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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

Postal Subscription Code 80-975

2018 Impact Factor: 0.989

Front. Mech. Eng.    2015, Vol. 10 Issue (1) : 20-36    https://doi.org/10.1007/s11465-015-0328-z
RESEARCH ARTICLE
Preload characteristics identification of the piezoelectric-actuated 1-DOF compliant nanopositioning platform
Ruizhou WANG,Xianmin ZHANG()
School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China
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Abstract

Packaged piezoelectric ceramic actuators (PPCAs) and compliant mechanisms are attractive for nanopositioning and nanomanipulation due to their ultra-high precision. The way to create and keep a proper and steady connection between both ends of the PPCA and the compliant mechanism is an essential step to achieve such a high accuracy. The connection status affects the initial position of the terminal moving plate, the positioning accuracy and the dynamic performance of the nanopositioning platform, especially during a long-time or high-frequency positioning procedure. This paper presents a novel external preload mechanism and tests it in a 1-degree of freedom (1-DOF) compliant nanopositioning platform. The 1-DOF platform utilizes a parallelogram guiding mechanism and a parallelogram load mechanism to provide a more accurate actual input displacement and output displacement. The simulation results verify the proposed stiffness model and dynamic model of the platform. The values of the preload displacement, actual input displacement and output displacement can be measured by three capacitive sensors during the whole positioning procedure. The test results show the preload characteristics vary with different types or control modes of the PPCA. Some fitting formulas are derived to describe the preload displacement, actual input displacement and output displacement using the nominal elongation signal of the PPCA. With the identification of the preload characteristics, the actual and comprehensive output characteristics of the PPCA can be obtained by the strain gauge sensor (SGS) embedded in the PPCA.

Keywords nanopositioning      preload characteristic      packaged piezoelectric ceramic actuator      compliant mechanism     
Corresponding Author(s): Xianmin ZHANG   
Online First Date: 15 February 2015    Issue Date: 01 April 2015
 Cite this article:   
Ruizhou WANG,Xianmin ZHANG. Preload characteristics identification of the piezoelectric-actuated 1-DOF compliant nanopositioning platform[J]. Front. Mech. Eng., 2015, 10(1): 20-36.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-015-0328-z
https://academic.hep.com.cn/fme/EN/Y2015/V10/I1/20
Fig.1  (a) The brief functional schematic of the first common external preload mechanism; (b) the brief functional schematic of the second common external preload mechanism

1–Fixed plate of the positioning platform; 2–Moving wedge; 3–Fixed wedge; 4–PPCA; 5–Moving plate of the positioning platform; 6–Screw; 7–Preload block

Fig.2  Complete structure of the novel two-level external preload mechanism

1–Tiny reflector of the laser interferometer; 2–Support of the tiny reflector; 3–Support of the capacitive sensor; 4–Capacitive sensor; 5–Head of the micrometer; 6–Fixed plate of the 1-DOF nanopositioning platform; 7–Spacer of the fixed plate; 8–Second-level screw; 9–Second-level steel ball; 10–First-level screw; 11–First-level steel ball; 12–Preload block which has a hemispherical pit; 13–Force sensor; 14–PPCA; 15–Moving plate of the positioning platform

Fig.3  (a) Adjustable bracket of the capacitive sensor; (b) 3-D model of the preload block; (c) cross-sectional view of the preload block
Fig.4  The 3-D structure of the guiding mechanism and the load mechanism
Fig.5  1-DOF positioning platform. (a) Overall view; (b) sectional view
Fig.6  (a) Key points of the guiding mechanism and load mechanism; (b) structural stiffness element model
Fig.7  (a) Sizes of the guiding mechanism and the load mechanism; (b) circular flexure hinge
Fig.8  Equivalent static stress of the 1-DOF nanopositioning platform
Fig.9  The dynamic model of the 1-DOF nanopositioning platform
Fig.10  The first-order natural frequency of the 1-DOF nanopositioning platform
Items Input stiffness/(N·μm-1) Output compliance/(μm·N-1) 1st-order frequency/Hz
Calculation 2.0223 0.4897 1707.9
Simulation 2.1076 0.4641 1600.0
Error/% 4.05 5.52 6.74
Tab.1  Results confrontation of matrix and FEA
Fig.11  (a) Test setup of the whole nanopositioning system and some components; (b) other components

1–Capacitive sensor controller; 2–PPCA controller of PI; 3–PC; 4–dSPACE controller; 5–PPCA controller of HCTST; 6–Single-electrode capacitive-position sensor; 7–Anti-vibration isolation table; 8–1-DOF nanopositioning platform; 9–PPCA

Fig.12  PSt, open-loop. (a) Preload displacement, nominal input displacement, actual input displacement and output displacement during the whole positioning procedure; (b) tiny difference between the actual input displacement and the output displacement; (c) the detailed curve of the preload displacement
Fig.13  PSt, closed-loop. (a) Preload displacement, nominal input displacement, actual input displacement and output displacement during the whole positioning procedure; (b) tiny difference between the actual input displacement and output displacement; (c) detailed curve of the preload displacement
Fig.14  PI, open-loop. (a) Preload displacement, nominal input displacement, actual input displacement and output displacement during the whole positioning procedure; (b) tiny difference between the actual input displacement and output displacement; (c) detailed curve of the preload displacement
Fig.15  PI, closed-loop. (a) Preload displacement, nominal input displacement, actual input displacement and output displacement during the whole positioning procedure; (b) tiny difference between the actual input displacement and output displacement; (c) detailed curve of the preload displacement
Order PSt, open-loop PSt, closed-loop PI, open-loop PI, closed-loop
Rising Downward Rising Downward Rising Downward Rising Downward
1 17.5 14.1 12.0 11.1 17.6 15.7 13.2 14.1
2 7.7 7.9 11.4 10.9 11.8 11.8 11.6 11.9
3 7.7 7.8 11.4 10.9 11.6 11.8 11.6 11.9
4 7.7 7.8 11.4 10.9 11.6 11.8 11.6 11.9
5 7.7 7.8 11.3 10.9 11.6 11.7 11.6 11.9
Tab.2  Standard deviation of the n-order polynomial to fit the preload displacement
Order PSt, open-loop PSt, closed-loop PI, open-loop PI, closed-loop
Rising Downward Rising Downward Rising Downward Rising Downward
1 77.4 58.1 75.9 50.2 46.3 52.5 43.1 73.2
2 16.7 10.1 19.5 13.3 18.9 12.8 8.2 10.1
3 9.8 9.9 13.1 13.0 18.9 11.8 8.2 8.2
4 9.8 9.9 13.1 13.0 12.9 11.3 8.0 8.0
5 9.7 9.6 13.1 13.0 12.9 11.1 8.0 8.0
Tab.3  Standard deviation of the n-order polynomial to fit the actual input displacement
Order PSt, open-loop PSt, closed-loop PI, open-loop PI, closed-loop
Rising Downward Rising Downward Rising Downward Rising Downward
1 74.2 66.7 70.1 59.3 46.9 46.4 25.0 64.0
2 14.9 8.2 18.3 12.1 17.3 12.8 12.4 11.9
3 8.1 8.1 11.8 12.0 17.3 12.8 12.3 11.7
4 8.0 8.1 11.8 11.9 13.1 11.8 12.0 11.6
5 8.0 8.0 11.8 11.9 13.1 11.8 12.0 11.6
Tab.4  Standard deviation of the n-order polynomial to fit the output displacement
Order PSt, open-loop PSt, closed-loop PI, open-loop PI, closed-loop
Rising Downward Rising Downward Rising Downward Rising Downward
apr2 -0.0563 0.0459 -0.0121 0.0059 -0.0935 0.0819 -0.0432 0.0519
apr1 -5.3159 -11.2567 -5.3250 -6.4717 -5.9862 -12.6513 -5.7784 -9.5929
apr0 -6.9883 -23.8002 -4.3828 2.2582 2.6120 -44.9610 -1.0018 -22.5378
Tab.5  Coefficients of the 2-order polynomial to fit the preload displacement
Order PSt, open-loop PSt, closed-loop PI, open-loop PI, closed-loop
Rising Downward Rising Downward Rising Downward Rising Downward
aai2 -0.2705 0.2241 0.2447 0.1605 -0.3006 0.4023 0.2882 0.4947
aai1 416.4972 421.0419 425.7895 432.0343 472.9322 454.0321 442.5777 435.6577
aai0 -53.3152 -130.8355 -74.1318 -100.7710 -59.5895 -532.9812 13.8089 -90.2022
Tab.6  Coefficients of the 2-order polynomial to fit the actual input displacement
Order PSt, open-loop PSt, closed-loop PI, open-loop PI, closed-loop
Rising Downward Rising Downward Rising Downward Rising Downward
aao2 0.2602 0.2591 0.2257 0.1924 -0.3100 0.3520 0.1479 0.4289
aao1 407.5656 409.0933 410.7467 413.9241 463.9914 446.2845 443.3160 433.1276
aao0 -4.1002 -68.3572 -70.6057 -100.4592 -53.5528 -518.0316 35.3560 -66.7681
Tab.7  Coefficients of the 2-order polynomial to fit the output displacement
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