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Technical Brief

The Fundamental Bandwidth Limit of Piezoelectrically Actuated Nanopositioners With Motion Amplification

[+] Author and Article Information
G. R. Jayanth

Department of Instrumentation and Applied Physics,
Indian Institute of Science,
Bangalore 560012, India
e-mail: jayanth@isu.iisc.ernet.in

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 28, 2016; final manuscript received March 16, 2017; published online June 28, 2017. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 139(11), 114501 (Jun 28, 2017) (3 pages) Paper No: DS-16-1467; doi: 10.1115/1.4036550 History: Received September 28, 2016; Revised March 16, 2017

This paper proposes a simple reduced-order model for a general flexure-guided piezoelectrically actuated nanopositioner and employs it to derive the upper limit of achievable bandwidth for a specified travel range. It is shown that flexure-based motion amplification enables achieving higher bandwidth than that obtained when they are used for guiding motion alone. The optimal amplification and the corresponding maximum bandwidth are studied as functions of the mass carried by the positioner and the stiffness of the flexure. Simple analytical expressions are derived for the two in case of stiff flexures carrying small mass. The proposed reduced-order model is validated by means of finite element analysis.

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Figures

Grahic Jump Location
Fig. 1

(a) Schematic of a general single-axis flexure-guided nanopositioner actuated piezoelectrically and (b) reduced-order model of the nanopositioner

Grahic Jump Location
Fig. 2

Graphs showing (a) the dependence of f̃0 on G for different values of k̃f for the case z0=10 μm. The parameters assumed for the piezo-actuator were: E=36 GPa, ρ=7800 kg/m3, α=10−3, and Ac=49 mm2. (b) The dependence of z̃0f̃r on G for different values of m̃s for the case ℓ=10 mm. (c) The dependence of f̃0max on m̃s for different values of k̃f. (d) The dependence of Gopt on m̃s for different values of k̃f.

Grahic Jump Location
Fig. 3

Graph showing the maximum achievable eigenfrequency f0max as a function of the travel range z0 using the optimally designed nanopositioner carrying a sample of mass ms=0.1×10−3 kg. The stiffness of the flexure was assumed to be kf=176 N/μm. The corresponding graphs are also plotted for a piezo-actuator with and without a sample of same mass placed on it.

Grahic Jump Location
Fig. 4

(a) Model of a flexure-guided nanopositioner simulated using finite element analysis. (b) Mode shape of the platform at its first eigenfrequency f0=42.9 kHz.

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