LA PEREGRINACIÓN DE LA MECA

There are a large n u m b e r of different piezoelectric m aterials w ith different properties available an d th ese are described in ref. 4 an d 5. T hese m aterials ca n be u se d to fabricate tu b e s of varying length, w all th ic k n e ss a n d d iam eter. T he axial deform ation of a radially poled tu b e is given by:

0L = d3iV L /e (1)

w here L is th e len g th of th e tu b e a n d e th e th ic k n e ss. d3i is a c o n sta n t (charge density a t axis one divided by th e stre ss along axis three). By changing the m aterial type, th e wall th ic k n e ss e an d th e length of th e tu b e the expansion for a given voltage can be changed. The lin e ar piezoelectric eq u atio n (1) provides a phenom enological d e s c rip tio n of th e p ro p e rtie s of th e tu b e , b u t piezo electric m aterials can display a considerable am o u n t of hy steresis an d creep w hich depend on th e geom etry an d m aterial type. Fig. 4 show s the extension of a n u m b e r of piezoelectric tu b e s w ith applied voltage. 3 M odern piezoelectric m a te ria ls s u c h a s lead z irc o n ate tita n a te (PZT) can be grouped into one of two types.

1) H ard PZT m a terials have a high C urie te m p e ra tu re (the te m p e ra tu re above w hich th e dipoles in th e cry stal are ran d o m ly oriented) an d are n o t easily poled or depoled.

2) Soft PZT m aterials have a C urie te m p e ra tu re s below 200° C an d are readily poled an d depoled a t high electric fields a t room te m p e ra tu re .

H ard PZT m a terials have good lin e arity an d low h y ste re sis (2% defined as th e m axium th ic k n e ss of th e h y ste re sis loop over

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Figure (4). The expansion and contraction of a piezo electric tubes

with applied voltage? The arrows indicate the tube contracting. All

tubes were 25mm long and with a 38 mm outside diameter. The

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th e overall extension) w h ereas th e softer m a terials display m u c h la rg e r h y s te re s is (20%) b u t p ro d u ce larg er d isp la c e m e n ts for a given voltage. U nfortunately, th e h ig h er stabilities of th e h a rd PZT are also accom panied by a relatively low expansion p e r volt. H ard PZT m a te ria ls give a m u c h m ore lin e a r re sp o n se w ith applied voltage th a n do th e ir soft m aterial c o u n te rp a rts. N onlinearity arises b e c a u s e a t th e h ig h en d of electric field s tre n g th no fu rth e r alignm ent of dipoles in the m aterial ca n occur.

All piezoelectric m a terials exhibit a sh o rt-te rm dim ensional stab ilizatio n or “creep ” w hich ta k e s place after a ste p change in voltage (see Fig. 5). The initial resp o n se of th e tu b e (in a fraction of a m illisecond) is followed by a sm aller change in extension over a m u ch longer tim e scale (up to 100s).

T here is very little effect of th e ex p an sio n of piezoelectric m a te ria ls u n d e r applied load (this p ro p erty is of u s e later) an d th e ir th e rm a l p ro p erties are sim ilar to o th er ceram ics. The poling p ro cess is su sc e p tib le to ageing w hich c a u se s a g ra d u a l loss in sensitivity w ith tim e. In general, ageing in h a rd m aterials is alm ost negligible w hereas softer m aterials can age quite quickly.

T he only p iezo electric tu b e w h ich h a d a low e n o u g h hy steresis an d w as relatively free from creep b u t w ith a significantly in c re a se d ran g e w as a tu b e of len g th 50m m a n d w all th ic k n e ss 3.18m m m ade from PZT-4 m aterial. T his tu b e gave a n expansion of a t le a st 1.2 pm a n d th e d isp lacem en t w ith voltage w as highly lin e a r (Fig. 6). W ith th is tu b e a lm o st an y force curve c a n be m easured, b u t an interm ediate fine m echanical control is n ecessary to m e asu re very stro n g forces. C h a p ter 4 show s how th e h y steresis and creep can be corrected for any piezoelectric device.

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Figure(5). The effect of creep in piezo electric materials is illustrated schematically. A step change in voltage causes an immediate change in the extension of the device followed by a slowly decaying dimensional change. The amount of creep is defined as the ratio of Axc to Ax.

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Figure(6). The expansion (filled circles) of the piezo electric tube as determined by FECO interferometry plotted against the voltage applied to the tube. The surface separation on contraction of the piezo is shown by the empty circles.

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The piezo tu b e s were incorporated into a new m o u n t w hich isolates th e tu b e from the liquid b ath in g the surfaces. One type of m o u n t is required for tu b es of a sta n d a rd length and an o th er for the extended tu b e. B oth th ese m o u n ts are show n in cross section in Fig.7. B oth m o u n ts operate on th e sam e principle. A tu b e w hich fits inside th e piezo or outside th e piezo slides ag a in st a tightly fitting m achined teflon seal. This tightly fitting seal in no w ay im pairs the m otion of th e tube, there is no b ac k lash an d no h y steresis b ec au se th e piezo expansion is in d ep en d en t of sm all loads.