II. How To Use ATILA

3.2 Unimorph (Homework 4)
Unimorph Optimized Design


PROBLEM - 3D Rectangular Plate, PZT4 = 40mm x 6mm x 1mm, Brass plate, Cantilever Support


  • We will decide the Brass plate thickness to obtain the maximum tip displacement under the same voltage applied.
1.
By keeping the PZT 4 thickness as 1 mm, change the Brass plate thickness from 0.2 mm to 1.2 mm (as many as possible).
2.
Calculate the tip displacement for a Cantilever support configuration, under 1 volt applied on the PZT plate.
3.

Plot the tip displacement (1 V) as a function of the Brass plate thickness, and obtain the optimized thickness for the Brass plate.

HINT:

When a piezoceramic plate is bonded to a metallic shim, a unimorph bending device can be fabricated. The tip deflection d of the unimorph supported in a cantilever style is given by
 
d = (d31E) L2Yc tc / [Ym{t02 - (t0 - tm)2} +Yc{(t0 + tc)2 - t02}]
 
Here E is the electric field applied to the piezoelectric ceramic, d31, the piezoelectric constant, L, the length of this unimorph, Yc or Ym, Young's modulus for the ceramic or the metal, tc or tm is the thickness of each material. In addition, t0 refers to the distance between the strain-free neutral plane and the bonding surface, which is represented as
 
t0 = [tc tm2(3 tc + 4 tm) Ym + tc4Yc] / [ 6 tc tm(tc + tm) Ym].
 
If Yc = Ym, the maximum displacement is obtained when tm = tc/2.

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