超精密气体静压轴系部分关键技术研究
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摘要
气体静压轴系的研究一直是超精密机床研究的重点内容之一,随着气体静压导轨与主轴在超精密机床上的广泛运用,高刚度、高精度、结构简单和阻尼特性良好的静压轴承成为超精密机床轴系设计追求的目标。小孔节流和全多孔质材料节流是气体静压轴承主要的节流形式之一,目前均存在轴承刚度不高和加工制造困难等方面的问题。局部多孔质节流作为一种新的节流方式,结合了小孔节流和全多孔质节流的特点,因而具有简单结构、高刚度和易于制造的特点,且已经受到大家所关注,遗憾的是对这一类型轴承的研究还比较少。另外气体静压轴系回转精度的评价也存在着理论评价体系不完善的缺陷。本论文针对气体静压轴系设计和检测评价方面存在的问题,选择局部多孔质气体静压轴承设计理论和单圈非重复轴系回转精度的测评作为主要的研究内容,具体开展以下研究:
在极薄膜润滑和层流的假设下,基于Beavers-Joseph模型及简化Stokes方程,并考虑轴承交界面处速度滑移影响,推导建立了稳态条件下局部多孔质气体静压轴承气膜压力分布的数学模型,结合由Darcy定律及气体连续性方程建立的多孔质内气体的流动模型,为研究局部多孔质气体静压轴承稳态特性奠定了理论基础。
利用伽辽金原理和格林公式,将局部多孔质气体静压轴承气体流动的数学方程转换为“弱”积分方程。通过有限元数值计算,发现局部多孔质节流器的直径、厚度、渗透系数、个数及位置的分布等参数都会对轴承的静态特性产生重要影响,发现只有按照一定的规律选择合适的参数,轴承才能得到较高的承载能力及刚度。系列的止推轴承实验结果,证明了所建立数学模型及数值求解方法的正确性,同时也证明了局部多孔质气体静压轴承具有更高刚度和易加工等优良特性。
对局部多孔质气体静压轴承气膜压力分布的数学模型进行了数值求解的收敛性研究,提出改进型比例分割法,并给出了比例分割因子G的求解公式,从而较好地解决了有限元方程的收敛性问题。
轴系回转误差广泛具有单圈非重复性的特点,目前的评价理论和评价方法非常有限。针对这个问题建立了轴系回转误差评价的数学模型。提出集合转换的方法,并利用极差极小化原理,分别建立了基于计算机处理的最小区域法和作用表面的统一判别准则。为了提高评价速度,还建立了统一的步长求解公式。编制的算法软件,在实验中已得到了验证,大大提高了误差的评价精度及效率,从而完善了轴系回转精度的测评理论体系。
Study on ultra-precision aerostatic bearing axes system is always one of the major research subjects of ultra-precision machine tools. With the extensive use of aerostatic slideways and spindle in ultra-precision machine tools, aerostatic bearing axes system has become an object to be designed with higher stiffness, higher accuracy, more simple construction and better damping capacity. Orofice restrictor and porous restrictor are one of the main feeding types with which this kind of bearings have such disadvantages as low stiffness and difficult to be made at present. As a new feeding type, partial porous restrictor has the characteristics of orifice restrictor and porous restrictor. Partial porous aerostatic bearing has been concerned for its advantages of simple construction, higher stiffness and easy to be produced. It is a pity that few research works on this kind of bearings have been made. Moreover, there are defects to assess the spindle radial error motions in the appreciation theory. For these problems, the design theory study on partial porous aerostatic bearing and measurement appreciation study on the aperiodic spindle radial error motions in one circle are chose as the main content, in detail as follows:
With the usual assumptions of a thin lubricating film and the isothermal laminar flow conditions, the pressure distribution in the clearance space of an air lubricated partial porous bearing is given by the modified Reynolds equation derived from simplified Navier-Stokes equations satisfying the velocity slip boundary condition, following the Beavers-Joseph slip velocity model. Then the flow motion in the porous media is given by the equations governed by Darcy's law with the equation of continuity. Based on the two nonlinear equations, the theoretical analysis is presented to predict the steady state performance characteristics of partial porous aerostatic bearing.
Galerkin weighted residual method and Green's theorem are used to transform the above two equations into the corresponding weak integral forms. Then by the finite element method, the numerical calculation results show that the parameters have important effect on the static characteristic regularly, including diameter, height, permeability, number, position layout of porous restrictor and so on. Moreover, high load capacity or high stiffness can be achieved by choosing right parameters only according to the rules. By testing serialization partial porous aerostatic thrust bearings prototype workpiece, good agreement is achieved between the results from the present model and the experiment results. The comparison results not only proved that the present mathematical model and the numerical calculation method are valid, but also that there are some advantages of higher stiffness, easy to be made and so on for this kind of bearings.
The convergence is analyzed to obtain the pressure distribution in the clearance space of a partial porous aerostatic bearing during the process of solving the FEM equation. An improved proportional division method and the proportional division factor G are provided to get the true convergent roots during the whole working clearance space.
There are very few methods to appreciate extensively aperiodic spindle error motions. A new appreciation model is provided to asses spindle radial error motions, after the spindle radial error motions set transformed. Based on the minimax theory, the uniform evaluation criterion of Minimum Zone Reference Circles method is then established, and also the effects surface uniform evaluation criterion. Moreover, a uniform step equation is obtained to improved the speed of appreciation. The test of appreciation algorithm has proved that both the appreciation precision and the efficiency are improved greatly. Then the appreciation theory is completed for the spindle radial error motions.
在极薄膜润滑和层流的假设下,基于Beavers-Joseph模型及简化Stokes方程,并考虑轴承交界面处速度滑移影响,推导建立了稳态条件下局部多孔质气体静压轴承气膜压力分布的数学模型,结合由Darcy定律及气体连续性方程建立的多孔质内气体的流动模型,为研究局部多孔质气体静压轴承稳态特性奠定了理论基础。
利用伽辽金原理和格林公式,将局部多孔质气体静压轴承气体流动的数学方程转换为“弱”积分方程。通过有限元数值计算,发现局部多孔质节流器的直径、厚度、渗透系数、个数及位置的分布等参数都会对轴承的静态特性产生重要影响,发现只有按照一定的规律选择合适的参数,轴承才能得到较高的承载能力及刚度。系列的止推轴承实验结果,证明了所建立数学模型及数值求解方法的正确性,同时也证明了局部多孔质气体静压轴承具有更高刚度和易加工等优良特性。
对局部多孔质气体静压轴承气膜压力分布的数学模型进行了数值求解的收敛性研究,提出改进型比例分割法,并给出了比例分割因子G的求解公式,从而较好地解决了有限元方程的收敛性问题。
轴系回转误差广泛具有单圈非重复性的特点,目前的评价理论和评价方法非常有限。针对这个问题建立了轴系回转误差评价的数学模型。提出集合转换的方法,并利用极差极小化原理,分别建立了基于计算机处理的最小区域法和作用表面的统一判别准则。为了提高评价速度,还建立了统一的步长求解公式。编制的算法软件,在实验中已得到了验证,大大提高了误差的评价精度及效率,从而完善了轴系回转精度的测评理论体系。
Study on ultra-precision aerostatic bearing axes system is always one of the major research subjects of ultra-precision machine tools. With the extensive use of aerostatic slideways and spindle in ultra-precision machine tools, aerostatic bearing axes system has become an object to be designed with higher stiffness, higher accuracy, more simple construction and better damping capacity. Orofice restrictor and porous restrictor are one of the main feeding types with which this kind of bearings have such disadvantages as low stiffness and difficult to be made at present. As a new feeding type, partial porous restrictor has the characteristics of orifice restrictor and porous restrictor. Partial porous aerostatic bearing has been concerned for its advantages of simple construction, higher stiffness and easy to be produced. It is a pity that few research works on this kind of bearings have been made. Moreover, there are defects to assess the spindle radial error motions in the appreciation theory. For these problems, the design theory study on partial porous aerostatic bearing and measurement appreciation study on the aperiodic spindle radial error motions in one circle are chose as the main content, in detail as follows:
With the usual assumptions of a thin lubricating film and the isothermal laminar flow conditions, the pressure distribution in the clearance space of an air lubricated partial porous bearing is given by the modified Reynolds equation derived from simplified Navier-Stokes equations satisfying the velocity slip boundary condition, following the Beavers-Joseph slip velocity model. Then the flow motion in the porous media is given by the equations governed by Darcy's law with the equation of continuity. Based on the two nonlinear equations, the theoretical analysis is presented to predict the steady state performance characteristics of partial porous aerostatic bearing.
Galerkin weighted residual method and Green's theorem are used to transform the above two equations into the corresponding weak integral forms. Then by the finite element method, the numerical calculation results show that the parameters have important effect on the static characteristic regularly, including diameter, height, permeability, number, position layout of porous restrictor and so on. Moreover, high load capacity or high stiffness can be achieved by choosing right parameters only according to the rules. By testing serialization partial porous aerostatic thrust bearings prototype workpiece, good agreement is achieved between the results from the present model and the experiment results. The comparison results not only proved that the present mathematical model and the numerical calculation method are valid, but also that there are some advantages of higher stiffness, easy to be made and so on for this kind of bearings.
The convergence is analyzed to obtain the pressure distribution in the clearance space of a partial porous aerostatic bearing during the process of solving the FEM equation. An improved proportional division method and the proportional division factor G are provided to get the true convergent roots during the whole working clearance space.
There are very few methods to appreciate extensively aperiodic spindle error motions. A new appreciation model is provided to asses spindle radial error motions, after the spindle radial error motions set transformed. Based on the minimax theory, the uniform evaluation criterion of Minimum Zone Reference Circles method is then established, and also the effects surface uniform evaluation criterion. Moreover, a uniform step equation is obtained to improved the speed of appreciation. The test of appreciation algorithm has proved that both the appreciation precision and the efficiency are improved greatly. Then the appreciation theory is completed for the spindle radial error motions.
引文
[1]盛伯浩.我国数控机床现况与技术发展策略.制造技术与机床,2006,(2):17-28
[2]刘盛东.航空制造工程手册—机载设备精密加工分册.航空工业出版社,1996.
[3]王云飞.气体润滑理论与气体轴承设计.机械工业出版社,1999:1-3
[4]J.W.POWELL.空气静压轴承设计.北京:国防工业出版社,1978年12月
[5]刘暾,刘育华,陈世杰.静压气体润滑.哈尔滨:哈尔滨工业大学出版社,1990.
[6]杨福兴.高刚度、高精度空气静压轴承静、动态特性的研究:博士学位论文.哈尔滨:哈尔滨工业大学,1995.
[7]杜建军.狭缝节流气体静压轴径止推串接型轴承稳态特性的研究:博士学位论文.哈尔滨:哈尔滨工业大学,2002.
[8]齐乃明.高刚度精密静压气体径向轴承研究:博士学位论文.哈尔滨:哈尔滨工业大学,2001.
[9]潘晋.精密工作台气体静压轴承的研究:博士学位论文.北京:清华大学,1989.
[10]吴起.精密主轴气体静压轴承静、动态性能的研究:博士学位论文.哈尔滨:哈尔滨工业大学,1995.
[11]Keum-Mo KIM,Kyung-Woong KIM.An Analytical study on the Rotational Accuracy of Externally Presssurized Air Journal Bearing.JSME Int.Series Ⅲ,1992,35(3):485-492
[12]Hiroshi YABE.A Study on Run-Out Characteristics of Externallly Pressurized Gas Journal Bearing(Rotor Run-Out Charateristics).JSME Int.Series C,1994,37(2):355-361
[13]Hiroshi YABE.A Study on Run-Out Characteristics of Externallly Pressurized Gas Journal Bearing(Modified DF Method for Point-Source Solution).JSME Int.Series C,1994,371.2):362-368
[14]Shigeka YOSHIMOTO.Yoshiro ANNO and Yasushi HIRAKAWA,Aerostatic Thrust Bearing with a Self-controlled Restrictor Employing a Floating Disk(Static Characteriscics).JSME Int.SeriedC,1994,37(2):369-375
[15]F.A-Bender and H.Van Brussel,Tilt characteristics of circular centrally fed aerostatic bearings,TRIBOLOGY Int.1992,25(3):189-197
[16]D.K.Pal and B.C.Majumdar.Stability analysis of externally-pressurized gas-lubricated porous bearings with journal rotation(Partl.Cylindrical whirl).TRIBOLOGY Int.,1984,117(2):83-91
[17]杜金名,卢泽生.多孔质流体静压轴承润滑技术的研究:博士学位论文.哈尔滨:哈 尔滨工业大学,2003.
[18]蔡久田.小型气体静压主轴系统及其性能研究:硕士学位论文.哈尔滨:哈尔滨工业大学,2004.
[19]Changzhi Cui,Kyosuke Ono.Theoretical and Experimental Investigation of An Externally Pressurized Porous Annular Thrust Gas Bearing and Its Optimal Design.Transaction of the ASME Journal of Tribology,1997,(119):487-492
[20]Krzysztof Cieslicki.Investigations of the Effect of Inertia On Flow of Air Through Porous Bearing Sleeves.Wear,1994,(172):73-78
[21]Anjani Kumar.Conical Whirl Instability of Turbulent Flow Hybrid Porous Journal Bearings.Tribology International,1998,31(5):235-243
[22]Jaw-Ren Lin.Optimal Design of One-dimensional Porous Slider Bearings Using the Brinkman Model.Tribology International,2001,(34):57-64
[23]J.R.Lin,C.C.Hwang.Lubrication of Short Porous Journal Bearings-Use of the Brinkman-extended Darcy Model.Wear,1993,(161):93-104
[24]Abdallah A,Elsharkawy,Lotfi H.Guedouar.Hydrodynamic Lubrication of Porous Journal Bearings Using A Modified Brinkman-extended Darcy Model.Tribology International,2001,(34):767-777
[25]Jaw-RenLin.Squeeze Film Behavior In A Hemispherical Porous Bearing Using the Brinkman Model.Tribology Transactions,Journal of Tribology,1996,39(4):769-778
[26]Y.B.P.Kwan,J.Corbett.A Simplified Method for the Correction of Velocity Slip and Inertial Efects In Porous Aerostatic Thrust Bearings.Tribology International,1998,31(12):779-786
[27]S.P.Liaw,D.G Lin.Sliding Effect of Gas-lubricated Porous Rectangular Thrust Bearings.Wear,1991,(141):235-248
[28]J.L.Gupta,G.M.Deheri.Effect of Roughness On the Behavior of Squeeze Film In a Spherical Bearing.Tribology Transactions,1996,39(1):99-102
[29]Ram Turaga,A.S.Sekhar,B.C.Majumdar.The Effect of Roughness Parameter On the Performance of Hydrodynamic Journal Bearings With Rough Surfaces.Tribology International,1999,(32):231-236
[30]K.Tender.Dynamics of Rough Slider Bearings:Effects of One-sided Roughness/waviness.Tribology International,1996,29(2):117-122
[31]Prakash.K.Gururajan.Effect of Velocity Slip in An Infinitely Long Rough Porous Journal Bearing.Tribology Transactions,1999,42(3):661-667
[32]李兴华.空气静压轴承的静特性计算及其实际应用.同济大学学报,1999,22(1):71-73
[33]李树森,曲全利,张鹏顺.静压气体轴承稳定性计算方法的分析.机械工程师,1999,(5):54-55
[34]程雪梅,陈海滨.一种研究空气静压轴承工作特性的新方法.渝州大学学报(自然科学版),1995,12(3):11-16
[35]徐建民,陈明.边界元方法在研究气体静压轴承特性中的应用.润滑与密封,1997,(3):27-30
[36]刘墩,彭春野,葛卫平,齐乃明,费源明.小孔节流气体静压润滑的离散化和计算收敛.摩擦学学报,2001,21(2):139-142
[37]侯予,熊联友,林明峰,陈纯正.多数供气孔静压环形止推气体轴承的研究.机械设计,1999,(3):38-40
[38]郭良斌,王祖温,包钢,李军.新型环面节流静压气体球轴承动特性分析.中国机械工程,2004,15(23):2069-2073
[39]杜金明,卢泽生,孙雅洲.空气静压轴承各种节流方式的比较.航空精密制造技术,2003,39(6):4-7
[40]T.Nakamura,S.Yoshimoto.Static Tilt Characteristics of Aerostatic Rectangular Double-pad Thrust Bearings with Compound Restrictors.Tribology International,1996,29(2):145-152
[41]S.Yoshimoto,J.Tamura,TNakamura.Dynamic Tilt Characteristics of Aerostatic Rectan gular Double-pad Thrust Bearings with Compound Restrictors.T ribology International,1999,(32):731-738
[42]Jaw-Ren Lin.Static and Dynamic Characteristics of Externally Pressurized Circular Step Thrust Bearings Lubricated with Couple Stress Fluids.Tribology International,1999,(32):207-216
[43]K.Czolczynski.How to obtain stiffness and damping coefficient of gas bearings.Wear,1996,201:265-275
[44]Q.H.Zeng,D.B.Bogy.Stiffness and Damping Evaluation of Air Bearing Sliders and New Designs With High Damping.Journal of Tribology,1999,121:341-347
[45]刘墩,杜建军,姚英学,谢大刚.狭缝节流气体静压润滑方程式的离散化和相容性条件.机械工程学报,2002,38(10):144-148
[46]S.Yoshimoto.Static Characteristics of a Slot-Entry Gas Journal Bearing With Feeding Holes.Journal of Tribology,Trans.ASME,1988,110:587-591
[47]Shigeka YOSHIMOTO etc..Dynamic Properties of Externally-Pressurized Gas Journal Bearings with Circular Slot Restrictors.Bulletin of JSME,1984,27(229),1537-1543
[48]Shigeka YOSHITMOTO.Static Characteristics of an Aerostatic Journal Bearing with Partially Gas-fed Slot Restrictors.Bulletin of JSME,1986,29(252):1907-1912
[49]Shigeka YOSHIMOTO,Yukihisa NAKANO.Stability of a Rigid Rotor supported by Externally Pressurized Gas Journal Bearings with a Circular Slot Restrictor.Bulletin of JSME,1984,27(225):561-569
[50]Hiroshi Y.A.B.E etc..A Study on Angular Stiffness and Damping Properties of Externally Pressurized Gas Thrust Bearing with Surface-restriction Compensation.Bulletin of JSME,1983,26(222):2251-2257
[51]Hiroshi YABE etc..Fundamental Characteristics of an Externally Pressurized Gas-Lubricated Journal Bearing with Surface-restriction Compensation.Bulletin of JSME,1986,29(254):2711-2717
[52]王元勋,景岗,陈尔吕.新型表面节流气体润滑轴承的有限元分析.机床与液压,19 95,(1):16-19
[53]L.Brzeski and Z.Kazimierski.Infinite stiffness gas bearings for precision spindles.Precision Engineering,1992,14(2):105-109
[54]M.Vermeulen,N.Rosielle,P.Schellekens.Dynamic Behavior-Improvement and Miniaturisation of Passively Compensation Aerostatic Bearings.Precision engineering:nanotechnology,Proceedings-volumel(euspen),1999,36-39
[55]Hiroshi MIZUMOTO,Masafumi INOUE.An Ultraprecision Machine Tool using Twist-roller Drives and Active control Aerostatic Guideways.Precision engineering:nanotechnology,Proceedings-volumel(euspen),1999,28-31
[56]水本洋,松原十三生等.自动调整绞り付高刚性空气静压轴受の动特性に关ょゐ研究.精密工学会志,1989,55(9):146-151
[57]水本洋,松原十三生,薄术雅雄等.无限刚性静压气体轴受の开发.精密工学会志,1990,56(8):71-77
[58]#12
[59]#12
[60]刘暾,齐乃明.一种提高静压气体轴承刚度方法的初步分析自主式气体轴承.北京理工大学学报(气体润滑专辑增刊),1993,13(S1):52-55
[61]水本洋,田中久隆,奥野胜则等.排气制御绞りにょゐ空气静压轴受の无限刚性化.精密工学会志,1991,57(11):164-169
[62]S.Yoshimoto.A aerostatic thrust bearing with a stiffness of 1 N nm-1.Nanotechnology,1996,(7):52-57
[63]Y.B.P.Kwan,J.Corbett.Porous aerostatic bearings-an updated review.Wear,1998,222:69-73
[64]杜金明,田春祥.多孔质静压轴承概述.润滑与密封,2006,175(3):170-174
[65]侯予,熊联友等.国外多孔质静压气体轴颈轴承理论分析的发展.润滑与密封,1998,(1):62-65
[66]H.J.Sneck.A survey of gas-lubricated porous bearings.ASME Journal of Lubrication Technology,1968,90:804-809
[67]Ishizawa S,Hori E.The Flow of a Viscous Fluid through a PorousWall into a Narrow Gap.Bul.JSME,1966,9(36):810-817
[68]Y.B.P.Kwan and J.Corbett.A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearing.Tribology Instrumental,1998,31(12):779-786
[69]Jaw-Ren Lin,Chi-Chuan Hwang,Rong-Fuh Yang.Hydrodynamic lubrication of long,flexible,porous journal bearings using the Brinkman model.Wear,1996,198:156-164
[70]T.S.Luong,W.Potze,J.B.Post,R.A.J.van Ostayen,A.van Beek.Numerical and experimental analysis of aerostatic thrust bearings with porous restrictors.Tribology International,2004,37:825-832
[71]K.C.Singh,N.S.Rao,B.C.Majumdar.Hybrid Porous Gas Journal Bearings:Steady State Solution Incorporating the Effect of Velocity Slip.Transactions of the ASME,1984,106:322-328
[72]Y.Mitsuya,Stokes Roughness Effects on Hydrodynamic Lubrication,Part Ⅱ-Effects Under Slip Flow Boundary Conditions.Tribology,1986,108:159-166
[73]K.C.Singh,N.S.Rao,B.C.Majumdar.Effect of Slip Flow on the Steady-State Performance of Aerostatic Porous Journal Bearings.Tribology,1984,106:156-161
[74]Mongomery A G,Sterry F.A Simple AirBearing Rotor forVery High Rotation Speeds. AERE1 ED/R 1671 Harwell, Berkshire, England, 1955
[75] Sheinberg S A, ShusterVG. Resistance to vibration of hydrostatic thrust bearing. Machine Tool, 1960, 31(11): 24-291
[76] Mori H, Yabe H, Ono T. Theory of externally pressurized circular thrust bearings.Trans. ASME, Journal of Basic Tech, 1965, (9): 613—621
[77] Garguilo E P, Gilmour P W. A Numerical Solution for the Design of Externally Pressurized Porous Gas Bearings. Thrust Bearings, Trans. ASME Journal Lub Tech, 1968(10): 810—817
[78] G. S. Beavers and D. D. Joseph. Boundary condition at a naturally permeable wall. J. Fluid Mech, 1967, 30(1): 197-207
[79] G. S. Beavers, E. M. Sparrow and R. A. Magnuson. Experiments on couple parallel flows in a channel and a bounding porous medium. J. Basic Eng. , 1970, 92(4): 843—848
[80] G. I.Taylor. A model for the boundary condition of a porous material, part I. J. Fluid Mech, 1971, 49(Part II): 319-326
[81] S. Richardson. A model for the boundary condition of a porous material, part 2. J. Fluid Mech, 1971, 49(Part II): 327-336
[82] P. G. Saffman. On the boundary conditions at the surface of a porous medium. Stud. Appl. Math, 1971, 50(2): 93-101
[83] G. S. Beavers, E. M. Sparrow and B.A.Masha. Boundary conditions at a porous surface which bounds a fluid flow. AICHEJ. , 1974, 20(3): 596-597
[84] E. M. Sparrow, G. S. Beavers and I. T. Hwang. Effect of velocity slip on porous walled squeeze films. J. Lubr. Technol. , 1972, 94(3): 260-265
[85] K. C. Sing, N. S. Rao and B. C. Majumdar. Effect of slip folw on the steady state performance of aerostatic porous journal bearings. J. Tribol. , 1984, 106(1): 156—162
[86] M.Malik, R. Sinhasan, M.Chandra. Finite-element analysis of a porous slider. Wear,1983, 76(1): 1-13
[87] S. M. Robde, K. P. Oh. Higher order finite element methods for the solution of compressible porous bearing problems. Int. Numerical Methods Eng. , 1975, 9: 903—911
[88] Yong Tian. Static study of the porous bearings by the simplified finite element analysis.Wear, 1998, 218: 203-209.
[89] Majudar B C, Schmidt J. Design of Externally Pressurized Rectangular Porous Thrust Bearings. Wear, 1975, 32: 1—8
[90] Rao N S. Effect of slip flow in aerostatic porous rectangular thrust bearings. Wear, 1980,61: 77-86
[91] Rao N S. Analysis of Aerostatic Porous Rectangular Thrust Bearings with Offset Loads Wear. 1980, 59: 333-344
[92] S. P. Liaw and D. G. Lin, Sliding effect of gas-lubricated porous rectangular thrust bearings.Wear, 1991, 141: 236-248
[93] A. K. Mishra. Analysis of Pneumatic Instability of An aerostatic Rectangular Thrust Bearing with Offset Load. Wear, 1988, 122: 1 — 12
[94] Yaw-Dong Shih and Jang-Yih Yang. Analysis of narrow rectangular aerostatic porous thrust bearings moving with a uniform transverse velocity. Wear, 1990, 141: 125 — 136
[95] Gorez R. A Study of the Stability of Externally Pressurized Gas Bearings with Porous Wall by Liapunov's Direct Method. Trans ASME Journal Lubrication Technology, 1973, 95(4):204-207
[96] Dah-Chen Sun. Stability Analysis of an Externally Pressurized Gas-Lubricated Porous Thrust Bearing. Trans ASME Journal Lubrication Technology, 1973, 95(10): 457—468
[97] Dah-Chen Sun. On the Stability of Gas-lubricated Porous Thrust Bearings. Trans ASME Journal Lubrication Technology, 1975, 97(4): 332—334
[98] Gorez R, Szwarcman M. Externally Pressurized Gas Bearings with Partialiy PorousWall.16 th International GasBearing Symp At University of Southamp ton (U1K), March 1974,Paper C7: 89-102
[99] Taylor R, Lewis G K. The Dynamic Performance of Aerostatic Porous Thrust Bearings with Uniform Films. 7 th Int. Gas Bearing Symp At Churchill College, Cambridge, England,July 1976, Paper A4: 49-66
[100] Taylor R. A Numerical Solution of the Dynamic Characteristics of an Aerostatic, Porous Thrust Bearing having a Uniform Film Subject to Linear Axial Load Variations. I. Mech E,Journal Mech Eng. (Sci), 1977, 19(3): 122-127
[101] S.Yoshimoto, K. Kohno. Static and Dynamic Characteristics of Aerostatic Circular Porous Thrust Bearings. Journal of Tribology, 2001, 123: 501—508
[102] M. C. Majumder. Study Of the Pneumatic Instablity Of Externally Pressurized Porous Gas Thrust Bearings with Slip Velocity. Wear, 1988, 124: 261—277
[103] S. K. Ghua, N.S.Rao, B. C. Majumdar. Study of Conical Whirl Instability of Self-Acting Porous Gas Journal Bearings Considering Tangential Velocity Slip. Tribology, 1988, 110: 139-143
[104] C. H. Robinson and F. Sterry. The static strength of pressure fed gas journal bearings.AERE ED/R 1672, 1958 Atomic Energy Research Establishment, Harwell
[105] H. S. Chang, Z. S. Wang and D. C. Sun. An experimental investigation of the stability of externally pressurized gas lubricated porous thrust bearings. J. Lubr. Technol. , 1983, 105:630-637
[106] Gang Lin, Tojiro Aoyama, Ichiro Inasaki31(5). A Computer Simulation Method For Dynamic and Stablity Analysis of Air Bearings. Wear, 1988, 126: 307—319
[107] Mohamed Fourka, Marc Bonics. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems. Wear, 1997, 210: 311—317
[108] SCHEIDEGGER A E. The Physics of Flow Through Porous Media. 3rd ed. [s. I.]:University of Toronto Press, 1974.
[109] MEI C C, AUR1AUL T J L. The effect of weak inertia on flow through a porous medium.J. Fluid Mech, 1991(222): 647-663
[110] Donaldson I S. Patterson E BISome Experiments on Plain Externally Pressurized Air Bearings with Porous Inserts at Supply Pressures up to 311MN /m. 1st Gas Bearing Sympl At University of Southampton (U1K), March 1971, 26: 1—8
[111] Donaldson IS, Patterson E B. The Use of Porous Inserts in Plain Externally Pressurized Air Thrust Bearings at High Supply Pressures. 16th Int. Gas Bearing Sympl. At University of Southampton, March 1974, Paper C6: 75—88
[112] Mc Grea R J, Donaldson I S. The Significance of Fluid Inertial and Slip Velocity in the Steady State Analysis of Externally Pressurized Gas-Lubricated Partially Porous Thrust bearing. 17 th Int Gas Bearing Symp. , July 13-15, 1976, paper A1:1—20
[113] Murti P R K. Analysis of Externally Pressurized Gas Porous Bearings. Trans. ASME Journal of Lub. Tech., 1974, 94(7): 354—360
[114] Murti P R K. Effect of Velocity Slip in an Externally Pressurized Porous Thrust Bearing Working with an Incompressible Fluid. Trans. ASME Journal of Lubrication Technology,1976, 96(9): 404-408
[115] Mohamed Fourka, Marc Bonics. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems. Wear, 1997, 210: 311—317
[116] J Corbett.R J Almond, DJ Stephenson.et al. . Porous ceramic water bearings for improved for accuracy performance. Annals. of the CIRP, 47: 467—470
[117]卢泽生,杜金明,孙雅洲.气体静压多孔质球面轴承静态性能分析.机械工程学报,2004,40(12):115-119
[118]严晖,黄协清,顾崇衔.关于“主轴回转轴线”定义的探讨.振动与动态测试,1982,(6):14-15
[119]蔡鹤皋,赵天开.关于主轴回转运动基本概念问题的初步探讨.振动与动态测试,1983,(1):4-5
[120]严晖,顾崇衔.再论主轴回转轴线.振动与动态测试,1983,(4):26-27
[121]黄伯文,尹苟保,刘桂秋.高精度车床主轴回转误差运动数字式测量方法.精密机床动态检测与精度控制论文选集,1987,55-64
[122]李均.回转轴径向误差运动测量中标准球安装偏心的影响.精密机床动态检测与精度控制论文选集,1987,65-70
[123]黄长征.超精密车床主轴回转误差运动动态测试系统研究:硕士学位论文.长沙:国防科技大学,2001.
[124]王建敏.动力调谐陀螺仪驱动轴圆跳动动态测试研究:硕士学位论文.长沙:国防科技大学,2002.
[125]凌文玉.两传感器误差分离技术的原理与误芳分析.国防科技大学精密机床动态检测与精度控制论文选集,1987,81-92
[126]谭深.三点法测量圆度、轴跳动数据处理方法的商椎.振动与动态测试,1986,(1):3-6
[127]李均,戴瀛洲,袁洪祥.在线圆度测量装置.仪器仪表学报,国防科技大学精密机床动态检测与精度控制论文选集,1987,71-80
[128]戴瀛洲.关于三传感器测圆度的若干问题.振动与动态测试,1986,(1):6-10
[129]袁洪祥,李均,张峰等.超精密加工中的圆度在线测量与补偿技术.国防科技大学精密机床动态检测与精度控制论文选集,1987,119-131
[130]青木保雄,大园成夫.三点法圆度测量方法的研究.精密机械(日文),1966,32(12)
[131]大园成夫.三点法圆度测量.机械研究(日文),1981,(1):193-198
[132]青木保雄,大园成夫.三点法圆度测量机.机械研究(日文),1978,30(6):753-759
[133]李济顺,洪迈生.三点法圆度误差分离的近似方法及精度分析.计量技术,1998,(2):8-11
[134]张宇华,王晓林.三点法圆度测量精度分析.光学精密工程,1998,6(4):127-131
[135]王宝玉.三点法分离工件圆度误差与轴系径向运动误差数据处理的儿个问题.振动与动态测试,1986,(6):30-32
[136]Wei Gao,Satoshi Kiyono,Tadatoshi Nomura.A new multiprobe method of roundness measurements.Precision Engineering,1996,19(1):37-45
[137]T.Hatsuzawa.Automatic centring system for a roundness tester using force feedback techniques.Precision Engineering,1988,10(1):19-23
[138]张宇华,王晓琳,张国雄,李真.多点法圆度及轴系误差分离方法的若干问题.北京理工大学学报,1999,19(3)
[139]Wei Gao.Satoshi Kiyono and Takamitu Sugawara,High-accuracy roundness measurement by a new error separation method.Precision Engineering,1997,21:123-133
[140]三井公之.精度诊断技术的研究(三点式主轴回转精度测量装置的开发).日本机械学会论文集,1982,(1):115-122
[141]肖怀.三点测圆法形状失真向题的研究.吉林工业大学学报,1983,3
[142]赵维谦,谭久彬,扬文国,张杰.基于两步法超精密圆度仪误差分离系统.中国机械工程,2000,11(11):1206-1208
[143]许晓桢.机床主轴回转精度的动态法测量.郑州纺织工学院学报,1998,9(2):68-71
[144]INTERNATIONALSTANDARDISO/FDIS230-7:2005(E)
[145]熊有伦.精密测量的数学方法.北京:中国计量出版社,1989.
[146]曹麟祥,王丙甲.圆度检测技术.北京:国防工业出版社,1998.
[147]刘立邦、刘健.内、外接圆法评定圆度误差的快速电算法.计量技术,1991,(3):1-3
[148]扬雪,张英芝.最小条件求圆皮误差值的快速电算法.计量技术,2001,(3):5-6
[149]N.Cho,J.Tu.Roundness modeling of machined parts for tolerance analysis.Precision Engineering,2001,25:35-47
[150]Jay F.Tu,and Spring C.C.Hung.Modeling and error analysis for assessing spindle radial error motions.Precision Engineering,1997,21:90-101
[151]Shoji Noguchi,Tadao Tsukada and Atsushi Sakamoto.Evaluation method to determine radial accuracy of high-precision rotating spindle units.Precision Engineering,1995,17(4):266-273
[152]曹麟祥,邵大钟.圆度、圆柱度和同轴度的测量原理及数据处理的解析方法.机械工程学报,1983,19(1):86-95
[153]柴琳,胡光,李振芳.机床主轴回转精度测量数量处理的研究.西安公路交通大学学报,1998,18(2):81-84
[154]JENS W.Dynamics of system of rigid bodies.Stuttgart:Teubner,1977.
[155]王勖成,邵敏.有限单元法基本原理和数值方法.北京:清华大学出版社,1997:1-15
[156]邱吉宝.加权残值法的理论与应用.北京:宇航出版社,1991:164-195
[157]O.C.监凯维奇(著),尹泽勇,柴家振(译).有限元法(下).北京:科学出版社,1985:808-809
[158]彭旭麟,罗汝梅.变分法及其应用.武昌:华中工学院出版社,1983:35-42,136-148
[159]饶寿期.有限元法和边界元法基础.北京:航空航天大学出版社,1990:99-102
[160]李大潜等.有限元素法续讲.北京:科学出版社,1979:40-45
[161]程学梅,陈海斌,张显全.空气静压轴承工作特性的有限元分析.渝州大学学报(自然科学版),1996,13(3):18-24
[2]刘盛东.航空制造工程手册—机载设备精密加工分册.航空工业出版社,1996.
[3]王云飞.气体润滑理论与气体轴承设计.机械工业出版社,1999:1-3
[4]J.W.POWELL.空气静压轴承设计.北京:国防工业出版社,1978年12月
[5]刘暾,刘育华,陈世杰.静压气体润滑.哈尔滨:哈尔滨工业大学出版社,1990.
[6]杨福兴.高刚度、高精度空气静压轴承静、动态特性的研究:博士学位论文.哈尔滨:哈尔滨工业大学,1995.
[7]杜建军.狭缝节流气体静压轴径止推串接型轴承稳态特性的研究:博士学位论文.哈尔滨:哈尔滨工业大学,2002.
[8]齐乃明.高刚度精密静压气体径向轴承研究:博士学位论文.哈尔滨:哈尔滨工业大学,2001.
[9]潘晋.精密工作台气体静压轴承的研究:博士学位论文.北京:清华大学,1989.
[10]吴起.精密主轴气体静压轴承静、动态性能的研究:博士学位论文.哈尔滨:哈尔滨工业大学,1995.
[11]Keum-Mo KIM,Kyung-Woong KIM.An Analytical study on the Rotational Accuracy of Externally Presssurized Air Journal Bearing.JSME Int.Series Ⅲ,1992,35(3):485-492
[12]Hiroshi YABE.A Study on Run-Out Characteristics of Externallly Pressurized Gas Journal Bearing(Rotor Run-Out Charateristics).JSME Int.Series C,1994,37(2):355-361
[13]Hiroshi YABE.A Study on Run-Out Characteristics of Externallly Pressurized Gas Journal Bearing(Modified DF Method for Point-Source Solution).JSME Int.Series C,1994,371.2):362-368
[14]Shigeka YOSHIMOTO.Yoshiro ANNO and Yasushi HIRAKAWA,Aerostatic Thrust Bearing with a Self-controlled Restrictor Employing a Floating Disk(Static Characteriscics).JSME Int.SeriedC,1994,37(2):369-375
[15]F.A-Bender and H.Van Brussel,Tilt characteristics of circular centrally fed aerostatic bearings,TRIBOLOGY Int.1992,25(3):189-197
[16]D.K.Pal and B.C.Majumdar.Stability analysis of externally-pressurized gas-lubricated porous bearings with journal rotation(Partl.Cylindrical whirl).TRIBOLOGY Int.,1984,117(2):83-91
[17]杜金名,卢泽生.多孔质流体静压轴承润滑技术的研究:博士学位论文.哈尔滨:哈 尔滨工业大学,2003.
[18]蔡久田.小型气体静压主轴系统及其性能研究:硕士学位论文.哈尔滨:哈尔滨工业大学,2004.
[19]Changzhi Cui,Kyosuke Ono.Theoretical and Experimental Investigation of An Externally Pressurized Porous Annular Thrust Gas Bearing and Its Optimal Design.Transaction of the ASME Journal of Tribology,1997,(119):487-492
[20]Krzysztof Cieslicki.Investigations of the Effect of Inertia On Flow of Air Through Porous Bearing Sleeves.Wear,1994,(172):73-78
[21]Anjani Kumar.Conical Whirl Instability of Turbulent Flow Hybrid Porous Journal Bearings.Tribology International,1998,31(5):235-243
[22]Jaw-Ren Lin.Optimal Design of One-dimensional Porous Slider Bearings Using the Brinkman Model.Tribology International,2001,(34):57-64
[23]J.R.Lin,C.C.Hwang.Lubrication of Short Porous Journal Bearings-Use of the Brinkman-extended Darcy Model.Wear,1993,(161):93-104
[24]Abdallah A,Elsharkawy,Lotfi H.Guedouar.Hydrodynamic Lubrication of Porous Journal Bearings Using A Modified Brinkman-extended Darcy Model.Tribology International,2001,(34):767-777
[25]Jaw-RenLin.Squeeze Film Behavior In A Hemispherical Porous Bearing Using the Brinkman Model.Tribology Transactions,Journal of Tribology,1996,39(4):769-778
[26]Y.B.P.Kwan,J.Corbett.A Simplified Method for the Correction of Velocity Slip and Inertial Efects In Porous Aerostatic Thrust Bearings.Tribology International,1998,31(12):779-786
[27]S.P.Liaw,D.G Lin.Sliding Effect of Gas-lubricated Porous Rectangular Thrust Bearings.Wear,1991,(141):235-248
[28]J.L.Gupta,G.M.Deheri.Effect of Roughness On the Behavior of Squeeze Film In a Spherical Bearing.Tribology Transactions,1996,39(1):99-102
[29]Ram Turaga,A.S.Sekhar,B.C.Majumdar.The Effect of Roughness Parameter On the Performance of Hydrodynamic Journal Bearings With Rough Surfaces.Tribology International,1999,(32):231-236
[30]K.Tender.Dynamics of Rough Slider Bearings:Effects of One-sided Roughness/waviness.Tribology International,1996,29(2):117-122
[31]Prakash.K.Gururajan.Effect of Velocity Slip in An Infinitely Long Rough Porous Journal Bearing.Tribology Transactions,1999,42(3):661-667
[32]李兴华.空气静压轴承的静特性计算及其实际应用.同济大学学报,1999,22(1):71-73
[33]李树森,曲全利,张鹏顺.静压气体轴承稳定性计算方法的分析.机械工程师,1999,(5):54-55
[34]程雪梅,陈海滨.一种研究空气静压轴承工作特性的新方法.渝州大学学报(自然科学版),1995,12(3):11-16
[35]徐建民,陈明.边界元方法在研究气体静压轴承特性中的应用.润滑与密封,1997,(3):27-30
[36]刘墩,彭春野,葛卫平,齐乃明,费源明.小孔节流气体静压润滑的离散化和计算收敛.摩擦学学报,2001,21(2):139-142
[37]侯予,熊联友,林明峰,陈纯正.多数供气孔静压环形止推气体轴承的研究.机械设计,1999,(3):38-40
[38]郭良斌,王祖温,包钢,李军.新型环面节流静压气体球轴承动特性分析.中国机械工程,2004,15(23):2069-2073
[39]杜金明,卢泽生,孙雅洲.空气静压轴承各种节流方式的比较.航空精密制造技术,2003,39(6):4-7
[40]T.Nakamura,S.Yoshimoto.Static Tilt Characteristics of Aerostatic Rectangular Double-pad Thrust Bearings with Compound Restrictors.Tribology International,1996,29(2):145-152
[41]S.Yoshimoto,J.Tamura,TNakamura.Dynamic Tilt Characteristics of Aerostatic Rectan gular Double-pad Thrust Bearings with Compound Restrictors.T ribology International,1999,(32):731-738
[42]Jaw-Ren Lin.Static and Dynamic Characteristics of Externally Pressurized Circular Step Thrust Bearings Lubricated with Couple Stress Fluids.Tribology International,1999,(32):207-216
[43]K.Czolczynski.How to obtain stiffness and damping coefficient of gas bearings.Wear,1996,201:265-275
[44]Q.H.Zeng,D.B.Bogy.Stiffness and Damping Evaluation of Air Bearing Sliders and New Designs With High Damping.Journal of Tribology,1999,121:341-347
[45]刘墩,杜建军,姚英学,谢大刚.狭缝节流气体静压润滑方程式的离散化和相容性条件.机械工程学报,2002,38(10):144-148
[46]S.Yoshimoto.Static Characteristics of a Slot-Entry Gas Journal Bearing With Feeding Holes.Journal of Tribology,Trans.ASME,1988,110:587-591
[47]Shigeka YOSHIMOTO etc..Dynamic Properties of Externally-Pressurized Gas Journal Bearings with Circular Slot Restrictors.Bulletin of JSME,1984,27(229),1537-1543
[48]Shigeka YOSHITMOTO.Static Characteristics of an Aerostatic Journal Bearing with Partially Gas-fed Slot Restrictors.Bulletin of JSME,1986,29(252):1907-1912
[49]Shigeka YOSHIMOTO,Yukihisa NAKANO.Stability of a Rigid Rotor supported by Externally Pressurized Gas Journal Bearings with a Circular Slot Restrictor.Bulletin of JSME,1984,27(225):561-569
[50]Hiroshi Y.A.B.E etc..A Study on Angular Stiffness and Damping Properties of Externally Pressurized Gas Thrust Bearing with Surface-restriction Compensation.Bulletin of JSME,1983,26(222):2251-2257
[51]Hiroshi YABE etc..Fundamental Characteristics of an Externally Pressurized Gas-Lubricated Journal Bearing with Surface-restriction Compensation.Bulletin of JSME,1986,29(254):2711-2717
[52]王元勋,景岗,陈尔吕.新型表面节流气体润滑轴承的有限元分析.机床与液压,19 95,(1):16-19
[53]L.Brzeski and Z.Kazimierski.Infinite stiffness gas bearings for precision spindles.Precision Engineering,1992,14(2):105-109
[54]M.Vermeulen,N.Rosielle,P.Schellekens.Dynamic Behavior-Improvement and Miniaturisation of Passively Compensation Aerostatic Bearings.Precision engineering:nanotechnology,Proceedings-volumel(euspen),1999,36-39
[55]Hiroshi MIZUMOTO,Masafumi INOUE.An Ultraprecision Machine Tool using Twist-roller Drives and Active control Aerostatic Guideways.Precision engineering:nanotechnology,Proceedings-volumel(euspen),1999,28-31
[56]水本洋,松原十三生等.自动调整绞り付高刚性空气静压轴受の动特性に关ょゐ研究.精密工学会志,1989,55(9):146-151
[57]水本洋,松原十三生,薄术雅雄等.无限刚性静压气体轴受の开发.精密工学会志,1990,56(8):71-77
[58]#12
[59]#12
[60]刘暾,齐乃明.一种提高静压气体轴承刚度方法的初步分析自主式气体轴承.北京理工大学学报(气体润滑专辑增刊),1993,13(S1):52-55
[61]水本洋,田中久隆,奥野胜则等.排气制御绞りにょゐ空气静压轴受の无限刚性化.精密工学会志,1991,57(11):164-169
[62]S.Yoshimoto.A aerostatic thrust bearing with a stiffness of 1 N nm-1.Nanotechnology,1996,(7):52-57
[63]Y.B.P.Kwan,J.Corbett.Porous aerostatic bearings-an updated review.Wear,1998,222:69-73
[64]杜金明,田春祥.多孔质静压轴承概述.润滑与密封,2006,175(3):170-174
[65]侯予,熊联友等.国外多孔质静压气体轴颈轴承理论分析的发展.润滑与密封,1998,(1):62-65
[66]H.J.Sneck.A survey of gas-lubricated porous bearings.ASME Journal of Lubrication Technology,1968,90:804-809
[67]Ishizawa S,Hori E.The Flow of a Viscous Fluid through a PorousWall into a Narrow Gap.Bul.JSME,1966,9(36):810-817
[68]Y.B.P.Kwan and J.Corbett.A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearing.Tribology Instrumental,1998,31(12):779-786
[69]Jaw-Ren Lin,Chi-Chuan Hwang,Rong-Fuh Yang.Hydrodynamic lubrication of long,flexible,porous journal bearings using the Brinkman model.Wear,1996,198:156-164
[70]T.S.Luong,W.Potze,J.B.Post,R.A.J.van Ostayen,A.van Beek.Numerical and experimental analysis of aerostatic thrust bearings with porous restrictors.Tribology International,2004,37:825-832
[71]K.C.Singh,N.S.Rao,B.C.Majumdar.Hybrid Porous Gas Journal Bearings:Steady State Solution Incorporating the Effect of Velocity Slip.Transactions of the ASME,1984,106:322-328
[72]Y.Mitsuya,Stokes Roughness Effects on Hydrodynamic Lubrication,Part Ⅱ-Effects Under Slip Flow Boundary Conditions.Tribology,1986,108:159-166
[73]K.C.Singh,N.S.Rao,B.C.Majumdar.Effect of Slip Flow on the Steady-State Performance of Aerostatic Porous Journal Bearings.Tribology,1984,106:156-161
[74]Mongomery A G,Sterry F.A Simple AirBearing Rotor forVery High Rotation Speeds. AERE1 ED/R 1671 Harwell, Berkshire, England, 1955
[75] Sheinberg S A, ShusterVG. Resistance to vibration of hydrostatic thrust bearing. Machine Tool, 1960, 31(11): 24-291
[76] Mori H, Yabe H, Ono T. Theory of externally pressurized circular thrust bearings.Trans. ASME, Journal of Basic Tech, 1965, (9): 613—621
[77] Garguilo E P, Gilmour P W. A Numerical Solution for the Design of Externally Pressurized Porous Gas Bearings. Thrust Bearings, Trans. ASME Journal Lub Tech, 1968(10): 810—817
[78] G. S. Beavers and D. D. Joseph. Boundary condition at a naturally permeable wall. J. Fluid Mech, 1967, 30(1): 197-207
[79] G. S. Beavers, E. M. Sparrow and R. A. Magnuson. Experiments on couple parallel flows in a channel and a bounding porous medium. J. Basic Eng. , 1970, 92(4): 843—848
[80] G. I.Taylor. A model for the boundary condition of a porous material, part I. J. Fluid Mech, 1971, 49(Part II): 319-326
[81] S. Richardson. A model for the boundary condition of a porous material, part 2. J. Fluid Mech, 1971, 49(Part II): 327-336
[82] P. G. Saffman. On the boundary conditions at the surface of a porous medium. Stud. Appl. Math, 1971, 50(2): 93-101
[83] G. S. Beavers, E. M. Sparrow and B.A.Masha. Boundary conditions at a porous surface which bounds a fluid flow. AICHEJ. , 1974, 20(3): 596-597
[84] E. M. Sparrow, G. S. Beavers and I. T. Hwang. Effect of velocity slip on porous walled squeeze films. J. Lubr. Technol. , 1972, 94(3): 260-265
[85] K. C. Sing, N. S. Rao and B. C. Majumdar. Effect of slip folw on the steady state performance of aerostatic porous journal bearings. J. Tribol. , 1984, 106(1): 156—162
[86] M.Malik, R. Sinhasan, M.Chandra. Finite-element analysis of a porous slider. Wear,1983, 76(1): 1-13
[87] S. M. Robde, K. P. Oh. Higher order finite element methods for the solution of compressible porous bearing problems. Int. Numerical Methods Eng. , 1975, 9: 903—911
[88] Yong Tian. Static study of the porous bearings by the simplified finite element analysis.Wear, 1998, 218: 203-209.
[89] Majudar B C, Schmidt J. Design of Externally Pressurized Rectangular Porous Thrust Bearings. Wear, 1975, 32: 1—8
[90] Rao N S. Effect of slip flow in aerostatic porous rectangular thrust bearings. Wear, 1980,61: 77-86
[91] Rao N S. Analysis of Aerostatic Porous Rectangular Thrust Bearings with Offset Loads Wear. 1980, 59: 333-344
[92] S. P. Liaw and D. G. Lin, Sliding effect of gas-lubricated porous rectangular thrust bearings.Wear, 1991, 141: 236-248
[93] A. K. Mishra. Analysis of Pneumatic Instability of An aerostatic Rectangular Thrust Bearing with Offset Load. Wear, 1988, 122: 1 — 12
[94] Yaw-Dong Shih and Jang-Yih Yang. Analysis of narrow rectangular aerostatic porous thrust bearings moving with a uniform transverse velocity. Wear, 1990, 141: 125 — 136
[95] Gorez R. A Study of the Stability of Externally Pressurized Gas Bearings with Porous Wall by Liapunov's Direct Method. Trans ASME Journal Lubrication Technology, 1973, 95(4):204-207
[96] Dah-Chen Sun. Stability Analysis of an Externally Pressurized Gas-Lubricated Porous Thrust Bearing. Trans ASME Journal Lubrication Technology, 1973, 95(10): 457—468
[97] Dah-Chen Sun. On the Stability of Gas-lubricated Porous Thrust Bearings. Trans ASME Journal Lubrication Technology, 1975, 97(4): 332—334
[98] Gorez R, Szwarcman M. Externally Pressurized Gas Bearings with Partialiy PorousWall.16 th International GasBearing Symp At University of Southamp ton (U1K), March 1974,Paper C7: 89-102
[99] Taylor R, Lewis G K. The Dynamic Performance of Aerostatic Porous Thrust Bearings with Uniform Films. 7 th Int. Gas Bearing Symp At Churchill College, Cambridge, England,July 1976, Paper A4: 49-66
[100] Taylor R. A Numerical Solution of the Dynamic Characteristics of an Aerostatic, Porous Thrust Bearing having a Uniform Film Subject to Linear Axial Load Variations. I. Mech E,Journal Mech Eng. (Sci), 1977, 19(3): 122-127
[101] S.Yoshimoto, K. Kohno. Static and Dynamic Characteristics of Aerostatic Circular Porous Thrust Bearings. Journal of Tribology, 2001, 123: 501—508
[102] M. C. Majumder. Study Of the Pneumatic Instablity Of Externally Pressurized Porous Gas Thrust Bearings with Slip Velocity. Wear, 1988, 124: 261—277
[103] S. K. Ghua, N.S.Rao, B. C. Majumdar. Study of Conical Whirl Instability of Self-Acting Porous Gas Journal Bearings Considering Tangential Velocity Slip. Tribology, 1988, 110: 139-143
[104] C. H. Robinson and F. Sterry. The static strength of pressure fed gas journal bearings.AERE ED/R 1672, 1958 Atomic Energy Research Establishment, Harwell
[105] H. S. Chang, Z. S. Wang and D. C. Sun. An experimental investigation of the stability of externally pressurized gas lubricated porous thrust bearings. J. Lubr. Technol. , 1983, 105:630-637
[106] Gang Lin, Tojiro Aoyama, Ichiro Inasaki31(5). A Computer Simulation Method For Dynamic and Stablity Analysis of Air Bearings. Wear, 1988, 126: 307—319
[107] Mohamed Fourka, Marc Bonics. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems. Wear, 1997, 210: 311—317
[108] SCHEIDEGGER A E. The Physics of Flow Through Porous Media. 3rd ed. [s. I.]:University of Toronto Press, 1974.
[109] MEI C C, AUR1AUL T J L. The effect of weak inertia on flow through a porous medium.J. Fluid Mech, 1991(222): 647-663
[110] Donaldson I S. Patterson E BISome Experiments on Plain Externally Pressurized Air Bearings with Porous Inserts at Supply Pressures up to 311MN /m. 1st Gas Bearing Sympl At University of Southampton (U1K), March 1971, 26: 1—8
[111] Donaldson IS, Patterson E B. The Use of Porous Inserts in Plain Externally Pressurized Air Thrust Bearings at High Supply Pressures. 16th Int. Gas Bearing Sympl. At University of Southampton, March 1974, Paper C6: 75—88
[112] Mc Grea R J, Donaldson I S. The Significance of Fluid Inertial and Slip Velocity in the Steady State Analysis of Externally Pressurized Gas-Lubricated Partially Porous Thrust bearing. 17 th Int Gas Bearing Symp. , July 13-15, 1976, paper A1:1—20
[113] Murti P R K. Analysis of Externally Pressurized Gas Porous Bearings. Trans. ASME Journal of Lub. Tech., 1974, 94(7): 354—360
[114] Murti P R K. Effect of Velocity Slip in an Externally Pressurized Porous Thrust Bearing Working with an Incompressible Fluid. Trans. ASME Journal of Lubrication Technology,1976, 96(9): 404-408
[115] Mohamed Fourka, Marc Bonics. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems. Wear, 1997, 210: 311—317
[116] J Corbett.R J Almond, DJ Stephenson.et al. . Porous ceramic water bearings for improved for accuracy performance. Annals. of the CIRP, 47: 467—470
[117]卢泽生,杜金明,孙雅洲.气体静压多孔质球面轴承静态性能分析.机械工程学报,2004,40(12):115-119
[118]严晖,黄协清,顾崇衔.关于“主轴回转轴线”定义的探讨.振动与动态测试,1982,(6):14-15
[119]蔡鹤皋,赵天开.关于主轴回转运动基本概念问题的初步探讨.振动与动态测试,1983,(1):4-5
[120]严晖,顾崇衔.再论主轴回转轴线.振动与动态测试,1983,(4):26-27
[121]黄伯文,尹苟保,刘桂秋.高精度车床主轴回转误差运动数字式测量方法.精密机床动态检测与精度控制论文选集,1987,55-64
[122]李均.回转轴径向误差运动测量中标准球安装偏心的影响.精密机床动态检测与精度控制论文选集,1987,65-70
[123]黄长征.超精密车床主轴回转误差运动动态测试系统研究:硕士学位论文.长沙:国防科技大学,2001.
[124]王建敏.动力调谐陀螺仪驱动轴圆跳动动态测试研究:硕士学位论文.长沙:国防科技大学,2002.
[125]凌文玉.两传感器误差分离技术的原理与误芳分析.国防科技大学精密机床动态检测与精度控制论文选集,1987,81-92
[126]谭深.三点法测量圆度、轴跳动数据处理方法的商椎.振动与动态测试,1986,(1):3-6
[127]李均,戴瀛洲,袁洪祥.在线圆度测量装置.仪器仪表学报,国防科技大学精密机床动态检测与精度控制论文选集,1987,71-80
[128]戴瀛洲.关于三传感器测圆度的若干问题.振动与动态测试,1986,(1):6-10
[129]袁洪祥,李均,张峰等.超精密加工中的圆度在线测量与补偿技术.国防科技大学精密机床动态检测与精度控制论文选集,1987,119-131
[130]青木保雄,大园成夫.三点法圆度测量方法的研究.精密机械(日文),1966,32(12)
[131]大园成夫.三点法圆度测量.机械研究(日文),1981,(1):193-198
[132]青木保雄,大园成夫.三点法圆度测量机.机械研究(日文),1978,30(6):753-759
[133]李济顺,洪迈生.三点法圆度误差分离的近似方法及精度分析.计量技术,1998,(2):8-11
[134]张宇华,王晓林.三点法圆度测量精度分析.光学精密工程,1998,6(4):127-131
[135]王宝玉.三点法分离工件圆度误差与轴系径向运动误差数据处理的儿个问题.振动与动态测试,1986,(6):30-32
[136]Wei Gao,Satoshi Kiyono,Tadatoshi Nomura.A new multiprobe method of roundness measurements.Precision Engineering,1996,19(1):37-45
[137]T.Hatsuzawa.Automatic centring system for a roundness tester using force feedback techniques.Precision Engineering,1988,10(1):19-23
[138]张宇华,王晓琳,张国雄,李真.多点法圆度及轴系误差分离方法的若干问题.北京理工大学学报,1999,19(3)
[139]Wei Gao.Satoshi Kiyono and Takamitu Sugawara,High-accuracy roundness measurement by a new error separation method.Precision Engineering,1997,21:123-133
[140]三井公之.精度诊断技术的研究(三点式主轴回转精度测量装置的开发).日本机械学会论文集,1982,(1):115-122
[141]肖怀.三点测圆法形状失真向题的研究.吉林工业大学学报,1983,3
[142]赵维谦,谭久彬,扬文国,张杰.基于两步法超精密圆度仪误差分离系统.中国机械工程,2000,11(11):1206-1208
[143]许晓桢.机床主轴回转精度的动态法测量.郑州纺织工学院学报,1998,9(2):68-71
[144]INTERNATIONALSTANDARDISO/FDIS230-7:2005(E)
[145]熊有伦.精密测量的数学方法.北京:中国计量出版社,1989.
[146]曹麟祥,王丙甲.圆度检测技术.北京:国防工业出版社,1998.
[147]刘立邦、刘健.内、外接圆法评定圆度误差的快速电算法.计量技术,1991,(3):1-3
[148]扬雪,张英芝.最小条件求圆皮误差值的快速电算法.计量技术,2001,(3):5-6
[149]N.Cho,J.Tu.Roundness modeling of machined parts for tolerance analysis.Precision Engineering,2001,25:35-47
[150]Jay F.Tu,and Spring C.C.Hung.Modeling and error analysis for assessing spindle radial error motions.Precision Engineering,1997,21:90-101
[151]Shoji Noguchi,Tadao Tsukada and Atsushi Sakamoto.Evaluation method to determine radial accuracy of high-precision rotating spindle units.Precision Engineering,1995,17(4):266-273
[152]曹麟祥,邵大钟.圆度、圆柱度和同轴度的测量原理及数据处理的解析方法.机械工程学报,1983,19(1):86-95
[153]柴琳,胡光,李振芳.机床主轴回转精度测量数量处理的研究.西安公路交通大学学报,1998,18(2):81-84
[154]JENS W.Dynamics of system of rigid bodies.Stuttgart:Teubner,1977.
[155]王勖成,邵敏.有限单元法基本原理和数值方法.北京:清华大学出版社,1997:1-15
[156]邱吉宝.加权残值法的理论与应用.北京:宇航出版社,1991:164-195
[157]O.C.监凯维奇(著),尹泽勇,柴家振(译).有限元法(下).北京:科学出版社,1985:808-809
[158]彭旭麟,罗汝梅.变分法及其应用.武昌:华中工学院出版社,1983:35-42,136-148
[159]饶寿期.有限元法和边界元法基础.北京:航空航天大学出版社,1990:99-102
[160]李大潜等.有限元素法续讲.北京:科学出版社,1979:40-45
[161]程学梅,陈海斌,张显全.空气静压轴承工作特性的有限元分析.渝州大学学报(自然科学版),1996,13(3):18-24