SLAAEP2 January   2026 ULC1001

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Acronyms
  5. 2Introduction
  6. 3Simulation Environment
  7. 4Simulation of Lens
  8. 5Simulation of Piezo Transducer
  9. 6Simulation of Lens Cover System (LCS)
    1. 6.1 Physics and Boundary Conditions
      1. 6.1.1 Glue
      2. 6.1.2 Thin Film
      3. 6.1.3 Housing
    2. 6.2 Results
  10. 7Resources

5 Simulation of Piezo Transducer

The dimensions of the piezo used in the LCS are listed in Table 5-4.

Table 5-1 Piezo Dimensions
ParamtersUnitValue
Inner Diametermm15
Outer Diametermm21
Thicknessmm1.5

PZT8 is used in the LCS and its material properties are listed in Table 5-2. Other common piezo materials and their material properties are also listed in the table.

Table 5-2 Materials Properties of the PZT8 in the Simulation

Symbol

Description

Unit

Navy Type VI (PZT 5H)

Navy type I (PZT 4)

Navy Type II (PZT 5A)

Navy Type III (PZT 8)

e1,rX

Relative permittivity

1

3244.97

1193.04

1795.99

1219.69

e3,rXRelative permittivity

1

3984.62

1325.63

1802.77

989.52

tan d (3X)

dielectric dissipation factor

1

0.016

0.003

0.017

0.004

d31

piezoelectric charge constant

C/N

-2.59e-10

-1.28e-10

-1.70e-10

-1.14e-10

d33

piezoelectric charge constantC/N

6.4e-10

3.28e-10

4.25e-10

2.75e-10

d15

piezoelectric charge constantC/N

6.16e-10

3.27e-10

5.06e-10

4.03e-10

Qm,t

mechanical quality factor

1

59

373

74

1088

p

density

kg/m3

7780

7700

7700

7700

s11e

compliance matrix

m2/N

1.82e-11

1.30e-11

1.7e-11

1.26e-11

s12ecompliance matrixm2/N

-7.76e-12

-4.35e-12

-6.6e-12

-3.71e-12

s13ecompliance matrixm2/N

-6.85e-12

-7.05e-12

-8.61e-12

-6.6e-12

s33ecompliance matrixm2/N

1.8e-11

1.96e-11

2.32e-11

1.83e-11

s44e,s55e

compliance matrixm2/N

3.8e-11

3.32e-11

4.35e-11

3.77e-11

s66e

compliance matrixm2/N

5.2e-11

3.47e-11

4.71e-11

3.26e-11

The transducer is a ring shape and is poled in the top/bottom direction. Figure 5-1 shows the geometry drawing in COMSOL.

Transducer Geometry in COMSOLFigure 5-1 Transducer Geometry in COMSOL

Figure 5-2 shows the coordinate system selection, where the Material XZ-plane System is selected.

Piezo: Coordinate System SelectionFigure 5-2 Piezo: Coordinate System Selection

Properly setting the damping is crucial in mechanical modeling. Two types of damping are incorporated: mechanical damping and dielectric loss. The damping factor is calculated automatically based on the material properties. Figure 5-3 and Figure 5-4 show the damping settings of the piezo in the COMSOL.

Piezo: Mechanical DampingFigure 5-3 Piezo: Mechanical Damping

The loss factor related to electrical permittivity is calculated automatically based on the properties of the piezo material.

Piezo: Dielectric LossFigure 5-4 Piezo: Dielectric Loss

The piezo electrodes are situated on both the top and bottom surfaces of the piezo component, leading us to designate Terminal 2 and Terminal 3 as the two terminals for the electrostatics. Figure 5-5 shows the screenshot of the terminal selection.

Piezo: Terminal SelectionFigure 5-5 Piezo: Terminal Selection

By conducting the Frequency Domain study, we can observe the impedance response ranging from 20 kHz to 700 kHz, as illustrated in Figure 5-6 below. The first mode, occurring at 59 kHz, is identified as a radial mode, where both the inner and outer diameters of the piezo change uniformly while maintaining a constant width. In contrast, the second mode at 525 kHz represents the thickness mode, characterized by variations in both thickness and width.

Impedance Response of the Piezo Transducer.Figure 5-6 Impedance Response of the Piezo Transducer.