Useful Equations (Equation 3) Axial contraction and radialdisplacement of piezo tube actuators can be estimated by the following equations: (Equation 1) r___r d
31 U___d L d L U––d
where:r= tube radius

Piezo · Nano · Positioning

31 where: d
31 = strain coefficient (dis-placement normal to polarization direction) [m/V]U= operating voltage [V]d= wall thickness [m] d
31 = strain coefficient (displa-cement normal to polari-zation direction) [m/V]L= length of the ceramictube [m]U= operating voltage [V] d= wall thickness [m] The quartered electrodes op-tion makes XY scanning possi- ble. These industrial scanner tubes,which flex in X and Y, are wide-ly used in scanning-probe microscopes manufacturer. The scan range of these components is esti- mated by: (Equation 4) (Equation 2) d d
33 U
where: PT Tube dimensions, in mm (see table forfurther information) d
= change in wall thickness[m] d
33 = strain coefficient (fieldand displacement inpolarization direction) [m/V]U= operating voltage [V] x 2 _______________ 2 d
31 L2 U ID d
Typical values for d where: 31 and d 33 x
= scan range in X and Y(for symmetrical electro- des) [m] are -200 pm/V and 500 pm/V,respectively.The radial contraction is thesuperposition of the increase in wall thickness and the tangen- tial contraction; it can be esti-mated by the following equa- tion: d
31 = strain coefficient (dis-placement normal topolarization direction) [m/V] U= symmetric operatingvoltage [V]L= length [m] ID= inner diameter [m]d= wall thickness [m] Technical Data / Product Order Numbers Order Dimensions Max. Electrical Axial Radial XY deflec- numberL x OD x ID**operatingcapacitance contractioncontractiontion [µm voltage [V][nF ±20%]µm @ max. Vµm @ max. V@ ±200 V] PT120.0020 x 2.2 x 1.050035 PT130.0030 x 3.2 x 2.25001090.9 PT130.9030 x 3.2 x 2.25001290.9 PT130.94*30 x 3.2 x 2.2±2004 x 2.490.9±18PT130.1030 x 6.35 x 5.355001891.8 PT130.14*30 x 6.35 x 5.35±200 4 x 3.891.8±9 PT130.2030 x 10.0 x 9.05003693 All models available with 40 mmlength, except PT120.00 Other specification on request* Quartered electrodes for XYdeflection** OD, ID ±0.05 mm all modelsexcept PT120 / PT 130.00 (±0.1 mm) PT130.24*30 x 10.0 x 9.0±2004 x 8.593±6PT130.3030 x 10.0 x 8.010001893 PT130.4030 x 20.0 x 18.010003596 PT140.7040 x 40.0 x 38.01000701512 27