Theoretical analysis and experimental study of the characteristics of magnetic fluid seal with a large diameter at high/low temperatures

Abstract

The sealing of large diameter rotating shaft in some special applications especially in aerospace and military industry needs to be sealed with magnetic fluids. However, the major problems of restricting the application of large diameter magnetic fluid rotary seal is the decrease of the pressure-resistance capacity of magnetic fluid seal at high temperatures and the bigger breakaway torque at low temperatures. To research effect of the temperature on the pressure-resistance capacity and breakaway torque of large diameter magnetic fluid seal, a sealing device with the diameter size of rotary shaft for 190 mm and the sealing gap for 0.1 mm was designed. Through the experimental test studied on the pressure-resistance capacity at −55 °C–70 °C and the breakaway torque at −55 °C–20 °C, exploring the influence rules of injection volumes of magnetic fluid and the standing time on the breakaway torque under at −55 °C. The experimental results show that the decrease of the saturation magnetization of magnetic fluid at high temperatures result in the pressure-resistance capacity falls, and the increase of the magnetic fluid viscosity at low temperatures is the key factors which causes the bigger breakaway torque. In theory, the analytical expression of between the viscous drag torque and the temperatures were derived, which could qualitatively explain the experimental rules of between the breakaway torque and the temperature at −55 °C–20 °C. In addition, the breakaway torque of magnetic fluid seal increases as the addition of the standing time and eventually becomes stable at −55 °C, and between the breakaway torque and the injection volumes of magnetic fluid showed a linearly change.

Keywords

magnetic fluid seal high/low temperature large diameter breakaway torque pressure-resistance capacity

1. Introduction

Magnetic fluids, also called ferrofluids or magnetic liquids, are a kind of colloidal soft materials whose behaviors can be strongly influenced by the presence of an external magnetic field, which is composed of magnetic solid particles with a size of 8–10 nm diffusely distributed in a nonmagnetic carrier fluid [1,2]. As the nanoparticles are thoroughly coated with the chain-like surfactant and dispersed evenly in the carrier fluid, magnetic fluids can remain stable without clumping and sedimentation in a long period when a strong magnetic field gradient is applied to the magnetic fluids [3]. And magnetic fluids will be moved to the place with highest magnetic flux density in the seal gap under the external magnetic field. Thus the magnetic fluid seal belongs to non-contact technical seals, which is a new type of fluid sealing technology. Compared with other conventional seals, which has prominent advantages: no leakage, long life, high rotational speed capability and low viscosity friction, so it has a broad development prospect and important value of engineering applications in aerospace, military equipment, mechanical engineering and other fields [4,5].

Magnetic fluid seal is one of the earliest and most successful applications of magnetic fluids. At present, magnetic fluid seals have been used in a wide variety of sealing applications to solve the leakage problems between two different pressure regions of vacuum or gas sealing in the medium and low rotational speed, also in the medium and small shaft diameter [6]. Also, the experimental results of sealing liquids have made great progress, such as Y. Mitamura of Japan [7,8], Leszek Matuszewski, and Zbigniew Szydlo of Polan [9,10], Y. S. Kim of South Korea [11,12], Decai Li of China [13,14]. However, the large shaft diameter, high/low temperatures and other complicated working conditions for important engineering application problems of magnetic fluid seals need to be solved, exploring the experimental laws of a large diameter magnetic fluid seal at high/low temperatures, which can be applied to solve the sealing problems of large diameter rotating shaft in aerospace, military industry equipment and other fields. The pressure-resistance capacity of magnetic fluid seal drops linearly with the temperature rises, and the breakaway torque of large diameter magnetic fluid seal increases sharply with the temperature decreases, the above mentioned these problems severely affect the engineering application of magnetic fluid seals. Therefore, in this paper the experimental investigation of sealing performance of large diameter magnetic fluid seal will provide an important practical reference basis for the engineering applications at high/low temperatures.

Though many experts have studied the sealing problems of magnetic fluid, but the pressure-resistance capacity of magnetic fluid seal at high temperatures and the breakaway torque of magnetic fluid seal at low temperatures are rarely researched especially on the large diameter magnetic fluid seals. At −40 °C, the experimental investigation on the influence laws of number of sealing stages and the standing time at normal temperature on the breakaway torque of large diameter magnetic fluid seal by Decai Li et al., but lack of theoretical analysis on the experimental results at low temperatures [15]. The static seal of magnetic fluid with a diameter size of magnetic fluid ``O” ring larger than 600 mm of the flange was designed by Xinzhi He et al., the change rules of between the pressure-resistance capacity and number of sealing stages was experimentally studied at normal temperature, also the leakage rate of the large diameter flange was measured [16]. The pressure-resistance capacity of a static seal with the diameter of magnetic fluid ``O” ring larger than 390 mm was studied at 20 °C–120 °C by Decai Li et al., and the larger seal gap respectively was 1.0 mm, 1.5 mm, 2.0 mm and 2.5 mm [17].

The above mentioned mostly concentrated on the pressure-resistance capacity of large diameter magnetic fluid seal under at normal temperature or the large seal gap, which can’t fully reflect the change rules of the pressure-resistance capacity or the breakaway torque. And for the large diameter magnetic fluid seals, recent studies lack of the variation regularity of the breakaway torque at −55 °C–20 °C and the pressure-resistance capacity at −55 °C–70 °C, this paper will fill this significant blank. In the paper, a sealing device with the diameter size of rotary shaft for 190 mm and the sealing gap for 0.1 mm was designed, the analytical expression of the viscous drag torque of magnetic fluid and the pressure-resistance capacity of magnetic fluid seal with the change of the temperature were deduced theoretically. We used a commercially engine oil-based, ester-based and kerosene-based magnetic fluid in Table 1, through the experimental research on the pressure-resistance capacity of magnetic fluid seals at −55 °C–70 °C and the breakaway torque of magnetic fluid seals at −55 °C–20 °C, the other the influence rules of injection volumes of magnetic fluids and standing time on the breakaway torque at −55 °C. Finally, the results of the experiments were analyzed and discussed.

Table 1
The main characteristic of the three fluids

Nanoparticles Freezing point

Magnetic Magnetic mean Viscosity Density of the carrier

fluid nanoparticles sizes (nm) (mpa ⋅ s) (g/cm³ ) liquid (°C)

Engine oil-based Fe₃O₄ 10 24 1.36 −33

Ester-based Fe₃O₄ 10 28 1.22 −20

Kerosene-based Fe₃O₄ 10 21 1.32 −40

		Nanoparticles			Freezing point
Engine oil-based	Fe₃O₄	10	24	1.36	−33
Ester-based	Fe₃O₄	10	28	1.22	−20
Kerosene-based	Fe₃O₄	10	21	1.32	−40

2. Theoretical derivation on the pressure-resistance capacity and viscous drag torque of magnetic fluid seal

2.1. The pressure-resistance capacity of magnetic fluid seal

The magnetic fluid Navier–Stokes equation is given in Eq. (1) [1]: $\begin{eqnarray}\displaystyle {\rho}_{f}\frac{dv}{dt} & = & \displaystyle {\rho}_{f}g-{\nabla}\left[p+{\mu}_{0}\int _{0}^{H}MdH-{\mu}_{0}\int _{0}^{H}{\rho}_{f}\frac{\partial M}{\partial {\rho}_{f}}dH\right]+{\mu}_{0}M\bullet {\nabla}H+{\mu}_{H}{\nabla}^{2}V\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle +∼\frac{1}{3}{\eta}_{H}{\nabla}({\nabla}\bullet v)+\frac{J}{2t_{s}}{\nabla}\times ({\omega}_{s}-{\omega}_{1}).\end{eqnarray}$ (1) The continuity Eq. (2) of magnetic fluid is given [1]: $\begin{eqnarray}\frac{\partial {\rho}_{f}}{\partial t}+{\nabla}\bullet ({\rho}_{f}\boldsymbol{v})=0.\end{eqnarray}$ (2)

Where 𝜌_f is the density of magnetic fluid, M is the magnetization intensity of magnetic fluid, v is the velocity of magnetic fluid, p is the pressure of magnetic fluid, g is the acceleration of gravity, 𝜇₀ is the magnetic permeability in vacuum, H is an external magnetic field strengthen, 𝜂_H is the dynamic viscosity of magnetic fluid, ω_s is the angular velocity of nanoscale magnetic particles t _s is the relaxation time of magnetic particles, ω₁ is the vortex velocity of magnetic fluid.

Assuming that the density of magnetic fluid is 𝜌_f = constant, the flow is irrotational, the relative motion of between magnetic nanoparticles in the carrier fluid is ignored. The Bernoulli equation of magnetic fluid is obtained in Eq. (3): $\begin{eqnarray}{\nabla}\left[-{\rho}_{f}\frac{\partial {\phi}_{s}}{\partial t}+\frac{1}{2}{\rho}_{f}v^{2}+{\rho}_{f}gh+p^{\ast }-{\mu}_{0}\int _{0}^{H}MdH\right]+{\mu}_{0}\int _{0}^{H}\frac{\partial M}{\partial T}{\nabla}TdH=0.\end{eqnarray}$ (3) If the flow of magnetic fluid is isothermal, 𝛻T = 0. Or the temperatures of flow field is much lower than the curie temperature, $\partial M/\partial T = 0$ ; The flow of magnetic fluid is steady, hence (3) can be simplified as into Eq. (4) $\begin{eqnarray}p^{\ast }+\frac{1}{2}{\rho}_{f}v^{2}+{\rho}gh-{\mu}_{0}\int _{0}^{H}MdH=C.\end{eqnarray}$ (4) Where C is an integral constant determined by the boundary condition, p ^∗ is the composite pressure of magnetic fluid, p ^∗ = p + p _m + p _s, p _m is the magnetization pressure of magnetic fluid, p _s is the magnetostrictive pressure of magnetic fluid $\begin{eqnarray}\displaystyle \mbox{}&\mbox{}& p_{m}={\mu}_{0}\int _{0}^{H}MdH & & \displaystyle \nonumber\\ \displaystyle \mbox{}&\mbox{}& p_{s}=-{\mu}_{0}\int _{0}^{H}{\rho}_{f}\frac{\partial M}{\partial {\rho}}dH. & & \displaystyle \nonumber\end{eqnarray}$

Besides, the boundary condition is given below $\begin{eqnarray}e_{n}^{0}({\tau}_{1}-{\tau}_{2})=-[(p_{1}^{\ast }p_{1n})-(p_{2}^{\ast }+p_{2n})]e_{n}^{0}.\end{eqnarray}$ (5) Where, $p_n=M^2_n/2,e^0_n$ is a normal unit vector, the subscript 1 and 2 represent the two group parameters of magnetic fluid in both adjacency sides, τ is the surface stress, p _c = σ(1∕𝜌₁ + 1∕𝜌₂) is the surface tension. $\begin{eqnarray}e_{n}^{0}({\tau}_{1}-{\tau}_{2})=-{\sigma}\left(\frac{1}{{\rho}_{1}}+\frac{1}{{\rho}_{2}}\right)e_{n}^{0}\end{eqnarray}$ (6) 𝜌₁ and 𝜌₂ represents the two principal radius of curvature. σ is a surface tension constant. Substituting p _c into the Eq. (6) $\begin{eqnarray}p_{1}^{\ast }+p_{1n}=p_{2}^{\ast }+p_{2n}+p_{c}.\end{eqnarray}$ (7) If subscript 2 denotes non-magnetic fluid and subscript 1 denotes magnetic fluid whose magnetization intensity M is proportional to the density, the Eq. (7) becomes $\begin{eqnarray}p_{1}^{\ast }+p_{1n}=p_{2}+p_{c}.\end{eqnarray}$ (8)

If the gravity of magnetic fluid is ignored. And Magnetic lines approximately are replaced by arcs and magnetic force lines are coincidence. In addition, without consider the surface tension of magnetic fluid.

Combining the magnetic fluid Navier–Stokes equation, the continuity equation of magnetic fluid with the boundary conditions and the assuming conditions, the one-stage pressure-resistance formula of magnetic fluid is derived in Eq. (9) $\begin{eqnarray}{\nabla}_{p}=p_{1}-p_{2}={\mu}_{0}\int _{H_{2}}^{H_{1}}MdH.\end{eqnarray}$ (9) Where 𝛻_p is the pressure value of one-stage magnetic fluid seal, H ₁ and H ₂ are the magnetic field intensity on the two sides of the interfaces.

2.2. The viscous drag torque for magnetic fluid seal

Magnetic fluid seal is a non-contact type seal without contact friction between solids, but the viscosity of magnetic fluid increases in the presence of an external magnetic field or at low temperatures. Therefore, the rotational motion of rotating shaft for magnetic fluid seal needs to overcome the viscous drag torque of magnetic fluid in the presence of an external magnetic field or at low temperatures. The pole pieces with sealing stages are stationary, and the rotating shaft of magnetic fluid seal is rotary, so magnetic fluid seal can be simplified as a two-dimensional motion model for the inner cylinder to rotate and the outer cylinder to remain stationary, as shown in Fig. 1.

Fig. 1.

The schematic diagram of two dimensional model of magnetic fluid seal.

The analytical solution of its tangential velocity for two-dimensional model is given $\begin{eqnarray}\frac{u}{u_{1}}=\frac{r_{1}/r_{2}}{1-(r_{1}/r_{2})^{2}}\cdot \frac{1-(r/r_{2})^{2}}{r/r_{2}};\quad u_{1}={\omega}r_{1}.\end{eqnarray}$ (10) In the cylindrical coordinate system, V _r = 0, V _𝜑 = 0, V _θ = u, the viscous shear stress is derived from Navier–Stokes equation for magnetic fluids $\begin{eqnarray}{\tau}_{r,{\theta}}={\eta}\left(\frac{\partial V_{{\theta}}}{\partial r}\frac{\partial V_{r}}{r\partial {\theta}}\frac{V}{r}\right)=2n\frac{{\omega}r_{1}^{2}r_{2}^{2}}{(r_{2}^{2}-r_{1}^{2})r^{2}}.\end{eqnarray}$ (11)

Therefore, the viscous drag torque of magnetic fluids acting on the cylinder surface of the rotary shaft can be obtained as follows $\begin{eqnarray}T_{n}=2{\pi}r_{1}\cdot l\cdot {\tau}_{r,{\theta}}\cdot r_{1}=4{\pi}\frac{{\eta}l{\omega}r_{1}^{2}r_{2}^{2}}{r_{2}^{2}-r_{1}^{2}}.\end{eqnarray}$ (12) Where 𝜂 is the dynamic viscosity of magnetic fluid; ω is the angular velocity of the rotating shaft, l is the total contact axial length between rotary shaft and magnetic fluid in the sealing gap; r ₁ is the radius of the rotating shaft; r ₂ is the inner radius of pole pieces.

3. Experimental System and Method

3.1. Experimental System

In Fig. 2 was presented the sealing structure of an large diameter magnetic fluid seal for testing the pressure-resistance capacity and the breakaway torque which was mainly composed of rolling bearings permanent magnets, hollow rotary shaft, magnetoconductive pole pieces magnetic shield, casing and end cover. In the test, using the shape dimensions of the cylinder neodymium iron boron (Nd–Fe–B) permanent magnet was 𝛷8 × 6 mm, the pole pieces and rotary shaft were manufactured with magnetic material of 2Cr13, the casing, end cover and magnetic shield were manufactured with non-conducted magnetic material of 304 stainless steel. The basic features of sealing structure used in the experiment is given as follows: the pole tooth of pole pieces are rectangular, the rotary shaft diameter is 𝛷 = 190 mm, the sealing gap is L _g = 0.1 mm, the width of single sealing tooth is L _t = 0.2 mm, the width of alveolus of pole pieces are L _s = 0.8 mm, the height of pole tooth is L _h = 0.7 mm (please see partial enlarged view A). The permanent magnet, pole pieces and rotary shaft composes a closed magnetic circuit, magnetic fluid is adsorbed in the sealing gap between the pole piece and rotating shaft under the presence of an external strong magnetic field, so on the top of the pole tooth will form multistage liquid “O” ring for achieving to the purpose of sealing. The experimental measurement device for measuring the pressure-resistance capacity and the breakaway torque of magnetic fluid seal is shown in Fig. 3 which mainly includes TD-G-C type nitrogen charging equipment, pressure reducing valve, precision pressure gauge, sealing test chamber, 8 m³ high/low temperature test box, etc.

Fig. 2.

The structure of the large diameter magnetic fluid seal.

Fig. 3.

The experimental apparatus for magnetic fluid seals.

3.2. Test methods for the pressure-resistance capacity of magnetic fluid seal

In the experiments, a commercially available engine oil-based, ester-based and kerosene-based magnetic fluid was used for studying the pressure-resistance capacity of magnetic fluid seal. In Fig. 4, shows the magnetization curves of the three magnetic fluids at normal temperature measured in a Lakeshore vibrating sample magnetometer (VSM). From Fig. 4, we can figure out that the saturation magnetization values of the engine oil-based and kerosene-based magnetic fluids are very close.

Fig. 4.

The magnetization curves of the three magnetic fluids.

Firstly, inject a certain quantity of magnetic fluid in the sealing gap. Then, install the sealing experimental device on the sealing test chamber and put into the 8 m³ high/low temperature test box for raising or lowering the temperature, through the control panel to adjust the temperature of 8 m³ high/low temperature test box respectively reached to 70 °C, 50 °C, 25 °C, 0 °C, −20 °C, −40 °C, −55 °C. The pressure value would be measured after the standing time of magnetic fluid seal reached to 2 hours under at the set temperature conditions In addition, filling the sealing test chamber with nitrogen, and by adjusting the pressure reducing valve to control the amount of gas was filled into the sealing test chamber, at the same time filling into the sealing test chamber with 0.01 MPa nitrogen every 30 s and observing 20s. And until the leakage occurs in the magnetic fluid seal, then recording the display value of the precision pressure gauge directly connected to the sealing test chamber.

3.3. Test methods for the breakaway torque of magnetic fluid seal

In the test, a commercially available engine oil-based, ester-based and kerosene-based magnetic fluid was applied to studying the effect of the temperature on the breakaway torque. The main contents of the experimental study included: (1) the magnetic fluid sealing device was respectively cooled to 20 °C, 0 °C, −10 °C, −20 °C, −30 °C, −40 °C, −55 °C in the 8 m³ high/low temperature test box, and standing time for 2 hours at each temperatures then measured the breakaway torque; (2) the magnetic fluid sealing device was respectively put in the 8 m³ high/low temperature test box for 1 h, 3 h, 5 h, and 7 h, then measured the breakaway torque; (3) through injected different volumes of magnetic fluid into the experimental seal device at −55 °C, then the standing time for 2 hours to measure the variation relationship of between the breakaway torque and volumes of magnetic fluid.

4. Analysis of results and discussion

4.1. The relation between the pressure-resistance capacity and the temperature

Fig. 5 reflects the overall variation of the pressure-resistance capacity of magnetic fluid seal, which gradually increases as the temperature decreases. At −29.5 °C, the two pressure-resistance capacity curves of engine oil-based and ester-based magnetic fluids intersect. At −55 °C–−29.5 °C, the pressure-resistance capacity of esterbased magnetic fluid seal is higher than engine oil-based magnetic fluid. At −29.5 °C–70 °C, the pressure-resistance capacity of esterbased magnetic fluid seal is lower than engine oilbased magnetic fluid. The pressure-resistance capacity curves of both ester-based magnetic fluid seal at 0 °C–70 °C and engine oil-based magnetic fluid seal at 20 °C–70 °C could be approximated as a linearly change, the former and the latter had a similar change rate.

Fig. 5.

The influence of temperature on the pressure resistance of magnetic fluid seal.

According to the pressure-resistance Eq. (9) without considering the viscosity change of the magnetic fluid or the effect of the temperature on the viscosity varies little the pressure-resistance capacity of magnetic fluid seal is related to the saturation magnetization intensity of magnetic fluid and the magnetic field intensity in the seal gap. However, the magnetic field intensity in the seal gap is mainly related to the size of the seal gap, the size of the seal gap was fixed in the experimental process. The experimental pressure value of the three magnetic fluids at normal temperature were measured in Table 2. From Table∼2, we can obtain that the pressure value of the engine oil-based and kerosene-based magnetic fluids are very close and higher than the ester-based magnetic fluid. Since the magnetization intensity of magnetic fluid is affected by the temperature, we will discuss the influence of temperature on the pressure-resistance capacity of magnetic fluid. The magnetization intensity of magnetic fluid M is obtained [2] $\begin{eqnarray}M(H)=mn\left[\coth \left(\frac{mH}{KT}\right)-\frac{KT}{mH}\right].\end{eqnarray}$ (13) Where m is the magnetic moment of single magnetic particle, n is the particles number per unit, K is Boltzmann constant, K =1.36 ×10⁻²³ J⋅K⁻¹, T is the absolute temperature. At the adjacent field of the pole tooth, there is a very strong magnetic field intensity H. So the below equation can be obtained $\begin{eqnarray}1\ll mH/KT.\end{eqnarray}$ Then coth (mH∕KT) ≈1, and the magnetization intensity at the adjacent field intensity of the pole tooth M is $\begin{eqnarray}M(H)=mn\left(1-\frac{KT}{mH}\right).\end{eqnarray}$ (14) When the magnetization intensity M(H) of magnetic fluid reaches the saturation state, the one-stage sealing pressure 𝛻p is $\begin{eqnarray}{\nabla}p\approx \int _{H(A)}^{H(B)}MdH\approx M[H(B)][H(B)-H(A)].\end{eqnarray}$ (15)

Table 2

The pressure values of the three magnetic fluids at normal temperature

Engine oil-based magnetic fluid	Kerosene based magnetic fluid	Ester-based magnetic fluid
0.109 MPa	0.105 MPa	0.09 MPa

Substitute M(H) into the Eq. (15) can be obtained $\begin{eqnarray}{\nabla}p\approx {\mu}_{0}mn[H(B)-H(A)]\frac{kn[H(B)-H(A)]}{H(B)}T.\end{eqnarray}$ (16)

In addition, the expression relations (14) of between the magnetization intensity M and the absolute temperature T can be expressed as $\begin{eqnarray}M(T)=K_{M}(T_{c}-T).\end{eqnarray}$ (17)

Where $\begin{eqnarray}\displaystyle K_{M} & = & \displaystyle \frac{nK}{H}\nonumber\\ \displaystyle T_{c} & = & \displaystyle \frac{mH}{K}.\nonumber\end{eqnarray}$

Derivatives for the Eq. (17) $\begin{eqnarray}\frac{\partial M}{\partial T}=-K_{M}.\end{eqnarray}$ (18)

K _M has nothing to do with the temperature, the negative sign on the right side of the Eq. (18) indicates that the magnetization intensity of magnetic fluid is inversely proportional to the temperature. Since the magnetic nanoparticles with a mean diameter of 10 nm diffusely distributed in the carrier liquid, so they are monodomain or subdomain, and similar to a magnetic gas molecules with a magnetic moment m [18]. The magnetization process of magnetic fluid can be explained that the effect of an external magnetic field causes the magnetic moment of magnetic particles will be as parallel as possible to the direction of an external magnetic field, due to the Brown moment is generated by the thermal motion of magnetic particles causes that the magnetic moment of magnetic particles cannot be completely parallel to the direction of an external magnetic field, thus there is an angle between them [19]. When the magnetic moment of magnetic particles is produced by the external magnetic field is balanced with the Brown moment is generated by the thermal motion of magnetic particles, magnetic fluid reaches a saturated magnetization state. At high temperatures, the thermal motion of magnetic particles increases resulting in the increase of the Brown moment, while the magnetic moment is generated by external magnetic field remains unchanged. Therefore, the angle of between the magnetic moment of magnetic particles and an external magnetic field becomes larger which mean that the saturation magnetization intensity of magnetic fluid will decrease. At low temperatures, the saturation magnetization intensity of magnetic fluid will increase.

From Eq. (16), it can be seen that there is a linear variation between the pressure-resistance capacity and the temperature. But the pressure capacity of experimental results in Fig. 5 show that the pressure capacity increases nonlinearly with the temperature decreasing. According to Eq. (18), it can be seen that there is a linear variation between the magnetization intensity and the temperature, and the effect of the saturation magnetization intensity with the temperature decreasing on the pressure capacity is that the pressure capacity increases linearly. Therefore, for the pressure capacity of experimental results at 0 °C–−55 °C with the temperature decreasing increases nonlinearly which can be attributed to the viscosity increases of magnetic fluid at low temperature besides the effect of the saturation magnetization on the pressure-resistance capacity. Compared with engine oil-based magnetic fluid, the pressure-resistance curve of ester-based magnetic fluid increases faster than that of engine oil-based magnetic fluid in the temperature drops process, which can be attributed to the viscosity of ester-based magnetic fluid increases faster than that of engine oil-based magnetic fluid with the temperature decreasing. In addition, the pressure-resistance capacity of the experimental results linearly decreases with the increase of the temperature at 0 °C–−70 °C, which can be attributed to the saturation magnetization falls with the temperature rising. And we can see the viscosity changes little with the temperature rising at 10 °C–60 °C from Fig. 7, thus the viscosity has little influence on the pressure-resistance capacity at high temperature

4.2. The relation between the breakaway torque and the temperature

As shown in Fig. 6 the difference of the breakaway torque between engine oil-based, ester-based and kerosene-based magnetic fluid is not significant at 20 °C, while it gradually increases as the temperature decreasing. At −55 °C, the difference of the breakaway torque between engine oil-based, ester-based and kerosene-based magnetic fluid is the largest In addition, the experimental results show that the bearing friction torque of the magnetic fluid sealing device without magnetic fluid almost the same with the temperature decreasing According to the viscous drag torque of magnetic fluid seal in Eq. (12), the influence factors on the viscous drag torque of magnetic fluid seal except for the radius r ₁, r ₂ and the angular velocity ω of rotary shaft, it is also related to the viscosity 𝜂 of magnetic fluid and the total contact axial length l of between rotary shaft and magnetic fluid in the sealing gap. However, the viscosity 𝜂 of magnetic fluid is mainly influenced by temperature T, magnetization intensity M, and shear rate 𝛾, so the viscosity 𝜂 can be expressed as $\begin{eqnarray}{\eta}={\eta}({\eta}_{0},M,H,T,{\gamma}).\end{eqnarray}$ When magnetic fluid is in low concentrations the viscosity 𝜂 of magnetic fluid can be expressed by Einstein’s formula $\begin{eqnarray}{\eta}={\eta}_{0}\left(1+\frac{5{\phi}}{2}\right).\end{eqnarray}$ (19)

Fig. 6.

The influence of temperature on the breakaway torque of magnetic fluid seal.

Fig. 7.

The viscosity-temperature curves of the three magnetic fluids.

When magnetic fluid is in high concentrations, the viscosity 𝜂 of magnetic fluid can be expressed as $\begin{eqnarray}{\eta}={\eta}_{0}(1-{\phi})^{-\frac{5}{2}}.\end{eqnarray}$ (20) Where 𝜙 is the volume fraction of magnetic particles in the magnetic fluid. According to the Eq. (19) or (20) we can be known that the viscosity of magnetic fluid is mainly affected by the viscosity 𝜂₀ of the carrier fluid and the volume fraction 𝜙 of magnetic particles. The viscosity 𝜂₀ of the carrier liquid can be expressed as [21] $\begin{eqnarray}{\eta}_{0}=A\cdot \exp \left(\frac{B}{T}\right).\end{eqnarray}$ (21) Where A represents a constant without physical meaning, B = E _a∕K, K is Boltzmann constant. Substituting (19) or (20) into (21) hence the viscosity 𝜂 of magnetic fluid becomes $\begin{eqnarray}{\eta}=A\cdot \exp \left(\frac{B}{T}\right)\left(1+\frac{5{\phi}}{2}\right)\quad \text{or}\quad {\eta}=A\cdot \exp \left(\frac{B}{T}\right)(1-{\phi})^{\frac{5}{2}}.\end{eqnarray}$ (22)

According to Eq. (22), we can be known that the change of viscosity of magnetic fluid with the temperature is mainly influenced by the viscosity of the carrier liquid and the volume fraction of magnetic particles. Substituting (22) into (12) the equation between the viscous drag torque T _n and the temperature T can be obtained in Eq. (23) $\begin{eqnarray}\displaystyle T_{n}=4{\pi}\frac{l{\omega}r_{1}^{2}r_{2}^{2}}{r_{2}^{2}-r_{1}^{2}}\cdot A\cdot \exp \left(\frac{B}{T}\right)\left(1+\frac{5{\phi}}{2}\right) & & \displaystyle \nonumber\\ \displaystyle \text{or}∼T_{n}=4{\pi}\frac{l{\omega}r_{1}^{2}r_{2}^{2}}{r_{2}^{2}-r_{1}^{2}}\cdot A\cdot \exp \left(\frac{B}{T}\right)(1-{\phi})^{-\frac{5}{2}}. & & \displaystyle\end{eqnarray}$ (23)

According to formula (23), we can draw a conclusion that the viscous drag torque of magnetic fluid seal increases with the temperature T decreasing, and it is consistent with the experimental results in Fig. 6, which can qualitatively explain that the increase of the breakaway torque at low temperatures are caused by the viscosity of magnetic fluid.

Since the rheological behavior of the magnetic fluids plays an important role in the increase of the breakaway torque of the magnetic fluid seals. To illustrate the rheological behavior of the magnetic fluids and study the breakaway torque of the magnetic fluid seals with the temperature changes, we measured the viscosity-temperature characteristics of the three magnetic fluids of zero magnetic field and an applied magnetic fields of 500 kA/m respectively in a temperature range from −10 °C to 60 °C with an Anton Paar MCR302 rotational rheometer, as shown in Fig. 7. In Fig. 7(a) and (b), we can both see that the viscosity of the magnetic fluid falls with the temperature rising and the viscosity falls sharply within the temperature range from −10 °C to 10 °C and then changes slowly afterwards, the temperature and an external magnetic fields have an huge influence on the viscosity characteristics of the magnetic fluid. And In Fig. 7(a), we can also see that the viscosity increase of the magnetic fluid under zero magnetic field with the temperature decreasing is very obvious. This can be attributed to the viscosity-temperature characteristics of the base carrier liquid of magnetic fluids. Therefore, the viscosity increase of magnetic fluids of an applied external magnetic fields at low temperature impact on the breakaway torque of the magnetic fluid seals. In the process of the temperature drops from 20 °C to −55 °C, the variation for the breakaway torque of ester-based magnetic fluid seal is the largest, the variation for the breakaway torque of kerosene-based magnetic fluid seal is the smallest, and the breakaway torque of magnetic fluid seal is mainly determined by the viscosity of magnetic fluid, which indicates that the viscosity of ester-based magnetic fluid increases with the temperature decreasing faster than engine oil-based and kerosene-based magnetic fluids. Besides, the viscosity of magnetic fluid at room temperature does not significantly change compared with at low temperatures, so the breakaway torque between the three magnetic fluid seals at 20 °C have little difference.

4.3. The relation between the breakaway torque and the standing time

As shown in Fig 8 the breakaway torque of magnetic fluid seal at −55 °C increases with the standing time increasing from 1 h to 4 h. While standing time exceeds 4 hours at −55 °C, the breakaway torque shows a decreasing trend with the increase of the standing time and eventually becomes stable, and the final value of the breakaway torque of esterbased magnetic fluid is larger than that of engine oil-based and kerosene-based magnetic fluids. In addition, in Fig. 8 also showed that the bearing friction torque of magnetic fluid sealing device without magnetic fluids almost the same at −55 °C. Cheng Yanhong et al. experimental investigation on the variation regularity of between the breakaway torque of perfluoropolyethers-based magnetic fluid rotating shaft seal and the standing time at normal temperatures, the experimental results showed that the breakaway torque increases with the standing time increasing and eventually becomes stable [22]. By the analysis of results showed that the viscosity was the major factor of affecting on the change of the breakaway torque with the standing time increases, agglomeration of magnetic particles were the essential reasons leading to the change and a slowly occurring process. Finally, under at normal temperatures and a strong external magnetic field, the sufficient time for the deposition of magnetic particles in perfluoropolyethers-based magnetic fluid was five days. Under the effect of a strong external magnetic field, the large magnetic particles will agglomerate as the standing time increasing, thus a large number of chain-like aggregates formed by nanoscale magnetic particles in the magnetic fluid, which will make the yield stress and the viscosity of magnetic fluid increase, thus the flow performance of magnetic fluid drops [23]. In addition, there are also reports that under specific conditions the linear chainlike aggregates are transformed to bulk dense droplike aggregates [24]. As an external magnetic field strengthen, the individual particles formed linear chains. The influence of chainlike and droplike aggregates on the rheology of ferrofluids was theoretically studied by Zubarev et al., who showed that droplike aggregates were formed in the magnetic fluids when the magnetic field exceeded a threshold value [25]. In Fig. 9(a) shows a schematic diagram of the drop-like structures model formed by nanoscale magnetic particles in the magnetic fluid, leading in the viscosity and yield stress of magnetic fluid increases, so the macroscopic appearance is that the breakaway torque increases. And in Fig. 9(b) shows a situation where the rotating shaft begins to rotate after standing for a period of time, the drop-like aggregates will be destroyed due to the rotation motion of the rotating shaft. The yield stress of magnetic fluids had an significantly influence on the breakaway torque especially at low temperatures, Chi Changqing et al. established a model in which the dipole chains were subjected to tensile action for studying on the yield stress [26], so it can be expressed as $\begin{eqnarray}{\tau}_{s}=n\frac{48{\mu}_{0}}{{\pi}d^{4}}m_{d}^{2}.\end{eqnarray}$ (24) Where n is the chains number of magnetic particles per unit, d is the diameter of magnetic particles, m _d is the mean magnetic moment of magnetic particles, 𝜇₀ is the vacuum permeability. The Brownian motion of liquid molecules of the carrier fluid reduces in the magnetic fluid at low temperatures, which causes the weakening of the thermal motion of magnetic particles, the mutual collision degree between magnetic particles in the magnetic fluid will reduce. Compared with at normal temperature, the flow performance of the carrier fluid and the thermal motion of magnetic particles in the magnetic fluid at low temperatures will decrease, this can help magnetic particles form more complex the chain-like and drop-like aggregates, resulting in the yield stress of magnetic fluid and the viscosity of magnetic fluid increases, thus the breakaway torque of magnetic fluid will significantly increase. When a strong external magnetic field gradient is applied to the magnetic fluids, the viscosity of the carrier fluid and the agglomeration of magnetic particles can reach the maximum degree at low temperatures, the complexity of the chain-like and drop-like structures will not increase, the magnetic fluid viscosity reaches its maximum value, so the breakaway torque of magnetic fluid seal will not increase and eventually becomes stable. When the standing time reaches to 4 h at −55 °C, the breakaway torque of magnetic fluid seal reaches its maximum value. The mainly reason is that the viscosity of the carrier fluid and the agglomeration of magnetic particles reaches to the maximum degree, resulting in that the viscosity and the yield stress of magnetic fluid will not increase, thus the breakaway torque of magnetic fluid seal will not increase with the standing time increasing at −55 °C and eventually becomes stable.

Fig. 8.

The influence of the standing time at −55 °C on the breakaway torque of magnetic fluid seal.

Fig. 9.

Sketch of the gap with nonseparated (a) and separated (b) domains.

4.4. The relation between the breakaway torque and injecting volumes of magnetic fluid

As shown in Figs 10, 11 and 12, the breakaway torque increases with the increase of the injection volumes of magnetic fluid at −55 °C, and between the breakaway torque and the injection volumes of magnetic fluid is almost a linear relation. The increase rate of the breakaway torque of ester-based magnetic fluid with the increase of the injection volumes of magnetic fluid is the fastest, while the increase rate of the breakaway torque of kerosene-based magnetic fluid with the increase of the injection volumes of magnetic fluid is the slowest. The breakaway torque with the increase of the injection volumes of magnetic fluid does not significantly increase at 20 °C. According to the viscous drag torque Eq. (12) the viscous drag torque is related to the total contact axial length l of between the rotating shaft and magnetic fluid in the sealing gap, and the main factor that determines the total contact axial length l is the injection volumes of magnetic fluid and the number of sealing stages. The more the number of sealing stages, the more the injection volumes of magnetic fluid, resulting in that the total length l becomes larger, and the surface contact area increases between the rotating shaft and magnetic fluid, so the rotary shaft needs to overcome the larger breakaway torque when the rotating shaft starts. For the magnetic fluid seal, when the injection volume of magnetic fluid gradually increases, the rise rate of the pressure-resistance capacity of magnetic fluid seal is faster. When the injection volume of magnetic fluid reaches a certain magnitude, the pressure-resistance capacity of magnetic fluid seal will not increase with the injection volume increases. When the injection volumes of magnetic fluid exceeds the certain magnitude, the pressure-resistance capacity of magnetic fluid seal does not increase significantly as the injection volume increasing, but the breakaway torque of magnetic fluid seal may be greater at low temperatures, which indicates that there is an optimal injection volumes of magnetic fluid in the magnetic fluid seal. According to different requirements of the magnetic fluid seal to design the size of sealing gap and the number of sealing stages, which can make the injection volumes in the sealing gap reach the optimal magnitude to improve the pressure-resistance capacity and the breakaway torque falls at low temperatures.

Fig. 10.

The influence of the injection volume of engine oil-based magnetic fluid on the breakaway torque of magnetic fluid seal.

Fig. 11.

The influence of the injection volume of ester-based magnetic fluid on the breakaway torque of magnetic fluid seal.

Fig. 12.

The influence of the injection volume of kerosene-based magnetic fluid on the breakaway torque of magnetic fluid seal.

5. Conclusion

In the paper, the author used an 8 m³ high/low temperature test box for simulating the actual high/low temperatures environment (at −55 °C–70 °C) to study on the performance of magnetic fluid seal with large diameter at high/low temperatures, such as the pressure-resistance capacity of the large diameter magnetic fluid seal at −55 °C–70 °C and the breakaway torque of the large diameter magnetic fluid seal at −55 °C–20 °C. As a result, the following some conclusions could be obtained:

(1) At high temperatures, the pressure-resistance capacity of magnetic fluid seal is mainly related to the saturation magnetization of magnetic fluid. At low temperatures, for the pressure capacity of experimental results at 0 °C–−55 °C with the temperature decreasing increases nonlinearly, which can be attributed to the viscosity increases at low temperature besides the effect of the saturation magnetization on the pressure-resistance capacity.

(2) The viscosity increases of magnetic fluid is a decisive factor for the increase of the breakaway torque with the temperature drops. The paper theoretically derived the analytical expressions of between the viscous drag torque and the temperature, which can qualitatively explain the experimental laws between the breakaway torque and the temperature (at −55 °C–20 °C).

(3) The breakaway torque increases at −55 °C as the standing time increases from 1 h to 4 h. While the standing time is more than 4 h at −55 °C, the agglomeration of magnetic particles and the viscosity of the carrier fluid reaches to the maximum degree in the magnetic fluid, resulting in that the viscosity and yield stress of magnetic fluid will not increase, thus the breakaway torque eventually becomes stable with the increase of the standing time.

(4) At −55 °C, the relation of between the breakaway torque and the injection volumes of magnetic fluid is linearly change. When the injection volumes of magnetic fluid exceeds the certain magnitude, the pressure-resistance capacity of magnetic fluid seal does not increase significantly as the increase of the injection volumes, but the breakaway torque may be greater at low temperatures. Therefore, we should rationally design the size of sealing gap and the number of sealing stages to improve its sealing performance according to the different requirements of the application situations and the pressure-resistance capacity.

Footnotes

Acknowledgements

The work was supported by the Fundamental Research Funds for the Central Universities (No. 2018YJS145) and the Creative Groups Development Program of the Ministry of Education of China (grant no. IRT17R07).

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		Nanoparticles			Freezing point
Magnetic	Magnetic	mean	Viscosity	Density	of the carrier
fluid	nanoparticles	sizes (nm)	(mpa ⋅ s)	(g/cm³ )	liquid (°C)
Engine oil-based	Fe₃O₄	10	24	1.36	−33
Ester-based	Fe₃O₄	10	28	1.22	−20
Kerosene-based	Fe₃O₄	10	21	1.32	−40