Piezo Engine for Nano Biomedical Science

ABSTRACT

For nano biomedical science the parameters and the characteristics of the piezo engine are obtained. The functions of the piezo engine are determined. The mechanical characteristic of the piezo engine is received.

KEYWORDS

Piezo engine; Deformation; Characteristic; Transfer coefficient; Nano biomedicale

INTRODUCTION

Piezo engine is used in tunnel microscopy, X-ray and photolithography [1-9]. Piezo engine is applied for adaptive optics, nano biomedical science and microsurgery for moving of instruments [8-20].

Differential Equation

For the piezo engine the equations [4-30] are written

where (T ), (E), (D), (S), (d ), (ε^T), (s^E), are matrixes of mechanical field intensity, strength of electric field, electric induction, relative deformation, piezo coefficient, dielectric constant, elastic compliance and t transposed index. For PZT engine these matrixes are received

Differential equation of the piezo engine [10, 31-50] is written

where are the Laplace transform of the deformation, the operator, the coordinate, the coefficient wave propagation, the speed at, the coefficient attenuation,

At decision of this differential equation is obtained

At elastic-inertial load for x = h the relative deformation is determined

the equation of the deformation is obtained

Functions

From this equation deformation the function of the piezo engine by E is determined in the form

where are the transforms of the deformation and the electric field intensity, the stiffness of the load and the piezo engine.

For the transverse piezo engine the function by U is obtained in the form

The relative deformation Si of piezo engine [1-20] has form

here d_mi - the piezo coefficient.

Mechanical characteristic of piezo engine is determined

here the maximums Δl_max and F_max of the deformation and the force are received.

For the reverse longitudinal piezo effect the equation [8-18] has form

here d₃₃ - the longitudinal piezo coefficient.

Mechanical characteristic is written

here maximums of deformation Δδ_max and force F_max are written

For = 1.5∙10⁵ V/m, S₀ = 1.5∙10^-4 m², δ = 2.5∙10^-3 m, d₃₃ = 4∙10^-10 m/V, s^E₃₃ = 15∙10^-12 m²/N the parameters PZT engine are determined Δδ_max = 150 nm, F_max = 600 N with error 10%.

The maximums of the deformation of the transverse piezo engine Δh_max and force max F_max are obtained

here d₃₁ - the transverse piezo coefficient.

The function of the transverse piezo engine by U at M>>m, M, m - the masses of load and piezo engine, has the form

here - its transfer coefficient, time constant, attenuation coefficient and conjugate frequency.

At C_l = 0.2∙10⁷ N/m, CE =2.3∙107 N/m, M = 1 kg its parameters are obtained T₇ = 0.2∙10^-3 s and ω₇ = 5∙10³ s^-1 with error 10%.

The steady-state deformation at elastic-inertial load has the form

At d₃₁ = 2∙10^-10 m/V, U =50 V the parameters are received k_U31 =3.6 nm/V and Δh = 180 nm with error 10%.

CONCLUSIONS

The deformation of the piezo engine is determined for nano biomedical science. Its functions are received. The characteristics of engine are obtained.

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