Author(s) LIU, Yanqing; MATSUHISA, Hiroshi; U. Citation Journal of Sound and Vibration (200.

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1 Title Sei-ative vibrati isolati sys and daping trol Authors LIU, Yanqing; MATSUHISA, Hiroshi; U Citati Journal of Sound and Vibrati Issue Date 8-6 URL Copyright 8 Elsevier; この論文は出版社 Right ん 引用の際には出版社版をご確認ご利用ください This is not the published versi. versi. Type Journal Artile Textversi author Kyoto University

2 Sei-ative vibrati isolati syste with variable stiffness and daping trol Yanqing LIU*, Hiroshi MATSUHISA, Hideo UTSUNO *Departent of Mehanial Engineering and Siene, Kyoto University Sayo-u, Kyoto ity 66-85, Japan, JSPS Researh Fellow Abstrat Sei-ative systes with variable stiffness and daping have destrated exellent perforane. However, vential devies for trolling variable stiffness are opliated and diffiult to ipleent in ost appliatis. To address this issue, a new figurati using two trollable dapers and two stant springs is proposed. This paper presents theoretial and experiental analyses of the proposed syste. A Voigt eleent and a spring in series are used to trol the syste stiffness. The Voigt eleent is oprised of a trollable daper and a stant spring. The equivalent stiffness of the whole syste is hanged by trolling the daper in the Voigt eleent, and the sed daper whih is parallel with the other eleents provides variable daping for the syste. The proposed syste is experientally ipleented using two agnetorheologial fluid dapers for the trollable dapers. Eight different trol shees involving soft suspensi, stiff suspensis with low and high daping, daping -off soft and stiff, stiffness -off low and high, and daping and stiffness -off trol are explored. The tie and frequeny respses of the syste to sinusoidal, ipulse and rando exitatis show that variable stiffness and daping trol an be realized by the proposed syste. The syste with daping and stiffness -off trol provides exellent vibrati isolati for a broad range of exitatis. Key Words: Sei-ative trol, Vibrati isolati, Variable daping, Variable stiffness, MR daper.. Introduti In reent years, vibrati isolati systes have been studied broadly and in great depth. The vibrati trol systes an be ategorized as: passive, ative and sei-ative. Sei-ative trol systes fill the gap between passive and ative trol syste and they represent a oproise between perforane iproveent and sipliity of ipleentati. They ly expend a sall aount of energy to hange syste paraeters, suh as daping and stiffness. The basi idea of variable daping systes have been proposed by any researhers to provide effetive vibrati trol [-]. However, there is still roo for further iproveent beause variable spring stiffness systes have not been thoroughly investigated in ters of their pratial ipleentati, despite the fat that vibrati systes with variable stiffness trol were proposed by a few researhers [5, 6]. Kobori proposed a variable stiffness syste to suppress buildings respse to earthquaes [6]. The ai of Kobori s wor was to ahieve a n-statiary and n-resant state during earthquaes. Youn and Ha used an air spring in a suspensi syste to vary the stiffness ag three disrete values [5]. The stiffness was hanged ly when the required trol fore ould not be generated by variable daping ale. A vehile syste with variable stiffness destrated a good perforane opared to a sei-ative syste * Correspding author, Tel.: , Fax.: E-ail: yqliu@eng.box.edia.yoto-u.a.jp

3 with variable daping and fixed stiffness. However, vential ipleentati of variable stiffness devie is opliated. On the other hand, the variable daping an be easily produed by a trollable daper, suh as a fluid daper with variable orifies or a agnetorheologial MR daper [7, 8]. The authors of this paper have proposed a struture using two Voigt eleents eah e oposed of a trollable daper and a stant spring in series to realize variable stiffness and daping [7]. In the syste, the stiffness ould be hanged easily by daper. The proposed struture was experientally ipleented using two MR fluid dapers. The sinusoidal and rando respses of e degree-of-freedo DOF and -DOF systes showed that the proposed daping and stiffness -off trol syste using MR fluid dapers exhibited good vibrati isolati perforane [9, ]. However, beause two trollable dapers were installed in series in the previous syste, the daping and stiffness ould not be hanged independently. In this paper, a new variable stiffness and variable daping syste in whih the stiffness and daping an be independently and easily trolled is proposed. The respses of the proposed systes to the sinusoidal and rando exitatis are studied in nuerial siulatis and experients.. Variable stiffness and daping syste. Mehanial struture A new odel of e-degree-of-freedo -DOF vibrati isolati syste with two trollable dapers daper and daper orrespding daping oeffiients of and and two springs spring and spring orrespding stiffnesses of and shown in Fig. a is proposed. Daper and spring oprise a Voigt eleent. The Voigt eleent and spring are in series. The stiffness values of the two springs are stant, however, the effetive stiffness of the net syste an be varied by the trollable daper. If the daping oeffiient of daper is sall enough, the total syste stiffness approahes the series stiffnesses of spring and. However, if the daping oeffiient of daper is large enough, the total stiffness approahes the stiffness of spring. The daper provides variable daping for the syste. F F x x x x x. Equatis of oti a Original odel b Equivalent odel Fig. Mehanial figurati of variable stiffness and daping. In Fig. a, F is an exitati fore, x, x, and x are displaeents of base, ass and the point between the Voigt eleent and spring, respetively. In the ase of a vehile suspensi, x orrespds to the road bupiness and F is produed by engine vibrati. Figure b shows the equivalent odel of the syste. Here and are equivalent stiffness and daping oeffiient, respetively. The equatis of oti for the syste shown in Fig. a are & x = x x x& x& x& x& F, x x = x x x& x&, where.. and. ean d /dt and d/dt. When ly the base exitati is sidered F=, the transfer funti of the syste is

4 = i i X X, 3 where x =X e it, x=xe it, t is the tie and is the exitati frequeny. When ly the fore exitati is sidered x =, the opliane is given by = i F X, where F=F e it. The orrespding transfer funtis of the equivalent odel shown in Fig. b are i i X X =, 5 i F X =. 6 Coparing Eqs. 3 and with Eqs. 5 and 6, the equivalent stiffness and daping oeffiient are = = r α α α, 7 = = α α α r, 8 where α= /, r=/ n, n =, =, and =. Equatis 7 and 8 show that is independent of, and and are influened by. If =, then = and =. If =, then = / and =. By letting = g, =π N/, / =/3, and =. these values give the natural frequenies of.5 Hz for = and Hz for =., Fig. shows frequeny respses of the syste. The resant frequeny an be varied by, and when is is sall <., the opliane in the low frequeny regi has large value n X/X =. =. =.5 =. = = = 5 a Base exitati

5 =. =. = X/F - =.5 = = 5 - = n b Fore exitati Fig. Frequeny respses of the vibrati syste varied by daper =...3 Equivalent stiffness and daping Figures 3 and show the values of and as funtis of and / for =.,.3 and.5 =π N/ and = g. When / = /3,. and 3., and =., and, the orrespding values of and are also shown by thi solid lines in the figures. The exiting frequenies are =. n, n, and n. N/ / - - N/ / - - N/ / - - a =. n b = n = n Fig. 3 Equivalent stiffness of the syste. Ns/ 5 Ns/ 5 Ns/ 5 / - - / - - / - - =. =. 3 =. 5 a = n

6 Ns/ 3 / - - Ns/ 3 / - - Ns/ 3 / - - =. =. 3 =. 5 b =. n Ns/ 5 Ns/ 5 Ns/ 5 / - - / - - / - - =. =. 3 =. 5 = n Fig. Equivalent daping oeffiient of the syste. Figure 3 shows that when the stiffness ratio / is sall / =., an be varied signifiantly by hanging. However, when it is large / =, an be hanged by a sall aount by varying. For pratial appliatis, the stiffness ratio / should be sall in order to ahieve a large variati of stiffness by hanging daper. In the following nuerial alulatis sidering the experiental apparatus, / =/3 is used. The equivalent stiffness an be hanged. ties. Based Fig., when = n, is alost independent, and when = n, is slightly affeted by. When =. n, has a high pea at = α α r. However, sine the isolati is designed for the high frequeny regi, the low frequeny regi an be negleted. Therefore, it an be luded that an be trolled by dependently when the value of is hanged fro a very sall value to a very large very value. On-off trol algoriths The -off trol algorith of daper uses the sign of the absolute veloity and the relative veloity []. The fore f d generated by daper is x& x& if x& x& x& fd =, 9 off x& x& if x& x& x& < where the daping oeffiient is equal to in the -state and off in the off-state. The trol algorith for daper uses the sign of x& x x [7]. The fore f d exerted by daper is x& x& if x& x x fd =, off x& x& if x& x x < Eight types of trol shees shown in Table are opared. In the Type syste, daper and daper are always in the off-sates and the total stiffness is the sall Soft suspensi. In the Type syste, daper is in the off-state and daper is in the -state Low daping. In the Type 3 syste, daper and are both in the -state High daping. Beause daper is always in the -state and the total

7 stiffness is large in the low and high daping systes, they are typially alled stiff suspensi. In the Type syste, daper is -off trolled as given by Eq. 9 and daper is in the off-state D -off soft. In the Type 5 syste, daper is -off trolled as given by Eq. 9 and daper is in the state D -off stiff. In the Type 6 syste, daper is in the off-state and daper is -off trolled as given by Eq. S -off low. In the Type 7 syste, daper is in the -state and daper is off trolled as given by Eq. S -off high. In the Type 8 syste, daper and are -off trolled DS -off. Types,, and 3 are passive systes, while Types, 5, 6, 7, and 8 are seiative trol systes. Table Ctrol systes Nae Daper Daper Type Soft syste off off Type Low daping off Type 3 High daping Type D -off soft -off off Type 5 D -off stiff -off Type 6 S -off low off -off Type 7 S -off high -off Type 8 DS -off -off -off 3. Frequeny and tie respses 3. Frequeny respses to a sinusoidal exitati Based the liitatis of experiental apparatus used in this wor, the following values were used in the nuerial alulati: off =.π Ns/ off =., =.π Ns/ =.5, off =.3π Ns/ off =., and =3.π Ns/ =. When X =., the values X/X of the syste with eight trol shees are shown in Fig. 5 a. When F =.π N, the values X/F of the syste are shown in Fig. 5 b. Beause the base does not ove in the fore exitati ase x& =, the ter x & x& x& is always positive or zero, and daper is always in the -state. Therefore, the D -off stiff trol syste behaves siilarly to the high daping syste, and the DS -off trol syste behaves siilarly to the S -off high trol syste in Fig. 5 b. Figure 5 a shows that DS -off and D -off soft trol systes have good perforanes, beause their respses do not exhibit resant peas at.5 n and n, and the X/X values are sall in the high frequeny regi. Based Fig. 5 b, DS -off, S -off high, D -off stiff and high trol systes have good perforanes in the resant and low frequeny regis. Therefore, the DS off trol syste ay have good perforanes in the both ases of base and fore exitatis.

8 S -off low Low Soft High X/X D -off stiff S -off high DS -off - D -off soft - n a Base exitati Soft S -off low - Low X/F - D -off soft High & D -off stiff S -off high & DS -off -3 - n b Fore exitati Fig. 5 Frequeny respses of the syste to a sinusoidal exitati.

9 3.3 Tie respses to a rando exitati The respse to a rando base exitati siulates a vehile traveling an atual road. It is oly aepted that the spetru of a geoetrial road profile, Pn, an be approxiated as w n P n, if n n = n P n, w n P n, if n > n n where w =. and w =.5, and n =/π /, n is a spatial frequeny, and Pn is the road roughness []. In this study, three lasses of roads are used: A sooth, Pn =6-6 3 /, B average, Pn =6-6 3 /, and C Rough, Pn = / []. Csidering a vehile traveling with speed υ, the road irregularity is desribed by N t = Ai sinit ϕi i= x, where φ i is a rando variable with a unifor distributi in the interval [, π], Ai = Pi n n, i=,, 3,, N, n=π/l, L is the length of the road segent [3]. The value of is deterined by π = υ. 3 L In this analysis, υ = /s, N=, L=, t=.5 s. Figure 6 desribes the tie histories and power spetral densities PSD of three lasses roads. In the alulati, the frequeny regi of the input signal is fro. Hz to Hz. The tie respses of the systes with B lass exitati are shown in Fig. 7, and the root ean square RMS values are showed in Table. Aording to Fig. 7 and Table, the displaeent of DS -off trol syste is the sallest ag the eight trol systes. The aelerati of DS -off trol syste is larger than those of Soft, D -off soft and S -off low trol systes, however, these systes have bad X/F perforanes in the low frequeny as shown in Fig. 5 b. Therefore, the DS -off trol has good perforanes in a rando exiting ase. x 5 A Sooth x x B Average C Rough Tie s a Tie history PSD of x /Hz A C B - Frequeny Hz b PSD values Fig. 6 Three lass exitatis.

10 x x x x x x x x x Soft Low High D -off soft D -off stiff S -off low S -off high DS -off - 6 Tie s 8 x& & /s x& /s & x& & /s & x& /s x& & /s & x& /s x& & /s & x& /s & x& /s Soft Low High D -off soft D -off stiff S -off low S -off high DS -off - 6 Tie s 8 b Aeleratis a Displaeents Fig. 7 Tie respses to a rando base exitati.

11 Table RMS values of the syste with a rando base exitati. A Sooth B Average C Rough x x& & /s x x& & /s x x& & /s Soft syste Low daping High daping D -off soft D -off stiff S -off low S -off high DS -off Experients. Experiental setup Figure 8 shows the experiental setup of the proposed vibrati syste. The ass is supported by leaf springs spring and ; and the syste base is shaen in horiztal direti using an eletroagneti vibrati exiter and a signal generator. Two MR fluid dapers RD 97 Lord Cooperati, daper and, are used to provide the variable daping. Daper is loated between the ass and idpoint; oreover, daper nets the ass with the base by steel stays. Beause the stays are very stiff, their deforatis in these experients are negligible. Daper and spring oprise a Voigt eleent. The Voigt eleent and spring are in series. In these experients, the displaeents x and x are easured by laser displaeent sensors. The veloities x& and x& are obtained by differentiating the displaeents in the troller. The voltages to DC power supplies trol the urrents to MR dapers.

12 Displaeent sensor Spring Daper x x θ Spring Daper Stay A/D Board θ Ctroller Vibrati exiter Platfor Displaeent sensor Signal generator I I DC power supply DC power supply D/A Board a Experiental syste b Photograph of the experiental apparatus Fig. 8 Experiental setup.. Paraeter values in experients The values orrespding to the paraeters of the experiental setup are listed in Table 3. The equivalent ass of the experiental struture is inluded in. In general, MR fluid dapers have friti fores [8, 9]. Therefore, the equivalent daping oeffiients are obtained by the syste s respses in other preliinary experients. Based

13 Eqs. 7 and 8, the values of,,, and resant frequeny f n for = n are shown in Table. Aording to Table, the total stiffness is hanged.8 ties by varying daper fro the off-state to the -state. The total daping oeffiient is varied 3.6 ties. The total daping and stiffness values are varied by daper and alost independently. Moreover, the natural frequeny f n is hanged fro.99 Hz to 3.35 Hz by altering the syste stiffness fro soft to stiff. Table 3 Paraeter values of experiental setup. Paraeters Values Paraeters Values A Paraeters Values Ns/ Paraeters Values.5 g I off off 3.6 off N/ I N/ I off off. off.6 θ o.8 I θ o.9 Table Values of equivalent stiffness and daping oeffiient in the experient. Daper Daper N/ Ns/ f n Hz off off off off Experiental results.3. Frequeny respses to a sinusoidal base exitati The steady-state respses of X/X are shown in Fig. 9, where the aplitude of a sinusoidal displaeent x is 5 and the exiting frequeny is hanged fro Hz to Hz. Beause of liitatis of the eletroagneti vibrati exiter, the experiental results are liited to the frequeny range fro Hz to Hz. Based Fig. 9, the alulati results are in good agreeent with those of the experient.

14 Low Soft X/X High DS -off D -off soft S -off low S -off high D -off stiff 5 Frequeny Hz Fig. 9 Frequeny respses to a sinusoidal base exitati experient:, alulati:..3. Respses to a rando base exitati Figure shows the tie respses to a rando base exitati. The RMS values of the respses are shown in the braets. The tie history of the input displaeent x is also shown in this figure. The respse of DS off trol syste is the sallest ag those of the eight trol systes.

15 x - x x x x x x Soft RMS:. Low RMS:.66 High RMS: 3. D -off soft RMS:.9 D -off stiff RMS:.98 S -off low RMS: 3. x - S -off high RMS:. x DS -off RMS: Tie s Fig. Rando input and tie respses. 5. Clusis A new variable stiffness and daping syste figurati using two trollable dapers was proposed. Sine the stiffness is trolled by hanging the daping oeffiient, this syste is very siple and easy to apply in

16 pratial systes. The syste is experientally investigated using the MR daper that the daping an be hanged easily. Based the experiental and alulati results, the proposed trol syste has good perforanes for the vibrati isolati, espeially, it has the sallest displaeent respses. The aelerati is a little larger than those of the soft spring systes, however, the soft spring systes has larger opliane and they are not appliable for the real systes whih has not ly the base exitati but also the fore exitati. Anowledgeents This wor was supported by Japan Soiety for the Prooti of Siene JSPS No Referenes [] D. Karnopp, M. J. Crosby, R. A. Harwood, Vibrati trol using sei-ative fore generators, ASME Journal of Engineering for Industry, Vol. 96, No. 97, p [] E. J. Krasnii, The experiental perforane of an -off ative daper, Sho and Vibrati Bulletin, No. 5 98, p [3] S. Raheja, S. Sanar, Vibrati and sho isolati perforane of a sei-ative -off daper, ASME Journal of Vibrati, Aoustis, Stress and Reliability in Design, Vol. 7, No. 985, p [] Y. Liu, H. Matsuhisa, H. Utsuno, J. G. Par, Ctrollable vibrati of the ar-body using agnetorheologial fluid daper, Internatial Journal of Vehile Syste Dynais Suppleent, Vol., No., p [5] I. Youn, A. Ha, Sei-ative suspensi with adaptive apability, Journal of Sound and Vibrati, Vol. 8, No , p [6] T. Kobori, M. Taahashi, T. Nasu, N. Niwa, K. Ogasawara, Seisi respse trolled struture with ative variable stiffness syste, Earthquae Engineering and Strutural Dynais, Vol., No. 993, p [7] Y. Liu, H. Matsuhisa, H. Utsuno, J. G. Par, Vibrati isolati by a variable stiffness and daping syste, Internatial Journal of Japan Soiety of Mehanial Engineering Series C, Vol. 8, No. 5, p [8] last aessed Aug. 7 th, 3. [9] Y. Liu, H. Matsuhisa, H. Utsuno, J. G. Par, Vibrati trol by a variable daping and stiffness with agnetorheologial dapers, Internatial Journal of Japan Soiety of Mehanial Engineering Series C, Vol. 9, No. 6, p. -7. [] Y. Liu, H. Matsuhisa, H. Utsuno, J. G. Par, Variable daping and stiffness trol with agnetorheologial dapers for a -DOF vibrati syste, Internatial Journal of Japan Soiety of Mehanial Engineering Series C, Vol. 9, No. 6, p [] O. Taniguhi, Vibrati Engineers Handboo in Japanese, The Copiling Coittee of Vibrati Engineers Handboo, Yoendo Press, Toyo, 976, p [] ISO 868: E, Mehanial vibrati -- road surfae profiles reporting of easured data, TC 8/SC Mehanial vibrati and sho/easureent and evaluati of ehanial vibrati and shos as applied to ahines, vehiles and strutures, ISO Standards, 995. [3] G. Verros, C. Natsiavas, Design optiizati of quarter-ar odels with passive and sei-ative suspensis under rando road exitati, Journal of Vibrati and Ctrol, Vol., No. 5 5, p