We obtained the structural scheme of the electro elastic actuator in the control system for nano research.
The transfer functions of the electro elastic actuator are used for the decision of the characteristics of the
actuator for nano research.
Keywords: Structural scheme; Electro elastic actuator; Piezo actuator; Transfer function
The application of the electro elastic actuator on the piezoelectric or electrostriction
effects is promising in the control system for nano research. The electro elastic actuator is
applied for nano research, adaptive optics, micro surgery, nano manipulator. The electro
elastic actuator for the control system in nano research is used in scanning microscopy,
nano injector, focus system, image stabilization [1-14]. The electro elastic actuator for nano
research have the displacement 1nm-10μm, fast response 1-10ms, force 100-1000N [15-31].
The structural scheme and transfer functions of the electro elastic actuator are calculated for
the decision of the dynamic and static characteristics of the actuator in the control system for
nano research [4-14].
We used the method of mathematical physics with Laplace transform for the decision the
wave equation. The structural scheme of the electro elastic actuator for the control system for
nano research is changed from Cady and Mason electrical equivalent circuits [7,8]. We have
the equation of the electro elasticity [5, 6,8,12,14] in the form
Where Si is the relative displacement along axis i, Ψm = {Em ,Dm is the control
parameter in the form of the electric field strength or the electric induction along axis m,
Tj is the mechanical stress along axis j, is the electro elastic module, Ψ
sij is the elastic compliance for Ψ = const , and the indexes i= 1, 2, … , 6; j=1, 2, … , 6; m=1, 2, 3.
We obtained the linear ordinary second-order differential equation by using Laplace
transform.
where Ξ(x, p) is the Laplace transform of the displacement of the section of the actuator,
γ = p/cΨ + α is the propagation coefficient, cΨ is the sound speed for Ψ = const , α is the
damping coefficient.
The structural scheme is received by using the linear ordinary second-order differential
equation, the boundary conditions, the equation of the electro elasticity in the form
Where
vmi is the electro elastic module, dmi, gmi are the piezo module
for the voltage-controlled actuator or the current-controlled
actuator, is the main size along axis i, so is the cross section area,
M1 , M2 are the mass of the load, Ξ1(p) , Ξ2 (p) and F1(p) , F2 (p)
are the Laplace transforms of the displacements and the forces on
the faces 1, 2 (Figure 1).
Figure 1: Structural scheme of electro elastic actuator
for nano research.
We obtained the structural scheme of the voltage-controlled
or current-controlled piezo actuator for nano research from its
mathematical model. The matrix transfer function [6,17,18,21,22-
31] of the electro elastic actuator for nano research is received in
the form
where (Ξ(p)) , (W(p)), (P(p))are the column-matrix of the
Laplace transforms of the displacements for the faces 1, 2 of the
actuator, the matrix transfer function, the column-matrix of the
Laplace transforms of the control parameter, the forces.
We received the structural scheme by using the linear ordinary
second-order differential equation, the boundary conditions, the
equation of the electro elasticity for the actuator in nano research.
We determined the structural scheme, the transfer functions of
the electro elastic actuator in nano research for the decision of the
characteristics of the actuator in the control system.
Cady WG (1946) Piezoelectricity: An introduction to the theory and applications of electro mechanical phenomena in crystals. McGraw-Hill Book Company, p. 806.
Mason W (1964) Physical acoustics: Principles and methods. Methods and Devices. Academic Press, p515.
Zwillinger D (1989) Handbook of Differential Equations. Academic Press, p.673.
Afonin SM (2016) Decision wave equation and block diagram of elecromagnetoelastic actuator nano- and microdisplacement for communications systems. International Journal of Information and Communication Sciences 1(2): 22-29.
Afonin SM (2015) Structural-parametric model and transfer functions of electro elastic actuator for nano- and micro displacement. Piezoelectrics and Nanomaterials: Fundamentals, Developments and Applications. Nova Science, pp. 225-242.
Afonin SM (2017) A structural-parametric model of electro elastic actuator for nano and micro displacement of mechatronic system. Advances in Nanotechnology. Nova Science, pp. 259-284.
SM (Afonin 2018) Elecromagnetoelastic nano- and micro actuators for mechatronic systems. Russian Engineering Research 38(12): 938-944.
Afonin SM (2012) Nano- and micro-scale piezomotors. Russian Engineering Research 32(7-8): 519-522.
Afonin SM (2016) Solution wave equation and parametric structural schematic diagrams of elecromagnetoelastic actuators nano- and micro displacement. International Journal of Mathematical Analysis and Applications 3(4): 31-38.
Afonin SM (2018) Structural-parametric model of elecromagnetoelastic actuator for nano mechanics. Actuators 7(1): 1-9.
Afonin SM (2018) Structural-parametric model of electro elastic actuator for nanotechnology and biotechnology. Journal of Pharmacy and Pharmaceutics 5(1): 8-12.
Professor, Chief Doctor, Director of Department of Pediatric Surgery, Associate Director of Department of Surgery, Doctoral Supervisor Tongji hospital, Tongji medical college, Huazhong University of Science and Technology
Senior Research Engineer and Professor, Center for Refining and Petrochemicals, Research Institute, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia
Interim Dean, College of Education and Health Sciences, Director of Biomechanics Laboratory, Sport Science Innovation Program, Bridgewater State University