.H.

Zeng

and Yuan

L.H.

, Simulation and optimization design of disc magnetorheological brake, Journal of Agricultural Machinery 46 (2015), 364–369.

13.

Yuan

J.F.

and Wang

J.W.

, Design and research of circular groove disc magnetorheological fluid brake, Mechanical Science and Technology 37 (2018), 226–231.

14.

Zhao

B.S.

and Ma

, Magnetorheological brake controlled by shape memory alloy, Mechanical Strength 38 (2016), 231–235.

15.

Jiang

X.Z.

and Yao

, Design, simulation and testing of a novel radial multi-pole multi-layer magnetorheological brake, Smart Materials and Structures 27 (2018), 025016.

16.

Huang

Tian

and Ji

, Development of a novel magnetorheological fluids transmission device for high-power applications, Smart Materials and Structures 28 (2019), 055021.

17.

Qin

Song

Zeng

and Hu

, Design and evaluation of a small-scale multi-drum magnetorheological brake, Intelligent Material System and Structures 29 (2018), 2607–2618.

18.

Bucchi

Forte

Frendo

Musolino

and Rizzo

, A fail-safe magnetorheological clutch excited by permanent magnets for the disengagement of automotive auxiliaries, Journal of Intelligent Material Systems and Structures 25 (2014), 2102–2114.

19.

Rizzo

Musolino

Bucchi

and Forte

, A multi-gap magnetorheological clutch with permanent magnet, Smart Materials and Structures 24 (2015), 075012.

20.

Rizzo

, An innovative multi-gap clutch based on magnetorheological fluids and electrodynamic effects: magnetic design and experimental characterization, Smart Materials and Structures 26 (2017), 015007.

21.

Rizzo

Musolino

and Lai

H.C.

, An electrodynamic/magnetorheological clutch powered by permanent magnets, IEEE Transactions on Magnetics 53 (2017), 8000307.

22.

Chen

, Numerical simulation calculation and analysis of physical field of magnetorheological safety coupling under permanent magnet excitation, Journal of Applied Mechanics 38 (2021), 434–440.

23.

Böse

Gerlachm

and Ehrlich

, Magnetorheological torque transmission devices with permanent magnets, Journal of Physics: Conference Series 412 (2013), 012050.

24.

Moghaniand

and Kermani

M.R.

, A lightweight magnetorheological actuator using hybrid magnetization, IEEE/ASME Transactions on Mechatronics 25 (2019), 76–83.

25.

Xiao

Zhang

and Xu

B.Y.

, Halbach permanent magnet array axial modulation permanent magnet gear, Mechanical Science and Technology 38 (2019), 1373–1379.

26.

Kordonsky

, Elements and devices based on magneto-rheological effect, Journal of Intelligent Material Systems and Structures 4 (1993), 65–69.

27.

and Kwon

D.S.

, Modeling of a magnetorheological actuator including magnetic hysteresis, Journal of Intelligent Materials Systems and Structures 14 (2003), 541–550.

28.

Q.T.

Wang

and Liang

, Simulation and experimental investigation of a multi-pole multi-layer magnetorheological brake with superimposed magnetic fields – ScienceDirect, Mechatronics 65 (2020), 102314.

29.

Jiang

X.Z.

Yao

and Li

, Research on new double-layer multi coil magnetorheological brake, Journal of Sichuan University (Engineering Science Edition) 48 (2016), 201–209.

Research on the torque performance for two multi-pole bilayer magnetorheological fluid couplings

Abstract

Keywords

1. Introduction

2. Structural design of the multi-pole bilayer permanent magnets MR coupling

5.1. Magnetic analysis of the multi-pole bilayer MR coupling

Table 2 Parameters and values Parameters (mm) Values R 1 22 R 2 30 R 3 30.5 R 4 62 R 5 62.5 R 6 74.5 z 80

Footnotes

Acknowledgements

References

Table 2
Parameters and values

Parameters (mm) Values

R ₁ 22

R ₂ 30

R ₃ 30.5

R ₄ 62

R ₅ 62.5

R ₆ 74.5

z 80