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Physics & Astronomy International Journal

Research Article Volume 4 Issue 4

An actuator nano and micro displacements for composite telescope in astronomy and physics research

Afonin SM

National Research University of Electronic Technology, MIET, Russia

Correspondence: Afonin SM, National Research University of Electronic Technology, MIET, Moscow, Russia

Received: August 12, 2020 | Published: August 31, 2020

Citation: Afonin SM. An actuator nano and micro displacements for composite telescope in astronomy and physics research. Phys Astron Int J.2020;4(4):165-167. DOI: 10.15406/paij.2020.04.00216

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Abstract

We obtained the deformation, the structural diagram, the transfer functions and the characteristics of the actuator nano and micro displacements for composite telescope in astronomy and physics research. The mechanical and regulation characteristics of the actuator are received.

Keywords: actuator nano and micro displacements, piezo actuator, deformation, transfer function, regulation characteristic, mechanical characteristic, nano and micro displacements, composite telescope

Introduction

The electromagnetoelastic actuator nano and micro displacements at the piezoelectric, electrostriction, magnetostriction, piezomagnetic effects is used for the control system the adaptive optics of the composite telescope and the interferometer. The multilayer actuator is increased the range of the displacement from nm to tens microns.6–31 The structural model and the structural diagram of the multilayer actuator are determined by using the equation of the electromagnetoelasticity, the differential equation and the boundary conditions of the actuator. The piezo actuator is applied in adaptive optics for composite telescope, laser systems, interferometry, scanning microscopy, nano manipulators for physics and astronomy research The electromagnetoelastic actuator is provided displacement from 1 nm to 20 μm, force 10-1000 N, response 1-10 ms.11–31

Deformation and structural diagram of actuator

The structural diagram of the actuator for composite telescope is obtained in difference from Cady's and Mason's electrical equivalent circuits of the piezo transducer. Electromagnetoelasticity equation has the form of the equation of reverse effect for the deformation of the actuator

Si=νmiΨm+sΨijTjSi=νmiΨm+sΨijTj ,

where SiSi , νmiνmi , ΨmΨm , sΨijsΨij , TjTj  are the relative deformation; the module; the control parameter; the elastic compliance; the mechanical stress.10−25 The second order linear ordinary differential equation for the actuator.10−25,28 has the form

Figure 1 Structural diagram of actuator for composite telescopes in astronomy and physics research.

d2Ξ(x,p)dx2γ2Ξ(x,p)=0d2Ξ(x,p)dx2γ2Ξ(x,p)=0 ,

where Ξ(x,p)Ξ(x,p)  is transform of Laplace the displacement, pp , γγ , xx  are the parameter of transform, the propagation coefficient, the coordinate. For the structural diagram on Figure 1 and the structural model of the actuator for composite telescopes in astronomy and physics research the system of equations has the form

Ξ1(p)=(1/(M1p2))×{F1(p)+(1/χΨij)×[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ1(p)Ξ2(p)]]}Ξ1(p)=(1/(M1p2))×⎪ ⎪ ⎪⎪ ⎪ ⎪F1(p)+(1/χΨij)×[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ1(p)Ξ2(p)]]⎪ ⎪ ⎪⎪ ⎪ ⎪ ;

Ξ2(p)=(1/(M2p2))×{F2(p)+(1/χΨij)××[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ2(p)Ξ1(p)]]}Ξ2(p)=(1/(M2p2))×⎪ ⎪ ⎪⎪ ⎪ ⎪F2(p)+(1/χΨij)××[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ2(p)Ξ1(p)]]⎪ ⎪ ⎪⎪ ⎪ ⎪ ,

where χΨij=sΨij/S0χΨij=sΨij/S0 , νmi={d33,d31,d15d33,d31,d15νmi={d33,d31,d15d33,d31,d15 , Ψm={E3,E1H3,H1Ψm={E3,E1H3,H1 , sΨij={sE33,sE11,sE55sH33,sH11,sH55sΨij={sE33,sE11,sE55sH33,sH11,sH55 , E, H are the strengths of the electric and magnetic fields.

Therefore, the system of the equations for the structural model of the actuator has the form

Ξ1(p)=(1/(M1p2))×{F1(p)+CΨijl×[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ1(p)Ξ2(p)]]}Ξ1(p)=(1/(M1p2))×⎪ ⎪⎪ ⎪F1(p)+CΨijl×[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ1(p)Ξ2(p)]]⎪ ⎪⎪ ⎪ ;

Ξ2(p)=(1/(M2p2))×{F2(p)+CΨijl×[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ2(p)Ξ1(p)]]}Ξ2(p)=(1/(M2p2))×⎪ ⎪⎪ ⎪F2(p)+CΨijl×[νmiΨm(p)[γ/sh(lγ)]×[ch(lγ)Ξ2(p)Ξ1(p)]]⎪ ⎪⎪ ⎪ ,

where CΨij=S0/(sΨijl)=1/(χΨijl)CΨij=S0/(sΨijl)=1/(χΨijl)  is the stiffness of actuator.

The matrix equation of the actuator has form

(Ξ1(p)Ξ2(p))=(W11(p)W12(p)W13(p)W21(p)W22(p)W23(p))(Ψm(p)F1(p)F2(p))(Ξ1(p)Ξ2(p))=(W11(p)W12(p)W13(p)W21(p)W22(p)W23(p))Ψm(p)F1(p)F2(p) .

From the electromagnetoelasticity equation at F=CeΔlF=CeΔl  the regulation characteristic of the actuator has the form

Δll=dmiΨmsΨijCeS0ΔlΔll=dmiΨmsΨijCeS0Δl ,

where CeCe , F are stiffness and force of the load. Therefore, the regulation characteristic of the actuator has the form

Δl=dmilΨm1+Ce/CΨij=kΨijΨmΔl=dmilΨm1+Ce/CΨij=kΨijΨm ,

CΨij=S0/(sΨijl)CΨij=S0/(sΨijl) , kΨij=dijl/(1+Ce/CΨij)kΨij=dijl/(1+Ce/CΨij) ,

where CΨijCΨij , kΨijkΨij  are the stiffness and the transfer coefficient of the actuator. The transfer function with lumped parameter of the actuator7,11–30 has the form

W(p)=Ξ(p)/Ψm(p)=kΨij/(T2tp2+2Ttξtp+1)W(p)=Ξ(p)/Ψm(p)=kΨij/(T2tp2+2Ttξtp+1) ,

Tt=M/(C+eCΨij) ,

where Ξ(p) , Ψm(p)  are the transforms of the displacement and the control parameter, Tt , ξt  are the time constant and the damping coefficient of the actuator, M is the load mass. The transfer function with lumped parameter of the transverse piezo actuator7,11–30 has the form

W(p)=Ξ(p)/U(p)=kU31/(T2tp2+2Ttξtp+1) ,

kU31=(d31l/δ)/(1+Ce/CE11) , Tt=M/(C+eCE11) ,

where U(p)  is the Laplace transform of the voltage and kU31  is the transfer coefficient. At d31 =2×10-10 m/V, l/δ =12, M=1 kg, CE11 =3.4×107 N/m, Ce =0.2×107 N/m the transfer coefficient kU31 =2.27 nm/V and the time constant Tt =0.17×10-3 s are obtained for the transverse piezo actuator from ceramic PZT.

From the electromagnetoelasticity equation at elastic load the regulation characteristic of the multilayer longitudinal piezo actuator is obtained in the following form

Δl=d33nU1+Ce/CE33=kU33U ,

kU33=d33n/(1+Ce/CE33) , l=nδ ,

where kU33  is the transfer coefficient.

For the multilayer longitudinal piezo actuator from ceramic PZT at d33 =4∙10-10 m/V, n = 6, CE33  =4∙107 N/m, Ce =0.2∙107 N/m, U=100 V are received kU33  =2.29 nm/V and Δl =229 nm.

The mechanical characteristic of the actuator has form Si(Tj)  or Δl(F)  and the regulation line of actuator has form Si(Ψm)  or Δl(U) . The mechanical characteristic is obtained in the following form

Si|Ψ=const=dmiΨm|Ψ=const+sΨijTj .

The regulation characteristic of the actuator has the form

Si|T=const=dmiEm+sEijTj|T=const .

The mechanical characteristic of the actuator has the form

Δl=Δlmax(1F/Fmax) ,

Δlmax=dmiΨml , Fmax=dmiΨmS0/sΨij ,

where Δlmax  is the maximum displacement for F=0  and Fmax  is the maximum force forΔl=0 .

The maximum displacement and the maximum force of the transverse piezo actuator on Figure 2 have the form

Δhmax=d31E3h , Fmax=d31E3S0/sE11 .

At d31  =2∙10-10 m/V, E3 = 2∙105 V/m, h = 2.5∙10-2 m, S0 =1.5∙10-5 m2, sE11 =15∙10-12 m2/N parameters of the transverse piezo actuator are found Δhmax =1000 nm and Fmax =40 N. The discrepancy between the experimental data for the piezo actuators and the calculation results is 10%.

Figure 2 Mechanical characteristic of transverse piezo actuator for composite telescopes in astronomy and physics research.

Conclusion

The regulation characteristic, the transfer function and the structural diagram of the actuator nano and micro displacements are obtained for composite telescope in astronomy and physics research. The mechanical and regulation characteristics of the actuator nano and micro displacements are found for nano manipulators in physics and astronomy research. The mechanical characteristic of actuator and its maximum displacement and maximum force are obtained. For the elastic load the regulation characteristics of the electromagnetoelastic actuator and the multilayer piezo actuator are calculated.

Acknowledgments

None.

Conflicts of interest

The author declares there is no conflict of interest.

References

  1. Schultz J, Ueda J, Asada H. Cellular Actuators. Butterworth-Heinemann Publisher, Oxford, 2014. p. 382.
  2. Afonin SM. Piezo actuators for nanomedicine research. MOJ Applied Bionics and Biomechanics. 2019;3(2):56‒57.
  3. Afonin SM. Condition absolute stability of control system with electro elastic actuator for nano bioengineering and microsurgery. Surgery and Case Studies Open Access Journal. 2019;3(3):307–309.
  4. Zhou S, Yao Z. Design and optimization of a modal-independent linear ultrasonic motor. IEEE transaction on ultrasonics, ferroelectrics, and frequency control. 2014;61(3):535–546.
  5. Uchino K. Piezoelectric actuator and ultrasonic motors. Boston, MA: Kluwer Academic Publisher. 1997. p. 347.
  6. Afonin SM. Block diagrams of a multilayer piezoelectric motor for nano- and microdisplacements based on the transverse piezoeffect. Journal of computer and systems sciences international. 2015;54(3):424–439.
  7. Afonin SM. Structural parametric model of a piezoelectric nanodisplacement transduser. Doklady physics. 2008;53(3):137–143.
  8. Afonin SM. Solution of the wave equation for the control of an elecromagnetoelastic transduser. Doklady mathematics. 2006;73(2):307–313.
  9. Cady WG. Piezoelectricity: An introduction to the theory and applications of electromechancial phenomena in crystals. McGraw-Hill Book Company, New York, London, 1946. p. 806.
  10. Mason W. Physical Acoustics: Principles and Methods. Vol.1. Part A. Methods and Devices. Academic Press, New York, 1964. p. 515.
  11. Afonin SM. Structural-parametric model and transfer functions of electroelastic actuator for nano- and microdisplacement. 2015.Chapter 9 in Piezoelectrics and Nanomaterials: Fundamentals, Developments and Applications. In: Parinov IA editor. Nova Science, New York, p. 225–242.
  12. Afonin SM. A structural-parametric model of electroelastic actuator for nano- and microdisplacement of mechatronic system. Chapter 8 in Advances in Nanotechnology. Volume 19. In: Bartul Z et al., editors. New York: Nova Science, 2017. p. 259–284.
  13. Afonin SM. Stability of strain control systems of nano-and microdisplacement piezo transducers. Mechanics of solids. 2014;49(2):196–207.
  14. Afonin SM. Structural-parametric model electromagnetoelastic actuator nanodisplacement for mechatronics. International Journal of Physics. 2017;5(1):9–15.
  15. Afonin SM. Structural-parametric model multilayer electromagnetoelastic actuator for nanomechatronics. International Journal of Physics. 2015;7(2):50–57.
  16. Afonin SM. Solution wave equation and parametric structural schematic diagrams of electromagnetoelastic actuators nano- and microdisplacement. International Journal of Mathematical Analysis and Applications. 2016;3(4):31–38.
  17. Afonin SM. Structural-parametric model of electromagnetoelastic actuator for nanomechanics. Actuators. 2018;7(1):1–9.
  18. Afonin SM. Structural-parametric models and transfer functions of electromagnetoelastic actuators nano- and microdisplacement for mechatronic systems. International Journal of Theoretical and Applied Mathematics. 2016;2(2):52–59.
  19. Afonin SM. Parametric block diagrams of a multi-layer piezoelectric transducer of nano- and microdisplacements under transverse piezoelectric effect. Mechanics of Solids. 2014;52(1):81–94.
  20. Afonin SM. Multilayer electromagnetoelastic actuator for robotics systems of nanotechnology. Proceedings of the 2018 IEEE Conference EIConRus, 2018. p. 1698–1701.
  21. Afonin SM. Electromagnetoelastic nano- and microactuators for mechatronic systems. Russian Engineering Research. 2018;38(12):938–944.
  22. Afonin SM. Structural-parametric model of electro elastic actuator for nanotechnology and biotechnology. Journal of Pharmacy and Pharmaceutics. 2018;5(1):8–12.
  23. Afonin SM. Electromagnetoelastic actuator for nanomechanics. Global Journal of Research in Engineering. A: Mechanical and Mechanics Engineering. 2018;18(2):19–23.
  24. Afonin SM. Structural–parametric model electroelastic actuator nano– and microdisplacement of mechatronics systems for nanotechnology and ecology research. MOJ Ecology and Environmental Sciences.2018;3(5):306‒309.
  25. Afonin SM. Static and dynamic characteristics of multilayered electromagnetoelastic transducer of nano- and micrometric movements. Journal of Computer and Systems Sciences International. 2010;49(1):73–85.
  26. Afonin SM. Static and dynamic characteristics of a multi-layer electroelastic solid. Mechanics of Solids. 2009;44(6):935–950.
  27. Afonin SM. Structural-parametric model and diagram of a multilayer electromagnetoelastic actuator for nanomechanics. Actuators. 2019;8(3):1–14.
  28. Afonin SM. A block diagram of electromagnetoelastic actuator nanodisplacement for communications systems. Transactions on Networks and Communications. 2008;6(3):1–9.
  29. Afonin SM. Decision matrix equation and block diagram of multilayer electromagnetoelastic actuator micro and nanodisplacement for communications systems. Transactions on Networks and Communications. 2019;7(3):11–21.
  30. Afonin SM. Structural-parametric model actuator of adaptive optics for composite telescope and astrophysics equipment. Physics and Astronomy International Journal. 2020;4(1):18‒21.
  31. Springer Handbook of Nanotechnology. In: Bhushan B editor. Springer, Berlin, New York, 2004. p. 1222.
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