# Piezoelectric effect- tube scanner

## Main Question or Discussion Point

Hi,

i have been working on this problem for a while. i just need some guidance.

the question is: design a ztube scanner suitable for displacing ±1 micron displacement at 200V.

i am using this equation:

ΔL=([d]_{}[/31]×V×L)/t
ΔL=(d31 ×L×V)/t

ΔL=change in length = 1micron
d31=piezo strain constant (usually in pico range [10]^{}[/-12]
V=applied voltage
L=length
t=thickness (for a tube-- Outer diameter - inner diameter (OD-ID))

Rearranging the equation:

[ΔL]\frac{}{}[/V]=[L]\frac{}{}[/t×[d]_{}[/31]]

ΔL/V= L/(d×d31)

∴[ΔL]\frac{}{}[/V]=1micron/200=5nm/v

http://www.physikinstrumente.com/en/products/prdetail.php?sortnr=400800.00

I am trying to solve it by,
choosing V=200V
ΔL= 1micron

∴[ΔL]\frac{}{}[/V]=
ΔL/V=1micron/200=5nm/v

how do i proceed after this step? i tried picking a value for [d]_{}[/31]=1.27[10]^{}[/-12]
but then i got stuck on picking realistic diameters for the piezo tube.

I am also wondering is the d31 chosen arbitrary, or its specific to the material being used, and so is it a parameter i cant control in the equation.
Usually d31 is given in pico scale.
L=1-70mm
Max diameter__ OD=78mm, ID=70mm
MIn diameter__ OD=2mm, ID0.8mm
d31= ?

i might be missunderstanding the question or equation.

thnks