tangential drive

8/12/2019 Tangential Drive

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LARGE DISPLACEMENT LINEAR ACTUATORReid A. Brennen, Martin G. Lim, Albert P. Pisano, and Alan T. Chou

Berkeley Sensor Actuator CenterElectronics Research LaboratoryDepartment of Electrical Engineering and Computer ScienceUniversity of California, Berkeley CA 94720ABSTRACT

In this paper, a tangential drive (Tdrive) polysilicon, linearactuator is presented which produces large magnitude tangentialmotion by flexing a microstructure n an essentially straight line withmoderate input voltage. These devices have been designed, fabricated,and successfully tested to have substantial displacements even forstatic positioning. The working principle of the T-drive is that thestrong electrostatic forces of a ttraction between a fixed bar and a freebar are converted to large amplitude tangential motion by theparallelogram flexural suspension of the free bar. Operating devicesare capable of tangential displacements as great as 32 pm. Thisdisplacement is stable and easily varied, since the tangentialdisplacement can be controlled by adjusting the potential between thefixed electrode and the traversing bar. Static displacements aredetectable for voltages as low as 15VDC. Typical T-drives have freebars 200m ong, 12pn wide, with flexural suspensions450pn ongand2 pm wide. All component thicknesses are2 pn Theoretical models forboth the flexural suspension and electrostatic forces have been derivedand they predict the relation between tangential displacement andexcitation voltage.INTRODUCTION

Within the last two years, several designs of micro-actuatorshave emerged for specific applications. Among these, onemay findshape-memory allow diaphragms for micropumps 111, cantilevered,electrostatically actuated structures to guide probetips for scanningtunneling microscopes 121, bi-stable mechanical actuators for non-volitile logic elements [3], electrostatic linear actuators for microfriction evaluation [4], a linear micromotor for magnetic disk drives151,electrostatically-actuated tweezers [61 as well as grippers 171. Acommon design theme among these and other micro-actuators are theuse of electrostatic, piezoelectric,or shape-memory properties ofmaterials to actuate the micro structures through relatively smalldisplacements(0.01 to 10 pm) with respect to the microactuator size.Although actuation amplitudes and forces for these devices seem to beadequate, the design of higher performance microactuators will requirethe deve lopment of large r amplitude motion with no compromise ofactua tion force.

Among the electrostatic actuators, one may find two basicdesigns. The first basic design utilizes parallel plate capacitors withone moving plate that is allowed to displace in the direction of themajor field lines, yielding a large-force, small-amplitude actuator.The second basic design utilize s the fringe field of capacitors to drivethe moving plate parallel to the fixed plate and perpendicular to themajor field lines [81. This results in a low-force, large amplitudeactuator.

In this paper is described the design and performance of alarge-force, large-amplitude electrostatic actuator that exhibits thebest feature s of previous electrostatic actuator designs. Thus, themoving capacitor plate is allowed to move parallel to the electric fieldlines (genera ting large force) as well as displace parallel to the fixedcapacitor plate (generating large amplitude motion). This newelectrostatic actuator design utilizes tangential motion of the movingcapacitor plate, and thus, is called the T-drive.

Unoptimized designs of T-drive actuators show that lowvoltage, large force, and l arge displacement linear actuation ispossible.

DESIGNThe fore gene rat ing componentsof the Tdrive are made u p oftwo parallel bars which are separated by a small gap. When a voltageis applied across the gap, an electros tatic force is created that actsyrpendic ular to, and between, thebars. For convenience, thisdirection

IS called the normal direction. By fixing one of the bars and atta chingthe other bar (the free bar) to one side of a parallelogram flexuresuspcnsion, Fig. 1 this force can be utilized for motion both paralleland perpendicular to the fixed bar by adjusting the geomet ry of thesuspension. The parallelogram suspensionis used in order to constrainthe two bars to remain parallel. If the suspensionbeams of the flexureare not parallel to the norma l direction, the total perpendicula r forcegenerated, Ftotal, can be decomposed into two force components:onecomponent parallel to and the other component perpendicular to thesuspcnsion beams. The tangential force component acts at the end of theflexures and deflects them, resulting in lateral motion of the free bar.This lateral movement can only occur when the initial orientationofthe beams is not parallel to Ftotal, i.e. the normal direc tion. Gravi tyacting on a simple pendulumservesas an analogy to the concept of theT-drive.The two critical design featu res of the T-drive are the flexuregeometry, which controls the gap distanc eas the structure displaces,and the free bar length, which affects the magnitude of theelectrostatic force (Fig. 1). The flexure geometry parameters includethe offset angle of the beams, the beam dimensions (length, width, andthickness), and the initial gap distance between the free and fixedbars. Larger initial angles of the beams result in a more rapid decreasein gap width and a more rapid increase in applied force as thefreebarmoves laterally. However, if the initial angle is too large, he free barwill contact the fixed bar as it displaces, and thus short the circuitpreventing furthe r movement. The rate of approachof the free bartoward the fixed bar is a function of beam length. The initial gapbetween the bars determine s whether thebars will contact and, if sowhat maximum actuator displacement is possible before they meet.The width, thickness, and length of the beams determine the stiffnessof the flexure suspension and the magni tude of F totd is proportional othe free bar length.

initial bar/electrodesepamtion distance

Figure 1F tangential that deflects the structurein the Ydirection.Schematicof Tangential Drive Linear Actuator. Note hat it is

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Y

(2a)lateral displacement Yof the freebar

l foreshorten

Foreshortening of beamsas they deflectTypesofbeam displacementsShadedstructuresare in displaced position)

Figure2

F

Extensionof beamsdue to axial force

THEORYUsing a modified parallel-plate capacitance model, the total

electrostatic force Ftotal, generated between the facing sides of the barsis estimated by:

1)where A is the capacitor plate area, V is the applied potential, d isthe gap between the bars, E is the permittiv ity of air , and C1 is aconstant factor. The factor C1 is based on results from a electrostaticfinite element package, Maxwell [91 and improves the estimate forFtotal by including fringe fields in the capacitance analysis. For ourmodel, C1 is set to 1.15. Clearly the factor, C1 must be recalculated ifthe design of the device is modified.As the free bar moves laterally, it approaches the fixed bar.The rate of approach is governed by three separate phenomena ( Fig.2). The first, due to the initial angle of the support beams, is theapproach of the free bar as it moves laterally a distance Y Fig. 2a .The second is the foreshortening, Xf,n the nx i n l direction, of thesupport beams as they deflect (Fig. 2b). The third is the axialextension, X,, of the support beams as the axial component of the totalforce isapplied (Fig. 2c). If 8, is the angle of the beams with respect tothe normal direction, then the gap, d, can be expressed as:

d =do - Ysine, + (+ X,kose, (2)where do is the initial gap. Using small displacement beam theory,expressions for Y, , and X,can be derived [lo] and, expandingeach ofthe terms in Eq. :

taneosineo+ 4 h { hd 1+y2)+sinh(XL)[cosh(hLJ( + y 2 ) - 2ysinh(hL)])cosh(hL) - 1

sinh(hL) (4)here y =

Figure 3SEM of a single bar T-drive structure. The L-shapedbreakaway supportisremoved before testing.

I Figure 4SEM of the free bar of a single bar T-drive.The scale and pointer can be seen between the two swpension beams on the left. The dimples can be seen in thecenter of the free bar. Note the vertical side walls of thep o lys ~~~conn the gap.

(5)

and L is the length of the flexure beams, b is the width of the beams, tis the thickness of the beams, E is Young's modulus of elastic ity forpolysilicon, and I is the area moment of inertia of the beams.136

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Table Maximum Displacements attained for Single and Multiple-Bar T-drive structures each with its beams at differentangleswith respect to t he normal direction.I Maximum disdacement um

Multiple barT-drive(446Pbeam)

(volta e at maximum dis lacement)An leofbeams

single barT-drive 27.0 29.5 30.5 32.0(446~nbeam) (127v) (127v) (118)' (82V)*

22.0 20.0 22.0 21.0(57V)+ (53V)+ (50)t (45)t

since Ftangential = Ftotal sine. This arger Ftangential educed the gapmore for a given voltage than that of the lesser-angle beam designs.This increased Ftotal and correspondingly, Ftangential. Consequently,the displacements of the larger angle beam designs increased fasterthan the lower voltage designs as the voltage was increased.For a given voltage, the single bar structures deflected less thanthe multiple bar structures. The experimental results bear out theexpected proportionality between the length of the attracting surfaces(i.e. the bar lengths) and Ftotal.

The maximum static displacement amplitudes attained for thestructures are shown in Table 1. For an applied voltage of 127V, a staticdisplacement of 32 pm was measured for a single bar Tdriv e with 446pm beams at an angle of 5.2O. The 32pn displacement was the greatestdisplacement measured for any of the Tdrive structures. The maximumdisplacement increased with an increase in 8, Geometrical constraintslimited the maximum displacement of the structures with large 8 Inthese cases the bars contacted before the voltage reached 127V.

There was a significant difference between the maximumattainable displacements of the single and multiple bar structures. Themultiple bar design of the tree end was inherently more compliant thanthe single bar structures . It was noted during testing that the branchesdeflected towards their respective fixed bars due to the large forcesgenerated as the gap became smaller. When the gap decreased to acertain amount, the force balance between the electrostatic force andthe resisting force in one of the branches would become unstable and thebranch contact the fixed bar. The complexity of the tree may havecontributed to the less than predicted displacements.During testing of the single and multiple bar Tdrives, it wasnoted that the free bar section of the devices levitated out of plane.The amplitude of the levitation varied from device to devicedepending on the physical dimensions of each device. For most of thedevices, the out-of-plane levitation increased as the applied voltageincreased until about 30 V was reached, after which the levitationdecreased and was not perceptible above about 50 V. This evitation isdue to the interaction of the ground plane and the free and fixed bars1111. Theoretical calculations reveal that the forces that the T-drive would be able to generate are dependent on how much thesuspension has been displaced before the force is exerted. This effect isdue to the elastic forces required to deflect the suspension. For example,for one multiple bar design, an initial displacement of 10 pm wouldrequire approximately 36V (Fig. 8). Assuming the structure at thispoint contacts the the structure upon which it acts and the T-drive doesnot displace further, an increase of 8V would provide a force of 2 pN 1is the force exerted by a 350 pm cube of silicon in gravity). Lowerinitial displacements reduce the rate at which the applied force wouldincrease with voltage.The differences in displacements between the theoreticalmodel and the experimental data can be attributed to several causes.First, the structures not only have compliant suspension beams, but thefree bars could also deform. As noted above, this was of especial concemfor the multiple bar T-drive. Further, in the multiple bar freebar/fixed bar design, only part of each branch was near to the fixed bar,the nominal gap being 2 pm. However, the branch was surrounded byother features that were about 6 km distant that were at the oppositepotential. Since an electrostatic force was generated by this gap, thetotal force was actually less than the theoretical force.

:0 10 5P.m20 30 40 50 60 70Voltage (V)

Figure 8Theoretical force exerted by the T-drive versus appliedvoltage at f ixed lateral displacements. The fixed dis-placement is noted by each curve.

The model had several limitations. A s noted above, the beamtheory used to describe the Tdrive suspension was valid only for smalldisplacements, or more accurately, for small changes of slope of thebeams. TheseT-drive suspension beams did have Significant changesofslope when they deflected. The effect of this increased slope was toeffectively increase the stiffness of the system 1121. A second limitat ionof the model was that the model assumed perfect geometric dimensionswhereas the actual structures had dimensions that varied slightlywith the fabrication process. Since large displacements only occurredwhen the gap had become very small, the uniformity of the gap wasvery important.The motion generated by the Tdriv e is not perfectly linear, butsince the free bar travels in a very large radius arc as the beams deflect.but this non-linearity is very small.

CONCLUSIONElectrostatic large displacement structures have beendeveloped, fabricated, and tested. The Tdri ve concept demonstratesthat direct electrostatic attraction can be used to generate largedisplacements. These structures attained static displacements of u p to32 pm with an applied voltage of 82V and 22 pm with an appliedvoltage of 50V. Structures with longer beams show promise for evengreater displacements. A theoretical model has been developed whichclosely describes the experimental data. Using this model, a value hasbeen calculated for Young's modulus of 105 GPa. Further, it has beenshown that relatively large forces can be applied with small increasesin vol tage once the free bar undergoes a large displacementand the gapbetween the free and fixed bars is reduced.

ACK NO W LEDG EMENTThe authors would like to thank the industrial members of theBerkeley Sensor Actuator Center for the support and fundingprovided for this project.

REFERENCES[l] J.D. Busch and A.D. Anderson, Prototype Micro-ValveActuator , Proc. I Micro Electro Mechanical SystemsWorkshop Napa Valley, CA, Feb. 1989.


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S Akamine, T.R. Albrecht, M.J. Zdeblick, and C.F. Quate,Microfabrication of Integrated Scanning TunnelingMicroscopes , Transducers 89, 5th Internation al Conference onSolid-state Sensors and Actuators, Montreux, Switzerland, 25-30 une1989.P.L. Bergstrom, T. Tamagawa, and D.L. Polla, Design andFabrication of Micromechanical Logic Elements ,Proc. IEEEMicro Electro Mechanical Systems Workshop, pp. 15-20,NapaValley, CA, Feb. 1989.M. G. Lim, J. C. Chang,D. . Schultz, R. T. Howe, and R. M.White, Polysilicon Microstructures for Characterize StaticFriction. Proc. IEEE Micro Electro Mechanical SystemsWorkshop, pp. 82-88,N a p Valley, CA, Feb. 1989.Martin G. Lim, Roger T. Howe, and Roberto Horowitz, Designand Fabrication of a Linear Micromotor for Magnetic Disk FileSystems , ASME Winter Annual Meeting, San Francisco,December 10.15,1989L. Y. Chen, 2. L. Zhang, J. J. Yao, D. C. Thomas, and N. C.MacDonald, Selective Chemical Vapor Deposition of Tungstenfor Microdynamic Structures, Proc. IEEE Micro ElectroMechanical Systems Workshop, pp. 82-87, alt Lake City, UTFeb. 1989.Chang-J in Kim, Albert P. Pisano, Richard S Muller, andMartin G. Lim, Polysilicon Microgripper , to be presented atIEEE Solid-state Sensor and Actuator Workshop, Hilton HeadIsland, South Carolina, June 4-7,1990.William C. Tang, Tu-Cuong H. Nguyen, Michael W. Judy, andRoger T. Howe, Electrostatic-Comb Drive of LateralPolysilicon Resonators , Transducers 89,5th InternationalConference on Solid-state Sensors and Actuators, Montreux,Switzerland,25-30 une1989.Ansoft Corporation, Pittsburgh, PA 15123Maxwell Users Guide,January,1989Raymond J. Roark and Warren C. Young, Formulasfor Stress andStrain,5th Ed., McGraw-Hill, New York, 1975William C Tang, Martin G. Lim, and Roger T. Howe,Electrostatically Balanced Comb Drive ,to be presented atIEEE Solid-state Sensor and Actuator Workshop, Hilton HeadIsland, South Carolina, June4-7,1990Egor P. Popov, Introduction to Mechanics of Solids, PrenticeHall, Inc., Englewood Cliff, New Jersey, 1968

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