Piezoelectric constant d33 of piezoelectric ceramics is a linear response coefficient that reflects the mutual coupling between the mechanical quantity (stress or strain) and the electrical quantity (electrical displacement or electric field). When a compressive stress T3 is applied along the polarization direction (z-axis) of the piezoelectric ceramic, and a charge is generated on the electrode surface, there is a relationship: where d33 is a piezoelectric constant, and the first number in the foot indicates the direction of the electric field. Or the vertical direction of the electrode surface, the second number refers to the stress or strain direction; T3 is the stress; D3 is the electric displacement. It is the proportional constant of a piezoelectric medium that converts mechanical energy (or electrical energy) into electrical energy (or mechanical energy), reflecting the relationship between stress (T), strain (S), electric field (E), or electrical displacement (D). It reflects the coupling relationship of the electromechanical properties of the material and the strength of the piezoelectric effect, which leads to the piezoelectric equation. There are four common constants of Pzt4 material piezoelectric disc: dij, gij, eij, hij. 2 Electromechanical coupling coefficient Kp, electromechanical coupling coefficient K is a physical quantity that comprehensively reflects the coupling relationship between mechanical energy and electrical energy of piezoelectric ceramics, and is a reflection of piezoelectric-electric energy conversion capability of piezoelectric materials. The definition of electromechanical coupling coefficient is:
The mechanical energy of a PZT material piezoelectric ceramics vibrator (a piezoelectric ceramic body having a certain shape and size and covered with a working electrode) is related to its shape and vibration mode, and different vibration modes will have corresponding electromechanical coupling coefficients. For example, the coupling coefficient of the radial expansion mode of the thin wafer is Kp (plane coupling coefficient); the coupling coefficient of the thin long piece length expansion mode is K31 (transverse coupling coefficient); the coupling coefficient of the cylindrical axial expansion mode is K33 ( Longitudinal coupling coefficient) and so on. It is a reflection of the ability of piezoelectric materials to perform machine-to-electric energy conversion. It is related to the piezoelectric constant, dielectric constant and elastic constant of the material, and is a relatively comprehensive parameter. Its value is always less than.
Mechanical quality factor Qm Piezoelectric ceramics of consume energy in order to overcome internal friction when is vibrating. The mechanical quality factor Qm is a parameter that reflects the amount of energy consumption. The larger the Qm, the smaller is the energy consumption. The definition of the mechanical quality factor Qm is where fr is the resonant frequency of the piezo ceramic bimorph, fa is the anti-resonant frequency of the piezoelectric vibrator, R is the minimum impedance Zb min (resonant resistance) at the resonant frequency, C0 is the static capacitance of the piezoelectric vibrator, and C1 is the piezoelectric vibrator resonant capacitor.
Frequency constant N
For a piezoelectric vibrator, the probability of the resonant frequency and the length of the vibrator vibration direction is a constant, that is, the frequency constant. N=fr×l where: fr is the resonant frequency of the piezoelectric vibrator; and l is the length of the vibrating direction of the piezoelectric ceramics ring transducers. Radial vibration of thin disc: Np=fr×D (D is the diameter of the disc) Thin plate thickness stretching vibration: Nt=fr×t (t is the thickness of the thin plate) Slender rod K33 vibration: N33=fr×l(l For the length of the rod) Thin plate shear K15 vibration: N15 = fr × lt (lt is the thickness of the thin plate)
Determination of main parameters of piezoelectric ceramic materials,The determination of material parameters Kp, Qm, d33, ε33 and tgδ requires the radial vibration mode of thin discs. The diameter of the thin discs is required to be much larger than the thickness, and the ratio is greater than 10. The polarization direction is parallel to the thickness direction, the electrode surface is perpendicular to the thickness direction, and the sheet is a uniform circular shape. If the Δf value of the thin wafer is small, it can be directly calculated by the following formula: when ζ=0.27, Kp2≌2.51Δf/fs. When ζ=0.30, Kp2≌2.53Δf/fs ,When ζ=0.36, Kp≌2.55Δf /fs Qm=1/4ΠR1CΔf×1012 ε33=4Ctlt/ΠΦ. Ct is the low frequency capacitance (Fara) of the thin wafer, which can be measured by the capacitor bridge at 1KC frequency, lt is the thickness of the thin wafer (meter), Φ is the diameter of the thin wafer (meter), andε33 is the free medium. Electric constant (Fara / m). The tgδ is measured by a capacitor bridge or a universal bridge. D33 was measured by using a quasi-static tester.
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