Planar maglev positioning system

[0001] The present invention relates to a planar positioning system, and more particularly to an improved structure of a planar positioning system having maglev positioning system thereon.

[0002] In recent years, precision machining technologies and precision servo control technologies play vast important rules with the rapid growth of the computer information and electrics industries. Traditionally, DC or AC servo motors operated with screws are applied in most precision positioning systems to achieve the purpose of precision positioning. For example, by using piezoelectric actuator at 10 micrometer motion distance which can reach high precision of 10 nanometers (nm), and the piezoelectric actuator can also meet a rapid reacting request. However, the superior limit of piezoelectric actuator is the moving range. It can not be used if there needs a larger moving range condition. In order to meet the long distant request, most of them utilize server motor with screw bar or directly utilize linear motors in tradition. Nonetheless, it renders the whole positioning precision down because of backlash of screw bar and friction of bearings. Linear motors also influenced by the ripple and end effect which reduce the positioning precision.

[0003] In general, a method to solve said friction is not only strengthening the manufacture precision of the system hardware, but also lubricating oil which can reduce the friction. Furthermore, it utilizes many kind of ways to estimate the friction under controlling principle and utilizes reverse force to against the friction effect.

[0004] In millimicron semiconductor fabricating process, it has reached certain level of technology level. At 0.9 μm fabricating process, its surface examining technology will play an important role. Although it can use the method of reducing friction method which has mentioned above to the examining, but it would render the examining results imprecise due to the electrostatic or shift accuracy down by few friction. It's obvious that none-contacting force is a better way to solve the system problem above. Aerodynamic suspension system, electrostatic suspension system and maglev system are common examples which use none-contacting force. However, the first two are not suitable in some particular environment, e.g. clean room, vacuum room, etc. Therefore, in order to develop a positioning system with high accuracy and be able to use in many environments, a system which utilizes maglev theorem to be basic construction has been developed. Beyond the mature technologies of double axles maglev technology recently, Dr. Trumper, from MIT. USA, has published 6 DOF maglev positioning system which utilizes linear motors as basic construction that also provides vertical maglev and lateral impellent that the system needs at 1996. However, it is not easy to apply to relate industries for its complexity and difficulty.

[0005] Moreover, Dr. Trumper's student Kim, at Texas University, has designed a new 6 DOF micro-actuator which is still under developing. The system utilizes coils and permanent magnets to achieve 6 DOF motion. Although it is a high precision system, but it does not suit in large movement application for its hardware design. Kwang and Yoon, from Korea, have developed a construction that utilizes switching two dimensional electromagnet arrays and regulating current for rendering the platform moving on a plane. However, it still could not surmount the boundary problem between coils. On the other hand, it also means that it could not reach the large movement request.

[0006] Moreover, according to the disadvantage of the used maglev positioning systems, the inventor has invented a new planer maglev positioning system which could achieve large moving range and high 6 DOF moving accuracy.

[0007] A primary object of the present inviention is to provide a novel planar maglev positioning system that has large moving range and the motion of 6degrees of freedom (DOF) with high accuracy positioning.

[0008] To achieve the above object, the novel planar maglev positioning system of the present invention mainly comprises: a platform, which has three hanging arms fixed on the platform, wherein each hanging arm has two permanent magnets, one being located at one end of the hanging arm and another one being located at a middle part of the hanging arm; three impelling sets which set outside of the permanent magnet located at the end of each hanging arm, and there are impelling coils setting on each impelling set; three maglev sets, which are set corresponding each hanging arms, and there are maglev coils and permanent magnets setting on each maglev set.

[0009] Due to the maglev force from the maglev coils which input controlling current, and impelling force from the impelling coils which input controlling currents, it could control the platform that enables to do 6 DOF position moving and achieve the large moving range and the motion of 6 DOF with high accuracy positioning.

[0021] Please refer to FIG. 1 that is a magnetic field vector pattern which object generates in the space, and please refer to FIG. 2 that is a magnetic field vector pattern which cylinder electromagnet generates in the space, as shown:

[0022] According to Biot-Savart Law, the magnetic field vector which is generated in the space after connecting with current source is shown as:

[0023] $\begin{array}{cc}\stackrel{\rightharpoonup }{H}=\frac{1}{4\pi }{\int }_{v^{\prime }}\frac{\stackrel{\rightharpoonup }{J}\left(\stackrel{\rightharpoonup }{r^{\prime }}\right)\times {\stackrel{\rightharpoonup }{i_{r^{\prime }}}}_r}{{r^{\prime }-r}^2}d{v}^{\prime }& \left(1\right)\end{array}$
Wherein is a view point position vectors, is a surface current position vector, (¹) is the current density of the coil, _r,_r is a vector opposite of the view point and surface current. By applying the equation on the cylinder and rectangle electromagnets, we have got magnetic field vector in space as following equation:

[0024] $\begin{array}{cc}{\stackrel{\rightharpoonup }{H}}_{\mathrm{cyl}}=\frac{1}{4\pi }{\int }_{-h_{1/2}}^{h_{1/2}}{\int }_0^{2\pi }{\int }_{r_1}^{r_2}\left(\frac{{\mathrm{NI}}_{\mathrm{cyl}}}{\left(r_2-r_1\right)h_1}\right)\frac{\left({\stackrel{\rightharpoonup }{e}}_{{\varphi }^{\prime }}\times {\stackrel{\rightharpoonup }{e}}_{p^{\prime }p}\right)}{{\stackrel{V}{p}-{\stackrel{V}{p}}^{\prime }}^2}{r}^{\prime }d{r}^{\prime }d{\varphi }^{\prime }d{z}^{\prime }& \left(2\right)\end{array}$
Wherein h₁ is coil's height, N is coil's winding turns r₁ and r₂ represent internal and external diameter of the coils, I_cyl is an input current of the coil, _cyl is product of position function and current in space.

[0025] We rewrite the equation as following:

[0026] $\begin{array}{cc}{\stackrel{\rightharpoonup }{H}}_{\mathrm{cyl}}={\stackrel{\rightharpoonup }{h}}_{\mathrm{cyl}}\left(x,y,z\right)I_{\mathrm{cyl}}& \left(3\right)\end{array}$
With the same reason, we got the magnetic field that rectangular electromagnet generates is:

[0027] $\begin{array}{cc}{\stackrel{\rightharpoonup }{H}}_{\mathrm{rec}}={\stackrel{\rightharpoonup }{h}}_{\mathrm{rec}}\left(x,y,z\right)I_{\mathrm{rec}}& \left(4\right)\end{array}$

[0028] please refer to FIG. 3 that is a permanent magnet forced pattern in magnetic field space. From Lorentz force, we got a equation of a permanent magnet forced in magnetic field space:

[0029] $\begin{array}{cc}\stackrel{\rightharpoonup }{F}=\left(\stackrel{\rightharpoonup }{m}·\nabla \right)\stackrel{\rightharpoonup }{B}& \left(5\right)\end{array}$
Wherein is a dipole vector of the magnet.

[0030] From equation (3) and equation (4), it is not difficult to find that the magnet force that magnet generates in electromagnet field and can be shown as:

[0031] $\begin{array}{cc}\stackrel{\rightharpoonup }{F}=\stackrel{\rightharpoonup }{g}\left(x,y,z\right)I& \left(6\right)\end{array}$
Wherein (x,y,z) is a opposite position function of the magnetic in the electromagnet. In order to get the relating function of (x,y,z), we avoid complicated theory or finite element method (FEM) to get the force of the magnet in the coil. We use high precision machine device to measure the force in the coil and rid of current value to get the curve of (x,y,z).

[0032] Please refer to FIG. 4(a) and FIG. 4(b) that are the patterns of a rectangle-shaped electromagnet and the forced curve between a rectangle-shaped magnet and a rectangle-shaped electromagnet, as shown:

[0033] For rectangular magnet and rectangular electromagnet to be example, set 100 measuring points inside the coil and put the magnets on them, then get the force value of magnets in different current from those points, and utilize those measured data and multinomial curve to get:
F_rec,y=(a₆y⁶+a₅y⁵+a₄y⁴+a₃y³+a₂y²+a₁y+a₀)I_rec  (7)

[0034] Wherein a₆=−1.954×10⁹, a₅=4.39×10⁸, a₄=−3.385×10⁷, a₃=1.16×10⁶, a₂=−19338, a₁=214.8, a₀=−0.385. Therefore, we can get the relating function of (x,y,z) between rectangular magnet and rectangular Electromagnet.

[0035] Please refer to FIG. 5(a) and FIG. 5(b) that are the patterns of a circular-shaped electromagnet and the force curve between a cylinder-shaped magnet and a cylinder-shaped electromagnet, as shown:

[0036] Similarly, we get the relating function of (x,y,z) between circular magnet and cylinder electromagnet by using the same way as above:
F_cyl,z=(b₄z⁴+b₃z³+b₂z²+b₁z+b₀)I_cyl  (8)
Wherein b₄=−5.62×10⁶, b₃=−4.89×10⁵, b₂=−16659, b₁=−219.34, b₀=0.06619.

[0037] Please refer to FIG. 6 that is the structure of the invention, as shown:

[0038] The present invention, a novel planar maglev positioning system 1, comprises a platform 10, which has three hanging arms 101, 102, 103 at the edge, and each hanging arm 101, 102, 103 has set a permanent magnet 104 105 106 at the end; three impelling sets 11 12 13, which are set on the relative positions of the permanent magnets 104 105 106 located of the end of each hanging arms 101, 102, 103, and there are impelling coils 111 121 131 setting on each impelling sets 11 12 13 to provide impelling force when input control current into impelling coils 111 121 131 three maglev sets 14 15 16, which are set corresponding each hanging arms 101, 102, 103, and there are maglev coils 141 151 161 and permanent magnets 142 152 162 setting on each maglev set 14 15 16, to provide levitated forces when input control current into meglev coils 141 151 161. Wherein the material of the platform 10 and three hanging arms 101, 102, 103 and maglev coils 141, 151, 161 can be aluminum alloy, and these three hanging arms 101, 102, 103 can be “” shape strength structure. Besides, one of the three handing arms 101, 102, 103 can be bent shape.

[0039] Please refer to FIG. 7(a) and FIG. 7(b) that are the overlook and front-look patterns of the platform under force of the invention, as shown:

[0040] By Newtonian second mechanics law, we get forced equations and torque equations of the platform from the six magnetic force of FIG. 7(a) and FIG. 7(b):
ΣF_X=F₁−√{square root over (2)}/2F₃=M{umlaut over (X)}
ΣF_Y=F₂+√{square root over (2)}/2F₃=MŸ
ΣF_Z=F₄+F₅+F₆−Mg=M{umlaut over (Z)}
ΣT_X=−F₅l₁+√{square root over (2)}/2F₆l₂≅I_{XX{umlaut over (φ)}}
ΣT_Y=F₄l₁−√{square root over (2)}/2F₆l₂≅I_{YY{umlaut over (φ)}}
ΣT_Z=F₃L₃≅I_{ZZ{umlaut over (θ)}}  (9)
Wherein M is mass of the platform, g is acceleration of gravity, I_XX, I_YY and I_ZZ are rotating inertia of the platform along X, Y and Z axles. Go back to equation (7) and (8), we can rewrite the above matrix into:
M{umlaut over (W)}=B(W)U−G  (10)
Wherein M≡diag[M, M, M, I_XX, I_YY, I_ZZ], X≡[X, Y, Z, φ, φ, θ]^T, U≡[u₁, u₂, u₃, u₄, u₅, u₆]^T, G≡[0, 0, Mg, 0, 0, 0]^T.

[0041] From the equations above, utilizing impelling force F₁ F₂ F₃ when input control current into impelling coil 111 121 131 can precisely control the platform 10 moving along axle, and rotating along axle(θ), and utilizing meglev coils 141 151 161 to input control current to generate levitated forces F₄ F₅ F₆ can precisely control the platform 10 moving along axle and rotating along, axle(φ, ψ) utilizing maglev coils 141, 151, 161. Thus, it achieves large moving range and the motion of 6 DOF with high accuracy positioning.