Abstract
In order to solve the problem of reciprocating seal for hydraulic cylinder, a new structure of Magnetorheological fluid (MRF) reciprocating seal with increasing width of pole teeth and pole piece was designed. The theoretical analysis of MRF reciprocating seal is carried out. The magnetic field intensity distribution in the sealing gap of MRF reciprocating seal was analyzed by finite element method. According to the pressure capability formula of MRF, the theoretical pressure capability is calculated. The influences of structure parameters such as the number of magnetic sources, sealing gap height, pole teeth length, the ratio of permanent magnet height to its length, the ratio of pole piece height to shaft radius on the sealing capabilities were studied. The results showed that the pressure capability of MRF reciprocating seal increases with the increase of the number of magnetic sources and with the decrease of the sealing gap height. With the increase of the pole tooth length, the pressure capability of the reciprocating seal increases. With the increase of the ratio of permanent magnet height to its length, the pressure capability of the reciprocating seal increases first and then decreases. With the increase of the ratio of the pole piece height to shaft radius, the pressure capability of the MRF reciprocating seal increases first and then decreases.
Introduction
MRF is an intelligent material which can control the change of mechanical properties by external magnetic field [1]. It is composed of magnetic particles, base carrier and surfactant. One of the typical applications of MRF technology is sealing. As a non-contact seal, compared with traditional seal, MRF seal has the advantages of simple structure, high reliability, long life, zero leakage, no pollution, etc. And occupies an important position in the engineering field [2,3]. There are many researches on magnetic fluid seal [4–9], but the research on reciprocating seal of magnetic fluid is much less. Scholars have carried out research on reciprocating sealing technology of magnetic fluid. Reciprocating shaft sealing technology of magnetic fluid originated in the early 1980s. Goldowsky [10] first established a single-stage linear seal of magnetic fluid for the development of cardiac engines, and published the experimental results of magnetic fluid used in reciprocating shaft seals. Evsin et al. [11] obtained the operating conditions of multi-stage sealing system through the research on reciprocating seal, and developed a new sealing structure with damping volume and aerodynamic resistance. Li et al. [12] deduced the pressure capability formula of magnetic fluid seal with reciprocating shaft, established the test bench of reciprocating seal with magnetic fluid, and verified the influence of rotating speed and travel on the sealing pressure capability. Potoczny and Zachara [13] conducted several experiments to obtain the effect of the volume of magnetic fluid on the fracture pressure of seals. Chen and Yang [14] studied the effects of structural parameters of magnetic fluid with small gap on sealing capabilities. Chen et al. [15] studied the influence of reciprocating shaft speed and travel on seal life by experimental method. The results showed that the service life of reciprocating seal with magnetic fluid decreased sharply with the increase of reciprocating shaft travel and speed. At present, the research on the reciprocating sealing technology with magnetic fluid mainly focuses on the seal theory, mechanism research and experimental verification of sealing capability, but there are few reports on the numerical research of MRF reciprocating seal.
In order to solve the problem of reciprocating seal in hydraulic system, a MRF reciprocating sealing device with increasing width of pole teeth and pole piece is designed. The finite element method was used to study the magnetic field distribution in the seal gap corresponding to different number of magnetic sources, seal gap height, pole tooth length, ratio of permanent magnet height to its length, and ratio of pole piece height to shaft radius. According to the pressure capability formula of MRF, the theoretical pressure capability is calculated. The variation law between the key parameters of the seal and MRF reciprocating seal with increasing width of pole teeth and pole piece is revealed. The research results provide important theoretical guidance for the research of MRF reciprocating seal for hydraulic cylinder of construction machinery.
Formula of magnetic fluid seal capability for reciprocating shaft
In general, Bernoulli equation of magnetic fluid can be expressed by the following formula [16]
The sealing area under its pole piece is shown as Fig. 1(a). When the boundary pressure on both sides is the same, it can be expressed by the following formula:
H 1 is the magnetic field strength at the junction of the shaft and the high-pressure side of the magnetic fluid, H 2 is the magnetic field strength at the junction of the shaft and the low-pressure side of the magnetic fluid.
Model of magnetic fluid under the pole tooth: (a) allowable pressure and (b) burst pressure.
Physical model of magnetic fluid reciprocating seals.
Figure 1(b) shows that the magnetic fluid moves along the shaft direction in its pole piece under the action of high-pressure side pressure. Under the action of nonlinear magnetic field strength, the magnetic fluid will resist the differential pressure between the high-pressure side and the low-pressure side. Assuming that the magnetic fluid has reached the saturation magnetization state, the critical pressure of the MRF seal in the sealing gap between the pole piece and the shaft can be expressed by the following formula:
The 2D physical model of MRF reciprocating seal is shown in Fig. 2, where ABCD represents the shape and position of the magnetic fluid ring before the reciprocating shaft moves, and A’B’C’D’ represents the shape and position of the magnetic fluid ring after the reciprocating shaft moves. The pressure capability formula of MRF reciprocating seal can be expressed as [12]:
The influence of reciprocating motion on MRF seal is described quantitatively and qualitatively by Eq. (4), where p h , p L , H (x C ), H (x B ), μ0, M S , V, h c , 𝜂, σ are high pressure side pressure, atmospheric pressure, magnetic field strength at x C , magnetic field strength at x B , vacuum permeability, saturation magnetization of magnetic fluid, reciprocating shaft speed, thickness of magnetic fluid ring, viscosity of magnetic fluid and surface tension coefficient of magnetic fluid.
In order to study the influence of the key parameters of the MRF reciprocating seal on the sealing capability, a MRF reciprocating sealing structure of increasing width of pole teeth and pole piece with 11 magnetic sources is designed, as shown in Fig. 3. The structural parameters are shown in Table 1. The permanent magnetic material in MRF reciprocating seal is NdFeB, the coercive force is 1.356 × 106 A/m, and the relative permeability is 1.05. The material of pole piece and reciprocating shaft is 2Cr13. MRF with saturation magnetization of 35.6 KA/m was used.
Schematic diagram of two-dimensional physical model of magnetic fluid reciprocating seal.
Geometrical parameters of the sealing structure
The ANSYS analysis process is as follows. Firstly, the physical environment is created. In the analysis interface of ANSYS, select the environment of Magnetic-Nodal, the unit module is PLANE53. The whole model is symmetrical about the central axis, and the unit option “Element behavior” is set to “axisymmetric”. Therefore, in the finite element analysis software, it is transformed into a two-dimensional plane problem for analysis. According to the geometric parameters of the sealing structure in Table 1, the model as shown in Fig. 4 is established in ANSYS finite element, and the sealing structure is symmetrical with respect to y-axis. In this model, A1 is the magnetic shaft, A13 to A24 are the magnetic pole piece with the same material properties, A2 to A12 are permanent magnets, their structural properties are the same, A25 is air. The magnetic pole piece, shafts and permanent magnets in the sealing structure are overlapped in the air.
ANSYS analysis model.
Because the slope of B–H curve of magnetic shaft, magnetic pole piece, permanent magnet is not a straight line, the value of B–H needs to be input. The permeability of magnetic fluid is about 1. For permanent magnet, the parameters are as follows, Br = 14.40 KGs, Hc = 13.05 KOe. In addition, to define the properties of permanent magnets, we also need to define the coercive force of permanent magnets. In order to get the maximum magnetic energy product in the magnetic circuit, the coercive force of two adjacent permanent magnets must be opposite. In this design, permanent magnets are magnetized along the y-axis direction. According to the established physical structure model, the material properties are defined to the corresponding module. The grid in ANSYS is selected for intelligent division, and the accuracy of the grid is set to 1 to calculate the magnetic field results of the sealing gap. The part of the pole tooth must be very precise, so the grid is divided by four nodes to generate the grid as shown in Fig. 5. After that, the boundary conditions are set.
ANSYS analysis model meshing.
When the boundary condition is applied, the static analysis is selected “Static Analysis”. If the analysis results converge, the path is defined on the surface of the reciprocating shaft along the increasing direction of the pole piece, the magnetic field strength H and flux density B in the sealing gap can be solved.
Influence of the number of magnetic sources on sealing performance
Because the permanent magnet provides magnetic energy for the whole sealing device, the number of magnetic sources has an important influence on the MRF reciprocating seal. Taking into account the axial length of reciprocating shaft and the pressure capability of MRF reciprocating seal, the magnetic field finite element analysis was carried out for the sealing structure with the number of magnetic sources ranging from 8 to 11 and the sealing gap height is 0.1 mm, the pole tooth height is 0.7, ratio of permanent magnet height to its length is 1.7, ratio of the pole piece height to shaft radius is 0.7. The magnetic field distribution is shown in Fig. 6.
Magnetic flux densities under different number of magnetic sources. (I) 8; (II) 9; (III) 10; (IV) 11.
It can be seen from Fig. 6 that with the increase of the number of magnetic sources, the magnetic field strength in the sealing gap of MRF reciprocating seal increases with increasing width of pole teeth and pole piece also. The main reason is that the higher the number magnetic sources is, the greater the magnetic energy provided is, the stronger the corresponding magnetic field is. When the number of magnetic sources is 11, the magnetic flux density in the sealing gap between the leftmost and rightmost pole piece and the shaft is much smaller than that in the sealing gap between the other pole piece and the shaft. This is because the flux density of the other pole pieces is provided by the magnetic sources on the left and right, while the flux density of the leftmost and rightmost pole piece are provided by only one magnetic source.
According to the flux density corresponding to different number of magnetic sources shown in Fig. 6 and the magnetic fluid reciprocating seal pressure capability formula, the relationship between the sealing pressure capability ΔP and the number of magnetic sources can be calculated.
It can be seen from Fig. 7 that with the increase of the number of magnetic sources, the pressure capability ΔP of the MRF reciprocating seal also increases, and the relationship is basically linear. This is because with the increase of the number of magnetic sources, the magnetic flux density in the sealing gap will also increase, eventually leading to the increase of the sealing pressure capability.
Effect of number of magnetic sources on pressure capacity of the seal.
The theoretical pressure capability of MRF reciprocating seal is related to the difference of magnetic field strength or magnetic flux density in sealing gap. In order to get the influence of sealing gap height on the theoretical pressure capability of seal, it is necessary to calculate the magnetic field strength or flux density distribution in the sealing gap. When the number of magnetic sources is 11, the pole tooth height is 0.7, and the ratio of permanent magnet height to its length is 0.7, the magnetic field intensity distribution under different seal gaps height is shown in Fig. 8.
Magnetic flux densities under different gaps conditions. (I) 0.1 mm; (II) 0.2 mm; (III) 0.3 mm; (IV) 0.4 mm.
It can be seen from Fig. 8 that when the sealing gap height increases from 0.1 mm to 0.4 mm, the magnetic flux density in the gap of MRF reciprocating seal with increasing width of pole teeth and pole piece decreases. The reason is that the magnetic reluctance in the sealing gap increases with the increase of the sealing gap. According to the magnetic circuit theory, the magnetic flux density in the sealing gap decreases.
According to the flux density corresponding to different number of sealing gaps shown in Fig. 8 and the magnetic fluid reciprocating seal pressure capability formula, the relationship between the sealing pressure capability ΔP and the change of sealing gap can be calculated, as shown in Fig. 9.
Pressure capability of the seal as a function of sealing gap height.
It can be seen from Fig. 9 that with the increase of the sealing gap height, the pressure capability of the MRF reciprocating seal decreases continuously. This is because the larger the sealing gap is, the greater the magnetic reluctance of the whole sealing system will be without changing the sealing structure parameters. According to the magnetic circuit theory, the magnetic induction strength in the sealing gap decreases and the magnetic field gradient also decreases correspondingly, which leads to the pressure capability of the sealing structure decreases.
Without changing the inner diameter and outer diameter of the sealing device, the length of the pole teeth has an important influence on the sealing capability of the MRF reciprocating seal. The length of the pole teeth will affect the magnetic field gradient in the sealing gap, and then affect the pressure capability of the reciprocating seal. Figure 10 shows the magnetic field intensity distribution at different pole tooth heights when the seal gap height is 0.1, the number of magnetic sources is 11, and the ratio of permanent magnet height to its length is 0.7.
Magnetic flux densities under different pole tooth length. (I) 0.5 mm; (II) 0.7 mm; (III) 0.9 mm; (IV) 1.1 mm.
It can be seen from Fig. 10 that when the length of the pole teeth ranges from 0.5 mm to 1.1 mm, the minimum value of the magnetic flux density in the gap of MRF reciprocating seal with increasing width of pole teeth and pole piece basically remains the same, while the maximum value of the magnetic flux density increases with the increase of the pole teeth height. Therefore, when the pole teeth length is 0.5 mm, the magnetic field strength is the weakest, and when the pole teeth length is 1.1 mm, the magnetic field strength is the strongest. The main reason is that the magnetic field gradient in the sealing gap increases with the increase of the pole teeth length, and then the magnetic field intensity in the sealing gap increases. When the pole teeth length is zero, the magnetic induction line approaches to the level.
According to the flux density corresponding to different number of sealing gaps shown in Fig. 10 and the magnetic fluid reciprocating seal pressure capability formula, the relationship between the sealing pressure capability ΔP and the change of pole teeth length can be calculated, as shown in Fig. 11.
Pressure capability of the seal as a function of pole tooth length.
It can be seen from Fig. 11 that with the increase of pole teeth length, the pressure capability of reciprocating seal gradually increases. This is because the magnetic field gradient difference in the sealing gap between the pole teeth and the reciprocating shaft will also increase as the length of the pole teeth increases. According to the MRF pressure seal capability formula, the greater the magnetic field gradient difference is, the stronger the sealing pressure capability is. When the length of the pole tooth is from 0.9 mm to 1.1 mm, the increase of the sealing pressure capacity is very slow and basically remains unchanged. The main reason is that when the length of the pole tooth is 0.9 mm the sealing state tends to be saturated. So the magnetic gathering effect of the pole tooth will not be too obvious, so the sealing pressure capability in the sealing device increases slowly. In addition, it is necessary to consider that the length of the pole tooth in the actual working conditions, the longer the length of the pole tooth, the more difficult the processing will be. Therefore, it is very important to choose a suitable pole teeth length.
The ratio of permanent magnet height to its length is the key parameter affecting the reciprocating seal of MRF, which has a great influence on the sealing effect. Therefore, it is of great significance to study the change of the ratio of permanent magnet height to its length for the development of MRF reciprocating sealing device with high sealing capability. When the seal gap height is 0.1 mm, the number of magnetic sources is 11, the pole tooth height is 0.7, and the ratio of pole piece height to shaft radius is 0.7, the magnetic field intensity distribution under different ratio of permanent magnet height to its length is shown in Fig. 12.
Magnetic flux densities under different ratio of permanent magnet height to its length. (I)1.8; (II) 1.6; (III) 1.4; (IV) 1.2; (V) 1.0.
It is not difficult to see from Fig. 12 that with the decrease of the ratio of permanent magnet height to its length, the lowest point of the magnetic flux density in the sealing gap also decreases. The main reason is that when other sealing structure parameters remain unchanged and the axial length of the permanent magnet remains constant, the magnetic energy provided by the permanent magnet decreases with the decrease of the permanent magnet radial height. According to the theory of magnetic circuit, the magnetic flux density through the pole piece and the pole teeth will decrease.
According to the magnetic fluid reciprocating seal pressure capability formula and the magnetic flux density of different ratio of permanent magnet height to its length shown in Fig. 12, the relationship between the sealing pressure capability ΔP and the ratio of permanent magnet height to its length is calculated, as shown in Fig. 13.
Pressure capability of the seal as a function of ratio of permanent magnet height to its length.
It can be seen from Fig. 13 that with the increase of the ratio of permanent magnet height to its length, the pressure capability of MRF reciprocating seal first increases and then decreases, and reaches the maximum when the ratio of permanent magnet height to its length is 1.4. The main reason is that when the ratio of permanent magnet height to its length increases from 1.0 to 1.4, the magnetic energy product of the magnetic circuit increases continuously. When the ratio of permanent magnet height to its length increases to about 1.4, the total magnetic energy produced by the magnetic circuit reaches the maximum value, and the pressure capability also reaches the maximum. When the ratio of permanent magnet height to its length continues to increase, the magnetic field gradient provided in the slot becomes smaller and smaller, which leads to the decrease of sealing ability.
Without changing the size of the outer circle of the seals, the inner diameter of the pole piece and the outer diameter of the shaft are changed at the same time, and the ratio of the pole piece height to the shaft radius is in a dynamic change. When the seal gap height is 0.1 mm, the number of magnetic sources is 11, the pole tooth height is 0.7, and the ratio of permanent magnet height to its length is 1.7, the magnetic field intensity distribution under different the ratio of pole piece heights to shaft radius is shown in Fig. 14.
Magnetic flux densities under the different ratio of pole piece height to shaft radius. (I) 0.6; (II) 0.8; (III) 1.0; (IV) 1.2; (V) 1.4.
It can be seen from Fig. 14 that with the increase of the ratio of pole piece height to shaft radius, the magnetic flux density in the structure of MRF reciprocating seal with increasing width of pole teeth and pole piece gradually decreases. The main reason is that when the outer diameter of the seals remains unchanged and the ratio of the pole piece height to the shaft radius increases, which results in the increase of the magnetic reluctance inside the pole piece. According to the theory of magnetic circuit, the magnetic flux density in the sealing structure will decrease. It can also be seen from the Fig. 14. The magnetic field gradient difference of the pole teeth of the pole piece on both sides is obviously smaller than that of the pole teeth of the middle one. This is due to the fact that the magnetic energy of the pole piece on both sides is provided by a single magnetic source, while the magnetic energy of the middle one is provided by two magnetic sources.
According to the magnetic fluid reciprocating seal pressure capability formula and the magnetic flux density of different ratio of pole piece height to shaft radius shown in Fig. 14, the relationship between the pressure capability ΔP and the ratio of pole piece height to shaft radius is calculated.
It can be seen from Fig. 15 that with the increase of the ratio of pole piece height to shaft radius, the pressure capability of MRF reciprocating seal with increasing width of pole teeth and pole piece first increases and then decreases. When the ratio of pole piece height to shaft radius is about 1.0, the pressure capability reaches the maximum, because the maximum magnetic energy product is obtained in the magnetic circuit formed by permanent magnet, pole piece and reciprocating shaft in the sealing structure. Therefore, the ratio of pole piece height to shaft radius should be considered in the design of MRF reciprocating sealing device, and the appropriate size of pole piece and shaft should be selected.
Pressure capability of the seal as a function of the ratio of different pole piece height to shaft radius.
A structure of MRF reciprocating seal with increasing width of pole teeth and pole piece with 11 magnetic sources is designed. The magnetic flux density in the sealing gap is calculated by finite element method.
The important influence of sealing structure parameters on MRF reciprocating seal is obtained. The results show that the pressure capability of MRF reciprocating seal with increasing width of pole teeth and pole piece increases with the increase of the number of magnetic sources. When the number of magnetic sources is 11, the sealing pressure capability is the largest. When the sealing gap height is 0.1 mm, the pressure capability of MRF seal is about 22.5 MPa. When the sealing gap height is 0.4 mm, the sealing pressure capability is only 7.5 MPa.
With the increase of pole teeth length, the pressure capability of MRF seal also increases. When the length of pole teeth is 0.9 mm, the magnetic gathering capacity is almost the best. With the increase of the ratio of permanent magnet height to its length, the pressure capability of the MRF seal first increases and then decreases. When the ratio of permanent magnet height to its length is 1.4, the sealing pressure capability is the largest. With the increase of the ratio of pole piece height to shaft radius, the sealing pressure capability first increases and then decreases. When the ratio of pole piece height to shaft radius is about 1.0, the sealing pressure capability reaches the maximum value.
Footnotes
Acknowledgements
The authors gratefully acknowledge the support of the National Nature Science Foundation of China (Grant No. 51905114), the support of the Science and Technology Project of Guangxi Province (Grant No. 2019JJA160046), and the support of Science and Techology Project of Liuzhou (Grant No. 2017BC20204), the support of graduate student innovation Project of Guangxi University of Science and Technology (Grant No. GKYC202108).