Question

REPEAT QUESTION - first one was answered wrong. I am completing a project and having difficulty calculating the hysteresis of a piezo actuator. I am trying to calculate the power loss that occurs due to heat dissipation through hysteresis theoretically. I have know figures of voltage and frequency and trying to relate these back to the change of temperature. I only want to know how i can actually calculate the hysteresis - I dont want the background.

Voltage 100 Volts peak to peak

Frequency 128kHz

Capacitance 2.2nF

Starting Temp 17C

Time constant 100 s

Anymore info needed

Answer 1

Piezoelectric materials are a subset of a larger class of materials known as ferroelectrics. Ferroelectricity is a property of certain materials that have a spontaneous electric polarization that can be reversed by the application of an electric field. Like the magnetic equivalent (ferromagnetic materials), ferroelectric materials exhibit hysteresis loops based on the applied electric field and the history of that applied electric field. Figure 1 shows an illustration of a strain (X) versus electric field (E) “butterfly” curve for a PZT material driven to its excitation limits.

As the electric field is cycled from positive to negative to positive, the following transformations occur in the piezo actuator:

A: Initially, strain increases with electric field and is only slightly nonlinear. As the electric field is increased, the dipoles of all the grains will eventually align to the electric field as optimally as is possible and the distortion of the grains will approach a physical limit.

B: When the field is reversed, strain decreases more slowly due to the reoriented dipoles. As the field gets smaller, the dipoles relax into less ideal orientations and strain decreases at a faster rate.

C: As the field becomes negative the dipoles are forced away from their original orientation. At a critical point they completely reverse direction and the piezo actuator becomes polarized in the opposite direction. The electric field at the point of polarization reversal is known as the coercive field (E_c).

D: After polarization reversal, the piezo expands again until it reaches its physical strain limit.

E: The electric field is reversed again and the same hysteretic behavior that occurred along curve B occurs as strain decreases.

F: The electric field is driven to the coercive limit for the opposite polarization direction and the dipoles reorient to their original polarization.

G: The piezo actuator expands with the applied electric field to its physical limit.

For positioning applications, piezo actuators are generally operated with a semi-bipolar voltage over an area of the curve (ABC) away from the saturation and coercive field limits. An example of displacement versus applied voltage for a piezo actuator stack in this region of the curve is shown in Figure 2.



Aerotech amplifiers take full advantage of the semi-bipolar operation of piezoelectric stack actuators. Our actuators are designed to operate from -30 V to +150 V with very high voltage resolutions. Over this voltage range, open-loop hysteresis values can be as large as 10-15% of the overall open-loop travel of the piezo stage. Operation of the piezo stage in closed-loop effectively eliminates hysteresis of the actuator enabling positioning repeatabilities in the single-digit nanometer range.