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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.    2017, Vol. 12 Issue (2) : 265-278    https://doi.org/10.1007/s11465-017-0453-y
RESEARCH ARTICLE
Mechatronic design of a novel linear compliant positioning stage with large travel range and high out-of-plane payload capacity
Hua LIU, Xin XIE, Ruoyu TAN, Lianchao ZHANG, Dapeng FAN()
College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, China
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Abstract

Most of the XY positioning stages proposed in previous studies are mainly designed by considering only a single performance indicator of the stage. As a result, the other performance indicators are relatively weak. In this study, a 2-degree-of-freedom linear compliant positioning stage (LCPS) is developed by mechatronic design to balance the interacting performance indicators and realize the desired positioning stage. The key parameters and the coupling of the structure and actuators are completely considered in the design. The LCPS consists of four voice coil motors (VCMs), which are conformally designed for compactness, and six spatial leaf spring parallelograms. These parallelograms are serially connected for a large travel range and a high out-of-plane payload capacity. The mechatronic model is established by matrix structural analysis for structural modeling and by Kirchhoff’s law for the VCMs. The sensitivities of the key parameters are analyzed, and the design parameters are subsequently determined. The analytical model of the stage is confirmed by experiments. The stage has a travel range of 4.4 mm× 7.0 mm and a 0.16% area ratio of workspace to the outer dimension of the stage. The values of these performance indicators are greater than those of any existing stage reported in the literature. The closed-loop bandwidth is 9.5 Hz in both working directions. The stage can track a circular trajectory with a radius of 1.5 mm, with 40 mm error and a resolution of lower than 3 mm. The results of payload tests indicate that the stage has at least 20 kg out-of-plane payload capacity.

Keywords mechatronic design      linear compliant positioning stage      large travel range      high out-of-plane payload capacity      spatial parallelogram      voice coil motor      sensitivity analysis     
Corresponding Author(s): Dapeng FAN   
Just Accepted Date: 19 May 2017   Online First Date: 07 June 2017    Issue Date: 19 June 2017
 Cite this article:   
Hua LIU,Xin XIE,Ruoyu TAN, et al. Mechatronic design of a novel linear compliant positioning stage with large travel range and high out-of-plane payload capacity[J]. Front. Mech. Eng., 2017, 12(2): 265-278.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-017-0453-y
https://academic.hep.com.cn/fme/EN/Y2017/V12/I2/265
Fig.1  (a) Novel 2-DOF LCPS and its partitions: (b) X-axis and (c) Y-axis single-DOF LCPS
Performance indicatorDesign goals
Travel range, Sax×Say4 mm×4 mm
Area ratio, Ra≥0.15%
Closed-loop bandwidth, fc (without load)≥10 Hz
Out-of-plane payload capacity, PL≥15 kg
Tab.1  Performance goals of the LCPS
Fig.2  Planar schematics of the (a) X-axis and (b) Y-axis LGCMs; (c) simplified mass-spring model of LGCM
Fig.3  Schematic of the VCM magnetic circuit
Fig.4  Relationships of the LCPS parameters
Independent
parameter
Range/mmDependent
parameter
Constraints
Lower boundaryUpper boundary
LSi5575LrLr=LS4?2l3_r?2lg
tSi0.501.5WrWr=pRm_r2/Lr
bSi1025Sax(y)Eq. (26)
Rm_c(r)1020lca_x(y)lca=l3_c(r)+2.2Sax(y)
lg_c(r)2.06.0lpEq. (16)
l3_c(r)2.06.0WW=Wr+2lg_r+8l3_r
lm_c(r)6.014LS3-2LS3-2=80+8tSi+4Sax (i=1 to 3)
d0.200.37LS6-1LS6-1=W+8tSi+4Say (i=4 to 6)
PxPx=LS3-2+7l3_r+2lm_r
PyPy=LS6-1+4.5l3_c+lm_c
Tab.2  Ranges and relationships of the parameters
Fig.5  Results of the parameter sensitivity analysis: (a) Travel range, (b) first resonant frequency, and (c) area ratio
Spatial leaf spring parallelogram
LSi×bSi×tSi×LSi-1×LSi-2/mm5
Rectangular VCM
l3×lg×lm×Lr×Wr/mm5
Circular VCM
l3×lg×lm×Rm/mm4
Diameter
d/mm
S1: 59×14.8×1.3×34×82.54×4×10×50×304×4×10×150.28
S2: 59.4×14.8×1.3×34×91.6
S3: 59.4×14.8×1.3×34×100.7
S4: 63×20×1.05×68.1×104
S5: 67.5×20×1.05×76.4×104
S6: 64.5×20×1.05×84.7×104
Tab.3  Design values of the stage parameters
Fig.6  Experimental setup of the LCPS
Fig.7  Travel range test: (a) X-axis; (b) Y-axis
Fig.8  Frequency response of the stage: (a) X-axis frequency response and its coupled Y-axis response; (b) Y-axis frequency response and its coupled X-axis response
Fig.9  Tracking performance for a 1.5 mm circular trajectory at 0.25 Hz: (a) Tracking results; (b) tracking errors
Fig.10  Resolution test of the stage
Fig.11  Travel range test results under different payloads: (a) X-axis; (b) Y-axis
Performance indicatorDesign goals
Travel range, Sax×Say4.4 mm×7 mm
Area ratio, Ra0.16%
Close-loop bandwidth, fc (without load)9.5 Hz
Out-of-plane payload capacity, PL≥20 kg
Tab.4  Performance of the prototype
  Fig A1Division of SLSP: (a) Simple SLSP division and (b) compound SLSP division
EYoung’s modulus
GShear modulus
ACross-sectional area
IyY-axis area moment of inertia
IzZ-axis area moment of inertia
JxX-axis polar moment of inertia
LSiLeaf spring length of Si
bSiLeaf spring width of Si
tSiLeaf spring thickness of Si
LSi-1Leaf spring distance of Si
LSi-2Guiding beam length of Si
Rm_cRadius of circular magnet
lm_cCircular magnet thickness
l3_cCircular yoke thickness
l3_rThickness of rectangular yoke
LrLength of rectangular magnet
WrWidth of rectangular magnet
WWidth of rectangular motor
Rm_rEquivalent radius of rectangular magnet
l3_rRectangular yoke thickness
lcaAxial length of coil
lpCoil length per unit axial length of the coil
lgLength of the gap
dDiameter of wire
  
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