Structural Model of a Nano Drive for Biomedical Science

Introduction

A nano drive based on the piezomagnetic, magnetostriction, piezoelectric, electrostriction effects is used for biomedical science, nanomedicine, nanotechnology, nanobiology, microsurgery. The piezo drive is used in scanning microscopy, astronomy for alignment and focusing, image stabilization, in adaptive optics and work with the genes [1-9].

Structural Model

The expression of electromagnet elasticity [1-15] has the forn

here T_j - the mechanical stress, E_m - the electric field strength, H_m - the magnetic field strength, S_ij^E,H - the elastic compliance for E = const , H = const , d_mi^H - the piezo module, d_mi^E - the magnetostriction coefficient, S_i - the relative deformation, the axis i, j, m.

Therefore, the expression of the reverse piezo effect [1-15]

and the expression of the magneto strictive effect [1-15]

The expression of the shift inverses piezo effect [1-15]

The differential equation of a nano drive is calculated [4-58]

here Ξ(x,s) , x , s, γ are the transform of displacement, the coordinate, the parameter, the coefficient of propagation.

For the shif piezo drive at x = 0 Ξ(0,s) = Ξ₁ (s) and at x = b and the solution of this differential equation is calculated

At x = 0 and x = b the expressions [11-39] are written

The structural model

The expression of the shift magnetostrictive effect [1-15]

The structural model is transformed

The expression of the transverse inverse piezo effect [1-15]

The solution is calculated

The system at x = 0 and x = h is calculated

The structural model has the form

The expression of the transverse magneto strictive effect [1-15]

The structural model is transformed

In general atl = { δ, h, b the solution is calculated

The system is transformed

The structural model on Figure 1 is calculated 

The matrix of deformations is calculated

In static the longitudinal deformations

For d₃₃ = 4∙10^-10 m/V, U = 75 V, M₁ = 1 kg, M₂ = 4 kg the static deformations ξ₁ = 24 nm, ξ₂ = 6 nm and ξ₁+ξ₂ = 30 nm are calculated at error 10%.

The expression of the direct piezo effect has form [1-15]

here D_m- the electric induction, ε_mk^E- the permittivity.

The transform for the back electromotive force on Figure 2 is evaluated

In general the reverse and direct coefficients are calculated (Figure 2)

Figure 1: Scheme of nano drive.

Figure 2: Scheme of piezo drive.

At voltage control of the piezo drive its characteristis are evaluated

At current control of the piezo drive

here - the sectional area of the capacitor, - the capacitance, - the electromechanical coupling coefficient.

For a nano drive the mechanical and adjustment characteristics [11-26] are evaluated

The mechanical characteristic is written

Therefore, for the transverse piezo drive this characteristic is evaluated

At d₃₁ = 2∙10^-10 m/V, E₃ = 1.5∙10⁵ V/m, h = 2.5∙10^-2 m, S₀ =1.5∙10^-5 m², s₁₁^E = 15∙10^-12 m²/N the values Δh_max = 750 nm and F_max = 30 N are found at error 10%

In static the deformation of a nano drive

The adjustment characteristic of a nano drive is evaluated

here - the elastic compliance, k_s - the coefficient of the change of elastic compliance

 The expression for Figure 3 is evaluated

There k_v is the speed damping coefficient (Figure 3).

Figure 3: Scheme of piezo drive at one fixed face.

At R = 0 the expression is evaluated

For M = 4 kg, C_l = 0.1∙10⁷ N/m, C₁₁^E = 1.5∙10⁷ N/m the values T_t = 0.5∙10^-3 s, ω_t = 2∙10³ s^-1 are calculated at error 10%.

The static deformation

For d₃₁ = 2∙10^-10 m/V, h/δ = 22, C_l/C₁₁^E = 0.1 the coefficient k₃₁^U = 4 nm/V is determined at error 10%.

Conclusion

For a nano drive the structural model is evaluated. The matrix of the deformations is constructed. The characteristics of the piezo drive are determined for biomedical science.

Acknowledgement

None.

Conflict of Interest

None.

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