The FF seal uses the magnetic response properties of the FF to the magnetic field to seal. After injecting into the gap between the magnetic circuit formed by the magnetic pole pieces and the shaft, FF will become several “O”-shaped seals. The number of seal rings is also written as the seal stages. When the FF is affected by the external pressure, it moves in the heterogeneous magnetic field, but the uneven magnetic field will create a magnetic gradient to provide the magnetic force to fight against the external pressure, and reach a new balance in the end (Li, 2010; Yang and Li, 2016a).

Earlier, to get the maximum seal pressure of FF seals, WALOWIT, J A et al. (Szczech and Horak, 2017) had found the best structure of rectangular pole teeth, which can make the seal pressure equal at both sides of the pole teeth. Without being collided or scraped by the shaft, we can guarantee the seal performance of this structure easily. The sealing gap between the relatively rotating shaft and the pole shoes is the main working area of the FF seal. We often use a small seal gap such as 0.05–0.2 mm to improve the seal pressure of FF seals. However, the structure will be easily collided or scraped by the shaft, which could cause a decrease in the seal pressure or leakage. In particular, for the shaft with the big radial runout, the aforementioned structure is commonly unreliable. Most of the solutions to solve this problem are increasing the sealing gap between the relatively rotating shaft and pole shoes, but the seal pressure of the FF seal will decrease significantly. In Yang and Li (2016a), in order to solve this problem, X. Yang had studied a converging stepped FF seal for a large seal gap, which improves the seal pressure of the FF seal under the large gap. However, the complexity of the device and high requirements for installation reduce the reliability of the seal and add the difficulties of adding FF. In van der Wal et al. (2020), in order to solve the aforementioned problems, Karoen van der Wal proposed a FF seal whose magnetic source is an axial-charged ring magnet setting on the shaft. As shown in Figure 1A, the seal contains a nonmagnetic ring, an axial-charged ring magnet, and a nonmagnetic ring successively set on the shaft. Then, the FF will be injected into the seal gap to offer seal pressure. Inspired by this, we proposed a new structure of the FF seal using radial-charged magnetized magnetic rings as a magnetic source, as shown in Figure 1B. In terms of optimization of permanent magnets, many types of optimization are designed to avoid problems such as installation difficulties and uneven magnetization of the ring magnet. In He et al. (2014), to solve the aforementioned problems, D. Li had studied a magnet structure composed of many small cylindrical magnets and verified the seal pressure by experiments. It also certificated the feasibility of replacement with split magnets first. In publication (Wang) Szczech, M designed and analyzed the seal pressure of the FF seal by experiments, whose magnetic source is made up of a cylindrical magnet but did not propose the optimal design and application conditions of the magnetic source. In He et al. (2019) J. Liu made an optimized design and the simulation analysis of the various structures of the permanent magnets through the simulation analysis and provided a selection scheme for the magnetic source structure of large-diameter FF seals. However, the optimization design of the aforementioned scholars is only limited to the classic structure of the FF seal. There are still poor seal reliability and high scrap possibility caused by the shaft runout and installation difficulties. When the ring magnets have difficulties in processability, installation, and uneven magnetization, we can replace them with split magnets named FF split magnet seal, as shown in Figure 1C, which not only solve the problems but also provide enough magnetic field for seal.

As shown in Figure 3A, it is a classic rectangular pole teeth structure of FF seal whose seal gap (distance between pole teeth and shaft) is 0.1 mm. With this gap confirmed, we set the pole teeth width L_t, pole teeth distance L_s, and pole teeth height L_h as 0.2 mm,、0.8 mm,、and 0.7 mm, respectively. The design theory has been successfully applied to many FF seals (Chi, 1993; Zhao et al., 2006; Yang et al., 2013), which are well sealed and highly reliable under many situations. Due to their small size, pole teeth have poor processability and quality. The main shaft has unavoidable radial runout; therefore, when the seal gap is changing, the pole teeth get hurt easily and have poor sealing performance. So we let the newly structured FF radial-charged seal remove the pole teeth, as shown in Figure 3B. To solve the ring magnets’ problems of processability, installation, and uneven magnetization, we replaced ring magnets with split magnets. To install split magnets stably, we adjusted the structure of the nonmagnetic ring to a nonmagnetic foundation, as shown in Figures 3C,D, which can not only raise the magnetic field but also meet the positioning needs of split magnets.

At first, we found out the better structural parameter of the FF seal by FEA, as shown in Figure 4 and Table 1. Table 1 shows the structural size of the classic FF seal, the FF radial-charged seal, and the FF split magnet seal. We set the shaft of the seal as 30 mm to make the calculation more accurate and reduce the calculation time. Then, we used FEA to compare the seal pressure of these structures and analyze the best choice of split magnets, in order to get the optimal structural design of the FF split magnet seal. Here, we mainly discussed the diameter or thickness L_h1 of the split magnet, the space L_h2 between split magnets, and the length L_h3 of the split magnet. In order to reduce demagnetization, the magnet cross section of the working site should be designed as a square. We simulated the FF cuboid magnet seal with L_h1 = L_h3 = 3 mm and L_h2 = 3 mm under the sealing gap of 0.1 mm that has 0.1 MPa seal capacity. We considered such a structure as an example and used the control variable method to discuss the effects of L_h1 and L_h2 on seal capacity. The results are shown in Figure 4. Considering the restrictive condition of process accuracy, the strength of the wall between magnets, and magnet size restriction, we take L_h1 = 4 mm and L_h2 = 2 mm. Twenty small magnets can be installed on one nonmagnetic foundation.

Then, according to the parameter, we processed the FF split magnet seal device to test its seal capacity. During the test, the air pressure is delivered from a pressure cylinder and adjusted by a pressure-reducing valve. The pressure in the sealed chamber is measured with a pressure gauge to range from 0 to 2 MPa. The rotational speed of the motor is controlled and displayed by using a controller. (Li et al., 2021). To examine cuboid magnet and cylindrical magnet seal capacity, the experimental study on the FF split magnet seal is divided into two parts: a static pressure test and a dynamic pressure test. In the experiment table, the two kinds of magnets installed on a nonmagnetic foundation and their relevant sizes are shown in Figure 5 and Table 1, respectively. The device consists of a nonmagnetic shell, a shaft, bearings, nonmagnetic foundations, split magnets, and ferrofluids. About the choice of materials, magnetic parts, such as the shaft and the pole shoes, are made of magnetic materials, 2Cr13 here. Nonmagnetic sections, such as the nonmagnetic ring and the shell, are made of NdFeB with a relative permeability of 1.05 and a coercive force of 8.9 e⁵. The magnetization of the radial-charged ring magnet is shown in Figure 5.

For the classic FF seal and FF radial-charged seal, we used SolidWorks to draw the core of the sealing device of the aforementioned structure scheme. Then, we imported it to the Maxwell 2D module and set the geometry module as cylindrical about Z. The magnetization direction of radial-charged ring magnets is r in the cylindrical coordinate system. According to the Maxwell FEA, we can optimize the seal structure. It is not rigorous to analyze the FF split magnet seal by the Maxwell 2D module. So we decided to use the Maxwell 3D module to analyze, which can not only analyze the stability of FF “O"-shaped seals but also find the difference between the cuboid and cylindrical magnet, which are the most commonly used split magnets. The seal model, contour plot, and magnetic lines distribution are respectively shown in Figures 6–8. The classic FF seal, FF radial-charged seal, FF cuboid magnet seal, and FF cylindrical magnet seal are respectively shown in Figures (A), (B), (C), (D). In Figure 6, the blue part represents the magnet parts, the orange part represents the magnetic parts, and the gray represents the non-magnetic parts. Compared to Figures 7C,D, we can find the magnetic line distribution of a cuboid magnet is more centralized than a cylindrical magnet. So we can guess the magnetic fluid of the FF cuboid magnet seal is stronger and more uniform.

According to simulation and calculation, we get the magnetic field strength curve of all kinds of FF seals, which is shown in Figure 8. According to the aforementioned formula and the relevant knowledge of the magnetic fluid seal, in order to meet the saturation of the magnetic fluid, we observed that the magnetic field strength in the working gap, where magnetic fluid exists, should be greater than the 200 kA/m. In this condition, the difference in the axial magnetic field strength determines the maximum seal pressure. Then, we treated the simulation results by formula (2). The results are shown in Figure 8 and Table 2. From Figure 9, it is obvious to find out that the magnetic field strength curves in the seal gap of these new structures of FF seals are both similar to those of the classic FF seal, which has a significant magnetic field strength gradient. Therefore, we can preliminarily consider that these seals need to be analyzed. The seal pressure is calculated and analyzed in the following. In order to analyze the influence of the magnetic rings on the magnetic field distribution and choose the better split magnets between the cylindrical magnet and the cuboid magnet, we set two arcs at the mid and the edge of magnets in the seal gap to analyze the degree of magnetic field uniformity, which is shown in Figure 10. The results are shown in Figures 11,12, whose abscissa indicates the arc angle rotating around the shaft.

In terms of the experiment, the static pressure resistance experiment of the FF cuboid magnet seal and the FF cylindrical magnet seal were first carried out. Then, the experimental results and the simulation results are shown in Figure 13. The structure of the conductive ring is very important. If the conductive ring is removed, the small magnet will attach to the shaft and cannot form a uniform magnetic fluid o-ring in the sealing gap. So the pressure capacity of the seal group without a conductive ring is 0. In order to prevent the leakage from the gap between the magnets and conductive rings or magnets and nonmagnetic foundations, we used silicone sealant to fill these gaps. A rotational pressure resistance experiment for the FF cuboid magnet seal was performed subsequently. But no matter how we adjust the sealing device, it seems to have a little gap between the shaft and the ring, and the starting torque was much larger than we imagined. We cannot find any rational result in the rotational experiment.

In this study, we analyzed the magnetic field of the classic FF seal, FF radial-charged seal, FF cuboid magnet seal, and FF cylindrical magnet seal in the seal gap. 1) From the magnetic field strength curve of the seal gap in Figure 9, we can find that the new structures of FF radial-charged seal and the FF split magnet seal can form a magnetic field with an axial gradient in the seal gap. From formula (2), the magnetic field strength gradient can fix FF in the seal gap, which offers the seal pressure. According to the static experiment result in Figure 13, the seal capacity of the FF cuboid magnet seal and the FF cylindrical magnet seal can be proved. 2) From Table 2, in terms of seal pressure, the FF radial-charged seal is larger than the other two FF split magnet seals. In Figure 11, the magnetic field intensity along the split magnets in the seal gap has regular fluctuation. The reason for this phenomenon is the presence of small gaps between the split magnets, which is greatly different from ring magnets. If we do not use the magnetic ring, the small magnets will stick to the shaft and lead to the leakage of the seal. So we set a magnetic ring between FF and magnets to address these problems. The design allows the seal to form a uniform and dense FF “O"-shaped sealing rings in the seal gap. 3) According to the seal size in Table 2, compared with the FF cuboid magnet seal and the FF cylindrical magnet seal, the FF radial-charged seal has more seal stages in the same space, larger seal pressure, and stability. It seems that the FF radial-charged seal is the best choice to solve the problems of the radial beating of the main shaft and low seal pressure under the large gap. However, the ring magnet is facing the problems of processability, installation, and uneven magnetization, so the seal pressure will drop or even fail. For seal, the seal pressure is not an absolute criterion, but how to meet the actual needs is more important. 4) In Figure 13, we can find the FF cuboid magnet seal has a larger seal capacity than the FF cylindrical magnet seal. Meanwhile, the error of the latter is much larger than the former. The reason for the difference in error is probably that the FF liquid ring quality of the FF cylindrical magnet seal is poor. It can also be proved by Table 2 and Figure 12. So we can consider that the FF cuboid magnet seal is the better choice than the FF cylindrical magnet seal.