Pull-up operation of an aluminum ring by utilizing ac ampere type magnetic levitation method

Abstract

In general, the magnetic levitation (maglev) force on a nonmagnetic metal generated by an alternating magnetic field becomes a repulsive force; therefore, the nonmagnetic metal can only be pushed up from below by the repulsive force. In contrast, our prototype device succeeded in continuously pulling up a thin aluminum ring with a diameter of 120 mm by using ac electromagnetic force based on the ac ampere type maglev method we have proposed. This system operates just as if a permanent magnet attracts a magnetic material. This paper describes the configuration of the prototype device, derivation of exciting current conditions for generating the ac ampere force using finite element analysis and demonstration of steady levitation force and pull-up operation.

Keywords

Magnetic levitation ac ampere force pull-up operation aluminum ring finite element analysis

1. Introduction

Ac induction type magnetic levitation (maglev) has long been known as a method for generating electromagnetic force between a nonmagnetic metal and an ac electromagnet. This type of maglev is applied to electromagnetic levitation furnace and semiconductor wafer transfer table in manufacturing processes [1, 2, 3, 4]. In principle, the alternating magnetic flux from an ac electromagnet induces eddy current in a nonmagnetic metal and then repulsive force occurs between them. Therefore, electromagnets are inevitably arranged under a nonmagnetic metal and can only push up the metal from below to keep a steady levitation state. This constraint on the arrangement hinders the expansion of industrial applications.

On the other hand, we have proposed an ac ampere type maglev method [5, 6, 7]. In this method, the new electromagnetic force that we call ‘ac ampere force’ is generated by adjusting the phase of the magnetic flux from a separately prepared electromagnet to the phase of eddy current inside a nonmagnetic metal. In [5], it has already been suggested that the ac electromagnetic force could theoretically pull up a nonmagnetic metal by using our proposed maglev method. An industrial robot capable of grabbing an object from above such as parallel link robot or articulated robot has high industrial utility value. Therefore, if a nonmagnetic metal can be pulled up with the proposed maglev method, it will be used more widely in manufacturing processes.

First, this paper deals with the fundamental difference between the conventional ac induction type maglev and the proposed ac ampere type one and shows a conceptual diagram for pulling up a nonmagnetic metal. Next, we designed the configuration of the prototype device based on the diagram. In addition, we derived the exciting current conditions for generating ac ampere force using finite element analysis (FEA) and finally demonstrated the generation of sufficient levitation force and the actual pull-up operation to an aluminum (Al) ring.

2. Principle and prototype

2.1 Generation principle of ac ampere force

Figure 1 shows the basic configurations of two kinds of ac ampere type maglev. The configuration excluding ac electromagnet EM2 in Fig. 1a corresponds to a conventional ac induction type maglev. The force on a nonmagnetic metal plate (e.g. Al plate) generated by EM1 is naturally repulsive force. The basic idea of the ac ampere type maglev is to effectively utilize eddy current induced in the Al plate as secondary electromagnetic force. That is, the phase relation between the eddy current and the magnetic flux from newly installed EM2 determines the direction of ac ampere force $f_{A}$ as shown in Fig. 1. Even when EM1 is installed above the Al plate, it is possible to generate the ampere force upward (Fig. 1b).

Figure 1.

Stator position and ac ampere force direction.

Figure 2.

Conceptual diagram and actual prototype.

Figure 3.

Dimensions of prototype.

Table 1

Dimensions of prototype and numerical values for FE analysis

Aluminum ring	Size: 120 [mm ${}^{\phi}$ ] $\times$ 110 [mm ${}^{\phi}$ ] $\times$ 5 [mm ${}^{t}$ ], Mass: 24 [g] (Conductivity: 3.81e7 [S/m], Relative permeability: 1)
Pancake coil	No. of turns $N_{1}$ : 216 [turns] (72 [turns] $\times$ 3 layers) Cross sectional area $S_{1}$ : 280 [mm ${}^{2}$ ]
Side coil	No. of turns $N_{2}$ : 290 [turns] (145 [turns] $\times$ 2 pieces) Cross sectional area $S_{2}$ : 360 [mm ${}^{2}$ ] (Conductivity: 0, Relative permeability: 1)
Back iron	Size: 100 [mm ${}^{\phi}$ ] $\times$ 20 [mm ${}^{\phi}$ ] $\times$ 10 [mm ${}^{t}$ ]
Pole piece	Pole area: 46 [mm] $\times$ 10 [mm ${}^{t}$ ], 6 pieces
Yoke	Size: 210 [mm ${}^{\phi}$ ] $\times$ 190 [mm ${}^{\phi}$ ] $\times$ 10 [mm ${}^{t}$ ] (Conductivity: 1.03e7 [S/m], Relative permeability: 4,000)
Gap	$d$ =10 [mm] (b/w pancake coil and Al ring) (Initial position) 5 [mm] (b/w pole pieces and Al ring)
Exciting current	EM1: $i_{1}=\surd 2I_{1}\text{exp}(j2\pi ft)$ , EM2: $i_{2}=\surd 2I_{2}\text{exp}(j(2\pi ft+\theta))$ $I_{1}=$ 3.0 [A ${}_{\text{rms}}$ ], $I_{2}=$ 3.0 [A ${}_{\text{rms}}$ ], $f=$ 180 [Hz], $\theta=$ 60 [deg] (Set as Default) Current density: $J_{1}=\surd 2N_{1}I_{1}/S_{1}$ , $J_{2}=\surd 2N_{2}I_{2}/S_{2}$
No. of elements	43,000 (Triangle meshes)
Solution time	30 [s] (CPU: Intel® Core ${}^{\text{TM}}$ i7-4930, 3.40 GHz)

<Notes> Software: Ansoft Maxwell EM Ver. 3.1 (Axisymmetric analysis). Levitation force results are calculated with $A$ - $\phi$ method and Maxwell’s stress tensor.

2.2 Prototype for pulling up an aluminum ring

Figure 2 shows a conceptual diagram and actual prototype device. In Fig. 1b, the ac induction force $f_{I}$ must be reduced while sufficiently generating the eddy current $i_{e}$ ; therefore, an Al plate is replaced with an Al ring. In addition, to reinforce the upward ac ampere force $f_{A}$ , plural EM2s are installed around the Al ring. When the total amount of ac ampere force is greater than the sum of induction force and the own weight of Al ring, the ring is theoretically attracted to EM1 side. Figure 2b shows the prototype device manufactured based on the principle of ac ampere type maglev for pulling up an Al ring. An upper electromagnet EM1, which consists of a pancake coil and an iron disk, is installed to excite eddy current in the Al ring. All six pole pieces of EM2s installed every 60 degrees around the Al ring face the side of Al ring. Figure 3 shows the details of the dimensions and structure of the prototype device. The outer diameter, inner diameter, thickness, and mass of the Al ring are 120 mm, 110 mm, 5 mm, and 24 g, respectively. An acrylic resin spacer with a thickness of 5 mm is installed on the pancake coil surface of EM1. The distance between the pancake coil surface and the upper surface of the Al ring is defined as a gap $d$ , and the initial value of the gap is set to 10 mm. The distance between the pole piece surfaces of EM2s and the side surface of the Al ring is 5 mm and the effective arc length of the pole piece per EM2 is about 46 mm (equivalent to 40.5 ${}^{\circ}$ ). Other detailed dimensions are listed in Table 1.

3. Finite element analysis and experiments

3.1 Ac steady state analysis by FEM

The magnitude of the exciting current to each coil, phase difference, and frequency are important factors for successful generation of ac ampere force. For the prototype device shown in Fig. 2b, we derived the characteristics of ac steady state levitation force using axisymmetric FEA before levitation force tests. First, we extracted the cross section along axis A-A’ in Fig. 2b as an axisymmetric analysis model. In this case, since each component related to EM2 is regarded as a cylinder centered on the $z$ axis, the effect due to the effective arc length of pole piece is not reflected in calculated results. Therefore, we multiplied the calculated results by the coefficient $K$ corresponding to the effective arc length as follows:

$\displaystyle f_{z}=KF_{z\_\textit{calc}}=\frac{40.5}{60}\times F_{z\_\textit{% calc}},$ (1)

where $F_{z\_\textit{calc}}$ is a calculated levitation force and $f_{z}$ is the levitation force which corrected the calculated levitation force $F_{z\_\textit{calc}}$ . Numerical values, conditions, and pc and software specifications are listed in Table 1.

Figure 4a shows the characteristics of the levitation force $f_{z}$ and the phase difference $\theta$ of each exciting current when the current $I_{1}$ and $I_{2}$ are fixed to 3 A ${}_{\text{rms}}$ and 3 A ${}_{\text{rms}}$ , respectively. Here, $\theta$ denotes the lead phase of $i_{2}$ to $i_{1}$ . In addition, the excitation frequency $f$ is set at every 60 degrees up to 240 Hz. As excitation frequency increases, levitation force increases and the lead phase giving maximum levitation force decreases. The maximum levitation force is around 1.8 times larger than the own weight of Al ring (0.245 N) at a phase difference of 60 degrees and an excitation frequency of 180 Hz. Figure 4b shows the relationship among levitation force, $I_{1}$ , and $I_{2}$ when excitation frequency and phase difference are set to 180 Hz and 60 degrees, respectively. Even if only either the current $I_{1}$ or $I_{2}$ is applied, levitation force exceeding the Al ring weight is not generated. On the other hand, sufficient levitation force is generated to support the weight by applying both currents with the phase difference.

Figure 4.

FE analysis results.

Figure 5.

Circuit diagram and electrical parameters.

Figure 6.

Measurement results.

Figure 7.

Input voltage signals and actual input current of EM1 at pull-up tests.

Figure 8.

Each input current of EM2 at pull-up tests. (a) is step current and each of (b) to (d) is the ramp current reaching the final value (3 A ${}_{\text{rms}}$ ) in 3, 6, or 12 seconds.

Figure 9.

Pull-up response characteristics of Al ring to each input current.

3.2 Pull-up tests

3.2.1 Ac steady state levitation force

Power supply configuration and electric circuits for applying the same exciting currents $i_{1}$ and $i_{2}$ as in FEA are shown in Fig. 5. Ac signals generated by using the waveform generator composed of a PC and a DSP become the applied voltage of each circuit via power amplifiers. Regarding exciting currents, their magnitude and phase depend on the impedance of each circuit; therefore, we confirmed the information on these currents with digital power meters and then set the appropriate voltage signals on the PC. In the ac transient test described later, a step voltage and ramp voltages are applied. The time delay response of exciting current $i_{2}$ was observed due to high inductance caused by the series connection of six EM2s. A power factor correction (PFC) capacitor is inserted in series in the EM2 circuit to improve the current transient response. Ac steady state levitation force is measured by installing a digital force gauge (IMADA, ZTA-5N) on the Al ring. As for ac transient response characteristics, the position of the center of Al ring is measured using a laser displacement sensor (OMRON, ZX-LD40) as shown in Fig. 3a.

Figure 6a shows the measured ac steady state levitation force for the phase difference $\theta$ between $i_{1}$ and $i_{2}$ when both currents are fixed to 3 A ${}_{\text{rms}}$ . The maximum levitation force is around 2.0 times larger than the Al ring weight at a phase difference of 60 degrees and an excitation frequency of 180 Hz. Figure 6b shows the relationship among levitation force, $i_{1}$ , and $i_{2}$ when excitation frequency and phase difference are set to 180 Hz and 60 deg., respectively. The experimental results of Fig. 6 are in good agreement with the FE analysis results of Fig. 4, and thus the axisymmetric analysis method mentioned above is obviously reasonable.

3.2.2 Pull-up of Al ring using ac transient currents

Figure 7a shows the r.m.s. values of voltage signals applied to EM1 and EM2 at pull-up tests. These input voltages are set so that the final values of exciting currents would be $i_{1}=$ 3 A ${}_{\text{rms}}$ and $i_{2}=$ 3 A ${}_{\text{rms}}$ . Figure 7b shows the actual current waveform when the voltage and frequency of EM1 are set to 12 V and 180 Hz. The current $i_{1}$ instantaneously reached a constant value (3 A ${}_{\text{rms}}$ ) as expected. At 3 seconds after the current $i_{1}$ was applied to EM1, a step current or the ramp current which reached the final value after 3, 6, or 12 seconds was applied to EM2. Each actual input current of EM2 at pull-up tests is shown in Fig. 8. Here, current $i_{2}$ is set to $f=$ 180 Hz and $\theta=$ 60 deg. Each current waveform of EM2 coincides with each input voltage waveform in Fig. 7a owing to the PFC capacitor inserted in EM2 circuit. Figure 9 shows the pull-up response of Al ring to each input current. Pull-up tests were carried out at the initial gap $d=$ 10 mm. In this test, the Al ring was suspended at three points with threads to keep the ring horizontal. The Al ring was immediately pulled up by applying the step current. Furthermore, even when three kinds of ramp currents were applied, the Al ring was pulled up straight without swing in horizontal directions. That is, these results prove that the Al ring is pulled up by continuous upward electromagnetic force rather than instantaneous upward force.

4. Conclusions

Originally, it is common sense that only repulsive force acts between a nonmagnetic metal and an ac electromagnet. That is, the conventional ac induction type maglev can only push up the nonmagnetic metal, which reduces the degree of freedom of configuration. In this research, we succeeded in pulling up an Al ring by using the ac ampere force generation method, as if a permanent magnet attracts iron. By installing the presented system at the tip of industrial robots, a series of operations such as “grabbing, moving, releasing” a nonmagnetic metal object by electromagnetic force is expected. However, the size and shape of Al ring are strongly limited. Our future plan is to explore the configuration and arrangement of ac electromagnets for strengthening the ac ampere force while suppressing the effect of ac induction force to increase the flexibility of selection of the size and shape of Al ring. Moreover, we have a plan to try non-contact stabilization of the Al ring by feedback control in the near future.

Footnotes

Acknowledgments

This study was supported by a part of JSPS KAKENHI Grant Numbers JP25289014.

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