Study on torque density enhancement mechanism of elliptic arc multi-disk MRF coupling

Abstract

The transfer energy of a magnetorheological fluid (MRF) coupling can be dynamically regulated by changing the MRF mechanical properties of its input and output shafts. In addition, the dynamic characteristics of its drive system can automatically be in the tune with its load characteristics to effectively suppress vibration and shock responses, to achieve overload protection of the system, and to improve its mechanical performance and safety reliability. However, the weak mechanical properties of MRF materials result in so small a coupling torque density that the MRF coupling applications for high-torque transfer is restricted. Thus, to increase the coupling torque density is becoming an urgent key technological challenge in this field. A technique based on shear-pressure mixed mode was proposed here to increase the torque density by utilizing the formation mechanism of MRF arc flux linkage. Futhermore, a new high torque arc multi-disk MRF coupling structure was designed and its corresponding mechanical torque transfer model was established. A FEA electromagnetic simulation was performed to study the distribution of the magnetic field in the MRF chamber under different current excitations. Effects of the key parameters of the elliptical arc on its transfer torque were also investigated. Finally, experimental analysis of the mechanical properties of the elliptical disk MRF coupling was conducted to verify the feasibility of the proposed technique and the validity of the torque transfer model.

Keywords

Magnetorheological fluid multi-disk coupling arc flux linkage torque density

1. Introduction

A MRF drive as a new kind of power transfer devices based on controllable MRF rheological properties is primarily made up of a magneto-rheological (MR) brake [1], a MR clutch [2], a MR soft starter [3] and a MRF coupling [4]. Compared with other existing power transfer techniques, it is known for its fast response speed, less wear ability of its transfer components, simple control and low energy consumption. Therefore, it can become an ideal power transfer device. A MRF coupling can dynamically change the MRF mechanical properties in accordance with its loading conditions of its drive system to dynamically regulate its mechanical transfer energy. With such characteristics, the MRF coupling can effectively suppress the shock response and achieve overload protection to enhance its mechanical performance and safety reliability. This technology has broad application prospects in the engineering applications. Unfortunately, the weak mechanical properties of MRF materials will lead to such a low coupling torque density that the high torque transfer applications of MRF couplings is limited. Thus, how to improve the torque density of MRF couplings is becoming an urgent technological challenge in this field.

To increase the transfer torque without at the expense of other good qualities such as high power, speed and control accuracy of modern drives, some researchers studied and refined structures of MR torque drives (MRTDs). Senkal [5] utilized a magnetic isolation ring to design a cylindrical coupling in a serpentine magnetic circuit structure so that MRF can work in a larger area. Kikuchi [6] designed two multi-disk micro-distance MRF drives to investigate effects of the MRF gaps on their transfer torques. Francesco Bucchi [7] integrated a permanent magnet and MRF to design a MRF drive equipped in a diesel engine. Nguyen [8,9] designed various MRF drive structures in accordance with their coil arrangements to increase their transfer torques. Yu Jiangqiang [10] proposed a new structure in the spiral flow mode to improve the rotational torque performance by increasing the length of the effective area. As mentioned above, the torque output capacity of MRF drives can enhance by changing the effective working area of their MRFs or adding auxiliary structures. On the other hand, the torque increase is usually accompanied by a complicated structure, which results to an undesirable volume and mass.

Other researchers tried to improve the torque output capacity by exploiting the transfer mechanisms of MRFs. Sarkar [11] designed a spring squeezing device on the side of a single disk brake so that the MRF can be squeezed to increase the brake torque. Na Wang [12] changed the surface texture of a disk MRF brake to try to improve its torque output capability. Tian T [13] designed a MRF brake where a kind of shear thickening fluid (STF) was used as its liquid medium to increase its torque transfer capacity. Hui S [14] developed a cycloidal corrugated coupling to increase its transfer torque. The above findings show that various drive structures and surface texture styles can affect the torque transfer performances of MR transfer units. Following this line of thought, a curved multi-disk MRF coupling was designed here with a structural feature that an arc flux linkage can be generated in the MRF gap between the driving and driven disks by changing the corrugated surface shape of the driving disk. The curved flux linkage is not only sheared but also squeezed by the upper and lower plates so that its transfer torque may rise significantly compared to a common multi-disk MRF coupling in the same volume.

2. Analysis of formation of an arc flux linkage

The magnetic field is typically evenly distributed between two parallel plates with its direction perpendicular to them. In contrast, when a parallel magnetic field passes through a curved surface, the direction of magnetic line will also be curved as shown in Fig. 1.

Fig. 1.

Distribution of magnetic field lines in a curved surface.

Hui S’s findings on magnetic field distributions of curved surfaces [14] indicate that the arc-curve conductive magnetic field is more intensive at the center of the curved surface and the magnetic lines are in curved arcs in the surrounding surfaces. In such case, the flux linkage of the arc surface is not only sheared but also squeezed by the upper and lower plates so that the corresponding transfer torque can increase compared to that of a traditional shearing MRF drive.

An arc surface (Fig. 1) is locally magnified to obtain the shape of the flux linkage (Fig. 2). In the axisymmetric model of a micro flux linkage element (Fig. 3), a, b, c, d is its boundary; the element angle (φ) represents the angle between the tangent line of the curved surface and the horizontal plane; P represents the horizontal pressure to the arc element; h represents the height of the axisymmetrically expanded arc element; ds represents the lengths of the both end surfaces of the arc element; q represents the pressure of the arc element from the end face (ds); and k represents the horizontal friction force of the arc element, which is namely the shear yield stress of the arc flux linkage.

Fig. 2.

Shear-pressure mixed flux linkage.

Fig. 3.

Axisymmetric unfolding model of an arc element.

As the horizontal force is in balance, the following equation can be obtained: $\begin{eqnarray}\displaystyle ph+2k\cos {\varphi}\cdot ds+2q\sin {\varphi}\cdot ds=ph+d(ph). & & \displaystyle\end{eqnarray}$ (1)

The following equation can be obtained from the Orowan theory in metal plastic deformation theory: $\begin{eqnarray}\displaystyle p=q-\frac{{\pi}k}{2}. & & \displaystyle\end{eqnarray}$ (2)

Equation (2) can be converted into the following equation (q vs. k) in combination with the geometric model: $\begin{eqnarray}\displaystyle \frac{dq}{k}=\frac{{\pi}}{2}\cdot \frac{dh}{h}+\cot {\varphi}\frac{dh}{h}. & & \displaystyle\end{eqnarray}$ (3)

The magnetic density (B) changes with positions of the arc. For investigation of its rule and in accordance with the principle of the control variable method, the semi-minor axis (b) only changes in size at the media boundary ellipse but the coil current and the minimum gap do not vary for performance of simulation analysis (b = 0 mm, 1 mm, 2 mm, 3 mm and 4 mm) in view of the elliptical arc surface. The data were sorted to obtain the relationship between the ellipse parameter angle and the magnetic induction intensity distribution by integrating the ellipse parameter angle (φ). As shown in Fig. 4, the magnetic flux density reach the peak at the center of the elliptical interface while it is almost zero at the two sides; moreover, b varies significantly with positions of the interface.

Fig. 4.

φ vs. B.

Fig. 5.

Schematic illustration of a multi-disk MRF coupling.

It can be seen from the characteristic curve of the magnetorheological fluid that when the magnetic induction intensity is not saturated, the magnetic induction intensity, B, is almost proportional to the shear yield stress produced, k _e. That is, B can be represented by the k _e. Assuming that k ₀ is the shear yield stress of at b = 0 (flat disk surface) and k _e is the shear stress at other angles (elliptical disk surface), then an averaged k _e in some angle range can be represented by k ₀ times a constant (different at different angle range) from the simulation result, which is Eq. (4). It is worth noting, Eq. (4) is an empirical instead of analytical relationship, which serves to simplify later calculations. $\begin{eqnarray}\displaystyle k_{e}=\left\{\begin{array}{@{}ll@{}}1.1k_{0}\quad & 0<{\varphi}\leq {\displaystyle \frac{{\pi}}{6}}\\[10.0pt] 0.5k_{0}\quad & {\displaystyle \frac{{\pi}}{6}}<{\varphi}\leq {\displaystyle \frac{{\pi}}{3}}\\[8.0pt] 0.125k_{0}\quad & {\varphi}>{\displaystyle \frac{{\pi}}{3}}.\end{array}\right. & & \displaystyle\end{eqnarray}$ (4)

3. Theoretical analysis of a multi-disk elliptical MRF coupling

3.1. Structural principle

As shown in Fig. 5, our multi-disk MRF coupling is modified on the basis of the structures of general disk couplings. The half-section view (right) presents the rotating input and output ends; the former is made up of an input shaft (3), a driving disk (12) and an inner magnetic isolation ring (13) which are screwed together; while the latter consists of a shaft sleeve (4), a driven disk (6), an outer magnetic isolation ring (7) and an output shaft (11) which are bolted. The input and output shafts rotate against each other by means of the bearing (1). In between the driven disks, the space will serve as the chamber(10) to fill the MRF and it’s sealed by a rubber ring (5) at the end of the output shaft. An unclosed end face covering (2) is equipped with a dynamic seal ring at the inner ring to prevent dusts from entering the coupling, which is screwed in the shaft sleeve. An excitation coil (9) is equipped in the output end through an excitation coil base (14) and bolted to the housing (8). When the coil is powered on, the power torque is transmitted to the driving disk through the input shaft and then transferred to the driven disk by means of solidification of MRF. It is finally transmitted to the load end through the output shaft and the output torque can be adjusted by controlling the coil current.

Our elliptical disk coupling is designed to change the corrugated shape of the driving disk face (Fig. 6) and keep the driven disk face in planar state. The corresponding MRF gap between the disk and driven disks generates an arc flux linkage. Figure 7 presents sizes of our coupling.

Fig. 6.

Elliptical disk style.

Fig. 7.

Coupling dimensions.

3.2. Simulation analysis of magnetic circuits

The operating magnetic field of MRF significantly affects the transfer performance. To improve the magnetic field distribution and transfer efficiency, it is necessary to analyze the magnetic circuits of drives. Maxwell electromagnetic simulation was carried out and the magnetic field distribution in the elliptical arc face is shown in Fig. 8. The magnetic conductive part is made of Q235 steel and the gap is made of MRF-350.

Fig. 8.

FEM simulation cloud diagram of magnetic circuits of our multi-disk MRF coupling.

The data points were extracted and sorted to obtain the magnetic field distribution under the condition of a single gap in the radial direction (Fig. 9) and various gaps (Fig. 10). Figures 9 and 10 indicate that the magnetic fields are relatively evenly distributed in the operating gap of MRF and the magnetic density meets the design requirements.

Fig. 9.

Magnetic flux density of the operating gap (radial).

Fig. 10.

Magnetic flux density of the operating gap (axial).

3.3. Torque transfer mechanics model

The MRF coupling can be mathematically described in accordance with its geometric model. The elliptic curve equation can be described as: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}x=-a\sin {\varphi}\quad \\ y=-b\cos {\varphi}\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (5) where a and b represent the semi-major and semi-minor axe of the ellipse, respectively; φ represents the angle of the ellipse; and x and y are the coordinates of a point at the ellipse.

When the driving disk is expanded along the radius (r), the relationship between the corresponding arc circumference and the expanded radius can be expressed as l = 2πr = 2an, where n represents the number of elliptical waves of the expanded disk and r represents the radius of the expanded disk. Figure 11 schematica demonstration of the circumferential development of an elliptical waveform.

When φ falls in the range of $(0,\frac{{\pi}}{2})$ , the elliptic arc end and the disk face are perpendicular and the elliptic arcs are evenly distributed in the disk. According to the ellipse equation, the slope of the tangent at any point on the ellipse is: $\begin{eqnarray}\displaystyle k_{t}=-\tan {\theta}=y^{\prime } & = & \displaystyle -\frac{b^{2}}{a^{2}}\cdot \frac{x}{y}=-\frac{b^{2}}{a^{2}}\cdot \frac{-a\sin {\varphi}}{-b\cos {\varphi}}\nonumber\\ \displaystyle & = & \displaystyle -\frac{b}{a}\tan {\varphi}.\end{eqnarray}$ (6)

The following equation can be derived based on the geometric relationship: $\begin{eqnarray}\displaystyle \frac{h}{2} & = & \displaystyle b+h_{min}-b\cos {\varphi}\nonumber\\ \displaystyle & = & \displaystyle b(1-\cos {\varphi})+h_{min}.\end{eqnarray}$ (7)

From the shear-pressure mixing mechanism model, integration of Eq. (6) and Eq. (7) leads to the following expression: $\begin{eqnarray}\displaystyle \frac{dq}{k} & = & \displaystyle \frac{{\pi}}{2}\cdot \frac{2b\sin {\varphi}d{\varphi}}{2b(1-\cos {\varphi})+2h_{min}}+\frac{a}{b}\cot {\varphi}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \cdot \frac{2b\sin {\varphi}d{\varphi}}{2b(1-\cos {\varphi})+2h_{min}}.\end{eqnarray}$ (8)

Assuming $c=\frac{h_{min}}{b}+1$ , integration of φ in Eq. (8) results in the following equation: $\begin{eqnarray}\displaystyle \frac{q}{k}=\frac{{\pi}}{2}\ln (c-\cos {\varphi})+\frac{a}{b}\cdot \frac{2c}{\sqrt{(c-1)(c+1)}}\cot \left(\sqrt{\frac{c+1}{c-1}}\tan \frac{{\varphi}}{2}\right)-\frac{a}{b}{\varphi}+C & & \displaystyle\end{eqnarray}$ (9) where: the integral constant (C) can be obtained from the boundary condition (φ = 0, p = 0) and Eq. (2): $\begin{eqnarray}\displaystyle C=\frac{{\pi}}{2}-\frac{{\pi}}{2}\ln (c-1). & & \displaystyle\end{eqnarray}$ (10)

The relationship between the elliptic arc normal pressure and shear stress is reorganized as: $\begin{eqnarray}\displaystyle \frac{q}{k} & = & \displaystyle \frac{{\pi}}{2}-\frac{a}{b}{\varphi}+\frac{{\pi}}{2}\ln \left(\frac{c-\cos {\varphi}}{c-1}\right)+\frac{a}{b}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \cdot \frac{2c}{\sqrt{(c-1)(c+1)}}\cot \left(\sqrt{\frac{c+1}{c-1}}\tan \frac{{\varphi}}{2}\right).\end{eqnarray}$ (11)

For a single elliptic wave surface, its horizontal force (F) is the integral of the horizontal components of q and k on the element in each surface, which is expressed as: $\begin{eqnarray}\displaystyle F & = & \displaystyle \int (q\cdot \sin {\theta}ds+k\cdot \cos {\theta}ds)\nonumber\\ \displaystyle & = & \displaystyle \int _{0}^{{\alpha}}\left(q\cdot b\sin {\varphi}d{\varphi}+k\cdot \frac{a}{b}\cot {\varphi}\cdot b\sin {\varphi}d{\varphi}\right)\end{eqnarray}$ (12) where 𝛼 is the ellipse limit parameter angle, which is within the range of (0, π) in the ellipse disk.

Fig. 11.

Expanded view of the elliptical disk.

Since the circumferential length of the disk is the total of the semi-major axes of the ellipse, the following geometric relationship can be obtained: $\begin{eqnarray}\displaystyle n\cdot 2a\cdot \sin {\alpha}=2{\pi}r\Rightarrow a=\frac{{\pi}r}{n\sin {\alpha}}. & & \displaystyle\end{eqnarray}$ (13)

Then, one MRF gap can generate the magnetic transfer torque (T _H) as follows: $\begin{eqnarray} \displaystyle T_{H} & = & \displaystyle n\int _{R_{1}}^{R_{2}}F\cdot rdr\nonumber\\ \displaystyle & = & \displaystyle nk\left[\frac{{\pi}}{2}b(c-\cos {\alpha})\left(\frac{R_{2}^{2}}{2}-\frac{R_{1}^{2}}{2}\right)\ln \left(\frac{c-\cos {\alpha}}{c-1}\right)\right.\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle +\frac{2{\pi}c(c-\cos {\alpha})}{3n\sqrt{(c-1)(c+1)}\sin {\alpha}}(R_{2}^{3}-R_{1}^{3})\cot \left(\sqrt{\frac{c+1}{c-1}}\tan \frac{{\alpha}}{2}\right)\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \left.-\frac{{\pi}{\alpha}}{3n\sin {\alpha}}(R_{2}^{3}-R_{1}^{3})(c-\cos {\alpha})\vphantom{\frac{R_{2}^{2}}{2}-\frac{R_{1}^{2}}{2}}\right]. \end{eqnarray}$ (14)

The magnetic transfer torque (T _H) of a single elliptical disk surface under stable operation can be derived by the integration of the above elliptical surface magnetic field distribution into Eq. (14) derive, which is expressed as: $\begin{eqnarray}\displaystyle T_{H}=\left\{\begin{array}{@{}l@{}}1.1nk_{0}T({\alpha})\quad 0<{\alpha}\leq {\displaystyle \frac{{\pi}}{6}}\quad \\[8.0pt] 0.6nk_{0}T\left({\displaystyle \frac{{\pi}}{6}}\right)+0.5nk_{0}T({\alpha})\quad {\displaystyle \frac{{\pi}}{6}}<{\alpha}\leq {\displaystyle \frac{{\pi}}{3}}\quad \\[10.0pt] 0.6nk_{0}T\left({\displaystyle \frac{{\pi}}{6}}\right)+0.375nk_{0}T\left({\displaystyle \frac{{\pi}}{3}}\right)+0.125nk_{0}T({\alpha})\quad {\alpha}>{\displaystyle \frac{{\pi}}{3}}\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (15) where: $\begin{eqnarray}\displaystyle T({\alpha}) & = & \displaystyle \frac{{\pi}}{2}b(c-\cos {\alpha})\left(\frac{R_{2}^{2}}{2}-\frac{R_{1}^{2}}{2}\right)\ln \left(\frac{c-\cos {\alpha}}{c-1}\right)\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle +\frac{2{\pi}c(c-\cos {\alpha})}{3n\sqrt{(c-1)(c+1)}\sin {\alpha}}(R_{2}^{3}-R_{1}^{3})\cot \left(\sqrt{\frac{c+1}{c-1}}\tan \frac{{\alpha}}{2}\right)\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle -\frac{{\pi}{\alpha}}{3n\sin {\alpha}}(R_{2}^{3}-R_{1}^{3})(c-\cos {\alpha}).\end{eqnarray}$ (16)

When the MRF coupling remains unstable or the brake is powered off, there is a difference in angular velocity between the driving and driven disk, the corresponding viscous damping force cannot be ignored during this process. This process is similar to the lubrication process of a thrust bearing. The viscous damping force equation can be obtained from the Reynolds equation of hydrodynamic lubrication. Because the semi-major axis is much larger than the semi-minor axis in our ellipse, a general wedge-shaped slider, instead of an elliptical corrugated surface, was utilized for analysis. The inlet and outlet gaps are h _max and h _min, respectively. The convergence ratio is defined as: $\begin{eqnarray}\displaystyle K=\frac{h_{max}-h_{min}}{h_{min}}=\frac{h_{max}}{h_{max}}-1. & & \displaystyle\end{eqnarray}$ (17)

Then, the unit viscous damping force of a single corrugated face is: $\begin{eqnarray}\displaystyle F_{f}=\frac{{\eta}vl}{h_{min}K}\ln (K+1)+\frac{h_{min}K}{2l}\cdot \frac{W}{L} & & \displaystyle\end{eqnarray}$ (18) where: v represents the flow velocity between the outlet and the inlet, which is expressed as v = Δωr. (Δω is the speed difference between the driving and driven disks, l is the horizontal length of a single corrugated surface, $l=\frac{{\pi}r}{n}$ and $\frac{W}{L}$ is the wave surface carrying capacity). $\frac{W}{L}$ is defined as: $\begin{eqnarray}\displaystyle \frac{W}{L}=\frac{6v{\eta}l^{2}}{K^{2}h_{min}^{2}}\left[\ln (K+1)-\frac{2K}{K+2}\right]. & & \displaystyle\end{eqnarray}$ (19)

The viscous force of MRF is: $\begin{eqnarray}\displaystyle F_{{\eta}}=\frac{{\pi}{\eta}{\rm\Delta}{\omega}r^{2}}{h_{min}}\left[\frac{\ln (K+1)}{K}+3\left(\frac{\ln (K+1)}{K}-\frac{2}{K+2}\right)\right]. & & \displaystyle\end{eqnarray}$ (20)

The viscous torque of a single elliptical disk is: $\begin{eqnarray}\displaystyle T_{{\eta}} & = & \displaystyle \int _{R_{1}}^{R_{2}}F_{{\eta}}\cdot rdr\nonumber\\ \displaystyle & = & \displaystyle \frac{{\pi}{\eta}{\rm\Delta}{\omega}}{4h_{min}}(R_{2}^{4}-R_{1}^{4})\left[\frac{\ln (K+1)}{K}+3\left(\frac{\ln (K+1)}{K}-\frac{2}{K+2}\right)\right].\end{eqnarray}$ (21)

The multi-disk elliptical corrugated MRF coupling can transfer the torque as follows: $\begin{eqnarray}\displaystyle T=2m(T_{H}+T_{{\eta}})+T_{m} & & \displaystyle\end{eqnarray}$ (22) where m represents the number of elliptical driving disks; T _H and T _𝜂 represent the magnetic and viscous torques of a single elliptical driving disk, respectively; and T _m represents the dynamic friction resistance torque of the coupling.

4. Result and discussion

4.1. Analysis of mechanical properties of a coupling

The mechanical model of the above multi-disk MRF coupling indicates that the torque transfer capacity of MRF is closely related to these parameters such as the semi-major axis (a), semi-minor axis (b), the number of elliptical arcs (n) and minimum gap (h _min). The control variable method was applied here to investigate effects of these parameters on the torque performances such as the magnetic output torque, viscous drag torque and torque adjustable ratio of a coupling and obtain its optimal design parameters.

(1) Magnetic output torque

For a rotating transfer component (especially a MRF coupling), there is no speed difference between its input and output shafts. The MRF solidifies under the action of the magnetic field and then its transfer capacity primarily depends on the magnetic shearing force. Therefore, the magnitude of the magnetic output torque shall be considered. When the transfer torque is maintained, the inner and outer diameters (R ₁ and R ₂) are assumed as 65 mm and 120 mm, respectively.

As for an elliptical corrugated MRF coupling, its magnetic transfer torque (T _H) is closely related to the minimum gap (h _min) and the semi-minor axis (b). Therefore, effects of h _min and b on the transfer torque are discussed below.

As shown in Fig. 12, the calculation results indicate that an elliptical corrugated driving disk is better than a common flat disk at transferring torque. T _max are approaching to a constant while h _min reached 2 mm and increased with the semi-minor axis b.

Fig. 12.

T _max vs. h _min.

Actually, MRF remains unsolidified in some local areas. At this time, the excessive gap ensures that the number of arc flux linkages in the shear-pressure mixing mode will decrease, which lead to rapid magnetic density loss. Thus, it is necessary to reduce the maximum gap between the driving and driven disks and there are two ways as suggested in Figs 13 and 14: by increasing the number of ellipse wave n or by increasing the length of semi-major axis a.

Fig. 13.

Increasing the number of ellipse waves (n).

Fig. 14.

Increasing the length of the semi-major axis (a).

As shown in Fig. 13, the number of ellipse waves (n) rises.

As shown in Fig. 14, the semi-major axis (a) increases.

The magnetic torque variations under both measures (Fig. 15) indicate that a drive can transfer a greater torque when h _min decreases or b increases. While the excitation current is the same, the magnetic transfer torque has a more substantial increase along with the growth of n and a for the same h _min and b. On the other hand, the torque will reach the maximum and then gradually decrease along with their continued growth. Further analysis of Eq. (14) indicates that the curves will get closer for elliptical corrugated and common flat disks in case of n →∞ or a →∞; and that their corresponding transfer torques will gradually decrease to the level of the common multi-disk MRF couplings. In addition, their transfer torque almost peak in case of n = 15 and 25 which corresponds to the ellipse limit angles (φ = 60° and 30°). The shear stress (k) changes in accordance with Eq. (15) with a sharp needle-shaped peaks and the needle-shaped peaks of a are the same.

Fig. 15.

T _H2 vs. n and a.

Fig. 16.

Viscous damping torque vs. n and a.

(2) Viscous damping torque

MRF remains incompletely solidified while a MRF drive starts braking. At this time, there is a slip between the driving and driven disks and a corresponding viscous damping torque would occur due to the viscous characteristics of MRF. Thus, it is necessary to discuss its damping torque. A coupling whose MRF viscosity and semi-minor axis are 𝜂 = 0.37 Pa ⋅ s and b = 6 mm, respectively, is chosen for study. The viscous damping torque of MRF in the gap of a single disk (Fig. 16) indicates that the viscous damping torque (T _𝜂) in the elliptical corrugated disk face is larger than that in the common flat disk. This is consistent with the hydrodynamic lubrication mechanism. Moreover, T _𝜂 first increased to its peak with growth of n or a but then slowly decreased to a constant level. While n or a approaches infinity, the performances of the elliptical corrugated and common flat disks are almost the same with their damping force almost equal.

(3) Torque adjustable ratio

The ratio of the magnetic output torque and the viscous damping torque under normal working conditions is defined as the torque adjustable ratio (𝛽). It is generally utilized to evaluate the control performances of the output torque of a MRF drive. While the torque adjustable ratios (𝛽_t and 𝛽_p) for elliptical corrugated and common multi-disk MRF couplings are expressed as: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}{\beta}_{t}={\displaystyle \frac{T_{H}}{T_{{\eta}}}}\quad \\[10.0pt] {\beta}_{p}={\displaystyle \frac{4{\tau}_{H}h_{min}(R_{2}^{3}-R_{1}^{3})}{3{\eta}{\rm\Delta}{\omega}(R_{2}^{4}-R_{1}^{4})}}.\quad \end{array}\right. & & \displaystyle\end{eqnarray}$ (23)

The following parameters including the MRF viscosity (𝜂 = 0.37 Pa ⋅ s) and the semi-minor axis length (b = 6 mm) are given. The relationship 𝛽 vs. Δω can be calculated for a specific MRF drive while n or a changes.

Figure 17 indicates that 𝛽 is larger for the common multi-disk MRF coupling than for an elliptical disk MRF coupling and it is more pronounced while the speed difference is low. In contrast, 𝛽 is not much different for both MRF couplings while the speed difference increases. In addition, 𝛽 increases with the growth of n and a. Overall, 𝛽 is most sensitive to Δω. However, the fact that 𝛽 does not change greatly while Δω approaching a critical value indicates that couplings can be controlled more easily when Δω is high.

Fig. 17.

The relationship between adjustable torque ratio 𝛽 vs. speed difference Δω.

To sum up, the transfer torque performance of elliptical disk MRF coupling is significantly affected by n, a and b. The optimal values are n = 15 mm, a = 30 mm and b = 6 mm and at the limited angle φ = 60.

4.2. Experimental study of a multi-disk MRF coupling

According to the previous analysis of this paper, a Elliptic Arc Multi-disk MRF Coupling experimental prototype was designed and custom made. The comparative experiment was conducted between the structure designed here and the traditional planar structure.

Our couplings were fabricated in accordance with the dimensions specified in Table 1. Our test bench, as shown in Fig. 18, mainly consisted of a drive motor, a reducer, a high-speed power supply slip ring, a multi-disk MRF coupling, a magnetic powder brake, a temperature sensor, a torque/speed sensor and sampling circuit signals. Figure 19 and Fig. 20 show the physical setting of the test bench and the measurement equipment. Based on these optimized parameters, the flat disk and the elliptical disk were manufactured, as shown in Fig. 21.

Table 1
Main structural dimensions of our test prototype

Basic parameter Size (mm) Basic parameter Size (mm)

R ₁ 65 R ₅ 190

R ₂ 120 h _min 1

R ₃ 145 Disk thickness 8

R ₄ 170 Housing thickness 25

Basic parameter	Size (mm)	Basic parameter	Size (mm)
R ₁	65	R ₅	190
R ₂	120	h _min	1
R ₃	145	Disk thickness	8
R ₄	170	Housing thickness	25

Fig. 18.

Schematic illustration of the test bench.

Fig. 19.

The physical setting of the test bench.

Fig. 20.

The measurement equipment.

Fig. 21.

The real photos of the flat disk and elliptical disk.

The no-load and magnetic torque characteristics of the coupling were primarily verified by experiment following the above theory and simulation analysis. The results are presented as follows.

(1) No-load transfer torque

The no-load transfer torque is mainly composed of the bearing, seal ring and MRF slip friction torque which are relatively small. For reducing measurement errors of instruments, the pulse signals of the torque/speed sensor are processed by the acquisition circuit and then imported into the industrial computer software to measure the torque. Several experiments were repeated and the measurements were averaged. The final data are shown in Fig. 22.

Fig. 22.

No-load characteristics of our multi-disk MRF coupling.

Figure 22 indicates that the no-load torque of our elliptical disk coupling is always higher than that of the common multi-disk coupling but they kept the same trend. Their no-load torque gradually increases with the growth of Δω. Whereas, their no-load torque decreased when the slip speed reaches a certain level primarily due to the fact that the bearing, seal ring and MRF friction forces all increase with Δω and MRF would produces a shear thinning effect at such speed. Thus, the torque growth slows down.

(2) Magnetic transfer torque

When the MRF is at working, its magnetic transfer torque is dominant. The test results are shown in Fig. 23. Figure 23 indicates that the magnetic transfer torques of the elliptical and common disk MRF couplings and the multi-disk MRF coupling increases the current. When the current is less than 1 A, their magnetic transfer torques grow linearly with the current. When the current exceeds 1 A, their torque growth gradually slows down. This is caused by the magnetization characteristics of MRF. When the magnetic field is relatively low, the MRF’s shear stress increases linearly with the magnetic field. As the magnetic field gradually rises, MRF gradually approaches its magnetic saturation state and the corresponding MRF’s shear stress slows down with the magnetic field due to the rheological effect. It can be seen that, for the flat disk, the theoretical value and the experimental test value are relatively close. However, there is, for the elliptical disk, indeed an error between the theoretical value and the experimental test value. We believe the difference is probably caused by the fact that it is difficult for the magnetorheological fluid to fill up every corner of the gap in the elliptical disk surface, which is relatively easy in the flat disk surface. In addition, due to the error of the manufacturing accuracy of the energized coil, it is hard to guarantee that the magnetorheological fluid in each gap can reach magnetic saturation. The magnetic field generated by the fluid at the trough and peak is quite lower than when the fluid is in saturation state, resulting in the experimental value lower than the theoretical one. However, when the current increases and the magnetic field is larger, the test value is closer to the theoretical value.

Fig. 23.

Magnetic transfer torque vs. current.

At the same time, comparison between the elliptical disk and the flat disk MRF couplings indicates that a certain torque growth rate can still maintain at a large current for the elliptical corrugated disk while the torque increases more slowly for the flat disk coupling. The transfer torque of our elliptical disk MRF coupling, which is up to 905 N ⋅ m, is about 25% higher than that of the flat disk MRF coupling (720 N ⋅ m) when they are approaching saturation. The theoretical results do not completely correspond to the simulation results under different currents, but the trending for both are very close because they are basically the same when the magnetorheological fluid is in a magnetic saturation state.

(3) Comparison of their torque densities

The elliptical coupling is divided into the input, transfer and output parts in accordance with their radial radiuses, whose overall volume is 14856041.9 mm³. The torque density is 0.0609 N/mm² which is equal to the maximum transfer torque (905 N ⋅ m) divided by the volume. The torque densities were calculated for other MRF torque transfer units in the literature [14–17] and comparison was performed between theirs and ours. The comparison indicates that the torque density of our MRF coupling almost doubled, as shown in Fig. 24.

Fig. 24.

Comparison of the torque densities.

5. Conclusions

(1) An elliptical disk MRF coupling based on the mixed shear-pressure working mode was proposed here by harnessing the mechanism of arc flux linkages. Its torque transfer mechanical model was established and its performance was evaluated by theoretical simulation. Finally, the theoretical simulation results were experimentally verified in the test bench. (2) Simulation results indicate when the number of waves in the disk is 15 and the semi-major and semi-minor axes of the ellipse are 30 mm and 6 mm, the torque transfer performance reaches the optimal. (3) The experimental results showed that the maximum magnetic output torque of the elliptical disk can be up to 905 N ⋅ m, which increases by 25% compared to that of a flat multi-disk coupling (720 N ⋅ m) with the same dimensions. And the torque density of the proposed MRF coupling is 0.0609 N/mm² at least double-folded in comparison to that of the torque transmission devices in other literatures.

Footnotes

Acknowledgements

This research was supported by the Open Research Fund of Defense Key Disciplines Laboratory of Ship Equipment Noise and Vibration Control Technology, Shanghai Jiaotong University (Fund No. VSN201901). Their supports are gratefully acknowledged.

References

Kakoc

Park

E.J.

and Suleman

, Design considerations for an automotive magnetorheological brake, Mechatronics 18 (2008), 434–447.

Koichiro

Wataru

and Toshinobu

, Magnetic and rheological properties of monodisperse Fe₃O₄ nanoparticle/organic hybrid, Journal of Magnetism and Magnetic Materials 321(5) (2009), 450–457.

Bossis

Volkova

Lacis

and Meunier

, Magnetorheology: Fluids, structures and rheology, Lecture Notes in Physics 594 (2003), 202–230.

Ciocanel

Elahinia

M.H.

Molyet

K.E.

, Design analysis and control of a magnetorheological fluid based torque transfer device, International Journal of Fluid Power 9(3) (2008), 19–24.

Senkal

and Gurocak

, Serpentine flux path for high torque MRF brakes in haptics applications, Mechatronics 20(3) (2010), 377–383.

Kikuchi

Otsuki

Furushoet

, Development of a compact magneto rheological fluid clutch for human-friendly actuator, Advanced Robotics 25(10) (2010), 1362.

Bucchi

Forte

Franceschini

, Analysis of differently sized prototypes of an MR clutch by performance indices, Smart Materials & Structures 22(10) (2013), 105009.

Hung Nguyen

Diep Nguyen

and Bok Choi

, Design and evaluation of a novel magnetorheological brake with coils placed on the side housings, Smart Materials & Structures 24(4) (2015), 047001.

Nguyen

Q.H.

and Choi

S.B.

, Optimal design of a novel hybrid MR brake for motorcycles considering axial and radial magnetic flux, Smart Materials & Structures 21(5) (2012), 55003–55012.

10.

Dong

and Wang

, Prototype and test of a novel rotary magnetorheological damper based on helical flow, Smart Materials & Structures 25(2) (2016), 025006.

11.

Sarkar

and Hirani

, Theoretical and experimental studies on a magnetorheological brake operating under compression plus shear mode, Smart Materials & Structures 22(11) (2013), 5032.

12.

Wang

D.H.

Song

W.L.

, Effect of surface texture and working gap on the braking performance of the magnetorheological fluid brake, Smart Materials & Structures 25(10) (2016).

13.

Tongfei

and Nakano

, Design and testing of a rotational brake with shear thickening fluids, Smart Materials & Structures 26(3) (2017), 035038.

14.

Hui

Chunni

Long

, Design and research of a novel magnetorheological fluid coupling with cycloid corrugated surface, International Journal of Applied Electromagnetics and Mechanics 2 (2019), 1–24.

15.

Park

E.J.

Stoikov

da Luz

L.F.

and Suleman

, A performance evaluation of an automotive magnetorheological brake design with a sliding mode controller, Mechatronics 16(7) (2006), 405–416.

16.

Peng

, The design of high-torque disc-shaped magnetorheological clutch, Journal of Test and Measurement Technology 2 (2014), 119–122.

17.

Shiao

and Nguyen

Q.A.

, Development of a multi-pole magnetorheological brake, Smart Materials & Structures 22(6) (2013), 24–34, 065008.