- 综合性科技类中文核心期刊
- 中国科技论文统计源期刊
- 中国科学引文数据库来源期刊
- 中国学术期刊文摘数据库（核心版）来源期刊
- 中国学术期刊综合评价数据库来源期刊
| Citation: |
CHEN Dongju, ZHANG Xuan, SUN Kun, LI Tianbao, CHEN Fang. Review on Progress of Macro and Micro Scale Research of Aerostatic Spindles[J]. Journal of Beijing University of Technology, 2023, 49(5): 577-596. DOI: 10.11936/bjutxb2021090009
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As the key component of precision ultra-precision machine tools, the aerostatic spindle is characterized by high rotary accuracy, smooth operation, less vibration and noise than conventional bearings, and less temperature rise at high-speed rotation. However, it has poor stiffness and load-bearing capacity. Therefore, it is necessary to systematically summarize and analyze the existing important research results of aerostatic spindles. Reviewing the historical development and research results of aerostatic spindles, the primary research aims to improve the load capacity and stiffness, dynamic/static characteristics and stability of aerostatic spindles by improving the Reynolds equation and optimizing the structural parameters. At the same time, the microscale characteristics have also become a research hotspot, and the research results show that the microscale characteristics influence the load carrying capacity and stiffness of the spindle. The development history of aerostatic spindles, static/dynamic performance, and the factors that significantly affected the performance of aerostatic spindles, such as viscosity, velocity slip, and thinning effects in the microscale field was reviewed in this paper. Combined with existing numerical simulation methods, the measurement of spindle rotation accuracy and the state of spindle motion were analyzed. Finally, the research development trend of aerostatic spindles was forecasted.
| [1] |
郭东明, 刘战强, 蔡光起, 等. 中国先进加工制造工艺与装备技术中的关键科学问题[J]. 数字制造科学, 2005, 3(4): 1-36.
GUO D M, LIU Z Q, CAI G Q, et al. Crucial technical problems in China's advanced machining, manufacturing and relevant equipment technologies[J]. Digital Manufacture Science, 2005, 3(4): 1-36. (in Chinese)
|
| [2] |
中国机械工程学会. 中国机械工程技术路线图[M]. 北京: 中国科学技术出版社, 2011.
|
| [3] |
ROBERT W. On the pressure produced on a flat plate when opposed to a stream of air issuing from an orifice in a plane surface[J]. Transactions of Philosophical Society, 1828, 3: 129-140.
|
| [4] |
王云飞. 气体润滑理论与气体轴承设计[M]. 哈尔滨: 哈尔滨工业大学出版社, 1999.
|
| [5] |
李树森, 张鹏顺, 曲全利. 气体润滑轴承技术的应用及发展趋势[J]. 润滑与密封, 1999(2): 9-10. https://www.cnki.com.cn/Article/CJFDTOTAL-RHMF199902002.htm
LI S S, ZHANG P S, QU Q L. Application and development trend of gas lubricated bearing technology[J]. Lubrication Engineering, 1999(2): 9-10. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-RHMF199902002.htm
|
| [6] |
FULLER D D. A review of research in the field of gas-lubricated bearings[R]. Washington D.C. : NASA, 1970: 1-63.
|
| [7] |
于贺春, 马文琦. 气体轴承技术的研究与发展[C]// 第四届全国流体传动与控制学术会议论文集. 大连: 中国机械工程学会流体传动与控制分会, 2006: 541-544.
YU H C, MA W Q. Research and development of gas bearing technology[C]// Proceedings of the 4th National Conference on Fluid Transmission and Control. Dalian: Fluid Transmission and Control Branch of Chinese Society of Mechanical Engineering, 2006: 541-544. (in Chinese)
|
| [8] |
DEVITT A J. Porous vs. orifice air bearing technology[J]. New Way Air Bearing Company's Technical Paper, 1999, 26(6): 1-15
|
| [9] |
侯国安. 流体静压支承对超精密金刚石车床动态特性影响的研究[D]. 哈尔滨: 哈尔滨工业大学, 2013.
HOU G A. Research on influences of hydrostatic bearing on dynamic characteristics of ultra-precision diamond lathe[D]. Harbin: Harbin Institute of Technology, 2013. (in Chinese)
|
| [10] |
杜金名, 卢泽生, 孙雅洲. 空气静压轴承各种节流形式的比较[J]. 航空精密制造技术, 2003(6): 4-7, 17. doi: 10.3969/j.issn.1003-5451.2003.06.002
DU J M, LU Z S, SUN Y Z. Comparison of all types of restriction of aerostatic bearing[J]. Aviation Precision Manufacturing Technology, 2003(6): 4-7, 17. (in Chinese) doi: 10.3969/j.issn.1003-5451.2003.06.002
|
| [11] |
田富竟, 尹自强, 王建敏, 等. 多孔质节流空气静压轴承静态性能实验研究[J]. 航空精密制造技术, 2011, 47(5): 5-8. doi: 10.3969/j.issn.1003-5451.2011.05.002
TIAN F J, YIN Z Q, WANG J M, et al. Experimental research and analysis of aerostatic bearing[J]. Aviation Precision Manufacturing Technology, 2011, 47(5): 5-8. (in Chinese) doi: 10.3969/j.issn.1003-5451.2011.05.002
|
| [12] |
YOSHIMOTO S, KOHNO K. Static and dynamic characteristics of aerostatic circular porous thrust bearings (effect of the shape of the air supply area) [J]. Journal of Tribology, 2001, 123(3): 501-508. doi: 10.1115/1.1308027
|
| [13] |
FAN K C, HO C C, MOU J I. Development of a multiple-microhole aerostatic air bearing system[J]. Journal of Micromechanics and Microengineering, 2002, 12(5): 636-643. doi: 10.1088/0960-1317/12/5/319
|
| [14] |
BELFORTE G, RAPARELLI T, VIKTOROV V, et al. Discharge coefficients of orifice-type restrictor for aerostatic bearings[J]. Tribology International, 2007, 40(3): 512-521 doi: 10.1016/j.triboint.2006.05.003
|
| [15] |
MIYATAKE M, YOSHIMOTO S. Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed hole[J]. Tribology International, 2010, 43(8): 1353-1359. doi: 10.1016/j.triboint.2010.01.002
|
| [16] |
FUJII F. Friction characteristics of an aerostatic liner bearing[J]. Tribology International, 2006, 39(9): 888-896. doi: 10.1016/j.triboint.2005.07.040
|
| [17] |
OHISHI S, MATSUZAKI Y. Experimental investigation of air spindle unit thermal characteristics[J]. Precision Engineering, 2002, 26(1): 49-57. doi: 10.1016/S0141-6359(01)00097-6
|
| [18] |
PARK J K, KIM K W. Stability analyses and experiments of spindle system using new type of slot-restricted gas journal bearings[J]. Tribology International, 2004, 37(6): 451-462. doi: 10.1016/j.triboint.2003.12.014
|
| [19] |
VIKTOROV V, BELFORTE G, RAPARELLI T. Modeling and identification of gas journal bearins: externally pressurized gas bearing results[J]. Journal of Tribology, 2005, 127(3): 548-556. doi: 10.1115/1.1924425
|
| [20] |
卢泽生, 杜金名, 孙雅洲. 影响空气静压多孔质止推轴承静态性能的因素[J]. 哈尔滨工业大学学报, 2001(6): 729-731, 739. doi: 10.3321/j.issn:0367-6234.2001.06.002
LU Z S, DU J M, SUN Y Z. Factors having effect on static performance aerostatic porous thrust bearing[J]. Journal of Harbin Institute of Technology, 2001(6): 729-731, 739. (in Chinese) doi: 10.3321/j.issn:0367-6234.2001.06.002
|
| [21] |
柴辉, 龙威, 杨绍华, 等. 气固热耦合对微尺度气膜空气静压轴承承载特性的影响[J]. 昆明理工大学学报(自然科学版), 2018, 43(5): 52-59. doi: 10.16112/j.cnki.53-1223/n.2018.05.008
CHAI H, LONG W, YANG S H, et al. Effect of gas-solid thermal coupling on loading capacity of aerostatic bearing under micro-scale gas-film[J]. Journal of Kunming University of Science and Technology(Natural Sciences), 2018, 43(5): 52-59. (in Chinese) doi: 10.16112/j.cnki.53-1223/n.2018.05.008
|
| [22] |
赵晓龙, 张君安, 董皓, 等. 变截面节流器对空气静压轴承承载性能的影响[J]. 光学精密工程, 2018, 26(10): 2446-2454. https://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201810013.htm
ZHAO X L, ZHANG J A, DONG H, et al. Influence of variable section throttle on performance of aerostatic bearings[J]. Optics and Precision Engineering, 2018, 26(10): 2446-2454. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GXJM201810013.htm
|
| [23] |
DU J J, ZHANG G Q, LIU T, et al. Improvement on load performance of externally pressurized gas journal bearings by opening pressure-equalizing grooves[J]. Tribology International, 2014, 73: 156-166. doi: 10.1016/j.triboint.2014.01.012
|
| [24] |
FOURKA M, BONIS M. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems[J]. Wear, 1997, 210(1/2): 311-317.
|
| [25] |
RENN J C, HSIAO C H. Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings[J]. Tribology International, 2004, 37 (4): 309-315. doi: 10.1016/j.triboint.2003.10.003
|
| [26] |
BEIFORTE G, COLOMBO F, RAPARELLI T, et al. Comparison between grooved and plane aerostatic thrust bearings: static performance[J]. Meccanica, 2011, 46(7): 547-555.
|
| [27] |
CHEN Y S, CHIU C C, CHENG Y D. Influences of operational conditions and geometric parameters on the stiffness of aerostatic journal bearings [J]. Precision Engineering, 2010, 34(4): 722-734. doi: 10.1016/j.precisioneng.2010.04.001
|
| [28] |
ZHANG W M, ZHOU J B, MENG G. Performance and stability analysis of gas-lubricate journal bearings in MEMS[J]. Tribology International, 2011, 44(7/8): 887-897.
|
| [29] |
LI Y T, DING H. A simplified calculation method on the performance analysis of aerostatic thrust bearing with multiple pocketed orifice-type restrictors[J]. Tribology International, 2012, 56: 66-71. doi: 10.1016/j.triboint.2012.06.018
|
| [30] |
ALBENDER F, VANBRUSSEL H. A method of separation of variables for the solution of laminar boundary-layer equation of narrow-channel flows[J]. Journal of Tribology-Transactions of The ASME, 1992, 114(3): 623-629. doi: 10.1115/1.2920927
|
| [31] |
ALBENDER F. On the modelling of dynamic characteristics of aerostatic bearing film: from stability analysis to active compensation[J]. Precision Engineering, 2009, 33(2): 117-126. doi: 10.1016/j.precisioneng.2008.06.003
|
| [32] |
PROHL M A. A general method for calculating critical speed of flexible rotors[J]. Journal of Applied Mechanics, 1945, 12(3): 142-148. doi: 10.1115/1.4009455
|
| [33] |
FOPPL A. Das problem der lavalschen turbinenwelle[J]. Der Civilingenieur, 1985, 4: 335-342.
|
| [34] |
KASHIMURA Y, YAMASAKI S, FURUTANI K, et al. A study on air spindle unit for NC milling machine-detection of cutting forces and failure using displacement detectors[J]. Journal of the Japan Society of Precision Engineering, 1990, 56(3): 527-532.
|
| [35] |
CZOLCZYŃSKI K. How to obtain stiffness and damping coefficients of gas bearings[J]. Wear, 1996, 201(1/2): 265-275.
|
| [36] |
LIN J R. Surface roughness effect on the dynamic stiffness and damping characteristics of compensated hydrostatic thrust bearings [J]. International Journal of Machine Tools & Manufacture, 2000, 40(11): 1671-1689.
|
| [37] |
TALUKDER H M, STOWELL T B. Pneumatic hammer in an externally pressurized orifice-compensated air journal bearing[J]. Tribology International, 2003, 36(8): 585-591. doi: 10.1016/S0301-679X(02)00247-5
|
| [38] |
WARDLE F P, BOND C, WILSON C, et al. Dynamic characteristics of a direct-drive air-bearing slide system with squeeze film damping[J]. The International Journal of Advanced Manufacturing Technology, 2010, 47(9): 911-918.
|
| [39] |
CHEN X D, ZHU J C, CHEN H. Dynamic characteristics of ultra-precision aerostatic bearings [J]. Advances in Manufacturing, 2013, 1(1): 82-86. doi: 10.1007/s40436-013-0013-6
|
| [40] |
YU P, CHEN X, WANG X, et al. Frequency-dependent nonlinear dynamic stiffness of aerostatic bearings subjected to external perturbations [J]. International Journal of Precision Engineering & Manufacturing, 2015, 16(8): 1771-1777.
|
| [41] |
NAKAMURA T, YOSHIMOTO S. Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with double row admissions[J]. Tribology International, 1997, 30(8): 605-611. doi: 10.1016/S0301-679X(97)00030-3
|
| [42] |
YOSHIMOTO S, TAMURA J, NAKAMURA T. Dynamic tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors [J]. Tribology International, 1999, 32: 731-738. doi: 10.1016/S0301-679X(00)00004-9
|
| [43] |
SU J C, LIE K N. Rotation effects on hybrid air journal bearings[J]. Tribology International, 2003, 36(10): 717-726. doi: 10.1016/S0301-679X(03)00034-3
|
| [44] |
ZHAO G, LIU P N, YU H C, et al. Research on gas film force of aerostatic gas bearing and its coupled dynamics with rotor [J]. Journal of Aerospace Power, 2012, 27(2): 472-480.
|
| [45] |
HUNG J P, LAI Y L, LIN C Y, et al. Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide[J]. International Journal of Machine Tools & Manufacture, 2011, 51(9): 731-739. doi: 10.1016/j.ijmachtools.2011.05.002
|
| [46] |
MARSH E R, ARNESON D A, LIEBERS M J, et al. Effects of gas composition on asynchronour error motion in externally pressurized spindle[J]. Precision Engineering, 2008, 32(2): 143-147. doi: 10.1016/j.precisioneng.2007.04.007
|
| [47] |
BOU S B, GRAU G, IORDANOFF I. On nonlinear rotor dynamic effects of aerodynamic bearings with simple flexible rotors[J]. Journal of Engineering for Gas Turbines and Power, 2008, 130(1): 82-93.
|
| [48] |
RUDLOFF L, ARGHIR M, BONNEAU O, et al. Experimental analysis of dynamic characteristics of a hybrid aerostatic bearing[C]// ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. Vancouver: International Gas Turbine Institute, 2011: 587-595.
|
| [49] |
YABE H, YAMAMOTO M. A study on the running accuracy of an externally pressurized gas thrust bearing: bearing stiffness and damping coefficient[J]. The Japan Society of Mechanical Engineers, 1989, 32(4): 618-624.
|
| [50] |
YABE H. A study on run-out characteristics of externally pressurized gas journal bearing(modified DF method for point-source solution) [J]. The Japan Society of Mechanical Engineers, 1994, 37(2): 362-368.
|
| [51] |
JING G, ZHANG L P, ZHANG S J, et al. Research and test on rotary accuracy of high precision spindle[J]. Manufacturing Technology & Machine Tool, 1996(6): 24-26.
|
| [52] |
CHEN G, MAO F H, WANG B K. Effects of off-sized cylindrical rollers on the static load distribution in a cylinder roller bearing[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2012, 226(8): 687-696. doi: 10.1177/1350650112441747
|
| [53] |
ADOLPH T, SCHONAUER W, KOCH R, et al. Capability of FDEM for journal bearings with microstructured surface[M]. Berlin Heidelberg: Springer, 2010.
|
| [54] |
BHAT N, BARRANS S, KUMAR A S. Performance analysis of Pareto optimal bearings subject to surface error variations[J]. Tribology International, 2010, 43(11): 2240-2249. doi: 10.1016/j.triboint.2010.07.012
|
| [55] |
边新孝, 李谋渭, 李威. 加工误差对气体静压径向轴承的影响[J]. 工程科学学报, 2005, 27(3): 331-333. doi: 10.3321/j.issn:1001-053X.2005.03.019
|
| [56] |
陈小安, 陈文曲, 康辉民, 等. 偏心电主轴动力学分析[J]. 重庆大学学报, 2012, 35(3): 26-32.
BIAN X X, LI M W, LI W. Influence of machining error on Aerostatic radial bearing[J]. Chinese Journal of Engineering, 2005, 27(3): 331-333. (in Chinese)
|
| [57] |
翟鹏程, 何青, 彭慧春. 横向裂纹深度和质量不平衡方向对转子振动影响的实验研究[J]. 电力科学与工程, 2016, 32(12): 32-37. https://www.cnki.com.cn/Article/CJFDTOTAL-DLQB201612007.htm
CHEN X A, CHEN W Q, KANG H M, et al. Dynamic analysis of high speed motorized spindles with eccentrics[J]. Journal of Chongqing University, 2012, 35(3): 26-32. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DLQB201612007.htm
|
| [58] |
WANG X K, XU Q, WANG B R. Effect of surface waviness on the static performance of aerostatic journal bearings[J]. Tribology International, 2016, 103: 394-405. doi: 10.1016/j.triboint.2016.07.026
|
| [59] |
杨小高. 考虑加工误差的油膜轴承动态性能研究[D]. 重庆: 重庆大学, 2015.
YANG X G. Study on the dynamic performances of oil film bearing with consideration of machining errors[D]. Chongqing: Chongqing University, 2015. (in Chinese)
|
| [60] |
孙岩辉, 洪军, 刘志刚, 等. 考虑零部件制造误差的精密主轴几何回转精度计算方法[J]. 机械工程学报, 2017, 53(3): 173-182. https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201703023.htm
SUN Y H, HONG J, LIU Z G, et al. A calculating method for the geometric rotation accuracy of precision spindles considering the manufacturing errors of component parts[J]. Journal of Mechanical Engineering, 2017, 53(3): 173-182. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXXB201703023.htm
|
| [61] |
孟曙光. 轴颈误差和电磁偏心对动静压电主轴回转精度的影响研究[D]. 长沙: 湖南大学, 2016.
MENG S G. Research on the rotary accuracy of the hydrostatic-dynamic spindle affected by journal geometric error and electromagnetic eccentricity[D]. Changsha: Hunan University, 2016. (in Chinese)
|
| [62] |
梅雄. 制造误差对多孔质静压轴承静动态特性的影响规律研究[D]. 成都: 电子科技大学, 2017.
MEI X. Influence of manufacturing error on static and dynamic characteristics of porous aerostatic bearings[D]. Chengdu: University of Electronic Science and Technology of China, 2017. (in Chinese)
|
| [63] |
郑艳伟. 轴承零件几何误差对圆柱滚子轴承动态性能的影响研究[D]. 洛阳: 河南科技大学, 2019.
ZHENG Y W. Research on influence of gcometric error of bearing parts on dynamic performance of cylindrical roller bearings[D]. Luoyang: Henan University of Science and Technology, 2019. (in Chinese)
|
| [64] |
王凯, 韩大勇, 韦增战. 动不平衡对高速主轴回转运动的影响[J]. 南京理工大学学报, 2000, 24(4): 341-344. doi: 10.3969/j.issn.1005-9830.2000.04.014
WANG K, HAN D Y, WEI Z Z. The influence of dynamic imbalance on high speed rotary spindle[J]. Journal of Nanjing University of Science and Technology, 2000, 24(4): 341-344. (in Chinese) doi: 10.3969/j.issn.1005-9830.2000.04.014
|
| [65] |
POWELL J W. Design of aerostatic bearing [M]. London: The Machinery Publishing Co. Ltd., 1970: 12-18.
|
| [66] |
CROSS W A, LEE A M. Fluid film lubrication [M]. New York: John Wiley & Sons, 1980: 1-5.
|
| [67] |
VEIJOLA T, TUROWSKI M. Compact damping models for laterally moving microstructures with gas-rarefaction effects[J]. Journal of Micro-Eletromechanical Systems, 2001, 10(2): 263-273. doi: 10.1109/84.925777
|
| [68] |
KENNARD E H. Kinetic theory of gases[M]. New York: McGr-aw-Hill, 1938.
|
| [69] |
张海军, 祝长生, 杨琴. 有效黏度效应对气体径向微轴承性能的影响[J]. 中国电机工学报, 2009, 29(29): 84-88. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGDC200929018.htm
ZHANG H J, ZHU C S, YANG Q. Effect of effective viscosity on performance of micro gas journal bearings[J]. Proceedings of the CSEE, 2009, 29(29): 84-88. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGDC200929018.htm
|
| [70] |
SUN A, MA W Q, WANG Z W. A review on the application equation in gas lubrication of high supply pressure [J]. China Mechanical Engineering, 2012, 19(17): 2090-2094.
|
| [71] |
GUSTAFSSON T, RAJAGOPAL K R, STENBERG R, et al. Nonlinear reyonds equation for hydrodynamic lubrication[J]. Electronic Journal of Differential Equations, 2014, 39(17): 5299-5309.
|
| [72] |
BARCOHEN A, KRAUS A D. Advances in thermal modeling of electronic components and systems, Vol 1[J]. Journal of Electronic Packaging, 1989, 111(2): 162-163.
|
| [73] |
BITSANIS I, VANDERLICK T, TIRRELL M. A tractable molecular theory of flow in strongly inhomogeneous fluids[J]. The Journal of Chemical Physics, 1988, 89(5): 3152-3162. doi: 10.1063/1.454972
|
| [74] |
ROWLEY R L, PAINTER M M. Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations [J]. International of Thermophysics, 1997, 18(5): 1109-1121. doi: 10.1007/BF02575252
|
| [75] |
何庆东. 纳米尺度流体粘度计算的新方法研究[D]. 秦皇岛: 燕山大学, 2012.
HE Q D. Research on a new method to calculate flow viscosity in nanoflow problems[D]. Qinhuangdao: Yanshan University, 2012. (in Chinese)
|
| [76] |
骆双双, 包福兵, 林建忠. 纳米尺度通道中气体粘度的分子动力学模拟[J]. 低温工程, 2015(2): 32-36. https://www.cnki.com.cn/Article/CJFDTOTAL-DWGC201502006.htm
LUO S S, BAO F B, LIN J Z. Molecular dynamics simulation of gas viscosity in nano-scale channels[J]. Cryogenics, 2015(2): 32-36. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DWGC201502006.htm
|
| [77] |
韩文彬, 冯涓, 武园浩, 等. 基于二次优化策略的约束环内稀薄气体粘度修正[J]. 真空科学与技术学报, 2015, 35(1): 38-43. doi: 10.13922/j.cnki.cjovst.2015.01.08
HAN W B, FENG J, WU Y H, et al. Viscosity correction of rarefied gas in confinement ring based on quadratic optimization[J]. Chinese Journal of Vacuum Science and Technology, 2015, 35(1): 38-43. (in Chinese) doi: 10.13922/j.cnki.cjovst.2015.01.08
|
| [78] |
岳向吉, 巴德纯, 刘坤, 等. 干式罗茨真空泵吸气级内流动的瞬态模拟[J]. 真空科学与技术学报, 2012, 32(9): 850-855. doi: 10.3969/j.issn.1672-7126.2012.09.18
QIU X J, BA D C, LIU K, et al. Transient numerical simulation of gas flow in suction stage of dry roots-type vacuum pump[J]. Chinese Journal of Vacuum Science and Technology, 2012, 32(9): 850-855. (in Chinese) doi: 10.3969/j.issn.1672-7126.2012.09.18
|
| [79] |
NETO C, EVANS D R, BUTT H J, et al. Boundary slip in Newtonian liquids: a review of experimental studies[J]. Reports on Progress in Physics, 2005, 68(12): 2859-2897. doi: 10.1088/0034-4885/68/12/R05
|
| [80] |
GADELHAK M. The fluid mechanics of microdevices—the freeman scholar lecture[J]. Journal of Fluids Engineering, 1999, 121(1): 5-33. doi: 10.1115/1.2822013
|
| [81] |
GADELHAK M. Flow physics in MEMS[J]. Mécanique & Industries, 2001, 2(4): 313-341.
|
| [82] |
NAVIER M. Memoire sur les lois du mouvement des fluids[J]. Memoires of Academia Royale des Sciences, 1823, 6: 389-440.
|
| [83] |
MAXWELL J C. On stresses in rarefied gases arising from inequalities of temperature[J]. Philosophical Transactions of the Royal Society of London, 1879, 170: 249-256.
|
| [84] |
BURGDORFEI A. The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings[J]. Journal of Basic Engineering, 1958, 81(1): 94-100.
|
| [85] |
WINER W O, BAIR S. Shear strength measurement of lubricants at high pressure[J]. Journal of Lubrication Technology, 1979, 101(3): 251-257. doi: 10.1115/1.3453339
|
| [86] |
HSIA Y T, DOMOTO G A. An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances[J]. Journal of Lubrication Technology, 1983, 105(1): 120-129. doi: 10.1115/1.3254526
|
| [87] |
SHI B J, YANG T Y. Pressure simulation of sliders with ultra-low flying heights in hard disk drives by using finite volume method[J]. Advanced Science Letters, 2011, 4(4/5): 1578-1582.
|
| [88] |
YANG Q, ZHANG H, LIU Y. Improved modified Reynolds equation for thin-film gas lubrication from an extended slip velocity boundary condition[J]. Microsystem Technologies, 2016, 22(12): 2869-2875. doi: 10.1007/s00542-015-2667-4
|
| [89] |
KARIMIPOUR A. Provide a suitable range to include the thermal creeping effect on slip velocity and temperature jump of an air flow in a nanochannel by lattice Boltzmann method[J]. Physica E: Low-dimensional Systems and Nanostructures, 2017, 85: 143-151. doi: 10.1016/j.physe.2016.08.021
|
| [90] |
MITSUYA Y. Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient[J]. Transactions American Society of Mechanical Engineers Journal of Tribology, 1993, 115: 289-294.
|
| [91] |
ZHOU J F, GU B Q, SHAO C L. Boundary velocity slip of pressure driven liquid flow in a micron pipe[J]. Science Bulletin, 2011, 56(15): 1603-1610. doi: 10.1007/s11434-010-4188-y
|
| [92] |
SPIKES H A. The half-wetted bearing, part 1: extended Reynolds equation[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2003, 217(1): 1-14.
|
| [93] |
FUKUI S, KANEKO R. Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report derivation of a generalized lubrication equation including thermal creep flow[J]. Journal of Tribology, 1988, 110(2): 253-262. doi: 10.1115/1.3261594
|
| [94] |
SHARMA R, ISHAK A, POP I. Stagnation point flow of a micropolar fluid over a stretching/shrinking sheet with second-order velocity slip[J]. Journal of Hydrologic Engineering, 2016, 29(5): 04016025.
|
| [95] |
THOMPSON P A, TROIAN S M. A general boundary condition for liquid flow at solid surfaces[J]. Nature, 1997, 389(6649): 360-362. doi: 10.1038/38686
|
| [96] |
MITSUYA Y. Nano-technologies for head-medium interface in magnetic disk storage[C]// International Symposium on Micromechatronics and Human Science. Nagoya: IEEE Xplore, 1997: 27-32.
|
| [97] |
CHENG F, JI W. Identification of dynamic coefficients of the journal bearing considering velocity slip of cavitation zone in the rotating spindle unit[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2018, 232(10): 1304-1317. doi: 10.1177/1350650117752987
|
| [98] |
ZANZI C, PEDRERO J I. Application of modified geometry of face gear drive[J]. Computer Method in Applied Mechanics and Engineering, 2005, 194(27/28/29): 3047-3066.
|
| [99] |
江甫炎. 近代齿轮制造工艺[M]. 北京: 航空工业出版社, 1996.
|
| [100] |
BOLTZMANN L. Further studies on the thermal equilibrium of gas molecules[M]//The Kinetic Theory of Gases: an Anthology of Classic Papers with Historical Commentary. Leipzig: Stephen G B, 2003: 262-349.
|
| [101] |
ERINGEN A. Simple microfluids[J]. International Journal of Engineering Science, 1964, 2(2): 205-217. doi: 10.1016/0020-7225(64)90005-9
|
| [102] |
FUKUI S, KANEKO R. Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation[J]. Transactions of the Japan Society of Mechanical Engneering Series C, 1987, 30(268): 1660-1666.
|
| [103] |
FUKUI S, KANEKO R. A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems[J]. Journal of Tribologgy, 1990, 112(1): 78-83 doi: 10.1115/1.2920234
|
| [104] |
BIRD G A. Recent advances and current challenges for DSMC[J]. Computers & Mathematics with Applications, 1998, 35(1/2): 1-14.
|
| [105] |
陈杰, 赵磊. 高超声速流存在局部稀薄效应的一个判据及相应的流动特性[J]. 空气动力学学报, 2018, 36(1): 4-11. https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201801003.htm
CHEN J, ZHAO L. A criteron for the existence of local rarefaction effect in a hypersonic flow field and the corresponding flow characteristics[J]. Acta Aerodynamica Sinica, 2018, 36(1): 4-11. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-KQDX201801003.htm
|
| [106] |
SUN H W, FAGHRI M. Effects of rarefaction and compressibility of gaseous flow in microchannel using DSMC[J]. Numerical Heat Transfer, Part A: Applications, 2000, 38(2): 153-168. doi: 10.1080/10407780050135388
|
| [107] |
MORINI G L, SPIGA M, TARTARINI P. The rarefaction effect on the friction factor of gasflow in microchannels[J]. Superlattices and Microstructures, 2004, 35(3/4/5/6): 587-599.
|
| [108] |
COLIN S. Rarefaction and compressibility effects on steady and transient gas flows in microchannels[J]. Microfluidics and Nanofluidics, 2005, 1(3): 268-279. doi: 10.1007/s10404-004-0002-y
|
| [109] |
唐桂华, 何雅玲, 陶文铨. 粗糙度与气体稀薄性对微尺度流动特性的影响[J]. 工程热物理学报, 2006, 27(2): 304-306. doi: 10.3321/j.issn:0253-231X.2006.02.040
TANG G H, HE Y L, TAO W S. Roughness and rarefaction effects on flow characteristics in microchannels[J]. Journal of Engineering Thermophysics, 2006, 27(2): 304-306. (in Chinese) doi: 10.3321/j.issn:0253-231X.2006.02.040
|
| [110] |
TANG G H, LI Z, HE Y L, et al. Experimental study of compressibility, roughness and rarefaction influences on microchannel flow[J]. International Journal of Heat and Mass Transfer, 2007, 50: 2282-2295. doi: 10.1016/j.ijheatmasstransfer.2006.10.034
|
| [111] |
KHADEM M H, SHAMS M, HOSSAINPOUR S. Effects of rarefaction and compressibility on fluid flow at slip flow regime by direct simulation of roughness[J]. World Academy of Science, Engineering and Technology, 2008, 2(5): 639-645.
|
| [112] |
SHI B J, YANG T Y. Simplified model of Reynolds equation with linearized flow rate for ultra-thin gas film lubrication in hard disk drives[J]. Microsystem Technologies, 2010, 16(10): 1727-1734. doi: 10.1007/s00542-010-1107-8
|
| [113] |
SADEGHI A, SAIDI M H. Viscous dissipation and rarefaction effects on laminar forced convection in microchaneel[J]. Journal of Heat Transfer, 2010, 132(7): 271-291.
|
| [114] |
RIABOV V V. Rarefaction effects in hypersonic aerodynamic[J]. International Symposium on Rarefied Gas Dynamics Aip, 2011, 1333: 1331-1336.
|
| [115] |
BIGHAM S, SHOKOUHMANO H, ISFAHANI R N, et al. Fluid flow and heat transfer simulation in a constricted microchannel: effects of rarefaction, geometry, and viscous dissipation[J]. Numerical Heat Transfer Part A: Application, 2011, 59(3): 209-230. doi: 10.1080/10407782.2011.541203
|
| [116] |
YE J J, YANG J, ZHENG J, et al. Rarefaction and temperature gradient effect on the performance of the Knudsen pump[J]. Chinese Journal of Mechanical Engineering, 2012, 25(4): 745-752. doi: 10.3901/CJME.2012.04.745
|
| [117] |
ROVENSKAYA O, CROCE G. Numerical investigation of the effect of boundary conditions for a highly rarefied gas flow using the GPU accelerated Boltzmann solver[J]. Computer & Fluids, 2013, 110: 77-87.
|
| [118] |
PAN S, GAO Z, LEE C. Numerical investigation of rarefaction effects in the vicinity of a sharp leading edge[J]. American Institute of Physics Conference Series, 2014, 1628(1): 185-191.
|
| [119] |
ZUPPARDI G, MORSA L, SAVINO R, et al. Rarefied aerodynamic characteristics of aero-space-planes: a comparative study of two gas-surface interaction models[J]. European Journal of Mechanics-B/Fluids, 2015, 53: 37-47. doi: 10.1016/j.euromechflu.2015.04.003
|
| [120] |
CHEN D J, ZHOU S, YANG Z, et al. Influence of flow factor in gas rarefied effects to aerostatic thrust bearing performance [J]. Advanced Engineering Sciences, 2016, 48(1): 194-199.
|
| [121] |
CHEN M F, LIN Y T. Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearing by modified resistance network method[J]. Tribology International, 2002, 35: 329-338. doi: 10.1016/S0301-679X(02)00012-9
|
| [122] |
CUI H L, GONG W W, ZHENG Y Q, et al. A simplified FEM analysis on the static performance of aerostatic journal bearings with orifice restrictor[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2021, 235(7): 1379-1389. doi: 10.1177/1350650120957132
|
| [123] |
FOURKA M, TIAN Y, BONIS M. Prediction of stability of air thrust bearings by numerical, analytical and experiment methods [J]. Wear, 1996, 198(1/2): 1-6.
|
| [124] |
BHAT N, KUMAR S, TAN W, et al. Performance of inherently compensated flat pad aerostatic bearings subject to dynamic perturbation forces [J]. Precision Engineering, 2012, 36(3): 399-407. doi: 10.1016/j.precisioneng.2012.01.002
|
| [125] |
NEVES M T, SCHWARZ V A, MENON G J. Discharge coefficient influence on the performance of aerostatic journal bearings [J]. Tribology International, 2010, 43(4): 746-751. doi: 10.1016/j.triboint.2009.11.001
|
| [126] |
FOURKA M, BONIS M. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems[J]. Wear, 1997, 210(1/2): 311-317.
|
| [127] |
CHOI J, LEE D G. Thermal characteristic of the spindle bearing system with a gear located on the bearing span[J]. International Journal of Machine Tools & Manufacture, 1998, 38(9): 1017-1030
|
| [128] |
ALMAS E A M, DESILVA F A P. Finite different automatically generated non-uniform grids in the numerical solution of the Reynolds' compressible one dimensional squeeze-film equation[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2003, 217(3): 243-249. doi: 10.1243/135065003765714908
|
| [129] |
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. doi: 10.1016/j.triboint.2004.04.008
|
| [130] |
GAO S Y, CHENG K, CHEN S J, et al. CFD based investigation on influence of orifice chamber shapes for the design of aerostatic thrust bearings at ultra-high speed spindles[J]. Tribology International, 2015, 92: 211-221. doi: 10.1016/j.triboint.2015.06.020
|
| [131] |
ZHU J C, CHEN H, CHEN X D. Large eddy simulation of vortex shedding and pressure fluctuation in aerostatic bearings [J]. Journal of Fluids and Structures, 2013, 40: 42-51. doi: 10.1016/j.jfluidstructs.2013.03.012
|
| [132] |
XIONG W L, HOU Z Q, LV L. Study on the mechanism of hydrostatic spindle rotational error motion [J]. Chinese Journal of Mechanical Engineering, 2014, 50(7): 112-119. doi: 10.3901/JME.2014.07.112
|
| [133] |
ELESHAKY M E. CFD investigation of pressure depressions in aerostatic circular thrust bearings[J]. Tribology International, 2009, 42(7): 1108-1117. doi: 10.1016/j.triboint.2009.03.011
|
| [134] |
NISHIO U, SOMAYA K, YOSHIMOTO S. Numerical calculation and experimental verification of static and dynamic characteristic of aerostatic thrust bearings with small feedholes[J]. Tribology International, 2011, 44(12): 1790-1795. doi: 10.1016/j.triboint.2011.07.004
|
| [135] |
陈东菊, 董丽华, 周帅, 等. 稀薄效应下空气静压主轴动态特性分析及试验研究[J]. 四川大学学报(工程科学版), 2016, 48(5): 180-185. doi: 10.15961/j.jsuese.2016.05.025
CHEN D J, DONG L H, ZHOU S, et al. Dynamic performance analysis and experiment research of aerostatic spindle under the rarefaction effects[J]. Advanced Engineering Sciences, 2016, 48(5): 180-185. (in Chinese) doi: 10.15961/j.jsuese.2016.05.025
|
| [136] |
ARGHIR M, ROUCOU N, HELENEN M. Theoretial analysis of the incompressible laminar flow in a micaro-roughness cell[J]. Journal of Tribology, 2003, 125(2): 309-318. doi: 10.1115/1.1506328
|
| [137] |
袁哲俊, 王先逵. 精密和超精密加工技术[M]. 北京: 机械工业出版社, 2007.
|
| [138] |
MURALIKRISHNAN B, VENKATACHALAM S, RAJA J. Aroundness measurement[J]. Precision Engineering, 2005, 2: 257-260. doi: 10.3969/j.issn.1672-6030.2005.04.003
|
| [139] |
GAO W, SATO E, OHVMA T, et al. Roundness and spindle error measurement by angular three-probe method [J]. Journal of the Japan Society of Precision Engineering, 2002, 68(9): 1195-1199.
|
| [140] |
李硕, 栗新. 机械制造工艺基础[M]. 北京: 国防工业出版社, 2006.
|
| [141] |
ANANDAN K P, OZDOGANLAR O B. A multi-orientation error separation technique for spindle metrology of miniature ultra-high-speed spindles[J]. Precision Engineering, 2016, 43: 119-131. doi: 10.1016/j.precisioneng.2015.07.002
|
| [142] |
HUANG P, LEE W B, CHAN C. Investigation of the effects of spindle unbalance induced error motion on machining accuracy in precision diamond turning[J]. International Journal of Machine Tools & Manufacture, 2015, 94: 48-56.
|
| [143] |
周菲, 王庆军. 机床主轴回转误差对加工精度的影响[J]. 煤矿现代化, 2002(5): 28. doi: 10.13606/j.cnki.37-1205/td.2002.05.014
ZHOU F, WANG Q J. Influence of spindle rotation error on machining accuracy[J]. Coal Mine Modernization, 2002(5): 28. (in Chinese) doi: 10.13606/j.cnki.37-1205/td.2002.05.014
|
| [144] |
LU X, JAMALIAN A, GRAETZ R. A new method for characterizing axis of rotation radial error motion: Part 1. Two - dimensional radial error motion theory, Part 2. Experimental results[J]. Precision Engineering, 2011, 35(1): 73 -94. doi: 10.1016/j.precisioneng.2010.08.005
|
| [145] |
王晓慧, 李占魁, 袁哲俊. 圆度、圆柱度在线测量及补偿控制实验研究[J]. 哈尔滨工业大学学报, 1995, 27(1): 114-117. https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX501.025.htm
WANG X H, LI Z K, YUAN Z J. The experimental study of on-line measurement and compensatory control for the roundness and cylindricity[J]. Journal of Harbin Institute of Technology, 1995, 27(1): 114-117. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HEBX501.025.htm
|
| [146] |
HORIKAWA O, MARUYAMA N, SHIMADA M. A low cost, high accuracy roundness measuring system [J]. Precision Engineering, 2001, 25(3): 200-205. doi: 10.1016/S0141-6359(01)00070-8
|
| [147] |
ZHANG G X, ZHANG Y H, YANG S M, et al. A multipoint method for spindle error motion measurement [J]. CIRP Annals-Manufacturing Technology, 1997, 46(1): 441-445. doi: 10.1016/S0007-8506(07)60861-0
|
| [148] |
OKUYAMA E, NOSAKA N, AOKI J. Radial motion measurement of a high-revolution spindle motor [J]. Measurement, 2007, 40(1): 64-74. doi: 10.1016/j.measurement.2006.04.004
|
| [149] |
SARHAN A A D, HASSAN M A, MATSUBARA A, et al. High-precision machining by measuring and compensating the error motion of spindle's axis of rotation in radial direction[J]. Electrical Engineering and Intelligent Systems, 2013, 130: 347-359.
|
| [150] |
ERIC M, JEREMIAH C, RYAN V. Nanometer-level comparison of three spindle error motion separation techniques[J]. Journal of Manufacturing Science and Engineering, 2006, 128(1): 180-187. doi: 10.1115/1.2118747
|
| [151] |
王世良. 超精密车床主轴回转误差测试系统的研究[D]. 哈尔滨: 哈尔滨工业大学, 2016.
WANG S L. Research on measurement system of ultra precision lathe spindle rotation error[D]. Harbin: Harbin Institute of Technology, 2016. (in Chinese)
|
| [152] |
黄长征, 李圣怡. 超精密车床主轴回转精度动态测试仿真[J]. 计算机仿真, 2002(6): 96-99. doi: 10.3969/j.issn.1006-9348.2002.06.031
HUANG C Z, LI S Y. Dynamic test and simulation of spindle rotation accuracy of ultra precision lathe[J]. Computer Simulation, 2002(6): 96-99. (in Chinese) doi: 10.3969/j.issn.1006-9348.2002.06.031
|
| [153] |
黄长征, 李圣怡. 超精密车床主轴回转误差运动的动态测试[J]. 航空精密制造技术, 2002(4): 1-3. doi: 10.3969/j.issn.1003-5451.2002.04.001
HUANG C Z, LI S Y. Dynamic measurement of spindle error motion of ultraprecision lathe[J]. Aviation Precision Manufacturing Technology, 2002(4): 1-3. (in Chinese) doi: 10.3969/j.issn.1003-5451.2002.04.001
|
| [154] |
GREJDA R, MARSH E, VALLANCE R. Techniques for spindles with nanometer error motion[J]. Precision Engineering, 2005, 29(1): 113-123. doi: 10.1016/j.precisioneng.2004.05.003
|
| [155] |
LEE D H, LEE W R. Easy measuring instrument for analyzing the radial and tilt error motions of a rotating shaft[J]. Journal of Engineering for the Maritime Environment, 2017, 231(2): 667-674.
|
| [156] |
FUJIMAKI K, MITSUI K. Error correction method in radial run out measurements based on laser autocollimation[J]. Optical Engineering, 2008, 47(1): 86-89.
|
| [157] |
马平, 李健洪, 欧建国, 等. 主轴回转精度多步误差分离研究[J]. 机械科学与技术, 2018, 37(6): 884-890. doi: 10.13433/j.cnki.1003-8728.2018.0610
MA P, LI J H, OU J G, et al. Study on multi-step error separation of spindle rotation precision[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37(6): 884-890. (in Chinese) doi: 10.13433/j.cnki.1003-8728.2018.0610
|
| [158] |
洪迈生, 邓宗煌. 圆度和回转运动误差的时域二点法分离技术[J]. 中国机械工程, 1997(2): 88-89, 92, 125. doi: 10.3321/j.issn:1004-132X.1997.02.025
HONG M S, DENG Z H. Separation of roundness and rotary motion errors by time domain two-point method[J]. China Mechanical Engineering, 1997(2): 88-89, 92, 125. (in Chinese) doi: 10.3321/j.issn:1004-132X.1997.02.025
|
| [159] |
苏恒, 李自军, 魏员雷. 机床主轴运动误差的在线高精度测量[J]. 现代制造工程, 2002(3): 46-47. doi: 10.3969/j.issn.1671-3133.2002.03.023
SU H, LI Z J, WEI Y L. Study on multi-step error separation of spindle rotation precision[J]. Modern Manufacturing Engineering, 2002(3): 46-47. (in Chinese) doi: 10.3969/j.issn.1671-3133.2002.03.023
|
| [160] |
GAO W, TANO M, ARAKI T, et al. Measurement and compensation of error motions of a diamond turning machine[J]. Precision Engineering, 2007, 31(3): 310-316. doi: 10.1016/j.precisioneng.2006.06.003
|
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