• Laser & Optoelectronics Progress
  • Vol. 60, Issue 21, 2112001 (2023)
Changjie Liu, Kaiming Fu*, and Yihan Guo
Author Affiliations
  • State Key Laboratory of Precision Testing Technology and Instruments, Tianjin University, Tianjin 300072, China
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    DOI: 10.3788/LOP222712 Cite this Article Set citation alerts
    Changjie Liu, Kaiming Fu, Yihan Guo. Novel Six-Probe Measurement System for Reconstructing Deep Hole Axes[J]. Laser & Optoelectronics Progress, 2023, 60(21): 2112001 Copy Citation Text show less

    Abstract

    A novel six-probe measurement system is proposed for reconstructing deep hole axes. This system is based on the two-point method in three dimensions. The probe can obtain the center position of the measured section and radius of the circle at each step. This novel approach has the following advantages. 1) The effects of the straightness error of the sensor motion device on the axis measurement and fitting results can be eliminated. 2) The approach has remarkable universality. The holes with different apertures can be measured by adjusting the relative position between displacement sensors. 3) Probe movement and data acquisition can be realized automatically which reduces the amount of labor and improves measurement efficiency. 4) The process of measurement is simple; the hole axis can be fitted using only a single scanning measurement, after which related parameters can be evaluated. These advantages were demonstrated by theoretical analyses and simulations. Further, experiments showed that this novel system can provide high lateral resolution.
    A':xA'=lAcos θAyA'=lAsin θA(1)
    B':xB'=xB+lBcos θByB'=yB+lBsin θB(1)
    C':xC'=xC+lCcos θCyC'=yC+lCsin θC(1)
    D':xD'=xD+lDcos θDyD'=yD+lDsin θD(1)
    E':xE'=xE+lEcos θEyE'=yE+lEsin θE(1)
    F':xF'=xF+lFcos θFyF'=yF+lFsin θF(1)
    x-o1x2+y-o1y2=r12
    x-o2x2+y-o2y2=r22
    o2xzi=o1xzi+d  
    o2yzi=o1yzi+d  
    m1xzi=o1xzi-rxzi
    m2xzi=o1xzi+d-rxzi
    m1yzi=o1yzi-ryzi
    m2yzi=o1yzi+d-ryzi
    Δmxzi=1dm2xzi-m1xzi=1do1xzi+d-o1xzi =ox'zi 
    Δmyzi=1dm2yzi-m1yzi=1do1yzi+d-o1yzi=oy'zi 
    Fxzi=Fxzi-1+Δmxzi-1s
    Fyzi=Fyzi-1+Δmyzi-1s
    Paxisxz=5sin(2πz/200)(1)
    Paxisyz=7cos(2πz/200)(1)
    exs=sinπz400(1)
    eys=cosπz400(1)
    u1x=o1xlA2ur2+o1xlB2ur2+o1xlC2ur2
    u2x=o2xlD2ur2+o2xlE2ur2+o2xlF2ur2
    o1x=13xB+xC+lAcos θA+lBcos θB+lCcos θC-r12-(lAsin θA-o1y)2-r12-(yB+lBsin θB-o1y)2-r12-(yC+lCsin θC-o1y)2
    o2x=13xD+xE+xF+lDcos θD+lEcos θE+lFcos θF-r12-(lDsin θD-o2y)2-r12-(yE+lEsin θE-o2y)2-r12-(yF+lFsin θF-o2y)2
    o1xlA=13cos θA+13r12-(lAsin θA-o1y)2-12·lAsin θA-o1ysin θA
    o1xlB=13cos θB+13r12-(yB+lBsin θB-o1y)2-12·yB+lBsin θB-o1ysin θB
    o1xlC=13cos θC+13r12-(yC+lCsin θC-o1y)2-12·yC+lCsin θC-o1ysin θC
    o2xlD=13cos θD+13r12-(yD+lDsin θD-o2y)2-12·yD+lDsin θD-o2ysin θD
    o2xlE=13cos θE+13r12-(yE+lEsin θE-o2y)2-12·yE+lEsin θE-o2ysin θE
    o2xlF=13cos θF+13r12-(yF+lFsin θF-o2y)2-12·yF+lFsin θF-o2ysin θF
    u1x=33.1865ur
    u2x=0.6724ur
    um=33.1933dur
    urFxzk=k·d233.19332d2ur2=33.1933kur
    m1x, zerozi=o1xzi-rxzi+e1
    m2x, zerozi=o1xzi+d-rxzi+e2
    m1y, zerozi=o1yzi-ryzi+e3
    m2y, zerozi=o1yzi+d-ryzi+e4
    Δmx, zerozi=1dm2xzi-m1xzi=1do1xzi+d-o1xzi+1d(e2-e1)=ox'zi+ζ  
    Δmy, zerozi=1dm2yzi-m1yzi=1do1yzi+d-o1yzi+1d(e4-e3)=oy'zi+ξ  
    ζ=1de2-e1, ξ=1de4-e3(1)
    Fx, zerozi=Fxzi+ζi
    Fy, zerozi=Fyzi+ξi
    Changjie Liu, Kaiming Fu, Yihan Guo. Novel Six-Probe Measurement System for Reconstructing Deep Hole Axes[J]. Laser & Optoelectronics Progress, 2023, 60(21): 2112001
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