Research Article Volume 4 Issue 4
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
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
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
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
d2Ξ(x,p)dx2−γ2Ξ(x,p)=0d2Ξ(x,p)dx2−γ2Ξ(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=dmiΨm−sΨijCeS0ΔlΔll=dmiΨm−sΨijCeS0Δl ,
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(1−F/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%.
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.
None.
The author declares there is no conflict of interest.
©2020 Afonin. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially.