一种关于静压气体轴承节流孔系数的计算方法
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摘要
基于层流边界层方程的分离变量算法和雷诺方程的解析算法,提出了一种关于单节流孔静压气体止推轴承的节流孔系数的计算方法。该方法通过比较层流边界层方程计算获得的气体轴承的质量流量和雷诺方程计算获得的质量流量计算获得了节流孔系数。将计算获得的节流孔系数和节流孔系数为常数0.8代入单节流孔气体止推轴承的雷诺方程中,计算获得的承载力与分离变量算法求解层流边界层方程获得的承载力进行对比,可以发现,相对于采用节流孔系数为0.8来说,采用该计算的节流孔系数求解雷诺方程的承载力与分离变量算法求解获得的承载力结果精度最大提高了8%。从而验证了该计算节流孔系数方法的正确性。
A calculation method combining the method of separation of variables(MSV)for laminar boundary-layer equations and the analytical solution of Reynolds equation was proposed to study the discharge coefficients of aerostatic bearings.The discharge coefficients were obtained by comparing the mass flow rate obtained by the laminar boundary-layer equations and by Reynolds equation.The bearing capacity from solution of Reynolds equation with the discharge coefficient at the constant 0.8 and laminar boundary-layer equations solved by MSV was studied comparatively.Results showed that the maximum precision of the bearing capacity obtained by the Reynolds equation with the discharge coefficient in this calculation was increased 8%than the bearing capacity from the Reynolds equation with discharge coefficient of 0.8,comparing with the results calculated by MSV.It means that the discharge coefficient is suitable and valid for solution of Reynolds equation.
A calculation method combining the method of separation of variables(MSV)for laminar boundary-layer equations and the analytical solution of Reynolds equation was proposed to study the discharge coefficients of aerostatic bearings.The discharge coefficients were obtained by comparing the mass flow rate obtained by the laminar boundary-layer equations and by Reynolds equation.The bearing capacity from solution of Reynolds equation with the discharge coefficient at the constant 0.8 and laminar boundary-layer equations solved by MSV was studied comparatively.Results showed that the maximum precision of the bearing capacity obtained by the Reynolds equation with the discharge coefficient in this calculation was increased 8%than the bearing capacity from the Reynolds equation with discharge coefficient of 0.8,comparing with the results calculated by MSV.It means that the discharge coefficient is suitable and valid for solution of Reynolds equation.
引文
[1]刘暾,刘育华,陈世杰.静压气体润滑[M].哈尔滨:哈尔滨工业大学出版社,1990.
[2]POWELL J W.Design of aerostatic bearings[M].London:Machinery Publishing,1970.
[3]HAN D,TANG C,HAO L,et al.Experimental studies on the effects of bearing supply gas pressure on the response of a permanent magnet disk-type motor rotor[J].Journal of Mechanical Science and Technology,2016,30(11):4887-4892.
[4]BELFORTE G,RAPARELLI T,VIKTOROV V.Discharge coefficients of orifice-type restrictor for aerostatic bearings[J].Tribology International,2007,40(3):512-521.
[5]LIU Z S,ZHANG G H,XU H J.Performance analysis of rotating externally pressurized air bearings[J].Journal of Engineering Tribology,2009,223(4):653-663.
[6]WANG X,XU Q,WANG B,et al.Numerical calculation of rotation effects on hybrid air journal bearings[J].Tribology Transactions,2016,60(2):195-207.
[7]DAL A,KARAAY T.Effects of angular misalignment on the performance of rotor-bearing systems supported by externally pressurized air bearing[J].Tribology International,2017,111:276-288.
[8]LO C Y,WANG C C,LEE Y H.Performance analysis of high-speed spindle aerostatic bearings[J].Tribology International,2005,38(1):5-14.
[9]MORI H.A theoretical investigation of pressure depression in externally pressurized gas-lubricated circular thrust bearings[J].Journal of Basic Engineering,1961,83(2):201-208.
[10]MORI H,MIYAMATSU Y.Theoretical flow-models for externally pressurized gas bearings[J].Journal of Tribology,1969,91(1):181-193.
[11]YOSHIMOTO S,SUGANUMA N,YAGI K,et al.Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet[J].Journal of Tribology,2007,129(2):384-390.
[12]ELESHAKY M E.CFD investigation of pressure depressions in aerostatic circular thrust bearings[J].Tribology International,2009,42(7):1108-1117.
[13]MIYATAKE M,YOSHIMOTO S.Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes[J].Tribology International,2010,43(8):1353-1359.
[14]NISHIO U,SOMAYA K,YOSHIMOTO S.Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes[J].Tribology International,2011,44(12):1790-1795.
[15]BELFORTE G,RAPARELLI T,TRIVELLA A,et al.CFD analysis of a simple orifice-type feeding system for aerostatic bearings[J].Tribology Letters,2015,58(2):1-8.
[16]CHANG S H,CHAN C W,JENG Y R.Discharge coefficients in aerostatic bearings with inherent orifice-type restrictors[J].Journal of Tribology,2015,137(1):1-7.
[17]CHANG S H,CHAN C W,JENG Y R.Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors[J].Tribology International,2015,90:157-163.
[18]AL-BENDER F,VAN BRUSSEL H.A method of‘separation of variables’for the solution of laminar boundarylayer equations of narrow-channel flows[J].Journal of Tribology,1992,114(3):623-629.
[2]POWELL J W.Design of aerostatic bearings[M].London:Machinery Publishing,1970.
[3]HAN D,TANG C,HAO L,et al.Experimental studies on the effects of bearing supply gas pressure on the response of a permanent magnet disk-type motor rotor[J].Journal of Mechanical Science and Technology,2016,30(11):4887-4892.
[4]BELFORTE G,RAPARELLI T,VIKTOROV V.Discharge coefficients of orifice-type restrictor for aerostatic bearings[J].Tribology International,2007,40(3):512-521.
[5]LIU Z S,ZHANG G H,XU H J.Performance analysis of rotating externally pressurized air bearings[J].Journal of Engineering Tribology,2009,223(4):653-663.
[6]WANG X,XU Q,WANG B,et al.Numerical calculation of rotation effects on hybrid air journal bearings[J].Tribology Transactions,2016,60(2):195-207.
[7]DAL A,KARAAY T.Effects of angular misalignment on the performance of rotor-bearing systems supported by externally pressurized air bearing[J].Tribology International,2017,111:276-288.
[8]LO C Y,WANG C C,LEE Y H.Performance analysis of high-speed spindle aerostatic bearings[J].Tribology International,2005,38(1):5-14.
[9]MORI H.A theoretical investigation of pressure depression in externally pressurized gas-lubricated circular thrust bearings[J].Journal of Basic Engineering,1961,83(2):201-208.
[10]MORI H,MIYAMATSU Y.Theoretical flow-models for externally pressurized gas bearings[J].Journal of Tribology,1969,91(1):181-193.
[11]YOSHIMOTO S,SUGANUMA N,YAGI K,et al.Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet[J].Journal of Tribology,2007,129(2):384-390.
[12]ELESHAKY M E.CFD investigation of pressure depressions in aerostatic circular thrust bearings[J].Tribology International,2009,42(7):1108-1117.
[13]MIYATAKE M,YOSHIMOTO S.Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes[J].Tribology International,2010,43(8):1353-1359.
[14]NISHIO U,SOMAYA K,YOSHIMOTO S.Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes[J].Tribology International,2011,44(12):1790-1795.
[15]BELFORTE G,RAPARELLI T,TRIVELLA A,et al.CFD analysis of a simple orifice-type feeding system for aerostatic bearings[J].Tribology Letters,2015,58(2):1-8.
[16]CHANG S H,CHAN C W,JENG Y R.Discharge coefficients in aerostatic bearings with inherent orifice-type restrictors[J].Journal of Tribology,2015,137(1):1-7.
[17]CHANG S H,CHAN C W,JENG Y R.Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors[J].Tribology International,2015,90:157-163.
[18]AL-BENDER F,VAN BRUSSEL H.A method of‘separation of variables’for the solution of laminar boundarylayer equations of narrow-channel flows[J].Journal of Tribology,1992,114(3):623-629.