Abstract—A novel velocity sensor based on electromagnetic induction was proposed in this paper. It was composed of four small inductor chips with circular symmetrical distribution on the bottom of a printed circuit board (PCB) and an elastic body with a permanent magnet embedded into on the top of the PCB. The output voltage of each inductor chip will change when an object moves on the top of sensor and drives the permanent to follow with a specific speed. The principle of velocity measurement was derived and simulation was carried out to determine size of the magnet and size of the whole sensor. Then, a prototype was developed and velocity experiments were executed to evaluate properties of the prototype. The result shows that the prototype was capable of following the velocity curve of a motion platform and measuring the velocity vector of the platform with nonlinear errors of 8.1% and 11.9% along its x-axis and y-axis respectively when the speed was from 1mm/s to 9mm/s.
I. INTRODUCTION Wafer transfer robot, which is an essential equipment of
integrated circuit manufacturing industry, takes a very important mission of transferring wafers precisely, fast and steadily from one position to another [1]. As an important part of wafer transfer robot, wafer transfer robot has a great effect on the efficiency of wafer transfer and wafer deformation because of contacting with wafer directly. In a vacuum environment, wafer transfer robot mainly depends on friction force between the end effector and the wafer to implement wafer transmission [2]. When the robot accelerates or decelerates, some serious problems will happen easily, such as wafer surface scratch, slope and stick-slip, which will decrease efficiency of wafer transfer obviously. In order to gain contact information on contact surface of wafer transmission, a small three-dimensional (3-D) tactile sensor based on piezo-resistive effect of piezo-resistive conductive ink (PRCI) was developed and was capable of measuring 3-D micro-force [3]. However, when transferring a wafer with high speed, it’s not enough to evaluate dynamic performance of wafer movement due to poor dynamic properties of the 3-D tactile sensor.
In order to obtain the dynamic information of wafer movement to control the robot moving more flexibly and high-efficiently, it is necessary to measure the wafer’s velocity
or acceleration. Due to the narrow spacing between layers of wafer cassette, 10mm for wafer with a diameter of 300 mm, the height of the sensor must be less than 10mm. Currently, most of available acceleration sensors integrate signal conditioning circuit, which make them difficult to be assembled in this narrow space.
Since acceleration is differential of velocity, acceleration information can be gained from velocity. In this paper, aim to measure velocity, a novel small velocity sensor based on electromagnetic induction was proposed. In 2009, Takenawa [4] developed a tactile sensor with similar structure, but it can only be used to detect slippage and three-axis force, not for velocity measurement directly.
II. MEASUREMENT PRINCIPLE The structure of the velocity sensor is shown in Fig. 1. The
whole sensor include an elastic body with a cylindrical permanent magnet embedded into on the top of a rigid substrate and four same small inductor chips (#1~#4) with circular symmetrical distribution on the bottom of the rigid substrate. H0 is the distant between the upper surface of permanent magnet and the plane of chip array, and R0 denotes the radius of the distribution circle of chip array. When a external force drives the elastic body deformed, the permanent magnet will make a movement of cutting magnetic induction line over the coil array and the output voltage of each inductor chip will change.
Figure 1. Mechanism of the sensor.
According to Faraday's law of electromagnetic induction, the amplitude of induction voltage Uout is proportional to the
This work was partly supported by the National Basic Research Program of China (973 Program) under grant 2009CB724206, the National ImportantProject on Technologies R&D under grant 2009ZX02012-002, the Program for Changjiang Scholars and Innovative Research Team in University under grant IRT0915.
change rate of the vertical component of magnetic flux density B⊥, shown as following equation
( ( ) )( ) Sout
d B s dsd d B SU N N Ndt dt dtφ ⊥⋅= − = − = − ∫ (1)
where N and S denote the number of coils of a inductor chip and the surface area of a coil, respectively. When S is very small (≤0.5mm2), it can be placed outside of the integral sign and the following equation can be got:
= z zout r
dB dB dBdrU NS NS NS Vdt dr dt dr
⊥≈ − − = − (2)
where Vr=dr/dt is the radial component of velocity of permanent magnet. When a very small displacement happens, dBz/dr can be regarded as a constant, dBz/dr ≈const, then
1out rU V
K≈ (3)
where K is a constant related to sensor structure, and it can be calibrated by experiments.
When four same chips are configured differentially and every two opposite inductor chips formed a differential output pair along two mutually perpendicular directions respectively, the following equations can be got:
1 3 13( )x x xv K U U K U= − = (4)
2 4 24( )y y yv K U U K U= − = (5)
where vx and vy are components of velocity of magnet along x-axis and y-axis respectively, Kx and Ky can be calibrated by experiments, U1~U4 are outputs of four chips.
III. DEVICE DESIGN According to the measurement principle, the key point is
that dBz/dr should be regarded as a constant. In order to find the qualified range, spatial magnetic field distribution of cylindrical permanent magnet would be derived and some simulation would be carried out by using commercial numerical processing software.
A. Magnetic Field Distribution As shown as Fig.2, a coordinate system is established on
the top of a cylindrical permanent magnet. Let R and L denote its radius and its height respectively, and let z1 and z2 denote the axial position of its bottom and top respectively. Assuming
Figure 2. Sketch of cylindrical permanent magnet.
that the magnet has a second quadrant demagnetization curve 0 ˆ( )sB H M zμ= + and using the current model [5], the radius component (Br) and the axial component (Bz) of magnetic flux density B can be got as follows:
2 20
01
( , , ) ( 1) cos( ') ( , , ; , ', )4
ksr k
k
MB r z g r z R z Rd
πμφ φ φ φ φ φπ =
= − −∑ ∫ (6)
where2 2 2 1/ 2
1( , , ; , ', )[ 2 cos( ') ( ') ]kg r z R zr R rR z z
φ φφ φ
=+ − − + −
.
2
1
2 2( 1)030
1' ( )
cos( ') ( )(x) ( 1) ( ) ' '
4 x x 'c
zjs cz cz
jr R j
M r R jB R j d dzπμ φ φ φ
π+
==
− −= −
−∑ ∫ ∫ (7)
According to (6) and (7), using numerical treatment method, simulation of magnetic field distribution of cylindrical permanent magnet with arbitrary size can be carried out to determinate the size of the permanent magnet and the size of the inductance chip array.
B. Size Determination of Permanent Magnet Considering that the sensor will be assembled on the
surface of end effector, the total height of sensor should be less than 5mm. According to deformation properties of general elastic materials, height restriction of sensor and volume restriction of sensor, H0 ( see Fig.1) was set to5.0 mm, and the height of the magnet L (see Fig.2) was set to 0.5mm, and R was limited to less than 2.5mm. Due to the need to lower cost and the uncertainty of production cycle, some available commercial permanent magnets with standard size series were chosen to make simulation analysis with (6) and (7) by using MATLAB (2010R, The MathWorks Co. USA). From Sangysupply Co. in Japan, R series satisfied the requirements are 0.5mm, 1.0mm, 1.5mm, 2.0mm and 2.5mm, whose material is NdFeB. Assuming that Ms is equal to 4.23×104A/m, when L=0.5mm, z=H0=3mm and φ =0°, the simulation result of Bz along radial direction of the permanent magnet with different R is shown in Fig. 3, where it can be got that when R=2.5mm the amplitude of Bz along radial direction is the biggest one, and its linear region is also the widest one. Thus, the permanent magnet with R=2.5mm and L=0.5mm was selected.
0 1 2 3 4 5 6 7 8 9 10-5
0
5
10
15
20x 10
-3
r (mm)
Bz
(T)
R=2.5mm
R=2.0mm
R=1.5mm
R=1.0mm
R=0.5mm
Figure 3. Bz distribution simulation of magnet with different R.
C. Size Determination of Inductance Chip Array The size of inductance chip array includes H0 and R0 (see
Fig.1) . According to precious analysis, H0=3mm, and then R0 will be determined in this part.
As analyzed in the part of measurement principle, to lower error, dBz/dr should be regarded as a constant, that is, dBz/dr≈const. In order to find the qualified range, calculate the distribution of dBz/dr of the permanent magnet with R=2.5mm and L=0.5mm along its radial direction, and the result is shown in Fig. 4. As seen in Fig. 4, there is an extreme point A, where r=2.33mm, so R0 is set to 2.33mm.
Assuming that the range of linearity is determined by Δd/d=0.1%, where d is the value of dBz/dr at point A, it can be got that the radial range is |Δr|=0.11mm.
Figure 4. dBz/dr distribution along radial direction.
D. Design of Elastic Body To make the magnet embedded into elastic body easily, a
sandwich structure was utilized to design elastic body. As shown in Fig.5(a), the elastic body contained four parts: rigid rubberⅠ, permanent magnet, hyper-elastic rubber and rigid rubber Ⅱ. The term of hyper-elastic material, which is from ANSYS, a finite element analysis software, is a description of nonlinearity of material with a capability of large deformation, such as silicone rubber, neoprene rubber.
Figure 5. Sketch of elastic body.
According to deformation properties of general hyper-elastic materials, the height of sensor and the volume restriction of sensor, the size of elastic body is determined finally as shown in Fig.5(b).
E. Prototype Making According to the previous analysis, a prototype of sensor
of this type was developed by using rigid rubber bump (see Fig. 6(a), made by Kinscem Co. in Japan), silicone rubber (see Fig. 6(b), made by Trusco Co. in Japan) and a cylindrical permanent magnet with R=2.5mm and L=0.5mm (see Fig. 6(c),
made by Sangyo Supply Co. in Japan). They were made in accordance with the size requirements as shown in Fig. 5(b), and then were glued with each other to become a whole body.
Figure 6. Materials of making the prototype.
As shown in Fig. 7, a printed circuit board (PCB) was made as rigid substrate, on the upper surface of which is the elastic body including the permanent magnet, the transparent part. The circuit was made on the lower surface of PCB, and four surface mounted device (SMD) inductor chips of 68uH were mounted on the same surface in the way of circular symmetrical distribution as chip array.
Figure 7. The prototype compared with a coin of 1 yen.
IV. EXPERIMENT STUDY
A. Experiment System To evaluate properties of the prototype, experiments of
following velocity curve and velocity measurement were carried out, respectively. Fig. 8 shows the experimental system with the prototype and the signal conditioning circuit. A 2-D motion platform (XMSG413-RA5 & ZMSG413-RA5, Suruga Seiki Co. in Japan) was fixed on the substrate and was able to move by standard trapezoidal speed-time curve and its speed range is from 1mm/s to 9mm/s. The signal conditioning circuit, which was specially designed for the prototype and included signal pre-amplification and filtering circuit, was utilized to deal with four outputs signal of chip array at the same time. Through signal pre-amplification and filtering, the micro signal, whose typical average voltage was about 0.1mV, would be amplified to a range of observation.
Figure 8. Experimental system.
B. Velocity Curve Following Experiment Study Let the prototype be fixed with its x-axis along x-axis of
the motion platform, and make the motion platform moving back and forth by standard trapezoidal speed-time curve with maximum speed of 5mm/s (see Fig. 9). The result of outputs of the prototype is shown in Fig. 10, where the bold line and the fine line indicate x-axis output of the prototype and y-axis output of the prototype, respectively. Then, let the prototype be fixed with its y-axis along x-axis of the motion platform, by the same method, the result of outputs of the prototype can be got as shown as Fig. 11.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10
-5
0
5
10
t/s
velo
city
/mm
/s
Figure 9. Standard trapezoidal speed-time curve.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-0.5
0
0.5
t/s
volta
ge/V
x-axis output y-axis output
Figure 10. The result of moving only along x-axis of the prototype.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.5
0
0.5
t/s
volta
ge/V
x-axis output y-axis output
Figure 11. The result of moving only along y-axis of the prototype.
Comparing above two results of outputs of the prototype with the velocity curve of the platform, it can be got that the prototype was capable of following the velocity curve of a motion platform.
C. Velocity Measurement Experiment Study Because the motion platform can move by standard
trapezoidal speed-time curve with specific maximum speed V=vmax, it can be used to carry out velocity calibration of the prototype, that is, let the platform move back and forth with a speed interval of 1mm/s from V=1mm/s to V=9mm/s and then corresponding outputs of the prototype were remembered under each movement process with a specific V.
First, let the prototype be fixed with its x-axis along x-axis of the motion platform, and then make the motion platform moving in the way described above. The result is shown in Fig.12 (a), and the expression of the bold regression line is
0.0607 0.6784xU v= + (10)
where Ux denotes x-axis output of the prototype and v denotes the x-axis velocity of the platform. And the nonlinear error is 8.19%.
1 2 3 4 5 6 7 8 90
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
x-axis velocity of the platform (mm/s)
Vol
tage
(V
)
1 2 3 4 5 6 7 8 90
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
y-axis velocity of the platform (mm/s)
Vol
tage
(V
)
x-axis output of the prototypey-axis output of the prototype
x-axis output of the prototypey-axis output of the prototype
(b) The result of moving only alongy-axis of the prototype
(a) The result of moving only alongx-axis of the prototype
Figure 12. The result of velocity experiments.
Next, let the prototype be fixed with its y-axis along x-axis of the motion platform, and make the motion platform moving in the same way. The result is shown in Fig.12 (b), and the expression of the bold regression line is
0.0656 0.7424yU v= + (11)
where Uy denotes y-axis output of the prototype and v denotes the x-axis velocity of the platform. And the nonlinear error is 11.90%.
V. CONCLUSION In this paper, a new type of velocity sensor based on
electromagnetic induction was proposed and its prototype was developed. It was composed of four small inductor chips with circular symmetrical distribution on the lower surface of a PCB and a elastic body with a permanent magnet embedded into on the upper surface of the PCB. The formula of magnetic flux density around a cylinder permanent magnet with arbitrary size was derived and some simulation analysis was carried out, then the size of the magnet and the size of elastic body were determined and a prototype was developed. In the end, an experimental system was established and the velocity following experiment and the velocity measurement experiment were carried out. The results shown that the prototype was capable of following the velocity curves of the motion platform and measuring velocity vector of the motion platform with 8.1% and 11.9% along its x-axis and y-axis respectively when the platform moved at a speed interval 1mm/s from 1mm/s to 9mm/s. Next step, the structure of senor will be optimized and a new prototype will be made to meet the requirement of wafer transmission.
REFERENCES [1] K. Takashi, “Vacuum manipulator for semiconductor equipment,”
Industrial Robot, Vol. 29(4), 2002, pp. 324–328 [2] Y. M. Cao, “Contact properties analysis and design of end effector for
larger-size wafer transfer robot,” Master’s degree paper of Harbin Institute of Technology, 2010, pp. 2–17
[3] Y. J. Liu, H. J. Han, Y. Inoue, T. Liu, K. Shibata, “A three-demensional tactile sensor based on piezoresistive conductive ink,” Procceding of 2011 4th IEEE International Conference on Computor Science and Information Technology, 2011 (9), pp. 486–490.
[4] S. Takenawa, “A soft three-axis tactile sensor based on electromagnetic induction,” Proceeding of the 2009 IEEE International Conference on Mechatronics, Malaga, Spain, April 2009, pp.1–6.
[5] E. P. Furlani, Permanent Magnet and Electromechanical Devices, Academic Press, 2001, pp. 126–131.
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