Shape memory alloy hysteresis

29

Sensors and Actuators A, 36 (1993) 29-35

Shape memory alloy hysteresis A Pruskl

and H Kohl

Loboratolre d’Autom&que (Recmed

et d’EIectronrque Industrrelles, Unwersrty of Metr. 57045 Metz (France)

July 18, 1991, m remed form May 8, 1992, accepted June 23, 1992)

Abstract Shape memory alloy (SMA) has Interesting properties which can be apphed to mlcrommlature to reduce the bulk and to make strain control possible, the internal electrical resistance vanatlon feedback vanable The strain has the disadvantage of having a large hysteresis, especially for describe m this paper some methods for removmg the hysteresis and some cases where controlled

1. Introduction Shape memory alloy (SMA) has properties which have interested robotics researchers for about ten years Indeed, it presents a very large usable energy/weight ratio that allows mlcrommlature actuators to be developed In the control field, a system 1s always characterlzed by the perception, decision and action tnlogy This concept needs perception sensors, control units and devices to perform the actions Generally these three units present a large bulk SMA 1s a solution for the mlcrommlature field, since it includes two parts out of the three action and perception Some research teams focused on the different problems caused by SMA mlcrommlature controlled actuators The first robotic apphcatlon used SMA as an actuator controlled by heat power (e g , the TOKI robot) [l] We call these devices first-generation actuators The second generation used SMA as a pure actuator to which an independent position sensor was associated Hashlmoto et al [2] designed two types of actuators The first was composed of SMA and a bias spring and the second one was a dfierentlal type composed of two antagonist SMA wires This actuator was fixed on a mechanical structure and allowed a biped robot to be made Feedback control was performed by a potentlometrlc posltlon sensor Bergamasco et a2 [3] described an SMA apphcatlon for a direct drive actuator The feedback loop was also made by a potentiometer position sensor The third SMA actuator generation used the internal SMA resistance to perform the posltlon control The 0924-4247/93/S 00

actuators In order may be used as the copper alloys We SMA may be used

SMA resistance replaced the strain estimation by heat power Indeed, the SMA reslstlvlty varied with respect to the amount of material transformed Honma et al [4] used the SMA resistance to control an actuator without overshoot with a 2% precision m the steady state Ikuta et al [5] achieved an active endoscope that constitutes a complex mechanism integrating some SMA actuator stages using electrical resistance feedback In [6] Ikuta described an apphcatlon for a mlcrommlature gnpper actuated by two antagonist SMA wires Takeda et al [7] analysed SMA features m order to make a displacement sensor Such a sensor 1s compact, light and has good linearity In all SMA apphcatlons where the deformation (or posltlon, or strain) 1s controlled by the electncal resistance, the authors specify that hysteresis exists It hrmts the performance of the mechanism We have studied the hysteresis phenomenon and offer some methods to remove it m the case of controlled SMA and an SMA sensor

2. The framework of the study The shape memory property IS induced by the phase transformation phenomenon m an NlTl or copper alloy A specific shape (or geometry) corresponds to the amount of martensite Two vanables induce the marten&e variation temperature and stress The relationship between strain and temperature 1s given by AE =6Aa-/i

A0 @ 1993 -

(1) Elsevler Sequoia All nghts reserved

-b-p-p

?-pi--~

-q-YL-jp

(a)

(‘3

(4

Fig 3 Different uses of SMA (a) thermal generator, (c) sensor

(b) actuator,

stress The SMA electrical resistance 1s of interest The martenslte and austemte reslstlvlties are drfferent This means that the resistance value 1s the mirror of the amount of martensite (or austenrte) and this gives the value of the strain A theoretical study [ 1l] shows that m a large area of the transformation phase, the reslstlvlty vanatlon 1s proportional to the amount of martensite The reslstlvlty behavlour 1s given by Apm = yAa - PA0

Fig I Stahc hehavlour

of SMA

where AE 1s the stram variation, Au the stress vanatlon, A0 the temperature vanatlon and S, p are posltlve constant coefficients This relationship 1s verified [ 8 - lo] m the hnear transformation phase as shown m Fig 1 The temperature after heatmg or the stress after removing the load mduces a large hysteresis that may reach 50% of the full-scale strain, or even more (see Fig 2) This characterlstlc makes it difficult to control the strain by measurmg the temperature or the

(2)

where (T 1s the stress, 0 the temperature, pm the martensite reslstlvlty and y, fi are positive coefficients We consider SMA as a multlvarlable system havmg two control variables and two output variables The three configurations, defined m Fig 3, descnbe different possible SMA uses The three vanables 0, E and c that define the SMA behavlour are reversible Any two inputs generate the third output However, the resistance may represent only one output We have Fig 3(a), a thermal generator, variation of E or 0 generates a temperature variation of the materials, Fig 3(b), a compound device displacement sensor/actuator, the inputs are temperature and stress and the effects are represented by strain and reslstance, Fig 3(c), a stress sensor, the system inputs constitute temperature and stram and the effects are resistance and stress variation, d the temperature 1s constant we assume that the system 1s a strain sensor In this paper, we present the results of our studies and experiments on both systems (b) and (c) The system (a) phenomenon 1s very margmal The generated effect 1s very weak and falls outside our study framework

3. Analysis of the resistance versus strain relationship E

Fig 2 Stress vs stram for constant

temperature

Most previous work has defined the various static as well as dynamic effects Our work 1s

31

n

POWER

’I C

Reference

J-U-L R

measure

Ftg 4 Outlme of the expenmental set-up

essentially focused on the material’s electrical reslstance m order to unprove the accuracy of an internal feedback-controlled SMA actuator We use a copper SMA (Cu-Zn-Al) whose performance 1s mfenor to TlNi ones for maxnnal strain and maximal admlsslble stress The hysteresis IS very large and constitutes an mterestmg framework for our study The first advantage 1s that the materials cost about ten tnnes less than TlN1 The expernnental SMA matenal 1s in the form of 0 5 mm diameter wre It presents the advantage of havmg a large electrical resistance compared to the stnp form (the reslstlvlty falls between 7 and 13 p.Q cm) as has a Marten&e Start (MS) of 28 “C The other advantage of SMA wire is a

traction stress which homogeneously mvolves all the matenals m the phase transformation, which 1s not the case for a torsion or flexlon stress The experunental device 1s represented m Fig 4 The strain measurement that we call displacement 1s performed by an optoelectronic sensor with a 3% linearity error on the full scale (8 mm) The stress 1s imposed by discrete masses that allow the displacement to be dlstmgulshed from the stress The temperature mcrease IS performed by a Joule effect A current signal IO, controlled by a pulsewidth modulator (PWM) and havmg the same shape, supphes the wu-e Another different constant-current source z supplies the wire For 1, = 0, the voltage at the terminals 1s proportional to the

32

SMA resistance The current magmtude 1s chosen so that the generated temperature does not affect the phase transformation The temperature 1s not permanently and accurately measurable and 1s estimated by the PWM signal average value A heat smk 1s associated with the wire to Increase the thermal inertia m order to avold the temperature fluctuation induced by the ambient temperature variation 3 1 SMA behavlour wzth respect to constant temperature As we have described above, we consider the SMA as a system having two input control vanables temperature and stress We intend to study the alloy’s behavlour by analysmg the effect mduced by each mput variable m an independent manner If we keep the temperature constant, we see that relations (I) and (2) become AE = kAp,

(3)

The expenments confirm relation (3) We see that the experimental curve does not show hysteresis despite its presence on the Ap, =f( Aa) and AE =f( Ao) features (Fig 5(a) and (b)) There are two reasons for this (1) The resistance measured by the experimental set-up represents the sum of the alloy resistance (which 1s a constant) and the resistance resulting from the phase transformation R=RO+R,

(4)

We see that the measured resistance variation only represents part of the vanatlon which 1s due to the phase transformation, AR = AR,

(11) There 1s a narrow bond between the SMA reslstlvlty variation pm and the stram The amount of martensite produced directly represents the strain and the reslstlvlty That 1s why the curves R =f(o) and E =f(~) have a symmetrical behavlour We see m Fig S(c) that the expertmental measurements confirm these hypotheses The measurements are performed at a temperature high enough (correspondmg to a heat power between 0 1 and 1 W) to put the alloy m active transformation phase The relative AR/R variation equals 10% for a maximal strain of 3% The proportional coefficient k = As/AR equals 0 6 mm/0 and does not change for any temperature This observation, which was made m [7], shows that SMA may be used as a sensor If the temperature 1s a constant (and 1s only valid m that case) Keeping the temperature constant 1s very difficult The least temperature variation resultmg from ambient temperature variation creates a disturbance, mducmg a change m the R measurement even d the temperature returns to the mltlal value This phenomenon 1s generated by the hysteresis on the temperature, as we shall see m the ne Section In T order to guarantee a greater immunity v&h respect to the ambient temperature, we suggest mcreasmg the thermal inertia (which 1s very weak for a wire) by assoclatmg a heat smk with the wire The alloy’s behavlour 1s mterestmg if we want to design a displacement sensor But if we want to design a resistance-controlled actuator, then it 1s not possible to keep the temperature constant since it constitutes the system control input variable 3 2 SMA behavzour wrth respect to a constant stress The SMA behavlour with respect to temperature makes another parameter appear m the reslstance measure The & value of expression (4) is no longer constant It 1s mtluenced by the temperature We may write R,,= Rb+k@+R,,,

(5)

We verify the effect of the k,O value m Fig 6(a) The resistance versus stram drawmg (Fig 6(c)) 1s not a linear charactenstlc without hysteresis R =f(O) and E =f(@) are not symmetnc We suggest deahng with the problem by removmg the value kO on the curve by the followmg expresslon Fig 5 SMA behavlour at constant temperature

R, = (AR - k, A@) =f( 0)

(6)

Fig 8 The R, measurement

Rm

Fig 6 SMA behawour

at constant stress

l &

Rg

k0

kl

k?.

k3 E v

Rg

7 SMA R =f[O)

rotation

9 Stress vs R,,, curve

measurement, obtained by filtering the pulsewidth-modulated signal (Fig 8) Figure 9 shows that the hysteresis has drsappeared for all values of the mput reference vanable We observe that an instantaneous ambient temperature vanatron affects the measurement but as soon as the temperature becomes stable, the measurement becomes exact The SMA behavrour study at a constant stress shows that rt 1s possrble to determine the alloy stram by measuring R,,,

by k, vanatlon

The idea consists m subtracting a value proporttonal to the temperature from all measured values R Introducing the k, value results m a rotatron of the AR =f(AO) curve (Fig 7) A good choice allows the two curves AR =f(AO) and AE = f(A0) to become symmetrrc, whrch removes the hysteresis on AR,,, =f(As) The expeIvnenta1 measurement of resistance vartation induced by the phase transformation is performed by subtracting the estimated temperature from the resistance

3 3 The differential sensor The simplest way of obtaining a displacement (or strain) sensor with SMA consists, as was shown above, m putting the materials m active phase transformatron by an appropnate current supply and then in measuring the resrstance The resistance 1s proportional to the strain without hysteresis But a temperature parasite wrll induce a measurement modrficatron We suggest removmg the parasitic mfluence of temperature by using a drfferentlal ctrcmt This sensor 1s achieved by a unique SMA wire whose displacement measuring

34 constsnt cltrrcnt supply > I( ,dtsplacemcnt 6

J

I

Ul

-> F2

L

Fl

u2

Ftg 10 The dtfferentlal sensor

point comcldes with the wire’s centre We obtain two parts Fl and F2 mechanically m opposttlon but electncally serially connected (Fig 10) From the mechanical pomt of view, the two parts (or wires) are submitted to the same stress A nudpoint displacement has the effect of submitting an increasing stress to one part (AG) and a decreasing stress of the same value to the second part, but with an opposite sign ( -AD) From the electrical point of view, the two parts are submitted to the same signal, which induces the same temperature m both Followmg eqns (3) and (5) above, AE = kAp,

Rg 11 The dlfferentlal reststance vs stram for d&rent tures

tempcra-

The expenmental results correspond to a 20 cm long wire The curve Ap =~(AE) obtained IS a lme whose measurement error with respect to imposed temperature variations IS not greater than 1% of the full scale (see Fig 11)

R=R;,+R,,,+k,O where for one wire

4. AN SMA sensor-actuator

AE = k( AR,,, + k,, A@)

We propose to design an SMA actuator whose strain IS half controlled, that IS to say that thermal disturbance does not influence the posltlon to be reached, which IS defined by an input reference value The stress disturbance IS considered to be insignificant The actuator static response IS drawn m Fig 12 The SMA device IS modelled by two inputs (input control signal 0 and the constant input control a) and the two outputs (strain reference E and the

For the two opposite parts AE, = kAR,l A.z2= kAR,2 AE, - AQ = k(AR,,

- AR&

As AE, = - AE?= AE we have AE = (k/2)(AR,1

- AR,&

C

reference

As the two parts are submitted to the same temperature (a temperature parasite equally mfluences the two parts) we have AR, = AR,,,, + k,O

a-“,

ARp = AR,,,, + k@ AR, - AR, = AER,,,~- AER,~

/

and AE = (k/2)(AR, - ARJ

(7)

Fig 12 The static response

35

measured resistance R) The SMA device feedback 1s controlled by the error between the input reference vanable (C refmna) representing the posltlon to be reached, and the mirror posltlon represented by the resistance induced by the phase transformation, R, As we have described,, the value R,,, IS obtained by the difference between the resistance R and a value proportional to the temperature estimate that 1s defined by filtermg the signal commg from the PWM The tnne constant 1s chosen so that the temperature estnnate represents the real temperature of the matenals as well as possible Figure 12 represents the actuator’s static response for a 7 N load The PWM generates a slgnal whose instantaneous magnitude rises up to 15 W The dynamic time constant ts roughly 0 3 s for the heating and 0 8 s for the cooling The obtained heating time constant 1s very low for a thermal device, because of the size of the heatmg power On coohng, the tune constant 1s 0 8 s, which seems equally weak The reason for this performance IS the heat smk used, which ensures that there 1s an nnportant thermal transfer with the environment

5. Conclusions We have shown m this paper different ways of usmg SMA The sun of usmg SMA as a rmcrominiature controlled actuator requires a good knowledge of the hysteresis behavlour m the reslstance measurement m order to determme the strain (displacement) The two inputs and two outputs of the model used allowed the hysteresis behavlour to be analysed with respect to 0 and (r The proposed solution allowed the removal of the hysteresis If one of the two inputs 1s constant But simultaneous vanatlon of the two inputs does not allow the hysteresis to be overcome m the strain control case A partial control may, however, be allowed If the temperature reference 1s clearly mcreasing or clearly decreasing As the hysteresis magmtude 1s known, It 1s possible to add or subtract a constant value to the feedback mformatlon according to the reference variation, m order to compensate the measurement error This 1s not the case if the SMA IS controlled by a constant mput reference vanable, a measurement devlatlon 1s then unavoidable We have performed all our ex-

penments mth Cu-Zn-Al SMA whose hysteresis 1s particularly unportant The results obtained may be reproduced on NlTl whose hysteresis 1s lower

References 1 K

2

3

4

5

6 I

J Gabriel, W S N Trmnner and J A Walker, A nncro rotary actuator usmg shape memory alloy, Sensors and Actuafors, 15 (1988) 95-102 M Hashlmoto, M Takcda, H Sagawa, I Chlba and K Sato, Apphcatlon of shape memory alloy to robotic actuators, / Robotzc Syst , 2( 1) (1985) 3-25 M Bergamasco, F Salsedo and P Dar~o, A hnear SMA motor as direct robotic actuator, IEEE Conf Robotzcs Automatron, Scottsdale, AZ, USA, 1989, pp 618-623 D Honma, Y Miwa and N Iguchl, Apphcatlon of shape memory effect to dlgtal control actuator, BUN Jpn Sot Mecb Eng, 27 (230) (Aug) (1989) K Ikuta, M Tsukamoto and S Hirose, Shape memory alloy servo actuator system wzth electnc reslstance feedback and apphcatIon for active endoscope, IEEE Conf Robotrcs Automatron, Phrlade!phza, PA, USA, 1988, pp 427-430 K Ikuta, Micro numature SMA actuator, IEEE Cons Robotzcs Automatron, Ctncmnatr, OH, USA, 1990, pp 2156-2161 M Takeda, M Hashnnoto and K Sate, A new displacement sensor usmg pseudoelastx tttane+mckel alloy wue, J Robotx Syst, 3(4) (1986) 44-450 H IhI, Etude et application des alhages a memolre de formes en robotlque, Ph D Thew, University of Metz, France (Nov 1990) A Pruskr and H K&l, Apphcauon des matenaux a memoire de formes a la robotique, Congres Gnmr, Parw, France, 1987 A Pruskl and H &hl, Actlonneurcapteur a matenaux a memoire de formes, Capteur ‘89, Pans, France, 1989, pp 207-215 J Perkms, Shape Memory E&cts m Alloys, Plenum, New York, 1975

Biographies Alarn Pruskl was born m France m 1955 and received his Ph D from the Umverslty of Metz (France) m 1984 He 1s a member of the Laboratolre d’Automatlque et d’Electromque Industnelles of the Umverslty of Metz He 1s interested m apphcatlons of mobile robots to disabled persons and m the robot sensor field Hubert Kohl was born m France m 1960 and received his Ph D from the Umverslty of Metz (France) m 1990 He 1s a member of the Laboratolre d’Automatlque et d’Electromque Industnelles of the Umverslty of Metz He 1s interested m the control of rmcrommlature mechanisms actuated by SMA and the apphcatlons to robots