• Optics and Precision Engineering
  • Vol. 31, Issue 12, 1761 (2023)
Rongwei LIN, Zhenying CHENG*, Yaxiong HE, Jie LI, and Ruijun LI
Author Affiliations
  • Anhui Province Key Laboratory of Measuring Theory and Precision Instrument,School of Instrument Science and Opto-electronic Engineering,Hefei University of Technology,Hefei230009,China
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    DOI: 10.37188/OPE.20233112.1761 Cite this Article
    Rongwei LIN, Zhenying CHENG, Yaxiong HE, Jie LI, Ruijun LI. On-line six-degree-of-freedom errors measurement and compensation for XY stages[J]. Optics and Precision Engineering, 2023, 31(12): 1761 Copy Citation Text show less

    Abstract

    An on-line six-degree-of-freedom (6-DOF) error measurement method and compensation model for XY stages were devised for improving the volumetric positional accuracy of the functional point. The positioning errors in the X- and Y-directions of the stage and the straightness error in the Z-direction were measured via laser interferometry, and the three angular motion errors around the X-, Y-, and Z-axes were measured using laser autocollimators. The volumetric positional errors of the functional point caused by the 6-DOF errors of the stage was analyzed, and an error compensation model based on the Abbe and Bryan principle was developed. An in-situ and on-line 6-DOF error measurement system based on the measurement method was developed and applied to a micro-nano coordinate measuring machine, which had high precision and a compact design. The capability of the system and the effectiveness of the model were experimentally verified, and the measurement uncertainty of the system was evaluated. SIOS laser interferometers were used as a reference. Experimental results indicated that the maximum positional errors at the reference functional point in the X-, Y-, and Z-directions were reduced from 1.7, 3.4, and 3 μm to 65, 81, and 109 nm, respectively, after error compensation, and the expanded uncertainty was 90, 98, and 158 nm (k=2), respectively. The proposed method and system can be used to increase the accuracy of XY stages.
    ΔXf=ΔXm+θymLz(Xa)-θzmLy(Xa)ΔYf=ΔYm-θxmLz(Ya)+θzmLx(Ya)ΔZf=ΔZm-θymLx(Zb)+θxmLy(Zb)(1)

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    Δd=N+Δφ2π×λ2n(2)

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    ΔX=dx-ΔdxΔY=dy-ΔdyΔZ=Δdz(3)

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    θX=ΔXQD22fθY=ΔZQD22fθZ=ΔYQD12f(4)

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    u1(x)=u2ΔX+uθyLz'(Xa)2+uθzLy'(Xa)2(5)

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    u1(y)=u2ΔY+uθxLz'(Ya)2+uθzLx'(Ya)2(6)

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    u1(z)=u2ΔZ+uθyLx'(Zb)2+uθxLy'(Zb)2(7)

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    u2(x)=θymaxuL2+θzmaxuL2=(8)

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    11.6 nm,

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    u2(y)=θxmaxuL2+θzmaxuL2=(10)

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    18.5 nm,

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    u2(z)=θymaxuL2+θxmaxuL2=(12)

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    u3(x)=u3(y)=u3(z)=δm3=(11)

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    u4(x)=u4(y)=δpd23=(12)

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    Rongwei LIN, Zhenying CHENG, Yaxiong HE, Jie LI, Ruijun LI. On-line six-degree-of-freedom errors measurement and compensation for XY stages[J]. Optics and Precision Engineering, 2023, 31(12): 1761
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