Support characteristics and application of permanent magnet suspension active mass drive system

Abstract

In this paper, a kind of permanent magnet (PM) suspension active mass drive mechanism is proposed, and its structure is designed. It has the advantages of non-contact, almost zero friction, small volume, and so on. Aiming at the active driving mass mechanism of PM suspension, the unidirectional PM suspension system and bi-directional PM suspension system are designed respectively, and their analytical models are established. By analyzing and calculating the magnetic force of the unidirectional and bi-directional PM suspension system, the support coefficient of the suspension system is deduced. After theoretical analysis, the structure is simulated and verified by ANSYS MAXWELL 3D in order to determine the correctness of the analytical calculation of the model. Finally, a test device is made and experiments are carried out in the constant temperature laboratory. The experimental results show that the Nd-Fe-B PMs used in the unidirectional suspension system can provide a maximum force of 260 N, which verify the feasibility of the PM suspension active mass drive system.

Keywords

Permanent magnet (PM)magnetic suspension AMD support characteristics

1. Introduction

Active Mass Driver (AMD), also known as moving heavy block device, is mainly used in structural vibration in the field of civil engineering. The mass is driven by passive, semi-active, active and intelligent control to change the dynamic characteristics and achieve the purpose of restraining single translation and torsional vibration under seismic and wind loads [1–4]. Literature [5] used active mass drivers to robust control the two-story building model. Scholars have also established servo actuators for hydraulically driven AMD mass block motion, and have also carried out active controlling of structural vibration [6] and direct-driven active mass control system. Other researchers have studied the structural vibration control system [7]. A large number of research results and practice have proved that the active mass driver is by far the most effective active control technology and means of structural vibration [8–12]. The traditional drive controlling device controls the movement of the mass block through the contact between the guide rail and the guide wheel, which has defects or deficiencies such as noise pollution and low running speed, especially when it is used to restrain ship rolling, its response speed cannot meet the requirements. It greatly limits the application and development of AMD active control technology. PM suspension has the advantages of non-contact force transmission, no energy consumption and small space consumption. It has been widely used in PM motors, mechanical vibration suppression and other fields [13,14]. However, the application of PM active drive mass device in ship anti-rolling has not been studied. In this paper, a PM suspension active drive mass device (AMD) is designed to verify the feasibility of the device through theoretical analysis, simulation and experiments.

Fig. 1.

Structure schematic diagram of PM suspension active drive mass device.

2. Calculation and analysis of support characteristics of PM active drive mass device

2.1. Structure diagram of PM suspension active drive mass device

In this paper, a PM suspension active drive mass device is designed, and its structure is shown in Fig. 1. PMs with opposite magnetizing directions are arranged at the upper ends of both sides of the fixed guide bracket and the upper ends of both sides of the mass block, and the structure is symmetric from left to right. Due to the repulsion between the PMs, the mass block obtains upward magnetic force. When the upward magnetic force on both sides is the same as the gravity of the mass block, the mass block can be suspended without contact. After stabilizing suspension, the mass block is driven by the linear induction motor, which is composed of the secondary on the fixed guide bracket and the primary on the mass block.

2.2. Analytical model of unidirectional PM

The stability of AMD is directly determined by the stiffness coefficient of PMs. In this paper, a unidirectional PM suspension system is designed, that is, the PMs on both sides of the fixed guide bracket and on both sides of the mass block are unidirectional. Because of the symmetry of the structure, the PMs on both sides of the mass block are exactly the same as the PMs on the fixed guide bracket, so only the vertical direction of the PMs on one side of the mass block and the PMs on the fixed guide bracket is analyzed. As shown in Fig. 2:

Fig. 2.

Structural schematic diagram of the unidirectional PM suspension system.

According to the magnetic charge theory, the interaction force between two point magnetic charges q ₁ and q ₂ in the vacuum can be expressed as: $\begin{eqnarray}\displaystyle F=\displaystyle {\displaystyle \frac{q_{1}q_{2}}{4{\pi}{\mu}_{0}r^{2}}}\vec{r}. & & \displaystyle\end{eqnarray}$ (1)

In formula (1), μ₀ is the vacuum permeability, r is the distance between two magnetic charges, and $\vec{r}$ is the unit vector of one magnetic charge pointing to the other.

In order to obtain the support characteristics of the mass block, the analytical model between the PMs on the mass block and the PMs on the fixed guide bracket must be analyzed.

Fig. 3.

Magnet configuration when the magnetizations of two PMs are parallel.

The two rectangular PMs are shown in Fig. 3. Their edges are, respectively, parallel. The magnetizations of the magnets J and J′ are supposed to be rigid and uniform in each magnet. Magnetization directions are parallel to each other but in the opposite directions. The central points of the magnets are O and O′, respectively. The geometric dimensions of the two magnets are a × b × h and a′× b′× h′, respectively. In the coordinate system OXYZ, the coordinates of O′ are (x, y, z). The magnetic charge density is ${\sigma}=\vec{J}\cdot \vec{n}$ because the direction of J is perpendicular to a × b, so ${\sigma}=|\vec{J}|$ . Then the magnetic interaction energy between two rectangular PMs is $\begin{eqnarray}\displaystyle E=\displaystyle {\displaystyle \frac{JJ^{\prime }}{4{\pi}{\mu}_{0}r}}\mathop{\sum }_{p=0}^{1}\mathop{\sum }_{q=0}^{1}(-1)^{p+q}\int _{-\frac{b}{2}}^{+\frac{b}{2}}dX\int _{-\frac{a}{2}}^{+\frac{a}{2}}dY\int _{-\frac{b^{\prime }}{2}}^{+\frac{b^{\prime }}{2}}dX^{\prime }\int _{-\frac{a^{\prime }}{2}}^{+\frac{a^{\prime }}{2}}dY^{\prime }. & & \displaystyle\end{eqnarray}$ (2)

Wherein, $r=\sqrt{(X-X\prime -x)^{2}+(Y-Y\prime -y)^{2}+z^{2}}$ .

After integral, we can get: $\begin{eqnarray} \displaystyle E=\displaystyle {\displaystyle \frac{JJ^{\prime }}{4{\pi}{\mu}_{0}}}\mathop{\sum }_{i=0}^{1}\mathop{\sum }_{j=0}^{1}\mathop{\sum }_{k=0}^{1}\displaystyle \mathop{\sum }_{l=0}^{1}\mathop{\sum }_{p=0}^{1}\mathop{\sum }_{q=0}^{1}(-1)^{{\varepsilon}}\varnothing(U_{ij},V_{kl},W_{pq},r). & & \displaystyle \end{eqnarray}$ (3)

In formula ((3)): $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}U_{ij}=x+(-1)^{j}\displaystyle {\displaystyle \frac{b^{\prime }}{2}}-(-1)^{i}\left(\displaystyle {\displaystyle \frac{b}{2}}\right)\\[7.0pt] V_{lk}=y+(-1)^{l}\displaystyle {\displaystyle \frac{a^{\prime }}{2}}-(-1)^{k}\left(\displaystyle {\displaystyle \frac{a}{2}}\right)\\[7.0pt] W_{pq}=z+(-1)^{q}\displaystyle {\displaystyle \frac{h^{\prime }}{2}}-(-1)^{p}\left(\displaystyle {\displaystyle \frac{h}{2}}\right)\\[7.0pt] r=\sqrt{U_{ij}^{2}+V_{lk}^{2}+W_{pq}^{2}}\\[7.0pt] {\varepsilon}=i+j+k+l+p+q\\ \end{array}\right. & & \displaystyle\end{eqnarray}$ (4) $\begin{eqnarray} \displaystyle \text{} & \text{} & \displaystyle \varnothing(U,V,W,r)={\displaystyle \frac{U(V^{2}-W^{2})}{2}}\ln (r-U)+{\displaystyle \frac{V(U^{2}-W^{2})}{2}}\ln (r-V)\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \quad +∼\mathit{UVW}\arctan \left({\displaystyle \frac{UV}{rW}}\right)+{\displaystyle \frac{r}{6}}(U^{2}+V^{2}-2W^{2}). \end{eqnarray}$ (5)

The force between PMs is a negative gradient of magnetic interaction energy, so the magnetic force formula between two cuboidal PMs can be obtained from the formula of magnetic interaction energy between PMs above. $\begin{eqnarray}\displaystyle F=\displaystyle {\displaystyle \frac{JJ^{\prime }}{4{\pi}{\mu}_{0}}}\mathop{\sum }_{i=0}^{1}\mathop{\sum }_{j=0}^{1}\mathop{\sum }_{k=0}^{1}\mathop{\sum }_{l=0}^{1}\mathop{\sum }_{p=0}^{1}\mathop{\sum }_{q=0}^{1}(-1)^{{\varepsilon}}{\Psi}(U_{ij},V_{kl},W_{pq},r). & & \displaystyle\end{eqnarray}$ (6) We get $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}c@{}}F_{X}\\ F_{Y}\\ F_{Z}\end{array}\right]=\left[\begin{array}{@{}c@{}}C\left[\displaystyle \frac{(V^{2}-W^{2})}{2}\ln (r-U)+UV\ln (r-V)+\mathit{VW}\arctan \displaystyle \frac{UV}{r\cdot W}+\displaystyle \frac{U\cdot r}{2}\right]\\[10.0pt] C\left[\displaystyle \frac{(U^{2}-W^{2})}{2}\ln (r-V)+UV\ln (r-U)+\mathit{UW}\arctan \displaystyle \frac{UV}{r\cdot W}+\displaystyle \frac{V\cdot r}{2}\right]\\[10.0pt] -C\left[UW\ln (r-U)+VW\ln (r-V)-\mathit{UV}\arctan \displaystyle \frac{UV}{r\cdot W}+W\cdot r\right]\end{array}\right]. & & \displaystyle\end{eqnarray}$ (7)

In above formula $C=\frac{JJ\prime }{4{\pi}{\mu}_{0}}\sum _{i=0}^{1}\sum _{j=0}^{1}\sum _{k=0}^{1}\sum _{l=0}^{1}\sum _{p=0}^{1}\sum _{q=0}^{1}(-1)^{{\varepsilon}}$ .

By derivation in three directions respectively, the obtained expressions of the bracing stiffness formulas of two PMs in the three directions of X, Y, Z are $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}K_{X}=C\left[\displaystyle \frac{V^{2}-W^{2}}{2(U-r)}+V\ln (r-V)+\displaystyle \frac{V^{2}W^{2}\cdot r}{W^{2}\cdot r^{2}+U^{2}V^{2}}+\displaystyle \frac{r}{2}\right]\\[12.0pt] K_{Y}=C\left[\displaystyle \frac{U^{2}-W^{2}}{2(V-r)}+U\ln (r-U)+\displaystyle \frac{U^{2}W^{2}\cdot r}{W^{2}\cdot r^{2}+U^{2}V^{2}}+\displaystyle \frac{r}{2}\right]\\[12.0pt] K_{Z}=-C\left[U\ln (r-U)+V\ln (r-V)+\displaystyle \frac{U^{2}V^{2}\cdot r}{W^{2}\cdot r^{2}+U^{2}V^{2}}+r\right].\end{array}\right. & & \displaystyle\end{eqnarray}$ (8)

The support diagram of the PM suspension AMD device designed in this paper is shown in Fig. 4.

Fig. 4.

Schematic diagram of mass block support.

The angles between the coordinate system (W, C, S) in which the mass block is located and the coordinate system (X, Y, Z) where the PMs are located on both sides of the above analysis are 𝛼 and 𝛽 respectively, so when the mass block is suspended near the equilibrium point, the displacement produced by the mass block is very small, and because there is no contact between the mass block and the auxiliary support, the damping force is negligible. When the structures on both sides are symmetrical, the PM support stiffness of the mass in the gravity direction is as follow. $\begin{eqnarray}\displaystyle K_{s}=K_{Lz}\cos {\alpha}-\displaystyle \sum (K_{LX},K_{LY})\sin {\alpha}+K_{RZ}\cos {\beta}-\sum (K_{RX},K_{RY})\sin {\beta}. & & \displaystyle\end{eqnarray}$ (9)

Wherein, K _LX, K _LY, K _LZ and K _RX, K _RY, K _RZ are the bracing stiffness of the left and right PMs in the coordinate system parallel to their three sides (Fig. 3), respectively.

On the basis of theoretical analysis, the unidirectional PM suspension system is simulated. Firstly, the simulation model is established in ANSYS MAXWELL3D, the excitation source is set up and meshed, and then the analysis and calculation are carried out. The results are as follows.

Table 1

Magnetic force in X, Y , Z directions with different air gaps between upper and lower magnets

Gap/mm	The biggest force in X, Y , Z directions/N	The force in X direction/mN	The force in Y direction/mN	The force in Z direction/N
0.5	152.4	34.83018	90.0734	152.3999
1	114.6592	−14.7313	−50.697	114.6592
1.5	90.84183	−125.545	−141.949	90.84163

Table 2

Magnetic force in X, Y , Z directions at different positions between upper and lower magnets

Position/mm	The biggest force in X, Y , Z directions/N	The force in X direction/mN	The force in Y direction/N	The force in Z direction/N
0	114.6592	−14.7313	−0.0507	114.6592
10	102.975	35.41168	50.31279	−89.8469
20	234.8738	−28.0222	−0.18936	−234.874
30	102.9861	−208.535	−50.5972	−89.6996

Note: The simulation conditions of Fig. 5 to Fig. 8, Table 1 and Table 2 are as follows: the PMs are Nd-Fe-35. The length is 20-mm, and the width is 12-mm. The height is 6-mm, and the direction of magnetization is 6-mm direction. The material of the iron core is electrical pure iron, the lower iron core size: the length is 160-mm, and the width is 18-mm. The height is 12-mm. The upper iron core size: the length is 80-mm, and the width is 18-mm. The height is 12-mm. In Figs 7, 8 and Table 2, the air gap between upper and lower magnets is 0.5-mm.

From Fig. 6 and Table 1, it can be concluded that for the same PM, when the gap between the PM is different, the magnetic flux density and magnetic force will also be different, they vary nonlinearly with the gap, and the waveform is non-standard sinusoidal, which is completely consistent with the theoretical calculation. For the same PM and structure, the smaller the gap is, the greater the magnetic flux density and magnetic force are, and the higher the machining precision is required. On the contrary, the larger the gap, the machining accuracy can be lower accordingly.

Fig. 5.

Magnetic field vector distribution with the air gap 0.5-mm between upper and lower magnets.

Fig. 6.

Magnetic flux density curve of centerline with different air gaps.

Fig. 7.

Schematic diagram at different positions of upper and lower magnets.

Fig. 8.

Magnetic flux density curve of centerline at different positions of upper and lower magnets.

From Fig. 8 and Table 2, it can be concluded that for the same PM and structure, when the position between the upper and lower structure is different, the magnetic flux density and magnetic force will also be different, they vary with the position. The biggest force is from 103.0N to 234.8N.

2.3. Analytical model of bidirectional PM

A bidirectional PM suspension system is also designed in order to form a more stable and continuous permanent magnetic field. The fixed guide bracket and the PMs on the mass block are bidirectional magnetized, and the PMs are formed in a Halbach array. Because of the symmetry structure, only the vertical direction of the structure is analyzed between the PMs on one side of the mass and the PM on the auxiliary guide, as shown in Fig. 9.

Fig. 9.

Structural schematic diagram of the bidirectional PM suspension system.

When the PM on one side of the mass is parallel to the magnetic polarization vector of the PM on the fixed guide bracket, the magnetic force between the PM is calculated as formula (6). When the magnetizations of the PMs on one side of the mass are perpendicular to the magnetizations of the PMs on the fixed guide bracket, model is shown in Fig. 10.

Fig. 10.

Magnet configuration when the magnetizations of two PMs are perpendicular.

Still according to the magnetic charge theory, the magnetic interaction energy between two PMs whose magnetic polarization vectors are perpendicular to each other is $\begin{eqnarray}\displaystyle E=\displaystyle \frac{JJ^{\prime }}{4{\pi}{\mu}_{0}r}\mathop{\sum }_{i=0}^{1}\mathop{\sum }_{p=0}^{1}(-1)^{i+p}\int _{-\frac{h^{\prime }}{2}}^{+\frac{h^{\prime }}{2}}dZ^{\prime }\int _{-\frac{b^{\prime }}{2}}^{+\frac{b^{\prime }}{2}}dX^{\prime }\int _{-\frac{b}{2}}^{+\frac{b}{2}}dX\int _{-\frac{a}{2}}^{+\frac{a}{2}}dY. & & \displaystyle\end{eqnarray}$ (10)

Like the calculation of the force between two rectangular PMs whose magnetic polarization vectors are parallel to each other, after quadruple integration and gradient transformation of the interaction energy, the forces between the two rectangular PMs whose magnetic polarization vectors are perpendicular to each other [15] are as follows: $\begin{eqnarray}\displaystyle F=\displaystyle \frac{JJ^{\prime }}{4{\pi}{\mu}_{0}}\mathop{\sum }_{i=0}^{1}\mathop{\sum }_{j=0}^{1}\mathop{\sum }_{k=0}^{1}\mathop{\sum }_{l=0}^{1}\mathop{\sum }_{p=0}^{1}\mathop{\sum }_{q=0}^{1}(-1)^{{\varepsilon}}{\Psi}(U_{ij},V_{kl},W_{pq}). & & \displaystyle\end{eqnarray}$ (11) Obtain $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}c@{}}F_{X}\\ F_{Y}\\ F_{Z}\end{array}\right]=\left[\begin{array}{@{}c@{}}C\bigg[-WV\ln (r-U)+UV\ln (r+W)+UW\ln (r+V)\\ -\displaystyle \frac{U^{2}}{2}\arctan \displaystyle \frac{WV}{U\cdot r}-\displaystyle \frac{V^{2}}{2}\arctan \displaystyle \frac{WU}{V\cdot r}-\displaystyle \frac{W^{2}}{2}\arctan \displaystyle \frac{UV}{W\cdot r}\bigg]\\ C\bigg[\displaystyle \frac{(U^{2}-V^{2})}{2}\ln (r+W)-WU\ln (r-U)-\mathit{UV}\arctan \displaystyle \frac{UW}{V\cdot r}-\displaystyle \frac{W\cdot r}{2}\bigg]\\ -C\left[VU\ln (r-U)+\mathit{UW}\arctan \displaystyle \frac{UV}{W\cdot r}+\displaystyle \frac{V\cdot r}{2}-\displaystyle \frac{(U^{2}-W^{2})}{2}\ln (r+V)\right]\end{array}\right]. & & \displaystyle\end{eqnarray}$ (12) Wherein, $C=\frac{JJ\prime }{4{\pi}{\mu}_{0}}\sum _{i=0}^{1}\sum _{j=0}^{1}\sum _{k=0}^{1}\sum _{l=0}^{1}\sum _{p=0}^{1}\sum _{q=0}^{1}(-1)^{{\varepsilon}}$ .

By derivation in three directions, the support stiffness formulas of two PMs in three directions (X, Y, Z) are obtained. $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}c@{}}K_{X}\\ K_{Y}\\ K_{Z}\end{array}\right]=C\left[\begin{array}{@{}c@{}}\displaystyle \frac{WV}{r-U}+V\ln (r+W)+W\ln (r+V)-\mathit{Uarctan}\displaystyle \frac{WV}{U\cdot r}+\displaystyle \frac{U^{2}VW.r}{2(W^{2}V^{2}+U^{2}\cdot r^{2})}\\ -\displaystyle \frac{V^{3}W.r}{2(W^{2}U^{2}+V^{2}\cdot r^{2})}-\displaystyle \frac{W^{3}V.r}{2(U^{2}V^{2}+W^{2}\cdot r^{2})}\\ -V\ln (r+W)-\mathit{Uarctan}\displaystyle \frac{UW}{V\cdot r}+\displaystyle \frac{U^{2}VW.r}{(U^{2}W^{2}+V^{2}\cdot r^{2})}\\ W\ln (r+V)-\displaystyle \frac{U^{2}VW.r}{U^{2}V^{2}+W^{2}\cdot r^{2}}\end{array}\right]. & & \displaystyle\end{eqnarray}$ (13)

Wherein, C is the same as in formula (12).

As shown in Fig. 4, when the structures on both sides are symmetrical, the support stiffness of the PMs in the gravity direction of the mass block is also same as in formula (9), but the difference is that when both the active mass block and the PMs on the fixed guide bracket are magnetized in both directions. The Halbach arrangement composed of PMs shown in Fig. 9 is adopted: $\begin{eqnarray}\displaystyle \left[\begin{array}{@{}c@{}}K_{LX\max }\\ K_{LY\max }\\ K_{LZ\max }\end{array}\right]=\left[\begin{array}{@{}c@{}}K_{RX\max }\\ K_{RY\max }\\ K_{RZ\max }\end{array}\right]=4\left[\begin{array}{@{}c@{}}K_{X}\\ K_{Y}\\ K_{Z}\end{array}\right]. & & \displaystyle\end{eqnarray}$ (14)

Wherein, K _X, K _Y, K _Z is the same as in formula (8), K _LXmax, K _{LY max}, K _LZmax is the maximum support stiffness of the left PMs of the mass block in the coordinate system parallel to its three sides (Fig. 3), and K _RXmax, K _{RY max}, K _RZmax is the maximum support stiffness of the right PMs in the coordinate system parallel to its three sides (Fig. 3), respectively.

On the basis of theoretical analysis, the bidirectional PM suspension system is simulated. Firstly, the simulation model is established in ANSYS MAXWELL3D, the excitation source is set up and meshed, and then the analysis and calculation are carried out. The results are as follows.

Table 3

Magnetic force in X, Y , Z directions at different positions between upper and lower magnets

Position/mm	The biggest force in X, Y, Z directions/N	The force in X direction/mN	The force in Y direction/N	The force in Z direction/N
0	99.41143454	8.517613343	19.61209155	97.45767855
20	113.3112741	−73.7192917	47.66478314	−102.7983845
40	273.9417015	−84.10793808	1.754634312	−273.9360692
60	99.15153169	−263.595717	−69.16899738	−71.0394718

Note: The simulation conditions of Fig. 11 to Fig. 13 and Table 3 are as follows: the PMs are Nd-Fe-35, the length is 20-mm, the width is 12-mm, the height is 6-mm, and the directions of magnetization are 6-mm direction and 20-mm direction respectively. The material of iron core is electrically pure iron, the lower iron core size: the length is 160-mm, the width is 18-mm, the height is 12-mm. The upper iron core size: the length is 80-mm, the width is 18-mm, the height is 12-mm.

Fig. 11.

Simulation model and magnetic field vector distribution diagram.

Fig. 12.

Schematic diagram at different positions of upper and lower magnets.

Fig. 13.

Magnetic flux density curve of centerline at different positions of upper and lower magnets.

It can be seen from Fig. 11 and Table 3, compared with the unidirectional PM suspension system, the relative position between the upper and lower structures of the bi-directional PM suspension system is different, the magnetic flux density and magnetic force are also different. The waveforms of the magnetic flux density and magnetic force are more non-standard sinusoidal, and they vary for different positions. The maximum force in the three directions varies greatly from 99.2 N to 273.9 N, but the force changes more gently, and the force curve tends to be more linear, which is more conducive to the stability of the system. Among them, the X direction force is small, and this direction is perpendicular to the running direction of the mass block, which is helpful to the stability of the whole system.

In order to obtain more stable PM suspension system, a four-way or multidirectional Halbach PMs array should be designed, so that when the mass block and the auxiliary guide bracket are at different relative positions, the force curve tends to be more linear, and the whole system will be more stable.

3. Experiments and results

3.1. Experiments

In order to verify the correctness of the theoretical analysis and simulation results, a simple PM suspension structure is designed in this paper. The components of test device are shown in Fig. 14, and the field test is shown in Fig. 15. The Specifications of test device are shown in Table 4.

Table 4
Test device specifications

Specifications Technique

Type: T315-200-Kg

Rated output: 2.0 ± 0.25%-mV/V

Force Sensor Zero balance: 0.01-mV/V

Non-linearity: 0.018%-F.S.

Repeatability: 0.018%-F.S.

Load Apparatus Standard load apparatus 2026

PMs Dimensions: 20-mm × 12-mm × 6-mm

Type: Nd-Fe-B-35

Gap 0.5-mm

Specifications	Technique
	Type: T315-200-Kg
	Rated output: 2.0 ± 0.25%-mV/V
Force Sensor	Zero balance: 0.01-mV/V
	Non-linearity: 0.018%-F.S.
	Repeatability: 0.018%-F.S.
Load Apparatus	Standard load apparatus 2026
PMs	Dimensions: 20-mm × 12-mm × 6-mm
	Type: Nd-Fe-B-35
Gap	0.5-mm

Fig. 14.

Test device components.

Fig. 15.

Experiments.

In the experiments, the upper magnets move in translation along the OY axis above the lower fixed magnets. The PMs are unidirectional. It can be obtained from serial data collector that the force between the upper and lower structures is different when the relative positions of them changes. When the gap of the upper and lower structures is 0.5-mm, the maximum repulsive force is approximately 260 N and the attractive force is much of a size. The force curve in test which is non-standard sinusoidal is almost the same in the simulation.

Fig. 16.

Force F _Z with the air gap 0.5-mm between upper and lower magnets. The PMs are unidirectional. Blue lines are for the analytical calculation, and red lines are the numerical results by ANSYS MAXWELL 3D. Pink lines are the experimental results.

3.2. Comparison between analytical calculation, numerical results and experimental results

Figure 16 shows the force calculation between the upper and lower magnets by three methods. For the first calculation method, the obtained analytical expressions are used. The second one is made by finite-element computation (ANSYS MAXWELL 3D software). The third one is obtained by experiments. The results are presented for displacement in the Y -direction. The comparison between the results shows that the three methods are in approximate agreement. The accuracy of the analytical calculation seems to be higher than the finite-element computation and experimental results. The numerical precision can probably be improved. One possibility is that the Nd-Fe-B-35 PM is not defined in the ANSYS MAXWELL 3D. The analytical results own more precision for ideal magnets, and can be calculated with a programmable pocket calculator. However, the analytical method is limit with uniform and rigid magnetization. The analytical results are proved to be correct by experimental result.

4. Conclusions

In this paper, unidirectional and bidirectional PM suspension systems are designed for the proposed permanent magnetic suspension AMD device, and their analytical models are established. By analyzing and calculating the magnetic force of the unidirectional and bidirectional PM suspension system, the support coefficient of the suspension system to AMD is deduced. On the basis of theoretical analysis, the structure is simulated by ANSYS MAXWELL3D, and experiments are carried out in the laboratory. The simulation and test results show that when the relative positions of the upper and lower structures of the PM suspension system are different, the magnetic induction intensity and magnetic force between them are also different, and the waveform is non-standard sinusoidal. The experimental results are close to the simulation results, which verify the effectiveness of the PM suspension AMD device designed in this paper and the method for further optimization.

Footnotes

Fund support

This project is supported by National Natural Science Foundation of China (51875275), the “Six Talent Summit” — high-level talent project in Jiangsu Province (JNHB-041) and the scientific research fund incubation project of Jinling Institute of Technology (jit-fhxm-201915).

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