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Nanomedicine & Nanotechnology Open Access Research Article 11 min read

An Engine for Nanomedicine and Nanotechnology

Afonin SM*
* Corresponding author
ISSN: 2574-187X  10.23880/nnoa-16000217  Received: March 28, 2022  Published: June 07, 2022
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Keywords
Piezo Engine Electro Elastic Engine Structural Model and Scheme Parameter Characteristic Nanomedicine and Nanotechnology
Abstract

For nanomedicine and nanotechnology the structural model of an engine is determined. The structural scheme of an engine is constructed. For an engine its matrix equation of the deformations is received for the decision of control systems. The parameters and characteristics of an engine are obtained.

Introduction

For control system of nanomedicine and nanotechnology an engine on piezoelectric or electrostrictive effect is applied [1, 2, 3, 4, 5, 6, 7, 8, 9]. For the structural schema of an engine its energy transformation is clearly [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. The piezo engine is used for precise movements in adaptive optics and microscopy [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26].

Structural Model and Scheme

The equations [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50] of an electro elastic engine have form $$ (D) = (d) (T) + \left(\varepsilon^ {T}\right) (E) $$ $$ \left(S\right) = \left(s ^ {E}\right) \left(T\right) + \left(d\right) ^ {t} \left(E\right) $$ $$ (D), (d), (T), \left(\varepsilon^ {T}\right), (E), (S), \left(s ^ {E}\right), \left(d\right) ^ {t}; $$ where are matrixes electric induction, piezo coefficient, strength mechanical field, dielectric constant, strength electric field, relative displacement, elastic compliance, transposed piezo coefficient.

For PZT engine its matrixes coefficients

0 0 0 0 0 d

$$ 0 = \left( \begin{array}{c c c c c c} 0 & 0 & 0 & 0 & d _ {1 5} & 0 \\ 0 & 0 & 0 & d _ {1 5} & 0 & 0 \\ d _ {3 1} & d _ {3 1} & d _ {3 3} & 0 & 0 & 0 \end{array} \right) $$

15 ( ) 0 0 0 0 0

d d

Figure 1: Mechanical characteristic an engine.
Click to enlarge
Figure 1: Mechanical characteristic an engine.

          =         −  

0 0 0 E E E

s s s

11 12 The equation of the mechanical characteristic of an engine is obtained $$ \Delta l = \Delta l _ {\max } \left(1 - F / F _ {\max }\right) $$

$$ \mathrm {w h e r e} \quad \Delta l _ {\max } = d _ {m i} E _ {m} l \mathrm {a t} F = 0 \mathrm {a n d} F _ {\max } = d _ {m i} E _ {m} S _ {0} / s _ {i j} ^ {E} \mathrm {a t} $$

0 = ∆l , mi d is the piezo module, m E is strength of electric field for m axis, E ijs is the elastic compliance, l is the length,

0 S is the area of an engine.

For the longitudinal PZT engine its relative displacement [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18] is written $$ S _ {3} = d _ {3 3} E _ {3} + s _ {3 3} ^ {E} T _ {3} $$ where d_33 is longitudinal piezo module, 3 _E is strength electric field for 3 axis, 33 E s is elastic compliance, 3 T is strength mechanical field for 3 axis.

In the mechanical characteristic of the longitudinal PZT engine for nanomedicine and nanotechnology its maximums values of displacement max δ ∆ and force max F are determined $$ \Delta \delta_ {\max } = d _ {3 3} \delta E _ {3} = d _ {3 3} U $$ $$ V, F _ {\max } = d _ {3 3} S _ {0} E _ {3} / s _ {3 3} ^ {E} $$ At 3

E = 0.75∙105 V/m, d33= 4∙10-10 m/V,

$$ \Delta \delta_ {\max } = 7 5 \mathrm {n m}, F _ {\max } $$

= 300 N on Figure

1 with error 10%.

Figure 2: Scheme an engine.
Click to enlarge
Figure 2: Scheme an engine.

Also for the mechanical characteristic of the transverse PZT engine its maximums values , max 31 3 0 11 / E F d E S s = At 5 3 1.2 10 V/m E = ⋅ , 10 31 2 10 m/V d − = ⋅ , 2 1 10 m h − = ⋅ , , 5 2 0 1 10 m S − = ⋅ , 12 2 11 12 10 m /N E S − = ⋅ for the transverse PZT engine are received $$ \delta = 0. 5 \cdot 1 0 ^ {- 3} \mathrm {m} $$ $$ \Delta h _ {\max } = 2 4 0 \mathrm {n m}, F _ {\max } = 2 0 \mathrm {N}. $$ The differential equation of an engine [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50] is written $$ \frac {d ^ {2} \Xi (x , s)}{d x ^ {2}} - \gamma^ {2} \Xi (x, s) = 0 $$ $$ \gamma = s / c ^ {E} + \alpha $$ here s, ( , ) x s Ξ , x , γ are the parameter, the Laplace transform of its displacement, the coordinate and the coefficient.

For the longitudinal PZT engine its displacements $$ \Xi (0, s) = \Xi_ {1} (s) \mathrm {f o r} x = 0 $$ $$ \Xi (\delta , s) = \Xi_ {2} (s) $$ for x= δ The decision of differential equation is determined $$ \Xi (x, s) = \left\{\Xi_ {1} (s) \mathrm {s h} \left[ (\delta - \mathrm {x}) \gamma \right] + \Xi_ {2} (s) \mathrm {s h} \left(\mathrm {x} \gamma\right) \right\} / \mathrm {s h} (\delta \gamma) $$ Also the Laplace transforms of forces on its faces are received $$ T _ {3} (0, s) S _ {0} = F _ {1} (s) + M _ {1} s ^ {2} \Xi_ {1} (s) $$ for x=0 $$ T _ {3} \left(\delta , s\right) S _ {0} = - F _ {2} (s) - M _ {2} s ^ {2} \Xi_ {2} (s) \mathrm {f o r} x = \delta $$ where 1_F_ , 2 F , 1 M , 2 M are the forces, the masses.

The Laplace transforms of the mechanical stresses for the longitudinal PZT engine are obtained $$ \left. \frac {1}{3} (0 , s) = \left(s _ {3 3} ^ {E}\right) ^ {- 1} \frac {d \Xi (x , s)}{d x} \right| - d _ {3 3} \left(s _ {3 3} ^ {E}\right) ^ {- 1} E _ {3} (s) $$ d x s T s s d s E s dx $$ = \left(s _ {3 3} ^ {E}\right) ^ {- 1} \frac {d \Xi (x , s)}{d x} \Bigg | - d _ {3 3} \left(s _ {3 3} ^ {E}\right) $$

1 1 3 33 33 33 3 0

x = $$ T _ {3} \left(\delta , s\right) = \left(s _ {3 3} ^ {E}\right) ^ {- 1} \frac {d \Xi (x , s)}{d x} \Bigg | _ {x = \delta} - d _ {3 3} \left(s _ {3 3} ^ {E}\right) ^ {- 1} E _ {3} (s) $$ Therefore, the structural model of the longitudinal PZT engine is determined

$$ \chi_ {3 3} ^ {E} = s _ {3 3} ^ {E} / S _ {0} $$

where 1 2 ( ), ( ) s s Ξ Ξ are the Laplace transforms of its displacements.

Also the system of the equations for the Laplace transforms of stresses an engine is written ( , ) (0, ) ( ) ( ) ( ) j ij mi ij m x d x s T s s v s s dx $$ = \left(s _ {i j} ^ {\Psi}\right) ^ {- 1} \frac {d \Xi (x , s)}{d x} \left| - v _ {m i} \left(s _ {i j} ^ {\Psi}\right) ^ {- 1} \Psi_ {n} \right| $$

1 1 $$ \left. s _ {i i} ^ {\Psi}\right) ^ {- 1} \frac {d \Xi (x , s)}{\left| \right.} - v _ {i i} \left(s _ {i i} ^ {\Psi}\right) ^ {- 1} $$

0 = $$ T _ {j} (l, s) = \left(s _ {i j} ^ {\Psi}\right) ^ {- 1} \frac {d \Xi (x , s)}{d x} \Bigg | _ {x = l} - v _ {m i} \left(s _ {i j} ^ {\Psi}\right) ^ {- 1} \Psi_ {m} (s) $$ where vmi is electro elastic coefficient, l is length.

The structural model of an engine Figure 2 for nanomedicine and nanotechnology is determined

Figure 3
Click to enlarge
Figure 3

$$ \chi_ {i j} ^ {\Psi} = s _ {i j} ^ {\Psi} / S _ {0} $$

, , , , m $$ v _ {m i} = \left\{ \begin{array}{l l} d _ {3 3}, d _ {3 1}, d _ {1 5} \\ g _ {3 3}, g _ {3 1}, g _ {1 5}, \end{array} \right. $$ $$ \Psi_ {m} = \left\{ \begin{array}{l l} E _ {3}, E _ {1} \\ D _ {3}, D _ {1}, \end{array} \right. $$

3 1 $$ s _ {i j} ^ {\Psi} = \left\{ \begin{array}{l l} s _ {3 3} ^ {E}, s _ {1 1} ^ {E}, s _ {5 5} ^ {E} \\ s _ {3 3} ^ {D}, s _ {1 1} ^ {D}, s _ {5 5} ^ {D}, l \end{array} \right. $$ , , , , E E E ij D D D s s s s s s s $$ c ^ {\Psi} = \left\{c ^ {E}, c ^ {D} \right. $$ $$ \gamma = \left\{\gamma^ {E}, \gamma^ {D} \right. $$

33 11 55 $$ l = \left\{\delta , h, b \right| $$

, , .

33 11 55

The structural scheme on Figure 2 is used for decision of deformations an engine for system of nanomedicine and nanotechnology.

Parameters and characteristics Therefore, the matrix of the deformations an engine for nanomedicine and nanotechnology is determined

The steady-state movements its faces are written The steady-state movements the faces of the longitudinal PZT engine are received $$ \begin{array}{l} \xi_ {1} = d _ {3 3} U M _ {2} / \left(M _ {1} + M _ {2}\right) \\ \xi_ {2} = d _ {3 3} U M _ {1} / \left(M _ {1} + M _ {2}\right) \\ \end{array} $$ $$ \mathrm {A t} U = 1 2 5 \mathrm {V}, M _ {1} = 1 \mathrm {k g}, M _ {2} $$

M = 4 kg, d33= 4⋅10-10 m/V the steady-state movements

$$ \xi_ {1} = 4 0 \mathrm {n m}, \xi_ {2} = 1 0 \mathrm {n m} \mathrm {a n d} $$ $$ \xi_ {1} + \xi_ {2} = 5 0 \mathrm {n m} $$ and error 10%.

The transfer equation of the transverse PZT engine for elastic-inertial load is determined E

31 2 2 ( ) ( ) ( ) 2 1

$$ W (s) = \frac {\Xi (s)}{U (s)} = \frac {k _ {3 1} ^ {E}}{T _ {t} ^ {2} s ^ {2} + 2 T _ {t} \xi_ {t} s + 1} $$ t t t $$ k _ {3 1} ^ {E} = d _ {3 1} \left(h / \delta\right) / \left(1 + C _ {l} / C _ {1 1} ^ {E}\right) $$

11 / ( ) E t l T M C C = + ,

is the transverse transfer coefficient, Cl, 11 E C are the where stiffness for load, engine, $T_i$, $\xi_i$, $\omega_i$ are the time constant, the attenuation coefficient, the conjugate frequency of the engine.

At $C_i = 0.1 \cdot 10^7$ N/m, $C_{11}^E = 1 \cdot 10^7$ N/m, $M = 2$ kg the parameters of the transverse PZT engine are obtained $T_i = 0.43 \cdot 10^{-3}$ s, $\omega_i = 2.3 \cdot 10^3$ s$^{-1}$ with error 10%.

The steady-state movement of the transverse PZT engine at elastic-inertial load is determined

$$\Delta h = \frac{d_{31}(h/\delta)U}{1 + C_i/C_{11}^E} = k_{31}^E U$$

At $h/\delta = 20$, $C_i/C_{11}^E = 0.1$, $d_{31} = 2 \cdot 10^{-10}$ m/V for the transverse PZT engine is received the transverse transfer coefficient $k_{31}^E = 3.6$ nm/V.

Conclusions

For control system the structural model an electro elastic engine is obtained. Its structural scheme is determined. The matrix of deformations an engine is constructed. The parameters and characteristics of an engine are obtained.

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@article{afonin2022,
  title   = {An Engine for Nanomedicine and Nanotechnology},
  author  = {Afonin SM},
  journal = {Nanomedicine & Nanotechnology Open Access},
  year    = {2022},
  volume  = {7},
  number  = {2},
  doi     = {10.23880/nnoa-16000217}
}
Afonin SM (2022). An Engine for Nanomedicine and Nanotechnology. Nanomedicine & Nanotechnology Open Access, 7(2). https://doi.org/10.23880/nnoa-16000217
TY  - JOUR
TI  - An Engine for Nanomedicine and Nanotechnology
AU  - Afonin SM
JO  - Nanomedicine & Nanotechnology Open Access
PY  - 2022
VL  - 7
IS  - 2
DO  - 10.23880/nnoa-16000217
ER  -