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Structural-parametric model and transfer functions of electroelastic actuator for nano- and microdisplacement

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Abstract

We developed a structural-parametric models, obtained solution for the wave equation of electroelastic actuators and constructed their transfer functions. Effects of geometric and physical parameters of electroelastic actuators and external loading on their dynamic characteristics determined. For calculation of automatic control systems for nanometric movements with electroelastic actuators, we obtained the parametric structural schematic diagrams and the transfer functions of piezoactuators. Static and dynamic characteristics of piezoactuators determined.

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... 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]. ...
... 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]. ...
... For the longitudinal PZT engine its relative displacement [8][9][10][11][12][13][14][15][16][17][18] For the longitudinal PZT engine its displacements ...
... The electromagnetoelastic actuator with the piezoelectric or electrostriction effect for nano robotics system is used in nanotechnology, nano manipulator, nano pump, scanning microscopy, adaptive optics. The use of the electromagnetoelastic actuator is promising in nano robotics system [1][2][3][4][5][6] and nano manipulator [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] for nanotechnology. The electromagnetoelastic actuator is the electromechanical device for actuating and controlling mechanisms, systems with the conversion of electrical signals into mechanical displacements and forces. ...
... The electromagnetoelastic actuator is the electromechanical device for actuating and controlling mechanisms, systems with the conversion of electrical signals into mechanical displacements and forces. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] The piezo actuator is used for nano scale motion in adaptive optics, laser systems, focusing and image stabilization systems, nano and micro surgery, vibration damping, nano and micro manipulation to penetrate the cell and to work with the genes. The electromagnetoelastic actuator is provided range of movement from nanometers to ten microns; force 1000 N, response 1-10 ms. ...
... For the piezo actuator from ceramic PZT at d 31 = 2⋅10 -10 m/V, l δ = 20, 11 E C = 2⋅10 7 N/m, e C = 0.5⋅10 7 N/m, U = 100 V we obtain values the transfer coefficient for voltage 31 U k = 3.2 nm/V and the displacement l ∆ = 320 nm. Therefore, we have the transfer function for voltage with lumped parameter of the transverse piezo actuator7,11,12,[16][17][18][19]27,31 with fixe one face for the elastic-inertial load in the form ...
... A precision electromagnetoelastic engines in the form of piezo engines or magnetostriction engines are applied in nanomanipulators, nanopumps, scanning microscopes for nanobiomedical research [1][2][3][4][5][6]. The piezo engine is used for nanodisplacements in photolithography, medical equipment of microsurgical operations, adaptive optics systems and fiberoptic systems for transmitting and receiving information [4][5][6][7][8][9][10][11][12]. ...
... The structural diagram of a precision engine for nanobiomedical research is changed from Cady and Mason electrical equivalent circuits [4][5][6][7][8]. For a precision engine the equation of electromagnetoelasticity [2][3][4][5][6][7][8][9][10][11][12][13][14] ...
... is the transform of Laplace for displacement; p ,  ,  c ,  are the operator of transform, the coefficient of wave propagation, the speed of sound, the coefficien of attenuation. The system of the equations for the forces on faces of a precision engine is written The matrix equation of a precision engine for nanobiomedical research has the form The equation of the direct piezoelectric effect for the piezo engine in nanobiomedical research [10][11][12][13][14] has the form ...
Article
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The transfer function and the transfer coefficient of a precision electromagnetoelastic engine for nanobiomedical research are obtained. The structural diagram of an electromagnetoelastic engine has a difference in the visibility of energy conversion from Cady and Mason electrical equivalent circuits of a piezo vibrator. The structural diagram of an electromagnetoelastic engine is founded. The structural diagram of the piezo engine for nanobiomedical research is written. The transfer functions of the piezo engine or are obtained.
... For a sectional electroelastic engine, the equation of the electroelasticity [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] has the form of the inverse piezoelectric effect ...
... where C e is the rigidity of the load. For a sectional piezoelectric engine at the transverse piezoeffect on Figure 1, the equation of the electroelasticity [6][7][8][9][10][11][12][13][14][15] has the form ...
... For a sectional piezoelectric engine at the longitudinal piezoeffect, the equation of the electroelasticity [6][7][8][9][10][11][12][13][14][15]28] has the form ...
Article
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This work determines the coded control of a sectional electroelastic engine at the elastic–inertial load for nanomechatronics systems. The expressions of the mechanical and adjustment characteristics of a sectional electroelastic engine are obtained using the equations of the electroelasticity and the mechanical load. A sectional electroelastic engine is applied for coded control of nanodisplacement as a digital-to-analog converter. The transfer function and the transient characteristics of a sectional electroelastic engine at elastic–inertial load are received for nanomechatronics systems.
... The piezoactuator for the nanomechanics is provided the displacement from nanometers to tens of micrometers, a force to 1000N. The piezoactuator is used for research in the nanomedicine and the nanobiotechnology for the scanning tunneling microscopes, scanning force microscopes and atomic force microscopes [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. ...
... In [6,7] was determined the solution of the wave equation of the piezoactuator. In the [14][15][16]30,31] were obtained the structural-parametric models, the schematic diagrams for simple piezoactuator and were transformed to the structural-parametric model of the electro magneto elastic actuator. The structural-parametric model of the electroelastic actuator was determined in contrast electrical equivalent circuit for calculation of piezoelectric transmitter and receiver [9][10][11][12]. ...
... For the electro elastic actuator its deformation corresponds to stressed state. For polarized piezoceramics PZT the matrix state equations [12,14] connected the electric and elastic variables have the form two equations, then the first equation describes the direct piezoelectric effect, the second -the inverse piezoelectric effect. ...
... The piezoactuator uses the inverse piezoeffect and serves for the actuation of mechanisms or the management and converts the electrical signals into the displacement and the force [1][2][3][4][5][6][7][8]. The piezoactuator is applied for the drives of the scanning tunneling microscopes, scanning force microscopes and atomic force microscopes [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. ...
... In the electroelastic actuator its deformation corresponds to stressed state. For polarized piezoceramics PZT, the matrix state equations [12,14] with the electric and elastic variables have the form two equations, where the first equation represents the direct piezoeffect, the second describes the inverse piezoeffect ...
... For calculation of the electroelastic actuator is used the wave equation [6,7,12,14] for the wave propagation in a long line with damping but without distortions. After Laplace transform is obtained the linear ordinary second-order differential equation with the parameter p, ...
... In References [6,7], the solution of the wave equation of the piezoactuator was determined. In References [6,14,15,28], the structural-parametric models and the schematic diagrams for the simplest piezoactuators were obtained, and these were transformed into the structural-parametric model of an electromagnetoelastic actuator with output displacements. ...
... In References [8,14,15], the transfer functions of the piezoactuator were used to overcome the problem of the absolute stability condition of the strain control system for an electromagnetoelastic actuator. ...
... For polarized piezoceramics PZT the matrix state equations [11,14] with electric and elastic variables can be given by two equations, where the first equation represents the direct piezoelectric effect, and the second describes the inverse piezoelectric effect: ...
Article
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The generalized parametric structural schematic diagram, the generalized structural-parametric model, and the generalized matrix transfer function of an electromagnetoelastic actuator with output parameters displacements are determined by solving the wave equation with the Laplace transform, using the equation of the electromagnetolasticity in the general form, the boundary conditions on the loaded working surfaces of the actuator, and the strains along the coordinate axes. The parametric structural schematic diagram and the transfer functions of the electromagnetoelastic actuator are obtained for the calculation of the control systems for the nanomechanics. The structural-parametric model of the piezoactuator for the transverse, longitudinal, and shift piezoelectric effects are constructed. The dynamic and static characteristics of the piezoactuator with output parameter displacement are obtained.
... The piezoactuator on the inverse piezoeffect is serves for the actuation of mechanisms or the management, converts electrical signals into displacement and force [1][2][3][4][5][6][7][8]. The piezoactuator for the nanomechanics is provided the displacement from nanometers to tens of micrometers, a force to 1000 N. The piezoactuator is used for research in the nanomedicine and the nanobiotechnology for the scanning tunneling microscopes, scanning force microscopes and atomic force microscopes [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. In the present paper the generalized structural-parametric model and the generalized parametric structural schematic diagram of the electromagnetoelastic actuator are constructed by solving the wave equation with the Laplace transform for the equation of the electromagnetolasticity, the boundary conditions on loaded working surfaces of the actuator, the strains along the coordinate axes. ...
... In [6,7] was determined the solution of the wave equation of the piezoactuator. In the [14][15][16]30,31] were obtained the structural-parametric models, the schematic diagrams for simple piezoactuator and were transformed to the structuralparametric model of the electromagnetoelastic actuator. The structural-parametric model of the electroelastic actuator was determined in contrast electrical equivalent circuit for calculation of piezoelectric transmitter and receiver [9][10][11][12]. ...
... For the electroelastic actuator its deformation corresponds to stressed state. For polarized piezoceramics PZT the matrix state equations [12,14] connected the electric and elastic variables have the form two equations, then the first equation describes the direct piezoelectric effect, the second -the inverse piezoelectric effect ...
... Drive on the piezoelectric or electrostriction effects are used for nanomovements. The energy conversion in the structural scheme of the drive is visibility and logical [7][8][9][10][11][12][13][14]. ...
... Two matrix equations [8,[11][12][13][14][15][16][17][18][19] for the piezo drive have the form ...
Article
Full-text available
The structural model of the drive for nanobiotechnology is obtained. The structural scheme of the drive is constructed. In nanobiotechnology for the control systems with the drive its deformations are determined.
... In structural schema of electro elastic engine its energy transformation is clearly [7][8][9][10][11][12]. The piezo engine is applied for precise adjustment for nanochemistry in adaptive optics and scanning microscopy [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. ...
... For an engine its equations in matrixes [8, For piezo engine Figure 1 its relative displacement for 3 axis [8,[11][12][13][14][15][16][17][18][19][20] has the form where d 33 is piezo coefficient, E 3 is strength electric field on 3 axis, s E 33 is elastic compliance, T 3 is strength mechanical field on 3 axis. The steady-state movement of the transverse piezo engine with fixed one face and at elastic-inertial load has the form For the transverse piezo engine at elastic-inertial load the expression has the form where C l , C E 11 are the stiffness of load and engine, T t , ξ t , ω t are the time constant, the attenuation coefficient and the conjugate frequency of the engine. ...
Article
Full-text available
The structural model of an engine for nanochemistry is obtained. The structural scheme of an engine is constructed. For the control systems in nanochemistry with an elecro elastic engine its characteristics are determined.
... A piezo engine based on the piezoelectric effect is used in the control systems for composite telescope and adaptive optics. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] A piezo engine is applied for precise adjustment, compensation the deformations of composite telescope and scanning microscope. [15][16][17][18][19][20][21] For decisions the displacements and the forces of a piezo engine in the control systems for composite telescope is used the structural model of a piezo engine. ...
... The matrix state equations [8,[11][12][13][14][15][16][17] of a piezo engine have the form ...
Article
The structural model of a piezo engine for composite telescope is constructed. This structural model clearly shows the conversion of electrical energy by a piezo engine into mechanical energy of the control element of a composite telescope. The structural scheme of a piezo engine is determined. For the control systems with a piezo engine its deformations are obtained in the matrix form. This structural model, structural scheme and matrix equation of a piezo engine are applied in calculation the parameters of the control systems for composite telescope.
... The piezo actuator is used in photolithography for nano-and microdisplacements when aligning templates, in medical equipment for precise instrument delivery during microsurgical operations, in optical-mechanical devices, in adaptive optics systems, and in adaptive telescopes [2]. It is also used in stabilization systems for optical-mechanical devices, systems for alignment and tuning of lasers, interferometers, adaptive optical systems and fiber-optic systems for transmitting and receiving information [3]. ...
... Innov. 2020, 3,53 ...
Article
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A electroelastic engine with a longitudinal piezoeffect is widely used in nanotechnology for nanomanipulators, laser systems, nanopumps, and scanning microscopy. For these nanomechatronics systems, the transition between individual positions of the systems in the shortest possible time is relevant. It is relevant to solve the problem of optimizing the nanopositioning control system with a minimum control time. This work determines the optimal control of a multilayer electroelastic engine with a longitudinal piezoeffect and minimal control time for an optimal nanomechatronics system. The expressions of the control function and switching line are obtained with using the Pontryagin maximum principle for the optimal control system of the multilayer electroelastic engine at a longitudinal piezoeffect with an ordinary second-order differential equation of system. In this optimal nanomechatronics system, the control function takes only two values and changes once.
... The method of the mathematical physics with Laplace transform we have to build the structural diagram of the electro magneto elastic actuator for nanotechnology and material science. The structural diagram of the electro magneto elastic actuator nano displacement for material science is difference from Cady and Mason electrical equivalent circuits [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. ...
... In the foundation the structural diagram actuator is used decision with Laplace transform the wave equation for the wave propagation in the long line with damping but without distortions. With Laplace transform the original problem for the partial differential equation of hyperbolic type using the Laplace transform is reduced to the simpler problem [8,13,14,18] for the linear ordinary differential equation ...
... The structural-parametric model of the piezoactuator is determined in contrast electrical equivalent circuit types Cady or Mason for the calculation of the piezoelectric transmitter and receiver, the vibration piezoactuator and the vibration piezomotor with the mechanical parameters in form the velosity and the pressure [2 − 5, 11, 12]. By using the method of mathematical physics and solving the wave equation with the Laplace transform for the corresponding equations of the piezoeffect [6,9,10,20], the boundary conditions on loaded faces of the piezoactuator, the strains along the coordinate axes, it is possible to construct the structural parametric model of the piezoactuator [14,15]. Its transfer functions and structural scheme are determined. ...
... In general the equation of electroelasticity [10,12,15] has following form For calculation of the electroelastic actuator nano-and microdisplacement is used the wave equation [10,12,16,19] for the wave propagation in a long line with damping but without distortions. After Laplace transform is obtained the linear ordinary second-order differential equation with the parameter p, where the original problem for the partial differential equation of hyperbolic type using the Laplace transform is reduced to the simpler problem [10,13,14] for the linear ordinary differential equation ...
... A piezoengine is used for nano displacement in tunnel microscopy, for the nano alignment in adaptive optics, microscopy and interferometers in nanomedicine and applied bionics, for the automatic adjustment of the constant optical parameter of the ring quantum generators, for the actively dampen mechanical vibrations in the laser system, for the deform mirrors and operations with penetration in a cells and for the works with a genes. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] A piezoengine with a compact design provides positioning of elements of adaptive systems with an accuracy of up to a nanometer in the range of hundreds of nanometers. These precise parameters of a piezoengine are provided by the use of the reverse piezoelectric effect. ...
Article
The mathematical models of a piezoengine are determined for nanomedicine and applied bionics. The structural scheme of a piezoengine is constructed. The matrix equation is obtained for a piezoengine.
... The electro magneto elastic actuator with the piezoelectric, piezomagnetic, electrostriction, magnetostriction effects is used for nanomedical research in the scanning tunneling microscopy [1][2][3][4][5][6][7][8][9]. For control system of the deformation of the electro magneto elastic actuator its structural diagram, transfer function, characteristics are calculated [9][10][11][12][13][14][15][16][17][18]. The structural diagram and matrix transfer function the electro magneto elastic actuator is applied to describe the dynamic and static characteristics of the electro magneto elastic actuator for nanomedical research with regard to its physical parameters and external load [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. ...
... The electromagnetoelastic actuator is the electromechanical device for actuating and controlling mechanisms, systems with the conversion of electrical signals into mechanical displacements and forces. The electromagnetoelastic actuator is provided range of movement from nanometers to ten microns, force 1000 N, response 1-10 ms [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. ...
Article
Full-text available
The regulation and mechanical characteristics of the electromagnetoelastic actuator are obtained for control systems in nano physics and optics sciences for scanning microscopy, adaptive optics and nano biomedicine. The piezo actuator is used for nano manipulators. The matrix transfer function of the electromagnetoelastic actuator is received for nano physics and optics sciences
... In this work the condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator is calculated. The control systems with electro magneto elastic actuator on piezoelectric, electrostrictive and magnetostrictive effects solves problems of the precise matching in the nano biomedicine, the compensation of the temperature and gravitational deformations of the equipment, the wave front correction in the adaptive laser system [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The piezo actuator for nano biomedicine is used in the scanning tunneling microscope, the scanning force microscope, the atomic force microscope, in the gene manipulator [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. ...
... We drew model of the actuator from decision the equation of electromechanics and the second order differential equation [12][13][14][15]. In result we have the mathematical model and the scheme of the actuator for nano biomedical research on Figure 1 with the piezoelectric or magneto strictive effect in the form ...
... The electro elastic actuator for the nanotechnology and the biotechnology is used in the scanning tunneling microscopes, the scanning force microscopes, the atomic force microscopes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . ...
... of equations(13) for mechanical stresses in piezoactuator yields the following set of equations describing the structural parametric model and the parametric block diagram of the voltage-controlled piezoactuator for the transverse piezoelectric effect onFigure 2 ...
Chapter
An electroelastic actuator on the piezoelectric or electrostriction effect is applied in nanotechnology, nanobiology, biomechanics and adaptive optics for the precision matching in nanomechatronics systems. For the analysis and calculation of nanomechatronics systems is used the harmonious linearization of the hysteresis characteristic for an electroelastic actuator. The piezo actuator works on the basis of the inverse piezoelectric effect due to its deformation when the electric field strength is applied. To increase the range of movement of the piezo actuator to tens of micrometers, the multilayer piezo actuator is applied. The piezo actuator is used in nanomechatronics systems for nanodisplacement in adaptive optics, nanotechnology, scanning microscopy, nanobiomechanics, multicomponent telescopes. The coefficients of harmonious linearization for the basic loop characteristic are determined by the method of the theory of nonlinear automatic systems. On the characteristic of the piezo actuator deformation from the electric field strength, the initial curve is observed, on which the vertices of the basic hysteresis loops lie. The basic hysteresis loops have a symmetric change in the electric field strength relative to zero, and partial loops have an asymmetric change in the strength relative to zero. The expressions for the hysteresis basic and local loops of piezo actuator are received. The coefficients of harmonious linearization for the basic loop characteristic of the piezo actuator for nanomechatronics systems are obtained. The basic and local loops for hysteresis characteristics of the piezo actuator are proposed. The expression is determined for the generalized frequency transfer function of the nonlinear link with the hysteresis characteristic of the basic hysteresis loop for the piezo actuator.KeywordsHarmonious linearizationHysteresisBasic and partial loopsDeformationElectroelastic actuatorPiezo actuatorNanomechatronics system
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Chapter
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Conference Paper
Structural-parametric models and parametric structural schematic diagrams of electromagnetoelastic actuators are obtained. The transfer functions of the actuators are determined from structural parametric models. For calculations robotics and mechatronics systems with piezoactuators the parametric structural schematic diagrams and the transfer functions of piezoactuators are obtained.
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