Parameters of a nanopiezoengine for astrophysics research

doi:10.15406/aaoaj.2024.08.00205

eISSN: 2576-4500

Aeronautics and Aerospace Open Access Journal

Short Communication Volume 8 Issue 3

Parameters of a nanopiezoengine for astrophysics research

Afonin SM

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National Research University of Electronic Technology, Russia

Correspondence: Afonin SM, National Research University of Electronic Technology MIET, Moscow, Russia

Received: August 08, 2024 | Published: August 21, 2024

Citation: Afonin SM. Parameters of a nanopiezoengine for astrophysics research. Aeron Aero Open Access J. 2024;8(3):175-177. DOI: 10.15406/aaoaj.2024.08.00205

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Abstract

The static and dynamic parameters of a nanopiezoengine for astrophysics research are determined. The function of the nanopiezoengine is obtained. The parameters of the transverse nanopiezoengine are written.

Keywords: nanopiezoengine, parameter, function, characteristic, astrophysics research

Introduction

For astrophysics research a nanopiezoengine is applied.^1–12 The energy transformation is clearly for a nanopiezoengine.^11–34. A nanopiezoengine is promising for nanotechnology, microscopy, interferometers, adaptive optics and astrophysics research.^20–42

Determination of parameters

The static and dynamic parameters of a nanopiezoengine for astrophysics research are written from piezoelasticity and its differential equation.

Piezoelasticity is determined^6–42

$S_{i} = v_{m i} Ψ_{m} + s_{i j}^{ψ} T_{j}$ $S_{i} = v_{m i} Ψ_{m} + s_{i j}^{ψ} T_{j}$

Here the control parameter is $E_{m}$ $E_{m}$ the strength electric field or $D_{m}$ $D_{m}$ the electric induction, $ν_{m i}$ $ν_{m i}$ the piezoconstant is $d_{m i}$ $d_{m i}$ the piezomodule or $g_{m i}$ $g_{m i}$ the piezocoefficient, $s_{i j}^{Ψ}$ $s_{i j}^{Ψ}$ the elastic compliance, $S_{i}$ $S_{i}$ is the relative displacement, $T_{j}$ $T_{j}$ the strength mechanical field.

Its differential equation^6–39

$\frac{d^{2} Ξ (x, s)}{d x^{2}} - γ^{2} Ξ (x, s) = 0$ $\frac{d^{2} Ξ (x, s)}{d x^{2}} - γ^{2} Ξ (x, s) = 0$

Here $Ξ (x, s)$ $Ξ (x, s)$ , s, x , $γ$ $γ$ are the Laplace transform of nanodisplacement, the parameter, the coordinate and the propagation coefficient.

The matrix of the nanodisplacements^6–39

$(\begin{matrix} Ξ_{1} (s) \\ Ξ_{2} (s) \end{matrix}) = (\begin{matrix} \begin{matrix} W_{11} (s) \\ W_{21} (s) \end{matrix} & \begin{matrix} W_{12} (s) \\ W_{22} (s) \end{matrix} & \begin{matrix} W_{13} (s) \\ W_{23} (s) \end{matrix} \end{matrix}) (\begin{matrix} Ψ_{m} (s) \\ F_{1} (s) \\ F_{2} (s) \end{matrix})$

Then the transverse static nanodisplacements

$ξ_{1} = d_{31} (h / δ) U M_{2} / (M_{1} + M_{2})$

$ξ_{2} = d_{31} (h / δ) U M_{1} / (M_{1} + M_{2})$

To the transverse PZT engine d₃₁= 0.2 nm/V, $h / δ$ = 10, U= 50 V, M₁= 0.25 kg, M₂= 1 kg its parameters are written $ξ_{1}$ = 80 nm, $ξ_{2}$ = 20 nm with 10% error.

If the boundary conditions

$Ξ (0, s) = Ξ_{1} (s) = 0$ for x = 0

$Ξ (h, s) = Ξ_{2} (s)$ for x = h

then the solution at fixed first end of the transverse nanopiezoengine

$Ξ (x, s) = \frac{Ξ_{2} (s) sh (x γ)}{sh (h γ)}$

and

$\frac{Ξ_{2} (s) γ}{th (h γ)} + \frac{Ξ_{2} (s) s_{11}^{E} M_{2} s^{2}}{S_{0}} + \frac{Ξ_{2} (s) s_{11}^{E} C_{1}}{S_{0}} = d_{31} E_{3} (s)$

Therefore, the function at the voltage control and $R = 0$ is determined

$W (s) = \frac{Ξ_{2} (s)}{U (s)} = \frac{d_{31} (h / δ)}{M_{2} p^{2} / C_{11}^{E} + h γ cth (h γ) + C_{e} / C_{11}^{E}}$

where $Ξ_{2} (s)$ , $C {}_{11}^{E}$ , $C_{e}$ are the transform the nanodisplacement its second end, the stiffness transverse piezo engine and its load.

At elastic-inertial load for $M_{2} ≫ m$ , $m$ the mass of the engine, its function is written

$W (s) = \frac{Ξ (s)}{U (s)} = \frac{k_{31}^{U}}{T_{t}^{2} s^{2} + 2 T_{t} ξ_{t} s + 1}$

$k_{31}^{U} = d_{31} (h / δ) / (1 + C_{e} / C_{11}^{E})$ , $T_{t} = \sqrt{M_{2} / (C_{e} + C_{11}^{E})}$

To the PZT engine $C_{e}$ = 0.33×10⁷ N/m, $C_{11}^{E}$ = 3×10⁷ N/m, $M_{2}$ = 1 kg its parameter is obtained $T_{t}$ = 0.17×10^-3 s with 10% error.

The transverse static nanodisplacement at voltage control

$Δ h = \frac{d_{31} (h / δ) U}{1 + C_{e} / C_{11}^{E}} = k_{31}^{U} U$

To the PZT engine $d_{31}$ = 0.2 nm/V, $h / δ$ = 10, $U$ = 50 V, $C_{e} / C_{11}^{E}$ = 0.11, $k_{31}^{U}$ = 1.8 nm/V its parameter is determined $Δ h$ = 90 nm at 10% error.

For the transverse nanopiezoengine mechanical characteristic with maximums values of its parameters are obtained

$Δ h = Δ h_{max} (1 - F / F_{max})$

$Δ h_{max} = d_{31} (h / δ) U$

$F_{max} = d_{31} S_{0} E_{3} / s_{11}^{E}$

To the PZT engine $h / δ$ = 10, $U$ = 50 V, $E_{3}$ = 1×10⁵ V/m, $S_{0}$ = 1×10^-5 m², $d_{31}$ = 0.2 nm/V, $s_{11}^{E}$ = 10×10^-12 m²/N its parameters are received $Δ h_{\max}$ = 100 nm, $F_{\max}$ = 20 N with 10% error.

Discussion

The transverse nanopiezoengine is used for astrophysics research, interferometers, adaptive optics. The parameters of the nanopiezoengine are obtained for astrophysics research.

Conclusion

The parameters of the nanopiezoengine are received. The function of the nanopiezoengine is obtained for astrophysics research. The parameters of characteristic the transverse nanopiezoengine are determined.