FEASIBILITY STUDY OF ACTIVE MICRO-VIBRATION CONTROL SYSTEM USING PIEZOELECTRIC ACTUATORS FOR FLOOR STRUCTURE OF PRECISION MANUFACTURING FACILITIES

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1 October -7, 8, Bejng, Chna FEASIBILITY STUDY OF ACTIVE MICRO-VIBRATION CONTROL SYSTEM USING PIEZOELECTRIC ACTUATORS FOR FLOOR STRUCTURE OF PRECISION MANUFACTURING FACILITIES Hrokazu Hora, Masash Yasuda, Tatsuya Osako, Yasuyuk Noguch, Hsao Kato Takafum Fujta, and Mamoru Shmazak ABSTRACT : Research and Development Dvson, Tokkyokk Corporaton, Tokyo, Japan Professor, Insttute of Industral Scence, The Unversty of Tokyo, Tokyo, Japan Insttute of Industral Scence, The Unversty of Tokyo, Tokyo, Japan Emal: hora@tokkyokk.co.jp As the semconductor processng technology keeps evolvng, the demand for vbraton-free envronment of semconductor manufacturng facltes keeps becomng severe. We develop an actve mcro-vbraton control system by usng pezoelectrc actuators to suppress the vbraton of the floor n precson manufacturng facltes. The system s a smart structure that ncludes the actuators put on the beams of the floor, acceleraton sensors and controllers. The man purpose s to suppress the vertcal vbraton of the floor where the machnes are nstalled. The smart structure actuator s sutable for mcro-vbraton control except earthquakes for the lmt of the capacty. Feasblty tests were executed by usng a large-scale expermental model, whch s a steel frame of two-dmensonal truss to represent as the floor structure of the manufacturng facltes. The weght of the model s 8kg and ts span s 6m. The sze of the pezoelectrc actuator s 5 x 5 x 6mm. The test result shows that the excepton vbraton control performance s acheved and expresses the feasblty of the control system for the real structure. KEYWORDS: Actve Vbraton Control, Pezoelectrc Actuator, Floor Structure. INTRODUCTION As the semconductor processng technology keeps evolvng and the desgn rule keeps becomng small rapdly, the demand for vbraton-free envronment of semconductor manufacturng facltes keeps becomng severe. Besdes, the semconductor manufacturng equpment mproves enlargement for large-sze wafers and ts operatonal speed becomes fast to rase the producton capacty durng the recent years, hence force that s generated by the manufacturng equpment grows and the equpment and the nstallaton floor are excted by the force. The producton capacty of the equpment and the adjacent machnes has been decreased by the nfluence of the vbraton. We developed an actve mcro-vbraton control system by usng pezoelectrc actuators to suppress the vertcal vbraton of the floor n precson manufacturng facltes. The system s a smart structure (FUJITA) that ncludes the actuators put on the beams of the floor, acceleraton sensors and controllers. The man purpose s to suppress the vertcal vbraton of the floor where the machnes are nstalled. The smart structure actuator s sutable for mcro- vbraton control except earthquakes for the lmt of the capacty. Partcpaton factor to the structure of the actuator, whch both ends are supported on the structure, was consdered usng a smple beam model analytcally. We dscuss where the both ends of the actuator are supported on the structure s very mportant for the partcpaton factor. Feasblty tests were executed by usng a large-scale expermental model, whch s a steel frame of two-dmensonal truss to represent as the floor structure of the manufacturng facltes. The weght of the model s 8kg and ts span s 6m. The sze of the pezoelectrc actuator s 5 x 5 x 6mm. The test result shows that the excepton vbraton control performance s acheved and expresses the feasblty of the control system for the real structure.

2 October -7, 8, Bejng, Chna. OUTLINES OF LARGE-SCALED EXPERIMENTAL MODEL Fgure shows a large-scaled expermental model, whch s a steel frame structure of two-dmensonal truss to represent as the floor structure of the semconductor manufacturng facltes. Table shows specfcatons of the expermental model. Total weght of the model s 8kg and ts span s 6m and ts heght s.7m. Fgure shows the nstallaton of a pezoelectrc actuator on the upper chord of the model. Two brackets are nstalled on the upper chord. The pezoelectrc actuator s held between the two brackets wth a rod and an adjustable bolt. The adjustable bolt pushes the pezoelectrc actuator and generates pre-compresson force between the two brackets. The rod s supported by two lnear bearngs. Fgure shows the pezoelectrc actuator and table summarzes ts specfcatons. Weght Actuator Steel frame Shaker Weght 6.m Bracket rod Upper chord Lnear Bearng.75m Actuator Bracket Fgure Installaton of actuator on upper chord Fgure Large-scaled expermental model Table Specfcatons of the expermental model Span x Heght 6.m x.7m Member Hxx6x8, Hx5x5x7 Total weghts 8kg st mode 6.Hz,.% nd mode 69.Hz,.8% rd mode 8.Hz,.5% Force drecton Fgure Pezoelectrc actuator Table Specfcatons of the pezoelectrc actuator Outer sze 5x 5x 6 H mm Rated voltage V Capactance 8µF Max. dsplacement µm Max. force kn

3 October -7, 8, Bejng, Chna. ANALYTICAL CONSIDERATION.. Consderaton Fxed Straght Beam wth Unform Secton To smplfy the problem, an analytcal model s treated as a fxed straght beam wth unform secton modulus. Fgure 4 shows the analytcal model for the smple beam wth pezoelectrc actuator. Vertcal vbraton of the contnuous system s expressed as modal coordnates, dφ ( x ) d ( x ) q + q + q = M φ & M ζ ω & ω * a a (.) m dx dx where q, ζ, ω and m * are modal dsplacement, modal dampng rato, modal frequency and modal mass of -th mode of the beam, correspondngly. x s poston of length drecton of the beam. φ ( x) s a modal shape functon as follow, cos kl cosh kl φ ( x) = cosh k x cos k x ( snh k x sn k x), cos k l cosh kl = (.) sn kl snh kl where k s a soluton of the frequency equaton. l s a length of the beam. x and x are ponts of the two brackets. M a s concentrated moment at x, -M a s concentrated moment at x, whch are caused by the control force of the actuator. st mode mode shape dervatve M a -f f -M a nd mode Fgure 5 Mode shape functons and ther dervatve x x d Fgure 4 Analytcal model of smple beam Partcpaton factor Installaton dstance d[m] Fgure 6 Relaton between nstallaton dstance and partcpaton factor Now, we consder carefully that the rght term of the Eqn... means a partcpaton factor for the -th mode of the equpped actuator on the beam. The magntude of the partcpaton factor depends on the dfference from x to x of the dervatve of the mode shape functon φ ( x) wth respect to x. Hence, t s very mportant where x and x are. Fgure 5 shows the mode shape functons and ther dervatve functons when =,. The partcpaton factor s maxmzed where x s the maxmum of the dervatve and x s the mnmum of the dervatve. The whte crcles ndcate a par of the ponts for the maxmum of the partcpaton factor n the st mode, two par of the ponts n the nd mode. However, a dstance of the par of the ponts, whch the partcpaton factor s maxmzed, s so long that t can be dffcult to realze n a practcal use. Here, the dstance and mean of x and x are defned as d and x a Hence Eqn... s transformed M d ( x d ) d ( x + d ) q + q + q = a φ a / φ a / & ζ ω & ω * (.) m dx dx Fgure 6 shows the relaton between the dstance d and the partcpaton factor n a case of the beam length

4 October -7, 8, Bejng, Chna l=.m, x a = l/ and for the st mode. The partcpaton factor becomes the maxmum where the dstance d s at 55% of the beam length l. As the partcpaton factor s proportonally ncreasng where the dstance d s less than 4% of the beam length l, t s preferable to lengthen the dstance d as far as possble n the practcal use... Analytcal Model for Complcated Structure An analytcal model for complcated structure s also expressed as modal coordnates as follows, φ A f φb f q& + ζ ωq& + ω q = (.4) * m where φ A and φ B are partcpaton factors of force f drecton, where the force f and f act. The modal parameters for the complcated structure are obtaned from fnte element method (FEM). Fgure 7 shows the modal analyss results of FEM for the expermental model, whch was composed of two dmensonal beam elements. Harmonc exctaton test was executed by the pezoelectrc actuator. Fgure 8 shows the outlnes of the harmonc exctaton test by the actuator. Fgure 9 shows the exctaton test results n the cases of the dstance d were 5, 75 and 5mm. The vertcal axs represents vertcal response acceleraton on the center of the upper chord of the model. It was confrmed that the tendency, whch the response acceleraton grows wth ncreasng the dstance d, was smlar to the smple beam partcpaton factor growng. It was also confrmed that the analytcal results are n good agreement wth the expermental results. 6.Hz Fgure 7 Modal analyss of FEM for the expermental model d M a -f f -M a Fgure 8 Outlnes of the harmonc exctaton test by the actuator (cm/s )/ N Cal. Exp Installaton dstance[mm] Fgure 9 Results of the harmonc exctaton by the actuator compared wth the analyss

5 October -7, 8, Bejng, Chna 4. VIBRATION CONTROL TEST 4.. Outlnes of Control System Fgure shows control system for the expermental model. The control system conssts of three vertcal acceleraton sensors and controller. The controller was desgned by a model-matchng method (FUJITA) to reduce a response of the st mode of the expermental model. A modal flter (MEIROVITCH) was also ncluded and calculated the st mode and the rd mode acceleraton. The rd mode acceleraton, whch obstructed a performance of the st mode controller, was elmnated. The modal fler was obtaned from the responses of the three sensors expermentally when the st mode and the rd mode were excted by the actuator. Eqn. 4.. shows the modal matrx φ, whch was obtaned expermentally. An nverse matrx of the modal matrx became the modal flter. aa.77. q&& q&& ab = [ φ ] =.4.5 (4.) q&& q && ac.8.56 where a A, a B and a C are the responses of the three sensors, q and q are modal dsplacements of the frst mode and thrd mode. Drver amplfer C Shaker st mode rd mode φ - Abs. Acc. A Abs. Acc. B Abs. Acc. C Ampltude[dB(cm/s /N)] Non-controlled(Exp.) Controlled(Exp.) Non-controlled(Cal.) Controlled(Cal.) Controller Fgure Control system for the expermental model Non-contorlled Frequency[Hz] Fgure Vbraton control performance Acceleraton[cm/s ] Acceleraton[cm/s ] Controlled Fgure Free vbraton test results Acceleraton[cm/s ] Non-controlled Controlled Fgure Tme hstory when no exctaton but ambent ground vbraton was affected

6 October -7, 8, Bejng, Chna 4.. Control Test Results Exctaton test was executed by a shaker, whch was nstalled on the lower chord of the expermental model. Fgure shows a comparson of non-controlled and controlled aganst a harmonc exctaton of the shaker, whch force was N. The horzontal axs represents frequency and the vertcal axs represents the vertcal response acceleraton on the center of the upper chord of the model. The controlled response acceleraton was reduced to / of the non-controlled n the harmonc exctaton of the shaker. Fgure shows the tme hstores of the response acceleraton on the center of the upper chord of free vbraton test n cases of the non-controlled and the controlled. The dampng rato of the st mode was calculated from the tme hstores, t became from.% to 7.6%. It s shown that the proposed system demonstrates good vbraton control performance. Fgure shows the tme hstory of the response acceleraton on the center of the upper chord n a case when no exctaton but ambent ground vbraton was affected. It was also confrmed an effectve reducton aganst small vbraton. 4.. Verfcaton of Analytcal Model Table summarzes the frst mode parameters of the large scaled expermental model, whch are obtaned from the modal analyss of the FEM model. The dsplacement of the actuator (x a ) s obtaned usng Eqn. 4.. Ampltude[dB(N/N)] Ampltude[dB(µ m/n)] Exp. Cal Frequency[Hz] Exp. Cal Frequency[Hz] f a k m x = (4.) where k m s the stffness of the mechancal part whch the pezoelectrc actuator s nstalled. The stffness k m s dentfed from an actual measurement of the mechancal part of the expermental model. Fgure also shows a comparson between the test results and the analytcal results of the vertcal acceleraton of the chord n the cases of non-controlled and controlled. In ths fgure, the lnes ndcate the analytcal results of non-controlled and controlled. Fgure 4 and 5 show the comparsons between the test results and the analytcal results of the force and the dsplacement of the pezoelectrc actuator n frequency doman. Fgure 6 shows tme hstory responses aganst random exctaton compared wth the analytcal results. Hgh and low frequency components of the tme hstores n ths fgure were elmnated by band-pass-flter. It s confrmed that the analytcal results are n good agreement wth the test results of the vertcal acceleraton, the actuator force and the actuator dsplacement n both frequency and tme doman. Valdty of the analytcal model for the proposed system s confrmed. Fgure 4 Actuator force response Fgure 5 Actuator dsp. response Acc.[cm/s ] Acc.[cm/s ] Shaker Acc Chord Acc.(Exp.) Actuator Force(Exp.) 5 Force[N] Dsp.[µ m] Actuator Dsp.(Exp.) Acc.[cm/s ] Chord Acc.(Cal.) Actuator Force(Cal.) 5 Force[N] Dsp.[µ m] Actuator Dsp.(Cal.) Fgure 6 Tme hstores of random exctaton

7 October -7, 8, Bejng, Chna Table Fst mode parameters of the expermental model (d=75mm) Modal mass 79.5kg Natural freq. 6.Hz Dampng rato.% Partcpaton factor A.86 Partcpaton factor B -.86 Partcpaton factor of shaker ESTIMATION OF THE SYSTEM FOR REAL STRUCTURE In order to estmate the system for real structure, we suppose a two-dmensonal truss structure n fgure 7 as the real floor structure of precson manufacturng facltes. Total weght of the structure s 4ton and span s 48m. Its natural frequency of the frst mode s 4.7Hz and dampng rato s supposed %. The nstallaton dstance d s desgned m. The stffness of the mechancal part whch the actuator s nstalled s estmated from the expermental model by usng a geometrcal smlarty. Fgure 5 shows the tme hstory responses when a certan random vertcal exctaton s affected to the center of the structure. The response acceleraton s reduced from.6cm/s to.cm/s. The maxmum values of the actuator force and dsplacement are 5.4kN and 5µm. The estmated specfcatons of pezoelectrc actuator for the real structure are summarzed n Table 4. The proposed system for the real structure can be realzed usng the pezoelectrc actuator on the market. Fgure 7 Supposed floor structure for the estmaton of the proposed system Acc.[cm/s ] Acc.[cm/s ] Non-controlled Chord Acc. 65 Controlled Actuator Force Controlled Chord Acc. Controlled Actuator Dsp Fgure 8 Estmated vbraton control performance and actuator responses Force[N] Dsp.[µ m]

8 October -7, 8, Bejng, Chna 6. CONCLUSIONS Table 4 Specfcatons of the estmated actuator Max. force 7kN Max. dsplacement 8µm Installaton number Number of parallel Number of seres In ths paper, the actve mcro-vbraton control system by usng the pezoelectrc actuators to suppress the vertcal vbraton of the floor n the precson manufacturng facltes was dscussed. The partcpaton factor of the actuator, whch both ends are supported on the structure, was consdered. It became clear where the best ponts for the both ends of the actuator were. Through the tests usng the large-scaled expermental model, the excepted vbraton control performance was acheved and the valdty of the analytcal model for the system was confrmed. The estmaton of the system for the real structure was shown. These expressed the large feasblty of the proposed system. REFERENCES Fujta T. (997) Smart Structures for Actve Vbraton Control of Buldngs. Proceedngs of the 997 Internatonal Symposum on Actve Control of Sound and Vbraton (ACTIVE 97),Budapest, Hungary, XIX-XXXIII. Fujta T., Tagawa Y., Mura N., Shbuya S., Takeshta A. and Takahash Y., (99) Study of Actve Mcrovbraton Control Devce Usng Pezoelectrc Actuator (st Report, Fundamental Study of One-Dmensonal Mcrovbraton Control). Transactons of the Japan Socety of Mechancal Engneers, Vol. 57, No. 54, (n Japanese) Merovtch L. and Baruh H. (985) On the Implementaton of Modal Flters for Control of Structures. Journal of Gudance, Control, and Dynamcs, 8, 6, 77-76