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# Piezoelectric Ceramic Stiffness

## Piezoelectric Ceramic Stiffness Last Updated on October 24, 2022 by You Ling

One of the basic characteristics of piezoelectric ceramics is the stiffness of piezoelectric ceramics.The stiffness of piezoelectric ceramics is an important parameter for the calculation of resonant frequency, output and other working states.More intuitively, piezoelectric ceramics can be described as mechanical springs with constant stiffness coefficients.The inherent stiffness of piezoelectric ceramics plays a very important role in resonant frequency and output characteristics of piezoelectric ceramics. The stiffness of piezoelectric ceramics is proportional to its cross-sectional area, and the stiffness of piezoelectric ceramics is inversely proportional to the length of the ceramics, that is, the stiffness of piezoelectric ceramics increases with the increase of the cross-sectional area, and decreases with the increase of the length of piezoelectric ceramics.Example: the cross-sectional area is 5×5mm2, the length is 9mm and the stiffness is 120N/ μm.The cross-sectional area remains unchanged, the length becomes 18mm, and the stiffness becomes 60N/ μm.If the cross-sectional area of the actuator is 10mm×10mm and the length is 18mm, the stiffness value is 240N/μm.However, the above example is only in the ideal state and can not fully feedback the actual situation.Because the piezoelectric ceramic stiffness also depends on how to use (dynamic, static operation), environment (voltage load, supply parameters, small signal or large signal operation, etc.) and different operating conditions.

So the example is only appropriate when all other factors are exactly the same.The example gives only a rough indication of the desired properties of piezoelectric ceramics.In practice, however, stiffness is affected by many other factors, such as how the electrodes are connected.If the electrodes are not connected, there is no way to consume energy, and the stiffness has a maximum.

For example, when a 10mm×10mm×20mm piezoelectric ceramic electrode is not short-circuited, the stiffness value is about 450N/μm, and when the electrode is short-circuited, the stiffness value is about 200N/μm.This is because the mechanical pressure creates a charge load, which can flow and be removed from the ceramic block when the electrodes short-circuit.In the open circuit, the electric charge keeps accumulating in the piezoelectric ceramics. The mechanical operation creates a voltage at the electrode, which is equivalent to generating an electric field inside the piezoelectric ceramics. This electric field stabilizes the piezoelectric ceramics and prevents them from compressing.

In summary, when the two ends of the piezoelectric ceramic leads are short connected, it is equivalent to voltage control. The charge generated by the machine flows relative to each other to keep the voltage at both ends of the piezoelectric ceramic constant, and the charge is consumed.When the two ends of the piezoelectric ceramic leads open circuit, the theory is equivalent to charge or current control, the mechanical force generated by the charge retained in the piezoelectric ceramic, the piezoelectric ceramic voltage changes with the change of the load.The advantage of open – circuit current control mainly lies in dynamic displacement control.Greater system stiffness can be obtained by closed-loop position control, and the response speed of open-circuit current control is faster than that of closed-loop control.