• Optics and Precision Engineering
  • Vol. 30, Issue 20, 2467 (2022)
Cong ZHANG, Wenzheng LIU, Fajie DUAN*, Xiao FU, and Xinxing WANG
Author Affiliations
  • State Key Laboratory of Precision Measuring Technology & Instruments, Tianjin University, Tianjin300072, China
  • show less
    DOI: 10.37188/OPE.20223020.2467 Cite this Article
    Cong ZHANG, Wenzheng LIU, Fajie DUAN, Xiao FU, Xinxing WANG. Accuracy improvement method and optimal design of straightness in five-degree-of-freedom measurement of long guide[J]. Optics and Precision Engineering, 2022, 30(20): 2467 Copy Citation Text show less

    Abstract

    To improve the straightness accuracy during the five-degree-of-freedom measurement (5DOFM) of long guide, the measurement light path, error model, and calibration method of the straightness measurement unit in the 5DOFM device were examined. During long distance measurement, the angle drift of the reference beam causes severe straightness error. Accordingly, a telescopic objective lens structure was adopted to measure the angle drift in the optical path. Compared with a single lens, the focal length can be increased in a limited space, such that the combined focal length is larger than the mechanical size, thereby improving the measurement accuracy, and compensating for the angle drift to improve the measurement stability. Additionally, the error introduced by angle crosstalk was analyzed, and a compensation model was established based on the angle measurement value in the device. A four-quadrant detector was used as the straightness measurement sensor. To solve the problems that the nonlinearity of the sensor increases as the range increases, and the sensitivity changes nonlinearly with the movement of the long guide, an interval calibration method combining polynomial fitting and cubic spline interpolation fitting was proposed. The experimental results showed that within the 5-m measurement distance and ±400-μm range, the error standard deviation was less than 0.3 μm compared with the measurement results of the laser interferometer, and the drift was less than ±0.5 μm within 3 h. Thus, the straightness measurement unit meets the requirements of large range, high precision, and high stability of long guide straightness measurement.
    δx=-Xδy=-Y(1)

    View in Article

    1f=1f2+1f3-df2f3(2)

    View in Article

    Δδx1=θy(l1+l2)=ΔzPSD2f(l1+l2)Δδy1=θz(l1+l2)=ΔyPSD2f(l1+l2)(3)

    View in Article

    Δδx2=-hεy1-1nΔδy2=hεx1-1n(4)

    View in Article

    εy=εy'-θy=ΔzPSD1f1-ΔzPSD2fεx=εx'+θz=-ΔyPSD1f1+ΔyPSD2f(5)

    View in Article

    δx'=δx+Δδx1+Δδx2δy'=δy+Δδy1+Δδy2(6)

    View in Article

    ω(z)=ω01+λ(z-z0)πω02212(7)

    View in Article

    σx=u1+u4-u2-u3u1+u2+u3+u4σy=u1+u2-u3-u4u1+u2+u3+u4(8)

    View in Article

    X=erf-1(σx)2ωY=erf-1(σy)2ω(9)

    View in Article

    XL=A4,Lσx4+A3,Lσx3+A2,Lσx2+A1,Lσx(10)

    View in Article

    XL1=A4,L1σx4+A3,L1σx3+A2,L1σx2+A1,L1σxXL2=A4,L2σx4+A3,L2σx3+A2,L2σx2+A1,L2σxXL3=A4,L3σx4+A3,L3σx3+A2,L3σx2+A1,L3σxXLn+1=A4,Ln+1σx4+A3,Ln+1σx3+A2,Ln+1σx2+A1,Ln+1σx(11)

    View in Article

    S(L1)=S(Ln+1)=0(12)

    View in Article

    A0,Li=XM,Li-XLi(13)

    View in Article

    A4=-146.37(L-1)3+403.60(L-1)-90.94,1L<2259.12(L-2)3-439.12(L-2)2-35.53(L-2)+166.29,2L<3-160.29(L-3)3+338.24(L-3)2-136.41(L-3)-49.24,3L<447.54(L-4)3-142.63(L-4)2+59.20(L-4)-7.69,4L5(14)

    View in Article

    A3=-24.44(L-1)3+79.48(L-1)+412.40,1L<222.73(L-2)3-73.32(L-2)2+6.16(L-2)+467.44,2L<329.61(L-3)3-5.12(L-3)2-72.27(L-3)+423.02,3L<4-27.91(L-4)3+83.72(L-4)2+6.33(L-4)+375.24,4L5(15)

    View in Article

    A2=23.02(L-1)3-51.76(L-1)+42.22,1L<2-44.29(L-2)3+69.07(L-2)2+17.31(L-2)+13.48,2L<327.96(L-3)3-63.81(L-3)2+22.57(L-3)+55.57,3L<4-6.69(L-4)3+20.07(L-4)2-21.16(L-4)+42.29,4L5(16)

    View in Article

    A1=4.26(L-1)3-7.02(L-1)+1227.18,1L<2-3.60(L-2)3+12.79(L-2)2+5.77(L-2)+1224.43,2L<3-1.49(L-3)3+1.99(L-3)2+20.55(L-3)+1239.39,3L<40.83(L-4)3-2.48(L-4)2+20.07(L-4)+1260.45,4L5(17)

    View in Article

    X2.5 m=71.13σx4+455.03σx3+33.87σx2+1230.06σxX3.5 m=-52.92σx4+389.31σx3+54.40σx2+1249.98σx(18)

    View in Article

    Cong ZHANG, Wenzheng LIU, Fajie DUAN, Xiao FU, Xinxing WANG. Accuracy improvement method and optimal design of straightness in five-degree-of-freedom measurement of long guide[J]. Optics and Precision Engineering, 2022, 30(20): 2467
    Download Citation