- Email: [email protected]
A six-component silicon micro force sensor
SE"ORS
AC'rUATORS A
ELSEVIER
Sensors and ActuatorsA 65 (1998) 109-115
PHYSICAL
A six-component silicon micro force sensor W.L. Jin a, C.D. Mote, Jr. b,, School of Mechanical and Production Engineering, Nanyang Technological University, Singapore, Singapore b Department of Mechanical Engineering, Universil3' of California at Berkeley, Berkeley, CA 94720-4200, USA
Received 22 May 1997;revised 12 August 1997;accepted20 August 1997
Abstract A six-component micro force sensor has been developed using silicon micromachining technology. The sensing and elastic elements of the sensor are fabricated separately through bulk silicon machining processes and bonded together using a Si-Au eutectic bonding technique. Calibration of the sensor is undertaken using Lorentz forces. High resolution and satisfactory linearity of the outputs of the sensor are obtained. © 1998 Published by Elsevier Science S.A. Ke)words: Microforce sensors;Micromachining;SiIicon
1. Introduction Micro force sensors are important components in microrobotic systems [ 1-3]. The minimum dimensions of multicomponent force sensors developed using conventional technology are limited by the size of the sensing elements [4-7]. A six-component miniature force sensor was developed by combining four micromachined silicon sensing elements and a conventionally machined elastic structure [8]. The use of conventional machining technology is an obstacle to batch production and further size reduction, and the bonding of the individual sensing elements is also time consuming. In calibration of a six-component force sensor, the magnitude, direction and position of the calibration force must be precisely controlled. Calibration through the use of gravitational or mechanical forces, which is a common practice with conventional multicomponent force sensors, requires development of a complex loading system [9]. When the sensor dimensions are scaled down to a few millimeters or less, fabrication and operation of a loading system become difficult. In the current design, a four-diaphragm sensing element is developed so that only one sensing element is needed for each sensor, and silicon micromachining technology is used to fabricate both the sensing and elastic elements of the sensor. By use of silicon micromachining technology, the dimensions * Correspondingauthor. Tel.: + 1510 642 7374. Fax: + 1510 643 6130. E-mai~"cdm@de,~.ure~.berke~e~.edu
of the sensor are reduced (4.5 mm ×4.5 ram× 1.2 ram) and batch production of the sensor becomes possible. The Lorentz force generated on a conductor carrying a current I in a magnetic field B, F=IIxB
is used to calibrate the sensor. I is the length of the conductor. As the vector product of current and magnetic field, force components in three orthogonal directions can be generated on a two-dimensional conductor. Therefore, the need for a micro-sized mechanical loading device is avoided. The linear relationship between the force and current makes the control of the force magnitude convenient.
2. Design The three components of the sensor shown in Fig. 1 are: (1) the elastic element, which is a bulk machined silicon cross suspended in a square frame; (2) the sensing element, which includes four diaphragms suspended between a silicon frame and a silicon cross; and (3) the load plate, which is a square silicon block with stages on the bottom side and aluminum stripes on the top side. A Si-Au eutectic bonding technology is used to bond the elastic and sensing elements, and the load plate is bonded to the sensing element using high-performance epoxy. On each of the four diaphragms of the sensing element, two Wheatstone bridges are integrated, as illustrated in Fig. 2. Forces applied to the load plate are transmitted through the silicon cross of the sensing element to the elastic element,
0924-4247/98/$I9.00 © 1998Published by Elsevier ScienceS.A. All rights reserved PII S0924-4247 ( 97 ) 01671-3
110
W.L. Jin, CD. Mote, Jr./Sensors and Actuators A 65 (1998) 109-115
the displacement of the elastic element is transmitted to the diaphragms of the sensing element, resulting in shear and axial strains on the diaphragms, which are then detected by the eight Wheatstone bridges shown in Fig. 2. Because the width of the bottom opening of the trapezoidal slots in the sensing element is larger than the width of the diaphragm (refer to Fig. 1), the strains obtained on the diaphragm are larger than that on the surface of the elastic element where the sensing diaphragms are located. The sensitivity of the sensor is therefore increased without decreasing its stiffness, which is highly desirable in robotic applications. The strain gai m which is about seven in the current design, is a function of the thickness of the sensing element, the width of the diaphragm and the property of the bonding interface [ 10]. The surface strains at the four ends of the cross beam, where the sensing diaphragms are located, are estimated using formulae from the elastic theory [11]. The relationships between the strains sensed by the bridges and the force and moment components are (refer to Fig. 3):
0n II
(a)
I
(b)]:
I
; ,Smm
\
1
Y.
m
m
m
El
"l
62 63
Fig. 1. Design of the sensor: (a) schematic view; (b) A-plane cross-sectional view.
64
= 0%
65 E6
which is approximately modeled as an elastic cross beam with clamped ends. The strain distributions in the cross beam under the application of unit force or moment components at its center are shown in Fig. 3. Through the bonding interface, bridge 7
67 6a
0 ex~ ~:,
%. 0 0
o e~ 0
0 0 0
0 -E~,.
- "/z, 0
0 6~
0 0
- ~¢.~
o
0
-e~.
0 %.. - e,~,. 0 o o o Ym: eS: -6, .... 0 0
bridge 6
bridge5
N
f,. Inx
L,"2:,j (1)
bridge 8
DD[2 D [~
o %: e,,v 0 0 "/m:
diaphragm 4 diaphragm 1
D ........1 D ,:j i
',,1
I~]~l
bridge 1
r bridge 2
_d aphragm 4 I ,ap~ag m 2
i
3 D D....... .
p'y
bridge 4 bridge 3 Fig, 2. Diaphragms and Wheatstone bridges on the sensing element.
i
ili
W.L. Jin, C.D. Mote, J r . / S e n s o r s and Actuators A 65 (]998) 109-115
~r~
~
.v x
X
]~'
b, under fz
(fI@ iiiiiili;i~?~
iiiii!i!i!i!i!ii~'~
/,
~
~r
x.
or' c, under rm (my)
f x d ~ x
a, underfx @)
d, under m z Fig. 3. Strain distribution in a cross beam with clamped ends.
where a~hd
ak:
efx = %. = 4EI
2EA
rT-nn
1 -- ~kf
Yfx= Try = 2GA
-0 1 0 A= 0 0 1
0 0 1 0 1 0
1 0 0 0 0 I
0 0 1 1 0 0
0 -1 0 0 0 1
0 0 1 0 -1 0
-1 0 0 0 0 1
00 I
(2)
-1 0 0
is introduced to examine the possibility of an interaction-free design of the bridge circuits. Multiplying both sides of Eq. ( 1 ) from the left by A, we have:
hl efz = 16 EI
O~kmh
e,,~ = e,~y = 4EI
¢ ¢ 6~
1
Ymz = 4lGA
and c<~is the strain gain coefficient of the sensing element. A is the cross-sectional area of the elastic element, d is the distance from the neutral axis of the elastic element to the force, E, G are the elastic and shear moduli of silicon, I is the second moment of the cross-sectional area, h is the distance from the neutral axis of the elastic element to the sensing element and l is the length of the elastic element. 0%.= Kf*/KN, a,m--Km*/K,~ where K/is the stiffness of the cross beam with respect to force component f,., Ks* is the stiffness of one of the crossed beams that is along the x direction with respect tof~, K,n is the stiffness of the cross beam with respect to the moment component m,, and K,~* is the stiffness of one of the crossed beams that is along the y direction with respect to t77x.
Considering the symmetrical structure of the sensor, a
~vaas~m~ati~amatrix
= OLs
I , I 65
i¢
2y::~
0
0
0
0
0
L
0 0 0 26fu 0
2yjS, 0 26g, 0 0
0 46/: 0 0 0
0 0 2e,,~ 0 0
0 0 0 26,,,>. 0
0 0 0 0 4ym~
f, L 17lx t7l>, fiT.
(3) where 6~ ~ 63 -- 67 6~ = 61 -- 65 6~ = 62 2- 64 ..+- 66 -.L 68
~=~-~ 65 = 62 -- 66
e* = el + e ~ + e s + e
7
A diagonal matrix can be expected when cek~,~hd cekf = 0 4EI 2EA
W.L. Jin, C.D. Mote, Jr. / Sensors and Actuators A 65 (1998) 109-1 t 5
112
•,,~---
magnetic field
-,"
Lorentz force from wires
electric current
~
Lorentz force on strips
aluminumsnipe .~,
J
connectionwires
z,
{
mz
my
t/l x
Fig. 4. Generation of six force components on the load plate (l).
However, restricted by the two-dimensional fabrication technology, a design for which this is true is not practical. The strategy for the independent generation of the six force and moment components on the load plate during calibration is shown in Fig. 4. Because each component is generated independently, the elements of the sensitivity matrix, s~j, are obtained directly from individual outputs, u~j, corresponding to the force components,f/
are the stiffnesses of the load plate with respect to a concentrated central load and a uniformly distributed load, respectively. The displacement of the sensor is
~_~ s
ks
where ks is the sensor stiffness. Letting 6o = 6s, we have
= oltql s,~=~@" i = 1 , 2 ..... 8 j = l , 2 ..... 6 JJ)
Connectors from the substrate to the load plate are arranged so that the Lorentz forces generated in them during calibration balance each other on the load plate, as illustrated in Fig. 4. The connectors also act as additional springs between the load plate and the substrate and therefore partially support the force generated on the load plate. A primary calibration system and its elastic model are shown in Fig. 5. Iffs is the force transmitted to sensor, the displacement of the center of the load plate is then
ql-A qt A where q is the toad density on the conductor, I is the length of the conductor, ko is the stiffness of the connections,
48EI k~o=
i3
384EI kcd--
5/3
where Og t --
ksko~( kod + 2k¢) kc~( 2kook¢ + 2kcks + ko~k~)
is the force transmission coefficient, c~t increases as ko decreases. When ko = 0, ~xt = 1. In the current design, aluminum wires with 25 ~m diameter are used as the connectors (see Fig. 7). The stiffness of the wires, kc, is estimated by modeling them as L-shaped elastic beams with clamped ends. Given the wire dimensions shown in Fig. 7, k¢ is found to be in the order of 101 N m-1, much smaller than that of the sensor and load plate, ks, k¢~. Therefore, a t is close to one.
3. Fabrication
The elastic element is fabricated using a double-side polished ( i00} silicon wafer. A layer of silicon nitride is deposited first. After a two-side alignment step, the nitride on both sides of the wafer is patterned with a 3 mm × 3 m m opening and four 1.2 mm × 1.2 mm openings, respectively. A twoside KOH etching step forms the suspended silicon cross
W.L. Jin, C.D. Mote, Jr./Se17sors and Acruators A 65 (]998) 709-775
i13
distributed Lorentz force, q = B f load plate ection wire (a) substrate
I q
(b)/-'/7~
Fig. 5. An elastic model of a calibration system using Lorentz forces: (a) composition; (b) model, kc, stiffness of the connection wire; ks, stiffness of the sensor; f~, force transferred to sensor; q, distributed Lorentz force.
Fig. 6. A fabricated prototype sensor before the bonding of the load plate.
structure. Then, undoped polysilicon and goId layers are deposited for the later Au-Si eutectic bonding. Fabrication of the sensing element starts with a back-side KOH etching step to form a diaphragm on the front side of a (100) wafer. Undoped polysilicon deposition follows to provide a proper substrate for later Si-Au eutectic bonding. Standard steps for insulation, strain gauge, metallization and protection layers are then carried out to build the Wheatstone bridges on the diaphragms. Finally, silicon and silicon nitride etching steps are used to shape the diaphragm into the designed square. The sensing and elastic elements are cleaned after fabrication in preparation for the bonding process. A 10 min sulfuric acid + hydrogen peroxide bath and a 30 s HF dip are used to remove organic residues and native oxide from the surfaces. The chips are then dipped in an ammonium fluoride solution for 30 s, which protects the cleaned surfaces from oxidation in air and allows alignment before the chips are clamped together. The contact pressure during bonding is controlled at about 50 kPa. Bonding is undertaken at atmospheric pressure of 10 -5 torr at 400°C. Photographs of a bonded prototype sensor are shown in Fig. 6. The load plate is fabricated through normal micromachining steps. An infrared two-side alignment technique is used to align the stages and aluminum strips on the two sides. During bonding of the load plate to the sensor, the stages on the bottom side of the plate fit with holes on the upper surface of the sensor (see Fig. 6) so that they are properly aligned. Photographs of a fabricated sensor with the load plate are shown in Fig. 7.
4. Calibration ~\g.]. 7~prototypesensor\v~thload plateand connectionwiresbonded.
Uniform magnetic fields of 2.5 tesla forf.~,fy, rnz, and 1.5 tesla for f~, m, my are provided by an electromagnet during
t 14
W.L. Jin, C.D. Mote, Jr. / Sensors and Actuators A 65 (1998) 109- ] 15
Table 1 Comparison of different multicomponent micro force sensors Reference
Fabrication technology
Batch production
Number of components
Dimension (ram)
Volume (ram3)
[4]
conventional
no
4
G 12 × 20
2260
[ 8]
conventional and silicon mieromaehining
partially
6
~5 × 5
98~
This paper
silicon micromachining
yes
6
4.5 × 4.5 × 1.2
25
0.4. 0.3-
.j/
g 0.2
N
~
A
0 -0.! f / . . . ~ -0.2 -400
"-
= -300
-200
-1130
0
100
200
300
400
current t m A )
Fig. 8. Output of bridge 2 vs. the calibration current during generation of m,. B = 1.5 tesla, t=3.8 mm and U = 5 V.
calibration of a prototype sensor. The current supply ranges from - 400 to 400 mA, and the bridge voltage is 5 V. The output of the bridge detecting axial deformation versus the current passing through the load plate, which produces M,., is shown in Fig. 8. Satisfactory linearity between load and output is seen. The elements of the sensitivity matrix are obtained by generating six force and moment components individually, as illustrated in Fig. 4. The calibrated relationship between the sensor outputs and applied forces is m
2.41
0.42
-0.70
2.01
1.61 -0.44 -0.55 11.9 12.2 --0.08
-0.15
-0.83 0.49 18.8
0.93 -0.0~
0.55 0.55
12.5
003
-0.10
0.84 0.64 -060
,0.53 0.86
7
0 2 3 7 [-I; 0.161 I : ; !
1.46 0.141 IA / - 0 3 5 00r//. d 12.8 0.27d l m ' t
0.17 4.o3A km:d
The diagonal and 4-2 and 5-1 elements of the transformed sensitivity matrix are significantly larger than the others, which coincides with the predicted relationship shown by Eq. (3). Resolutions of 1 mN for force components and 2 mN mm for moment components were observed. Table 1 compares this sensor with the existing multicomponent micro force sensors.
5. Conclusions A six-component, micro force sensor has been developed using silicon microfabrication and wafer-bonding technologies. A calibration method based on the Lorentz force is used to calibrate the sensor. A satisfactory linearity and high resolution are observed.
m
ltl It 2 R3 lA4 U5 II 6 It 7 ll 8
Acknowledgements m
u
-0.37 6.89 1.15 -0.23
0.95 0.i2 0.28 5.60
0.23 4.76 -0.45 5.23
- 0.38 0.i9 0.54 6.8
0.50 7.10 -0.25 -0.13
1.03 0.12 1.18 0.09
0.33 -1.06 -0.26 -5,37 0.20 4.21 - 1.26 -0.14 0.38 0.32 -6.36 4.68
-0.37 -0.45 -0.39 -5.70
-0.36 -5.73 -0,28 0.22
0.87 -0.15 0.95 0.08
f, '
x
/,n,/
The work reported in the paper was funded by FANUC Ltd, (Japan). The development of the sensor was carried out in the Micro-fabrication Laboratory of the University of California at Berkeley.
/m~J m
where the unit of force is the newton (N), of moments is N mm and the outputs are in millivolts. The transformed relationship using matrix A defined by Eq. (2) is
References [ 1] Y. Zhang, Y.M. Yang, H.R. Lin and Y.H. Wu, Research on MR-2 micro-robot, Proc. IEEE Int. Conf. IndustrialTechnotogy, Goangzhou, China, 5-9 Dec., 1994, pp. 589-592.
W.L. Jin, C.D. Mote, Jr./Sensors and Actuators A 65 (1998) 109-115
[2] T. Fukuda, A. Kawamoto, F. Arai and H. Matsuura, Steering mechanism and swimmingexperimentof micro mobile robot in water. Proc. IEEE Micro Electro Mechanical Systems, Amsterdam. Netherlands, 29 Jan.-2 Feb., 1995, pp. 300-305. [3] S. Cherian, W.O. TroxelI and M.M. Aii, Design of behavior-base micro-rover robot, Proc. Intelligent Vehicles '92 Syrup., Detroit, MI, USA, 29 June-1 July, 1992, pp. 280-287. [4] D. Diddens, D. Reynaerts and H. Van Bmssel, Design ofs ring-shaped three-axismicro force/torque sensor. Sensorsand ActuatorsA, (1995) 225-232. [5] V. Gass, B.H. Van der Schoot, S. Jeanneret and N.F. de Rooij, Microtorque sensor based on differential force measurement. Proc. IEEE Micro Electro Mechanical Systems, Oiso, Japan, 25-28 Jan., 1994, pp. 241-244. [6] J. Planert, H. Modler, K. Ludecke and M. Eger, A miniaturizedforcetorque sensor with six degrees of freedom for dental measurements, Clin. Phys. Physiol. Meas., 13 (1992) 241-248. [7] K. Peterson, C. Kowalski. J. Brown, H. Allen and J. Knutti, A t'orce sensing chip designed for robotic and manufacturing automation applications, in R.S. Muller (ed.), Micro Sensors, IEEE Press. New York, 1992, pp. 419-42I. [8] W.L. Jin and C.D. Mote, Jr., Development of a six-component miniature force sensor for robotic applications,Proc. ASME Dynamic Systems Control Division, Atlanta, GA, USA, 17-22 Nov., I996, DSC Vol. 58, ASME, I996, pp. 753-760. [9] H.H. Bau, N.F. de Rooij and B. Loeck, Sensors, A Comprehensive Survey, Voh7, Mechanical Sensors, VCH, Wienheim. 1994, pp. 455459. [ I0] W.L. Jin and C.D. Mote, Jr., A novel silicon sensing element for highnatural frequency, low-range dynamometrical sensors, Sensors and Actuators A, 62 (I997) in press. [ 11] S. Timoshenko,Strength of Materials, Van Nostrand,New York, 1956, pp. 95-I38,
Biographies Welin Jin graduated from the Hefei University of Technology, China, with a B.S. in 1982. He received the Ph.D. in mechanical engineering from Nanjing University of Aeronautics and Astronautics in China and joined the faculty of the same university in 1988. He worked in the City University of Hong Kong as a visiting scholar in 1992. From May 1994 to M a y 1997, he visited the University of California at Berkeley, USA. He is now a visiting fellow at the Nanyang Technological University in Singapore. Dr Jin's research interest includes machining process monitoring and optimization, multicomponent dynamometers and microelectromechanical systems. He published more than 20 papers in academic journals and holds two patents in China. C.D. Mote, Jr., is Vice C h a n c e l l o r - - University Relations, and F A N U C Chair in Mechanical Systems at the University of California, Berkeley. As Vice Chancellor he is responsible for all programs external to the campus. Beginning early in 1992, he conceived, designed and implemented a seven year
115
comprehensive, capital campaign with a goal of one billion dollars. The victory celebration is scheduled for the turn of the century. From 1987 to 1991 he served as Chair of the Department of Mechanical Engineering. He came to Berkeley from Carnegie Institute of Technology in 1967, where he was on the faculty in the Mechanical Engineering Department between 1964 and 1967. In addition, he has held research positions at the University of Birmingham, UK, in 1963, the Norwegian Institute for Wood Science and Technology, Oslo, on many occasions between 1972 and 1985, the Technical University of Darmstadt in 1989 and the Tokyo Institute of Technology in i99 i. Vice Chancellor Mote's research and technical interest lie in the fields of dynamical systems and control, instrumentation, design, vibration and acoustics, biomechanics and sport mechanics. He is internationally recognized for his research on vibration and stability control of gyroscopic systems, including axially translating and rotating systems like circular and band saws. His work on snow skis, skiing and the biomechanics of skiing injury spans more than two decades and has established the foundation of the skiing injury and mechanics fields. His research efforts have resulted in more than 250 publications in academic journals and patents in the USA, Norway, Finland and Sweden. Vice Chancellor Mote is a registered professional engineer in California and has served professional societies in a number of capacities. He served as Vice President of the Environment and Transportation Group of the American Society of Mechanical Engineers from I986 to 1990 and as Vice Chairman of the A S M E Council on Engineering in 1989-1990. He served on the National Academy of Engineering Peer Committee from 1990-1993, as its Chair in 1992-1993, and currently serves on the Program Committee. Vice Chancellor Mote has been recognized for his contributions on many occasions. He was lauded by the University of California (Berkeley) with its Distinguished Teaching Award in 1971. He is pleased to note that many of his more than 50 doctoral students have become leading contributors to engineering practice, teaching and research. He has been elected to Fellow grade by the International Academy of W o o d Science (1978); the A S M E ( 1984); the Acoustical Society of America ( i991 ); and the American Association for the Advancement of Science (1992). In 1988 he was elected to the US National Academy of Engineering and was awarded the Humboldt Prize by the Federal Republic of Germany. In 1991 the Japan Society for the Promotion of Science awarded him their fellowship, and he was appointed to the F A N U C Chair in Mechanical Systems at Berkeley. He is listed in a number of biographical volumes including W h o ' s Who it~ A m e r i c a since 1978. Vice Chancellor Mote received the B.S. in mechanical engineering in I959 and the Ph.D. in engineering mechanics in 1963 from the University of California, Berkeley.
AC'rUATORS A
ELSEVIER
Sensors and ActuatorsA 65 (1998) 109-115
PHYSICAL
A six-component silicon micro force sensor W.L. Jin a, C.D. Mote, Jr. b,, School of Mechanical and Production Engineering, Nanyang Technological University, Singapore, Singapore b Department of Mechanical Engineering, Universil3' of California at Berkeley, Berkeley, CA 94720-4200, USA
Received 22 May 1997;revised 12 August 1997;accepted20 August 1997
Abstract A six-component micro force sensor has been developed using silicon micromachining technology. The sensing and elastic elements of the sensor are fabricated separately through bulk silicon machining processes and bonded together using a Si-Au eutectic bonding technique. Calibration of the sensor is undertaken using Lorentz forces. High resolution and satisfactory linearity of the outputs of the sensor are obtained. © 1998 Published by Elsevier Science S.A. Ke)words: Microforce sensors;Micromachining;SiIicon
1. Introduction Micro force sensors are important components in microrobotic systems [ 1-3]. The minimum dimensions of multicomponent force sensors developed using conventional technology are limited by the size of the sensing elements [4-7]. A six-component miniature force sensor was developed by combining four micromachined silicon sensing elements and a conventionally machined elastic structure [8]. The use of conventional machining technology is an obstacle to batch production and further size reduction, and the bonding of the individual sensing elements is also time consuming. In calibration of a six-component force sensor, the magnitude, direction and position of the calibration force must be precisely controlled. Calibration through the use of gravitational or mechanical forces, which is a common practice with conventional multicomponent force sensors, requires development of a complex loading system [9]. When the sensor dimensions are scaled down to a few millimeters or less, fabrication and operation of a loading system become difficult. In the current design, a four-diaphragm sensing element is developed so that only one sensing element is needed for each sensor, and silicon micromachining technology is used to fabricate both the sensing and elastic elements of the sensor. By use of silicon micromachining technology, the dimensions * Correspondingauthor. Tel.: + 1510 642 7374. Fax: + 1510 643 6130. E-mai~"cdm@de,~.ure~.berke~e~.edu
of the sensor are reduced (4.5 mm ×4.5 ram× 1.2 ram) and batch production of the sensor becomes possible. The Lorentz force generated on a conductor carrying a current I in a magnetic field B, F=IIxB
is used to calibrate the sensor. I is the length of the conductor. As the vector product of current and magnetic field, force components in three orthogonal directions can be generated on a two-dimensional conductor. Therefore, the need for a micro-sized mechanical loading device is avoided. The linear relationship between the force and current makes the control of the force magnitude convenient.
2. Design The three components of the sensor shown in Fig. 1 are: (1) the elastic element, which is a bulk machined silicon cross suspended in a square frame; (2) the sensing element, which includes four diaphragms suspended between a silicon frame and a silicon cross; and (3) the load plate, which is a square silicon block with stages on the bottom side and aluminum stripes on the top side. A Si-Au eutectic bonding technology is used to bond the elastic and sensing elements, and the load plate is bonded to the sensing element using high-performance epoxy. On each of the four diaphragms of the sensing element, two Wheatstone bridges are integrated, as illustrated in Fig. 2. Forces applied to the load plate are transmitted through the silicon cross of the sensing element to the elastic element,
0924-4247/98/$I9.00 © 1998Published by Elsevier ScienceS.A. All rights reserved PII S0924-4247 ( 97 ) 01671-3
110
W.L. Jin, CD. Mote, Jr./Sensors and Actuators A 65 (1998) 109-115
the displacement of the elastic element is transmitted to the diaphragms of the sensing element, resulting in shear and axial strains on the diaphragms, which are then detected by the eight Wheatstone bridges shown in Fig. 2. Because the width of the bottom opening of the trapezoidal slots in the sensing element is larger than the width of the diaphragm (refer to Fig. 1), the strains obtained on the diaphragm are larger than that on the surface of the elastic element where the sensing diaphragms are located. The sensitivity of the sensor is therefore increased without decreasing its stiffness, which is highly desirable in robotic applications. The strain gai m which is about seven in the current design, is a function of the thickness of the sensing element, the width of the diaphragm and the property of the bonding interface [ 10]. The surface strains at the four ends of the cross beam, where the sensing diaphragms are located, are estimated using formulae from the elastic theory [11]. The relationships between the strains sensed by the bridges and the force and moment components are (refer to Fig. 3):
0n II
(a)
I
(b)]:
I
; ,Smm
\
1
Y.
m
m
m
El
"l
62 63
Fig. 1. Design of the sensor: (a) schematic view; (b) A-plane cross-sectional view.
64
= 0%
65 E6
which is approximately modeled as an elastic cross beam with clamped ends. The strain distributions in the cross beam under the application of unit force or moment components at its center are shown in Fig. 3. Through the bonding interface, bridge 7
67 6a
0 ex~ ~:,
%. 0 0
o e~ 0
0 0 0
0 -E~,.
- "/z, 0
0 6~
0 0
- ~¢.~
o
0
-e~.
0 %.. - e,~,. 0 o o o Ym: eS: -6, .... 0 0
bridge 6
bridge5
N
f,. Inx
L,"2:,j (1)
bridge 8
DD[2 D [~
o %: e,,v 0 0 "/m:
diaphragm 4 diaphragm 1
D ........1 D ,:j i
',,1
I~]~l
bridge 1
r bridge 2
_d aphragm 4 I ,ap~ag m 2
i
3 D D....... .
p'y
bridge 4 bridge 3 Fig, 2. Diaphragms and Wheatstone bridges on the sensing element.
i
ili
W.L. Jin, C.D. Mote, J r . / S e n s o r s and Actuators A 65 (]998) 109-115
~r~
~
.v x
X
]~'
b, under fz
(fI@ iiiiiili;i~?~
iiiii!i!i!i!i!ii~'~
/,
~
~r
x.
or' c, under rm (my)
f x d ~ x
a, underfx @)
d, under m z Fig. 3. Strain distribution in a cross beam with clamped ends.
where a~hd
ak:
efx = %. = 4EI
2EA
rT-nn
1 -- ~kf
Yfx= Try = 2GA
-0 1 0 A= 0 0 1
0 0 1 0 1 0
1 0 0 0 0 I
0 0 1 1 0 0
0 -1 0 0 0 1
0 0 1 0 -1 0
-1 0 0 0 0 1
00 I
(2)
-1 0 0
is introduced to examine the possibility of an interaction-free design of the bridge circuits. Multiplying both sides of Eq. ( 1 ) from the left by A, we have:
hl efz = 16 EI
O~kmh
e,,~ = e,~y = 4EI
¢ ¢ 6~
1
Ymz = 4lGA
and c<~is the strain gain coefficient of the sensing element. A is the cross-sectional area of the elastic element, d is the distance from the neutral axis of the elastic element to the force, E, G are the elastic and shear moduli of silicon, I is the second moment of the cross-sectional area, h is the distance from the neutral axis of the elastic element to the sensing element and l is the length of the elastic element. 0%.= Kf*/KN, a,m--Km*/K,~ where K/is the stiffness of the cross beam with respect to force component f,., Ks* is the stiffness of one of the crossed beams that is along the x direction with respect tof~, K,n is the stiffness of the cross beam with respect to the moment component m,, and K,~* is the stiffness of one of the crossed beams that is along the y direction with respect to t77x.
Considering the symmetrical structure of the sensor, a
~vaas~m~ati~amatrix
= OLs
I , I 65
i¢
2y::~
0
0
0
0
0
L
0 0 0 26fu 0
2yjS, 0 26g, 0 0
0 46/: 0 0 0
0 0 2e,,~ 0 0
0 0 0 26,,,>. 0
0 0 0 0 4ym~
f, L 17lx t7l>, fiT.
(3) where 6~ ~ 63 -- 67 6~ = 61 -- 65 6~ = 62 2- 64 ..+- 66 -.L 68
~=~-~ 65 = 62 -- 66
e* = el + e ~ + e s + e
7
A diagonal matrix can be expected when cek~,~hd cekf = 0 4EI 2EA
W.L. Jin, C.D. Mote, Jr. / Sensors and Actuators A 65 (1998) 109-1 t 5
112
•,,~---
magnetic field
-,"
Lorentz force from wires
electric current
~
Lorentz force on strips
aluminumsnipe .~,
J
connectionwires
z,
{
mz
my
t/l x
Fig. 4. Generation of six force components on the load plate (l).
However, restricted by the two-dimensional fabrication technology, a design for which this is true is not practical. The strategy for the independent generation of the six force and moment components on the load plate during calibration is shown in Fig. 4. Because each component is generated independently, the elements of the sensitivity matrix, s~j, are obtained directly from individual outputs, u~j, corresponding to the force components,f/
are the stiffnesses of the load plate with respect to a concentrated central load and a uniformly distributed load, respectively. The displacement of the sensor is
~_~ s
ks
where ks is the sensor stiffness. Letting 6o = 6s, we have
= oltql s,~=~@" i = 1 , 2 ..... 8 j = l , 2 ..... 6 JJ)
Connectors from the substrate to the load plate are arranged so that the Lorentz forces generated in them during calibration balance each other on the load plate, as illustrated in Fig. 4. The connectors also act as additional springs between the load plate and the substrate and therefore partially support the force generated on the load plate. A primary calibration system and its elastic model are shown in Fig. 5. Iffs is the force transmitted to sensor, the displacement of the center of the load plate is then
ql-A qt A where q is the toad density on the conductor, I is the length of the conductor, ko is the stiffness of the connections,
48EI k~o=
i3
384EI kcd--
5/3
where Og t --
ksko~( kod + 2k¢) kc~( 2kook¢ + 2kcks + ko~k~)
is the force transmission coefficient, c~t increases as ko decreases. When ko = 0, ~xt = 1. In the current design, aluminum wires with 25 ~m diameter are used as the connectors (see Fig. 7). The stiffness of the wires, kc, is estimated by modeling them as L-shaped elastic beams with clamped ends. Given the wire dimensions shown in Fig. 7, k¢ is found to be in the order of 101 N m-1, much smaller than that of the sensor and load plate, ks, k¢~. Therefore, a t is close to one.
3. Fabrication
The elastic element is fabricated using a double-side polished ( i00} silicon wafer. A layer of silicon nitride is deposited first. After a two-side alignment step, the nitride on both sides of the wafer is patterned with a 3 mm × 3 m m opening and four 1.2 mm × 1.2 mm openings, respectively. A twoside KOH etching step forms the suspended silicon cross
W.L. Jin, C.D. Mote, Jr./Se17sors and Acruators A 65 (]998) 709-775
i13
distributed Lorentz force, q = B f load plate ection wire (a) substrate
I q
(b)/-'/7~
Fig. 5. An elastic model of a calibration system using Lorentz forces: (a) composition; (b) model, kc, stiffness of the connection wire; ks, stiffness of the sensor; f~, force transferred to sensor; q, distributed Lorentz force.
Fig. 6. A fabricated prototype sensor before the bonding of the load plate.
structure. Then, undoped polysilicon and goId layers are deposited for the later Au-Si eutectic bonding. Fabrication of the sensing element starts with a back-side KOH etching step to form a diaphragm on the front side of a (100) wafer. Undoped polysilicon deposition follows to provide a proper substrate for later Si-Au eutectic bonding. Standard steps for insulation, strain gauge, metallization and protection layers are then carried out to build the Wheatstone bridges on the diaphragms. Finally, silicon and silicon nitride etching steps are used to shape the diaphragm into the designed square. The sensing and elastic elements are cleaned after fabrication in preparation for the bonding process. A 10 min sulfuric acid + hydrogen peroxide bath and a 30 s HF dip are used to remove organic residues and native oxide from the surfaces. The chips are then dipped in an ammonium fluoride solution for 30 s, which protects the cleaned surfaces from oxidation in air and allows alignment before the chips are clamped together. The contact pressure during bonding is controlled at about 50 kPa. Bonding is undertaken at atmospheric pressure of 10 -5 torr at 400°C. Photographs of a bonded prototype sensor are shown in Fig. 6. The load plate is fabricated through normal micromachining steps. An infrared two-side alignment technique is used to align the stages and aluminum strips on the two sides. During bonding of the load plate to the sensor, the stages on the bottom side of the plate fit with holes on the upper surface of the sensor (see Fig. 6) so that they are properly aligned. Photographs of a fabricated sensor with the load plate are shown in Fig. 7.
4. Calibration ~\g.]. 7~prototypesensor\v~thload plateand connectionwiresbonded.
Uniform magnetic fields of 2.5 tesla forf.~,fy, rnz, and 1.5 tesla for f~, m, my are provided by an electromagnet during
t 14
W.L. Jin, C.D. Mote, Jr. / Sensors and Actuators A 65 (1998) 109- ] 15
Table 1 Comparison of different multicomponent micro force sensors Reference
Fabrication technology
Batch production
Number of components
Dimension (ram)
Volume (ram3)
[4]
conventional
no
4
G 12 × 20
2260
[ 8]
conventional and silicon mieromaehining
partially
6
~5 × 5
98~
This paper
silicon micromachining
yes
6
4.5 × 4.5 × 1.2
25
0.4. 0.3-
.j/
g 0.2
N
~
A
0 -0.! f / . . . ~ -0.2 -400
"-
= -300
-200
-1130
0
100
200
300
400
current t m A )
Fig. 8. Output of bridge 2 vs. the calibration current during generation of m,. B = 1.5 tesla, t=3.8 mm and U = 5 V.
calibration of a prototype sensor. The current supply ranges from - 400 to 400 mA, and the bridge voltage is 5 V. The output of the bridge detecting axial deformation versus the current passing through the load plate, which produces M,., is shown in Fig. 8. Satisfactory linearity between load and output is seen. The elements of the sensitivity matrix are obtained by generating six force and moment components individually, as illustrated in Fig. 4. The calibrated relationship between the sensor outputs and applied forces is m
2.41
0.42
-0.70
2.01
1.61 -0.44 -0.55 11.9 12.2 --0.08
-0.15
-0.83 0.49 18.8
0.93 -0.0~
0.55 0.55
12.5
003
-0.10
0.84 0.64 -060
,0.53 0.86
7
0 2 3 7 [-I; 0.161 I : ; !
1.46 0.141 IA / - 0 3 5 00r//. d 12.8 0.27d l m ' t
0.17 4.o3A km:d
The diagonal and 4-2 and 5-1 elements of the transformed sensitivity matrix are significantly larger than the others, which coincides with the predicted relationship shown by Eq. (3). Resolutions of 1 mN for force components and 2 mN mm for moment components were observed. Table 1 compares this sensor with the existing multicomponent micro force sensors.
5. Conclusions A six-component, micro force sensor has been developed using silicon microfabrication and wafer-bonding technologies. A calibration method based on the Lorentz force is used to calibrate the sensor. A satisfactory linearity and high resolution are observed.
m
ltl It 2 R3 lA4 U5 II 6 It 7 ll 8
Acknowledgements m
u
-0.37 6.89 1.15 -0.23
0.95 0.i2 0.28 5.60
0.23 4.76 -0.45 5.23
- 0.38 0.i9 0.54 6.8
0.50 7.10 -0.25 -0.13
1.03 0.12 1.18 0.09
0.33 -1.06 -0.26 -5,37 0.20 4.21 - 1.26 -0.14 0.38 0.32 -6.36 4.68
-0.37 -0.45 -0.39 -5.70
-0.36 -5.73 -0,28 0.22
0.87 -0.15 0.95 0.08
f, '
x
/,n,/
The work reported in the paper was funded by FANUC Ltd, (Japan). The development of the sensor was carried out in the Micro-fabrication Laboratory of the University of California at Berkeley.
/m~J m
where the unit of force is the newton (N), of moments is N mm and the outputs are in millivolts. The transformed relationship using matrix A defined by Eq. (2) is
References [ 1] Y. Zhang, Y.M. Yang, H.R. Lin and Y.H. Wu, Research on MR-2 micro-robot, Proc. IEEE Int. Conf. IndustrialTechnotogy, Goangzhou, China, 5-9 Dec., 1994, pp. 589-592.
W.L. Jin, C.D. Mote, Jr./Sensors and Actuators A 65 (1998) 109-115
[2] T. Fukuda, A. Kawamoto, F. Arai and H. Matsuura, Steering mechanism and swimmingexperimentof micro mobile robot in water. Proc. IEEE Micro Electro Mechanical Systems, Amsterdam. Netherlands, 29 Jan.-2 Feb., 1995, pp. 300-305. [3] S. Cherian, W.O. TroxelI and M.M. Aii, Design of behavior-base micro-rover robot, Proc. Intelligent Vehicles '92 Syrup., Detroit, MI, USA, 29 June-1 July, 1992, pp. 280-287. [4] D. Diddens, D. Reynaerts and H. Van Bmssel, Design ofs ring-shaped three-axismicro force/torque sensor. Sensorsand ActuatorsA, (1995) 225-232. [5] V. Gass, B.H. Van der Schoot, S. Jeanneret and N.F. de Rooij, Microtorque sensor based on differential force measurement. Proc. IEEE Micro Electro Mechanical Systems, Oiso, Japan, 25-28 Jan., 1994, pp. 241-244. [6] J. Planert, H. Modler, K. Ludecke and M. Eger, A miniaturizedforcetorque sensor with six degrees of freedom for dental measurements, Clin. Phys. Physiol. Meas., 13 (1992) 241-248. [7] K. Peterson, C. Kowalski. J. Brown, H. Allen and J. Knutti, A t'orce sensing chip designed for robotic and manufacturing automation applications, in R.S. Muller (ed.), Micro Sensors, IEEE Press. New York, 1992, pp. 419-42I. [8] W.L. Jin and C.D. Mote, Jr., Development of a six-component miniature force sensor for robotic applications,Proc. ASME Dynamic Systems Control Division, Atlanta, GA, USA, 17-22 Nov., I996, DSC Vol. 58, ASME, I996, pp. 753-760. [9] H.H. Bau, N.F. de Rooij and B. Loeck, Sensors, A Comprehensive Survey, Voh7, Mechanical Sensors, VCH, Wienheim. 1994, pp. 455459. [ I0] W.L. Jin and C.D. Mote, Jr., A novel silicon sensing element for highnatural frequency, low-range dynamometrical sensors, Sensors and Actuators A, 62 (I997) in press. [ 11] S. Timoshenko,Strength of Materials, Van Nostrand,New York, 1956, pp. 95-I38,
Biographies Welin Jin graduated from the Hefei University of Technology, China, with a B.S. in 1982. He received the Ph.D. in mechanical engineering from Nanjing University of Aeronautics and Astronautics in China and joined the faculty of the same university in 1988. He worked in the City University of Hong Kong as a visiting scholar in 1992. From May 1994 to M a y 1997, he visited the University of California at Berkeley, USA. He is now a visiting fellow at the Nanyang Technological University in Singapore. Dr Jin's research interest includes machining process monitoring and optimization, multicomponent dynamometers and microelectromechanical systems. He published more than 20 papers in academic journals and holds two patents in China. C.D. Mote, Jr., is Vice C h a n c e l l o r - - University Relations, and F A N U C Chair in Mechanical Systems at the University of California, Berkeley. As Vice Chancellor he is responsible for all programs external to the campus. Beginning early in 1992, he conceived, designed and implemented a seven year
115
comprehensive, capital campaign with a goal of one billion dollars. The victory celebration is scheduled for the turn of the century. From 1987 to 1991 he served as Chair of the Department of Mechanical Engineering. He came to Berkeley from Carnegie Institute of Technology in 1967, where he was on the faculty in the Mechanical Engineering Department between 1964 and 1967. In addition, he has held research positions at the University of Birmingham, UK, in 1963, the Norwegian Institute for Wood Science and Technology, Oslo, on many occasions between 1972 and 1985, the Technical University of Darmstadt in 1989 and the Tokyo Institute of Technology in i99 i. Vice Chancellor Mote's research and technical interest lie in the fields of dynamical systems and control, instrumentation, design, vibration and acoustics, biomechanics and sport mechanics. He is internationally recognized for his research on vibration and stability control of gyroscopic systems, including axially translating and rotating systems like circular and band saws. His work on snow skis, skiing and the biomechanics of skiing injury spans more than two decades and has established the foundation of the skiing injury and mechanics fields. His research efforts have resulted in more than 250 publications in academic journals and patents in the USA, Norway, Finland and Sweden. Vice Chancellor Mote is a registered professional engineer in California and has served professional societies in a number of capacities. He served as Vice President of the Environment and Transportation Group of the American Society of Mechanical Engineers from I986 to 1990 and as Vice Chairman of the A S M E Council on Engineering in 1989-1990. He served on the National Academy of Engineering Peer Committee from 1990-1993, as its Chair in 1992-1993, and currently serves on the Program Committee. Vice Chancellor Mote has been recognized for his contributions on many occasions. He was lauded by the University of California (Berkeley) with its Distinguished Teaching Award in 1971. He is pleased to note that many of his more than 50 doctoral students have become leading contributors to engineering practice, teaching and research. He has been elected to Fellow grade by the International Academy of W o o d Science (1978); the A S M E ( 1984); the Acoustical Society of America ( i991 ); and the American Association for the Advancement of Science (1992). In 1988 he was elected to the US National Academy of Engineering and was awarded the Humboldt Prize by the Federal Republic of Germany. In 1991 the Japan Society for the Promotion of Science awarded him their fellowship, and he was appointed to the F A N U C Chair in Mechanical Systems at Berkeley. He is listed in a number of biographical volumes including W h o ' s Who it~ A m e r i c a since 1978. Vice Chancellor Mote received the B.S. in mechanical engineering in I959 and the Ph.D. in engineering mechanics in 1963 from the University of California, Berkeley.