Self-heating, i.e. heat generation within the piezoelectric actuator due to electrical and mechanical losses, is a major concern for high frequency applications. Properties (capacitance, stroke, etc.) will evolve with temperature, with the risk of unstable performance, increase stress and even degradation of the actuator.
In sinusoidal operation, the average power dissipation in a piezoelectric actuator can be estimated using the formula below:
Where:
tan (δ) = apparent dielectric dissipation factor
C = apparent PZT actuator capacitance [Farad]
Up-p = peak-peak drive voltage [V]
f = operating frequency [Hz]
Note that on datasheets, C and tan(δ) are specified for small signals. At 3kV/mm, the product C*tan(δ) is typically 7 to 10 times higher.
The knowledge of the average dissipation in the actuator is not sufficient to determine its temperature. It is necessary to know the geometry and thermal properties of the system, such as:
Generally speaking, small samples are easier to cool down because of the higher surface to volume ratio. Hard-doped ceramic is also advantageous at equivalent performance. Here are some indicative examples of temperature rise in natural convection conditions:
A small sample, hard-doped ceramic (NAC2024, 3*3*2mm, 200V), lying on a ceramic plate in ambient conditions, operated at 2kHz, full amplitude will heat-up by +30°C (picture).
A large sample, soft-doped ceramic (NAC2022-H50, 10*10*50mm, 200V), in the same ambient conditions, operated at 40Hz, full amplitude will heat-up by +70°C.
The best approach is to monitor temperature using a thermocouple, and eventually run thermal simulations during the design phase. The fact that large components can have a significant temperature gradient (core temperature is higher than surface temperature) should also be taken into account.
Piezoceramic material has a rather low heat conductivity but rather high heat capacity. Therefore, actuators tend to have a long thermal inertia, which means that they need a significant amount of time to heat-up or cool down. It is not uncommon that it takes one hour for a large stack to reach steady state.
If an actuator is operated for a short time at high power, it might not heat-up significantly. However, if that burst is repeated periodically, the long-term average power should be considered.
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