Time Response of Nitinol Ribbons

Transcription

1 Time Repone o Nitinol Ribbon Pavel L. Potapov, Techniche Univerität-Berlin, Germany preently with Antwerpen Univerity- RUCA, EAT, Croenenborgerlaan 7, Antwerpen, Belgium Key word NiTi, Nitinol, actuator, time repone, convection, tranormation latent heat Abtract Force/diplacement actuator with a high output power and time repone may be abricated rom thin hape memory ribbon. They are normally driven by Joule heating and air convection cooling. In the preent work, the time repone o our -um Nitinol ribbon having the dierent content o Cu or H and, thereore the dierent tranormation temperature, i tudied ytematically under condition o ree and orced air convection. The imple analytical model or calculating the time repone i developed which account the latent heat and thermal hyterei o tranormation. For all our ribbon, the calculated time repone i in a good agreement with that oberved experimentally. Finally, on the bae o the uggeted model, the time repone o a Nitinol ribbon i preented a a unction o it tranormation temperature and thickne. Introduction Shape memory linear actuator made rom Nitinol, Cu-Zn-Al or Cu-Al-Ni alloy are capable to produce a large actuation orce or diplacement due to the intrinic phae tranition. Thee alloy undergo the diuionle tranormation rom martenitic () to autenitic (A) phae on heating and the A tranormation on cooling. A typical method to trigger the tranition include the Joule heating or the A tranormation and air convection cooling or the A one. The Joule heating can be quite rapid at the uicient electric power applied. Thu, the time repone o actuator i controlled mainly by the eiciency o the cooling proce. Thi paper preent the experiment on air convection cooling o everal Nitinol ribbon having quite dierent tranormation temperature and geometrical ize. The oberved experimental reult can be reaonably itted by the imple analytical model that conit no calibration parameter. The model i uitable or imulation o the cooling proce in linear hape memory actuator uch a Nitinol ribbon. Experimental Procedure and Reult Nitinol ribbon containing 5, and 5% Cu were upplied by emry Co.-Europe (Belgium), RyazanTechProm (Ruia) and Dr.A.V.Shelyakov (ocow Engineering Phyic Int.) correpondingly. Ribbon containing H were manuactured by Dr. A.V.Shelyakov in collaboration with Pro. A.A.Gulyaev and Dr. P.L.Potapov. At room temperature, all ribbon how approximately the ame peciic heat capacity o about.5j/g/k. The tranormation temperature and latent heat a determined by DSC are lited in Table where ribbon are reerred a B, R, S and H type depending on their upplier. The tranormation tart and inih temperature are reerred a A and A or the A tranormation and and or the A one.

2 Table Compoition, cro ection, tranormation temperature and latent heat o Nitinol ribbon. Ribbon Supplier Chemical Cro-ection, mtranormation temperature Latent heat, Compoition A A J/g B emry-eu 5%Ni-5%Ti-.7x.. 5%Cu R RTP %Ni-5%Ti-.x %Cu S Shelyakov 5%Ni-5%Ti-.x %Cu H Shelyakov 5%Ni-5%Ti- 5%H.x Nitinol ribbon provide a diplacement or induce a load when heated in load-contant or delection-contant condition correpondingly. Experiment with thin ribbon in the load-contant mode can be ditorted by inertia and riction eect. Thu, the delection-contant mode wa elected in the preent work. To induce the hape memory eect the ribbon were pre-deormed at room temperature and then placed between two motionle grip with the inter-grip ditance o mm. One o the grip wa connected with a train-gage enor allowing u to control the load induced by the ribbon. For each ribbon, two erie o experiment were executed: quai-tatic and dynamic heating/cooling. B-ribbon S-ribbon experimental approximated Temperature ( C) R-ribbon H-ribbon Temperature ( C) experimental approximated Fig. Load-temperature curve o B, S and R, H ribbon obtained at heating/cooling rate 5 C/min in delection-contant condition. Cooling branche are itted by (). In quai-tatic experiment, the ribbon were lowly heated/cooled with the precie control o the temperature over the ribbon. On heating rom A to A point, the A tranormation occur and induce the load between the grip. On cooling rom to, the ribbon undergo A tranition reulting in a reet o the induced load. The maximal load lightly change with the heating/cooling cycling, however in 5 cycle it i tabilized. Fig. how the load-temperature curve o B, R, S and H ribbon obtained ater complete cycle. The hape o the tranormation loop i imilar in all examined ribbon although the tranormation point and hyterei vary igniicantly rom a ribbon to a ribbon due to their dierent compoition and treatment. We will ocu on the cooling branch o each curve. The degradation o the load on cooling i proportional to the amount o the martenite induced. For tre-contant condition, Liang and Roger [] uggeted the ollowing empirical dependence o the martenite raction n on temperature

3 n= at >T T n( T ) = co π + at <T< () n= at T< In train-contant condition, the coupling between the induced load and the martenite raction reult in an increae o tranormation point, a evident rom the comparion o the curve in Fig with the data in Table. However, Fig. demontrate that the empirical dependence () i till reaonable in train-contant condition with taking and parameter higher than thoe taken in tre-ree condition. Out o the tranormation range, ome ribbon how the mall negative lope o the load-temperature curve due to thermal expanion. R ribbon indicate the more complex behavior with a poitive lope o the load below temperature. oreover, a poitive lope i oberved even on cooling ar below room temperature. That i a reult o the tranition between dierent type o martenite reported in NiTi-%Cu alloy. In thi paper, we neglect the martenite martenite tranition becaue it i aociated with the much maller latent heat and induced load than the A one. 9 et: 7 C t H = t H =.5 t H =. 9% reet: C 7 5 et: C t H = t H = t H =.5 9% reet: 5 C - - et: 9 C t H = t H =.5 t H = et: C 7 t H = t H =.5 t H =. 5 9% reet: 57 C 9% reet: 75 C (c) (d) Fig. Impulive Joule heating o B, R, S (c) and H (d) ribbon ollowed by ree air convection cooling. For convenience, each curve i hited along the time-axi uch a cooling tart alway at t= regardle o the heating duration.

4 In dynamic experiment, heating wa executed by ending the hort rectangular DC impule through the ribbon ollowed by cooling with ree air convection. The load-time protocol wa continuouly recorded during heating/cooling while the temperature o the ribbon wa not controlled. Auming that the load-temperature curve do not change igniicantly with the heating/cooling rate, the temporal evolution o the temperature can be extracted rom the load-time protocol and the quai-tatic data in Fig.. Fig. how the reult o dynamic experiment when the duration o the heating impule wa varied rom. to. At each impule duration, the value o DC wa preciely adjuted in order to reach the ame maximal temperature a that or the quaitatic experiment (7 C in B, C in R, 9 C in S and 5 C in H ribbon). For intance, R ribbon were heated up to C or by ending.a and or. by ending 7.A. The load correponding to the maximal temperature i marked a a et point. Other marker indicate the level when 9% o the tranormation-induced load i reet by cooling. Note that in the cae o cooling H ribbon (Fig.d), the load lightly increae in the range o 9 5 C due to thermal contraction and then decreae in the 7 9 C range due to the A- tranormation. A een in Fig.d, thi peculiarity i reproduced in dynamic experiment. We reer the time required or cooling rom the et point to the 9% reet point a the cooling time. The cooling time varie rom a ribbon to a ribbon being the maximal in B ribbon and the minimal in H one. Alo the cooling time decreae lightly with decreaing the duration o DC impule. The cooling proce can be orced by lowing air rom an external an. Fig, how the example o the experiment when ribbon were expoed by a permanent airlow along their urace with the rate o.5m/. Comparing with ree convection, the cooling time decreae by a actor, but at the ame time, the higher thermal loe reult in approximately time higher power conumption during the heating phae. et: 7 C t H = t H =.5 t H =. et: 9 C t H = t H =.5 t H =. 9% reet: C 9% reet: 57 C Fig. Impulive Joule heating o B, and S ribbon ollowed by orced air convection cooling with a low rate.5m/. For convenience, each curve i hited along the time-axi uch a cooling tart alway at t= regardle o the heating duration. Simulation o Cooling Curve When no electrical power i upplied to the SA ribbon (cooling phae), the heat traner problem i deined by dt ( C + h( T )) = K( T T ) () dt

5 where C i the heat capacity o a Nitinol ribbon, h(t) i the tranormation heat releaed on cooling, K i the coeicient o the heat exchange between a ribbon and urrounding, T i the temperature o a Nitinol ribbon and T i the temperature o urrounding. Auming that the martenite volume raction depend on temperature a (), the tranormation heat v. temperature i π T h( T ) = in π H () where H i the integral latent heat or the tranormation on cooling. Equation () and () can be combined and written in dimenionle orm: π dt + H in( π T ) = T + dt S () T K H T where T =, t = t, H = and S = are dimenionle variable C C( ) and parameter introduced by Wirtz et al.[]. Integrating () with the boundary condition T'= at t'= we have t = ln π H ( T ) + ln( ) { co( πs )[ Si( π ( T ) Si( π ( + S )] in( πs )[ Ci( π ( T )) Ci( π ( + S )]} (5) x where Si() x = in y () y dy and x () y co Ci( x) = dy are the ine and coine integral unction y incorporated a tandard in ome mathematical otware, e.g. athematica.. The ormula (5) i valid at any S parameter. At S >, the heat traner problem can be olved even without uing the pecial unction. Dividing both the ide o () on (S'+T') and approximating the /(S'+T') term a a linear unction in the vicinity o the T =.5 point, the equation () can be rewritten a π + S T dt in( ) + H πt (.5 ) T + S + S dt = () Lineariation o the /(S`+T ) term i exact in the only mall vicinity o the point T =.5. However, the deviation o () rom () at T = and T = are till negligible becaue o in(πt ) goe to at thee point. Integrating () with the boundary condition T'= at t'= we have H t = ln( T ) + ln( ) + ( + S T ) co( π T ) + in( πt ) π (7) (.5 ) Fig. how the calculated dimenionle cooling curve with the variou H and S parameter. The S parameter indicate how big i the dierence between the tranormation and room temperature while the H parameter i the dimenionle meaure o the tranormation latent heat. The lower S reult in the lower cooling proce. The tranormation latent heat alo retard cooling with the maximal eect at T =.5. Note that the curve calculated with ormula (7) how the only minor deviation rom the exact olution (5).

6 , H =.5 calculated with [7] calculated with [5] S =.5, S = calculated with [7] calculated with [5] H =.5, S =, H = T, S = T, H =.5, S =, H = H = t t Fig. Calculated cooling proile in dimenionle term (ee deinition in text). Due to the thermal hyterei o the tranormation, Nitinol ribbon hould be heated at leat up to A A temperature, thu the cooling proce tart at T'=+G, where G = i the dimenionle hyterei. In the regime <T'<G, the heat traner equation i written a dt = T () dt Uing the ame boundary condition (T'= at t'=) we obtain the implet temperature-time curve ( T ) + ln( ) t = ln + S (9) The curve (9) can be moothly connected with (5) or (7) at T'= due to the equal derivative dt/dt at thi point. The analogou curve can be generated in the regime T <. So, the problem o the heat traner reduce to determination o the heat exchange coeicient K between a Nitinol ribbon and urrounding. In a tandard theory o the convective heat exchange, K i deined by K = lλnu () where l i the ribbon length (inter-grip ditance), λ i the thermal conductivity o air and Nu i the Nuelt number. In the cae o ree convection and orced convection with a laminar low, the ollowing expreion or Nu are recommended []: ( Pr) / (.9 / Pr) Nu = + Gr + ree convection () Nu =.( ωh / ν ) Pr orced convection () where h i the ribbon width, Pr i the Prandtl number o air, Gr i the Graho number, v i kinematic vicoity o air and ω i the air low rate. The Graho number i

7 gβ Th Gr = () ν where g i the gravitation contant, T i the dierence between the maximal temperature on a ribbon and the urrounding temperature, β i thermal expanion coeicient o air (or an ideal ga β=/t). The coeicient β reer to the maximal temperature o a ribbon while the other contant in (-) reer to the middle temperature between a ribbon and urrounding. Finally, the dimenionle time can be tranerred to the real one with the ormula K t = t () lhdρc where d i the ribbon thickne, ρ i the denity o Nitinol (about.5 g/m ) and c p i the Nitinol peciic heat capacity at room temperature. The calculated reult are ummarized in Table and plotted in Fig. 5 in comparion with the experimental cooling time. The temperature dependent thermal parameter employed in (-) are taken rom []. Depite o the rough aumption made, the calculation correctly reproduce the experimental data or all examined ribbon. oreover, a demontrated in Fig., the calculated time-temperature proile are in a good agreement with experimental one extracted rom Fig. and. Table Dimenionle latent heat (H ), temperature dierence actor (S ) and hyterei (G ) along with the calculated dimenionle cooling time (t C ), heat exchange coeicient (K), and real cooling time (t C ). The thermal contant or calculating K were taken rom []. Ribbon C C T, C Hyte rei, H S G t C Free convection Forced convection C K, mj/ t C, K, t C, ec. mj/ C ec. B * R ** S ** H ** * calculated with (5) ** calculated with (7) p R (exp) S (exp) H (exp) B (exp) R (calc) S (calc) H (calc) B (calc) R (exp) S (exp) H (exp) B (exp) R (cal) S (cal) H (cal) B (cal) Cooling Cooling. Heating.. Heating Fig. 5 Comparion o the experimental cooling time with the calculated one or ree and orced air convection.

8 Temperature ( C) 7 5 calculated 5 experimental, t H = experimental, t H =.5 Fig. Comparion o the experimental cooling proile with the calculated one or the R ribbon. The uggeted model doe not predict any dependence o the cooling time on the heating impule duration. That i becaue the olution (5), (7) and (9) aume K to be contant during the cooling proce and equal to the teady value deined by (-). In reality, thi condition can be valid in only the cae o relatively long impule applied. A een rom Fig., the load reache the teady level in ater witching DC on. Thi mean that the teady heat exchange between a ribbon and urrounding i only oberved when a heating impule i longer than. In the cae o the. and.5 impule, the current i cut beore the tationary condition are reached, and thu, urther cooling hould be rather modeled in the term o the unteady heat exchange. Unortunately, the unteady heat traner problem can not be olved analytically. We are now in running to develop the imple empirical approach reaonable or hort heating impule. The equation (5-) enable u to etimate the time repone o Nitinol ribbon a a unction o their geometrical ize and tranormation temperature. Fig.7 how the variation o the cooling time with the thickne and the temperature. So a the heating time can be extremely hort at the uicient DC power applied, the time repone o Nitinol ribbon i controlled mainly by the cooling time. To provide rapid actuation at room temperature, the hould tay in the range o - C while an increae o above C reult in an only mall urther improvement o the time repone. Thi concluion i conitent with the experimental data o Yaeger [5] who tudied the time repone when the urrounding temperature wa varied while the tranormation temperature wa ixed. A reduction o a ribbon thickne demontrate the more dramatic eect on the actuation time repone (note the logarithmic cale in Fig.b). However, it i alo true that the induced load decreae proportionally to the thickne. 5, Cooling thickne d=µm width h=mm A=+5 C =- C To= C Cooling, width h=mm width/thickne ratio h/d=5 A=75 C = C = C To= C temperature ( C), ribbon thickne d (µm) Fig.7 Predicted cooling time or a Nitinol ribbon a a unction o temperature and thickne. The tranormation latent heat i alway aumed to be J/g.

9 Concluion. The cooling proce in hape memory actuator uch a Nitinol ribbon can be reaonably imulated by the imple analytical model.. The actuation requency o Nitinol ribbon can be improved by increaing the temperature up to - C or/and by decreaing their thickne. Acknowledgement The project wa upported by Alexander von Humboldt-Stitung. Calorimetric tet were kindly perormed by E. Da Silva. The author would like to thank Dr. A.V.Shelyakov or providing ribbon and conultation. The author acknowledge dicuion with Pro. I.üller and other member o the Thermodynamik team in Techniche Univerität-Berlin. Reerence [] C.Liang and C.A.Roger, One-dimenional thermomechanical contitutive relation or hape memory material, Proc. AIAA nd Structure, Structural Dynamic and aterial Con.,, 99 Baltimore, (99) 7-CP. [] R.A.Wirtz, F.Gordaninejad and W.Wu, Free repone o a thermally driven, compoite actuator, J.Intell. at.sytem and Structure, 5 (995) pp.-7. [] W.Beitz and K.H.Küttner, Dubbel Tahenbuch ür den machinenbau, Springer-Verlag, Berlin (995). [] H.D.Baehr and K.Stephan, Wärme-und Stoübertragung, Springer-Verlag, Berlin (99). [5] J.R.Yager, Electrical actuator: alloy election, proceing and evaluation, in Engineering Apect o Shape emory Alloy, ed. T.W.Duerig et al., Butterworth-Heinemann, London (99) pp.9-.