• Optics and Precision Engineering
  • Vol. 29, Issue 9, 2158 (2021)
Qin LUO, Xiao-yan SHEN, Dong-sheng LI*, Jian-long Yin, and Jia-cheng Hu
Author Affiliations
  • College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, Zhejiang310018, China
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    DOI: 10.37188/OPE.20212909.2158 Cite this Article
    Qin LUO, Xiao-yan SHEN, Dong-sheng LI, Jian-long Yin, Jia-cheng Hu. Energy efficiency of aerostatic restrictor with orifice throttle[J]. Optics and Precision Engineering, 2021, 29(9): 2158 Copy Citation Text show less

    Abstract

    To address problems that have long been unsolved in the energy utilization efficiency and energy efficiency evaluation of aerostatic lubrication technology, this study uses three types of aerostatic restrictors for CMM, to establish the theoretical model of energy efficiency evaluation and experimental analysis. First, starting from the gas state, the compression factor is introduced based on the pneumatic power to establish a compression energy model of the compressed air flowing into the throttle. Second, using the pressure and bearing capacity of the air film field, the air flotation work model is determined. Third, the energy efficiency theory is established from the two functional models. Finally, an energy efficiency test for the three throttles is conducted through multi-parameter tests. The test results show that all three types of restrictors have the best energy efficiency when the inner diameter of the intake pipe is 2 mm and the supply pressure is 0.3 MPa. Among them, the double U A-type with the largest working area can reach a maximum energy efficiency of 17.8%. In conclusion, the energy efficiency of the device is inversely related to the supply pressure and intake flow, and positively related to the bearing capacity. Furthermore, when other conditions are equal, the device with a greater working area exhibits a greater energy efficiency. This thesis research has vital reference value for the gas source configuration and overall design of aerostatic systems.
    F=pA(1)

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    W=F·v·t=pA·v·t=p·Q·t(2)

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    W=pV(3)

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    E=pVlnppa(4)

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    P=dEdt=pQlnppa(5)

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    Z=pVnRT=pVm(real)RT(6)

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    pr=ppc(7)

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    Tr=TTc(8)

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    Vm(real)=ZRTp(9)

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    Vm(real)=Vrealn(10)

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    n=mM(11)

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    Vreal=nVm=ρQtM¯ZRTp(12)

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    ρreal=1.293×ppa273.15T(13)

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    Vreal=tZRTQρrealM¯p(14)

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    Ereal=pVreallnppa=tZRTQM¯ρreallnppa(15)

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    Preal=dErealdt=ZRTQM¯ρreallnppa(16)

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    pf=p1-p2(17)

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    2pf2x2+2pf2y2+3hhxpf2x+hypf2y=0(18)

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    M1=M2(19)

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    M1=ApsCφ2RT(20)

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    φ=k22k+1k+1k-1pmps2k+1kk-1kk-1pmps2k-pmpsk+1kpmps>2k+1kk-1(21)

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    M2=ρh312μ0Bpfxx=0+pfxx=Ldy+ρh312μ0Lpfyy=0+pfyy=Bdx.(22)

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    F=0B0L(pf-pa)dxdy(23)

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    EF=t0hFdh=tFh(24)

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    PF=dEFdt=Fh(25)

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    η=PFPreal=FhZRTQρreallnppa/M¯×100%(26)

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    Fi,j=1Bi,jFi+1,j+Fi-1,jΔx2+Fi,j+1+Fi,j-1Δy2+3hi,jhi+1,j-hi-1,j2ΔxFi+1,j-Fi-1,j2Δx+3hi,jhi,j+1-hi,j-12ΔyFi,j+1-Fi,j-12Δy(27)

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    F¯(i,j)r+1=λF(i,j)r+1+(1-λ)F(i,j)r(28)

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    i=0m-1j=0nF¯(i,j)r+1-F¯(i,j)ri=0m-1j=0nF¯(i,j)r+1δ(29)

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    1-M1M2<ζ(30)

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    Qin LUO, Xiao-yan SHEN, Dong-sheng LI, Jian-long Yin, Jia-cheng Hu. Energy efficiency of aerostatic restrictor with orifice throttle[J]. Optics and Precision Engineering, 2021, 29(9): 2158
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