超精密气浮定位平台动力学特性优化研究
|
摘要
基于静压气浮轴承支承和直线电机驱动技术的超精密气浮定位工作平台,是一种新型的精密运动机构,克服了传统上采用旋转电机和滚珠丝杠驱动方式所造成的传动环节多、响应滞后大以及存在非线性摩擦等缺点,实现了微纳米级加工定位和快速传输,被广泛应用于半导体光刻、精密测量和生物医学等领域。但是,当超精密定位平台的定位精度接近传统加工的极限时,其动力学特性难以满足高速运行时平台的稳定性和快速性要求。因此,本文对静压气浮轴承的支承刚度、空间位置和平台构型对平台动力学特性的影响以及相应的优化方法进行了深入系统的研究,研究成果已在100nm光刻机的研发中得以成功应用。
针对气浮支承刚度对定位平台动力学特性的影响,运用结构动力学建模的基本理论和有限元建模方法,对计算模型进行了气浮支承刚度波动的参数化修正,求解计算得到了系统的固有频率和广义刚度与气浮支承刚度之间的变化关系。采用最小二乘法,揭示了气浮支承刚度波动与平台固有频率之间的关系。基于气浮支承刚度变化对平台固有频率灵敏度的分析,提出了气浮支承刚度的优化方法。
提出了部分网格的空间移动技术,并对静压气浮轴承空间安装位置进行了优化研究。当静压气浮轴承安装在不同位置时,平台前5阶固有频率的比值的极限依次为:6.0961、5.4736、1.9246、1.6210、1.0917和1.2972,并且加速度响应的峰值具有明显的变化,最大的加速度响应峰值比达到了10倍左右。
利用拓扑优化技术,开展了超精密气浮定位平台驱动臂部分的优化研究。在进行动力学特性优化研究过程中,发现了现有驱动臂的设计不足,提出了驱动臂的设计优化方法,解决了超精密气浮定位平台驱动臂部分的设计问题。
基于上述研究成果对超精密气浮定位平台进行了动力学特性优化的实验研究。当静压气浮轴承在确定位置和支承刚度达到70N/μm时,对试验模态分析获得的平台固有频率,与有限元计算仿真结果进行对比分析,最大相对误差为3.24%,验证了静压气浮轴承支承刚度参数设置的正确性;调节静压气浮轴承的供气压力,对超精密气浮定位平台的动力学特征随静压气浮轴承支承刚度变化的实验研究,实验数据与仿真计算的结果进行对比分析,两者具有很好的一致性。
An ultra-precision positioning stage is a new type of precision motion mechanism, which is based on gas-lubricated bearing and linear motor driving. The stage can overcome the shortages result from the traditional positioning stage, such as more transmissions, bigger lag of response and existed nonlinear friction between moving parts and static ones. The stage can achieve the nanometer positioning accuracy and rapid moving, and has been widely used in semiconductor lithography, precision measurement and biomedical field. When the positioning accuracy approaches the tradition manufacturing limits, to meet with the more stability and faster response of the sateg have some difficulty. The factors, for example the stiffnesses of the gas-lubricated bearings, the location of the bearings and the configuration of stage, can influence the dynamics characteristic of the stage, obviously. The factors how to affect the dynamics characteristic of the stage is studied in the dissertation and carried out into optimization correspondingly. The performance has been applied in the development of 100 nm lithography successfully.
The structural dynamics and the finite element method are used to study the stiffness how to affect the dynamics characteristic of the stage. The stiffnesses are modified in the digital model. Natural frequencies and generalized stiffnesses of the stage are obtained by the calculation. The relationship between the supporting stiffness and the natural frequencies of the stage is obtained by least square method. The optimization methods of the stiffness accounting for the gas-lubricated bearing are obtained through the sensitivity analysis.
The partial grid mobile technology is put forward in the study firstly, and successed in applying the gas-lubricated bearing position optimization. When the air-bearings are installed in different positions, the maximal ratio between the optimal and worst position in the first 5 order natural frequencies is 6.0961, 5.4736, 1.9246, 1.6210, 1.0917 and 1.2972. And the response amplitude is changed manifestly, for example the maximal ratio is about 10 times in typical positions.
The drive arm is the key component of the ultra-precision positioning stage. The topology optimization technology is used to solve the design of the drive arm. The perfect design is proposed through the optimization. The drive arm design problem is solved.
Based on the results from the above research of the ultra-precision positioning stage with gas-lubricated bearings, the experimental modal analysis is conducted on the stage. When the bearing is on the given position and the stiffnesses of the bearings are equal to 70 N/μm, the maximal relative error is 3.24% compared with the results from the experiment and the finite element analysis. Regulated the supply pressure of the gas-lubricated bearings, the dynamics characteristic of the stage is changed. Compared with the results from the experimental model analysis and the finite element analysis under the different supply pressure or the stiffness, the results are in agreement with the experimental model analysis and the finite element analysis..
针对气浮支承刚度对定位平台动力学特性的影响,运用结构动力学建模的基本理论和有限元建模方法,对计算模型进行了气浮支承刚度波动的参数化修正,求解计算得到了系统的固有频率和广义刚度与气浮支承刚度之间的变化关系。采用最小二乘法,揭示了气浮支承刚度波动与平台固有频率之间的关系。基于气浮支承刚度变化对平台固有频率灵敏度的分析,提出了气浮支承刚度的优化方法。
提出了部分网格的空间移动技术,并对静压气浮轴承空间安装位置进行了优化研究。当静压气浮轴承安装在不同位置时,平台前5阶固有频率的比值的极限依次为:6.0961、5.4736、1.9246、1.6210、1.0917和1.2972,并且加速度响应的峰值具有明显的变化,最大的加速度响应峰值比达到了10倍左右。
利用拓扑优化技术,开展了超精密气浮定位平台驱动臂部分的优化研究。在进行动力学特性优化研究过程中,发现了现有驱动臂的设计不足,提出了驱动臂的设计优化方法,解决了超精密气浮定位平台驱动臂部分的设计问题。
基于上述研究成果对超精密气浮定位平台进行了动力学特性优化的实验研究。当静压气浮轴承在确定位置和支承刚度达到70N/μm时,对试验模态分析获得的平台固有频率,与有限元计算仿真结果进行对比分析,最大相对误差为3.24%,验证了静压气浮轴承支承刚度参数设置的正确性;调节静压气浮轴承的供气压力,对超精密气浮定位平台的动力学特征随静压气浮轴承支承刚度变化的实验研究,实验数据与仿真计算的结果进行对比分析,两者具有很好的一致性。
An ultra-precision positioning stage is a new type of precision motion mechanism, which is based on gas-lubricated bearing and linear motor driving. The stage can overcome the shortages result from the traditional positioning stage, such as more transmissions, bigger lag of response and existed nonlinear friction between moving parts and static ones. The stage can achieve the nanometer positioning accuracy and rapid moving, and has been widely used in semiconductor lithography, precision measurement and biomedical field. When the positioning accuracy approaches the tradition manufacturing limits, to meet with the more stability and faster response of the sateg have some difficulty. The factors, for example the stiffnesses of the gas-lubricated bearings, the location of the bearings and the configuration of stage, can influence the dynamics characteristic of the stage, obviously. The factors how to affect the dynamics characteristic of the stage is studied in the dissertation and carried out into optimization correspondingly. The performance has been applied in the development of 100 nm lithography successfully.
The structural dynamics and the finite element method are used to study the stiffness how to affect the dynamics characteristic of the stage. The stiffnesses are modified in the digital model. Natural frequencies and generalized stiffnesses of the stage are obtained by the calculation. The relationship between the supporting stiffness and the natural frequencies of the stage is obtained by least square method. The optimization methods of the stiffness accounting for the gas-lubricated bearing are obtained through the sensitivity analysis.
The partial grid mobile technology is put forward in the study firstly, and successed in applying the gas-lubricated bearing position optimization. When the air-bearings are installed in different positions, the maximal ratio between the optimal and worst position in the first 5 order natural frequencies is 6.0961, 5.4736, 1.9246, 1.6210, 1.0917 and 1.2972. And the response amplitude is changed manifestly, for example the maximal ratio is about 10 times in typical positions.
The drive arm is the key component of the ultra-precision positioning stage. The topology optimization technology is used to solve the design of the drive arm. The perfect design is proposed through the optimization. The drive arm design problem is solved.
Based on the results from the above research of the ultra-precision positioning stage with gas-lubricated bearings, the experimental modal analysis is conducted on the stage. When the bearing is on the given position and the stiffnesses of the bearings are equal to 70 N/μm, the maximal relative error is 3.24% compared with the results from the experiment and the finite element analysis. Regulated the supply pressure of the gas-lubricated bearings, the dynamics characteristic of the stage is changed. Compared with the results from the experimental model analysis and the finite element analysis under the different supply pressure or the stiffness, the results are in agreement with the experimental model analysis and the finite element analysis..
引文
[1] Yoichi Mochida, Masaya Tamura, Kuniki Ohwada. A micromachined vibrating rate gyroscope with independent beams for the drive and detection modes[J]. Sensors and Actuators, 2000(80):170-178.
[2] H Shinno, H Yoshioka, K Taniguchi. A newly developed linear motor-driven aerostatic X-Y planar motion table system for nano-machining[J]. CIRP Annals - Manufacturing Technology, 2007, 56(1):369-372.
[3] Jan Holterman, Theo J.A. de Vries, Frank, Auer. Active damping based on decoupled collocated control[J]. Proc. International Symposium on Active Control of Sound and Vibration Active 2002:827-838.
[4] T Kawai, K Ebihara, Y Takeuchi. Improvement of machining accuracy of 5-axis control ultraprecision machining by means of laminarization and mirror surface finishing[J]. CIRP Annals - Manufacturing Technology, 2005, 54(1): 329-332.
[5] Lee S Q, Gweon D G. A new 3-DOF Z-tilts micropositioning system using electromagnetic actuators and air bearings[J]. Precision Engineering, 2004(24):24-31.
[6] Chen X D, Yu X Z, He X M, et al. Dynamic characteristic analysis of precision long stroke linear motor with air-bearing in optical lithography[J]. Chinese Journal of Mechanical Engineering, 20008, 21(2):17-22.
[7]朱煜,尹文生,段广洪.光刻机超精密工件台研究.电子工业专用设备[J], 2004, 109(2):25-27.
[8]嵇钧生. X射线光刻机中应用的精密定位工作台[J].航空精密制造技术, 1998, 34(3):10-12.
[9]赵文宏,文东辉,戴勇等. IC硅片纳米级抛光专家控制技术的研究[J].金刚石与磨料磨具工程, 2006, 155(5):90-92.
[10]张从鹏,刘强.基于静压气浮导轨的直线电机高性能工作台的研制[J].机械科学与技术, 2006, 25(10):1212-1216.
[11]王文,李欣欣.超精密定位平台的测量系统研究[J],机电工程, 2006, 23(4):13-16.
[12] Mekid Samir. High precision linear slide part I: design and construction[J]. International Journal of Machine Tools & Manufacture, 2000, 40(3): 1039-1050.
[13] Akihisa Amada, Michio Tsunoda. High straightness positioning stage implementing real-time position compensation[J]. Motion & control, 2003, 12(5): 29-32.
[14] Mao Junhong, Tachikawa Hiroyuki, Shimokohbe Akira. Precision positioning of a DC-motor-driven aerostatic slide system[J]. Precision Engineering, 2003, 27(1): 32–41.
[15] Chen C L, Jang M J, Lin K C. Modeling and high-precision control of a ball-screw-driven stage[J]. Precision Engineering, 2004, 28(8): 483–495.
[16] Stout K J, Barrans S M. The design of aerostatic bearings for application to nanometer resolution manufacturing machine systems[J]. Tribology International, 2000, 33(10):803~809.
[17]冯伯儒,张锦,侯得胜等.微光刻技术的发展[J].微细加工技术, 2000, 36(l):1-9.
[18]陈开盛.亚微米光刻与光掩模新技术现状与研发前景[J].半导体技术, 2000, 25(5):18-21.
[19]苏雪莲.新世纪光刻技术及光刻设备的发展趋势[J].微电子技术, 2001, 29(2):8-17.
[20]王波,董申,赵万生.超精密定位中的几项相关关键技术[J].航空精密制造技术, 1998, 34(3):13-16.
[21]黄练伟,胡基士.直线感应电机推力及法向力的计算[J].机车电传动, 2005(1):36-39.
[22]李庆雷,王先奎,吴丹等.永磁同步直线电机推力及垂直力的有限元计算[J].清华大学学报(自然科学版), 2000, 40(5):20-23.
[23]张从鹏,刘强. H型直线电机工作台控制技术研究[J].机床与液压, 20007, 35(10):130-132.
[24]董吉洪,田兴志,李志来等. 100nm步进扫描投影光刻机工件台、掩模台的发展[J].微纳科学与技术, 2004,11(5):20-24.
[25]王继红,唐小平. 0.35微米分步重复投影光刻气浮工件台研究[J].微细加工技术, 1998, 13(3):20-24.
[26] Bert Vleeming, Barbra Heskamp, Hans Bakker. ArF step & scan with 0.75NA for the 0 .10μm node[J]. Proc. SPIE, 2001, 4346(4):634-652.
[27] Sluijk, Boudewijn, Castenmiller, Tom. Performance results of a new generation of 300mm lithography systems[J]. Proc. SPIE, 2001, 4346(3):544-557.
[28] Chensong Dong, Chuck Zhang, Ben Wang, et al. Reducing the dynamic errors of coordinate measuring machines[J]. Journal of Mechanical Design ASME, 2003, 125(7): 831-839.
[29]刘丹,程兆谷,高海军等.步进扫描投影工件台和掩膜台的进展[J].激光与光电子学进展, 2003, 40(5):14-20.
[30] H. Shinno, H. Hashizume, H. Yoshioka, et al. X-Y-θnano-positioning table system for a mother machine[J]. CIRP Annals-Manufacturing Technology, 2004, 53(1):337-340.
[31] Shigeki Goka, Seiji Hashimoto, Kiyoshi Ohishi, et al. Variable forgetting factor-based friction compensation method of precision stages[J]. SICE-ICASE International Joint Conference 2006, 10:18-21.
[32] Seiji Hashimoto, Kiyoshi Ohishi, Takuya Ohishi,et al. Ultra-precision stage control based on friction model of non-resonant ultrasonic motor[J]. AMC 2004, 1 (4):559-564.
[33] Heui Jae Pahk, Dong Sung Lee, Jong Ho Park. Ultra precision positioning system for servo motor–piezo actuator using the dual servo loop and digital filter implementation[J]. International Journal of Machine Tools and Manufacture, 2001, 41(1): 51-63.
[34] Z. Z Liu, F. L. Luo, M. H. Rashid. Robust high speed and high precision linear motor direct-drive XY-table motion system[J]. IEE Proc.–Control Appl. 2004, 151(2):166-173.
[35] Hongbo Lan, Yucheng Ding, Hongzhong Liu, et al. Review of the wafer stage for nanoimprint lithography[J]. Microelectronic Engineering, 2007,84(4):684-688
[36] Shuichi Dejima, Wei Gao, Hiroki Shimizu, et al. Precision positioning of a five degree-of-freedom planar motion stage[J]. Mechatronics, 2005, 15(8):969-987.
[37] Yung-Tien Liu, Rong-Fong Fung, Chun-Chao Wang. Precision position control using combined piezo-VCM actuators[J]. Precision Engineering, 2005, 29(4):411-422.
[38] H Shinno, H Yoshioka, K Taniguchi. A newly developed linear motor-driven aerostatic X-Y planar motion table system for nano-machining[J]. CIRP Annals-Manufacturing Technology, 2007, 56(1): 369-372.
[39] Chih-Liang Chu, Sheng-Hao Fan. A novel long-travel piezoelectric-driven linear nanopositioning stage[J]. Precision Engineering, 2006, 30(1):85-95.
[40] Wei Gao, Shuichi Dejima, Hiroaki Yanai, et al. A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning[J]. Precision Engineering, 2004, 28 (3):329-337.
[41] Shuichi Dejima, Wei Gao, Kei Katakura, et al. Dynamic modeling, controller design and experimental validation of a planar motion stage for precision positioning[J]. Precision Engineering, 2005, 29(3):263-271.
[42] Jooho Hwang, Chun-Hong Park, Chan-Hong Lee, et al. Estimation and correction method for the two-dimensional positionerrors of a planar XY stage based on motion error measurements[J]. International Journal of Machine Tools and Manufacture, 2006, 46(1):801-810.
[43] Wei Gao, Yoshikazu Arai, Atsushi Shibuya, et al. Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage[J]. Precision Engineering, 2006, 30(1):96-103.
[44] Mike Holmes, Robert Hocken, David Trumper. The long-range scanning stage: a novel platform for scanned-probe microscopy[J]. Precision Engineering, 2000, 24(3):191-209.
[45] Mike Holmes, David Trumper. Magnetic/fluid-bearing stage for atomic-scale motion control (the angstrom stage)[J]. Precision Engineering, 1996, 18(1):38-49.
[46] Won-Jong Kim, David L Trumper, James B Bryan. Linear motor-leviated stage for photolithography[J]. CIRP Annals-Manufacturing Technology, 1997, 46(1):447-450.
[47] Won-Jong Kim, David L Trumper. High-precision magnetic levitation stage for photolithography[J]. Precision Engineering, 1998, 22(2):66-77.
[48]何惠阳.微电子制芯领域中磁悬浮精密定位平台的研究[D].长春:中国科学院长春光学精密机械与物理研究所, 2004.
[49]黄欢,郁鼎文,刘向阳.超精密运动平台隔振系统性能分析与试验研究[J].科学技术与工程, 2006, 6(1):23-27.
[50]侯予,熊联友,林明峰等.多数供气孔静压环形止推气体轴承的研究[J].机械设计, 1999, 3:38-40.
[51] Y B P Kwan, J Corbett. A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings[J]. Tribology International, 1998, 31(12):779-786.
[52] L Li, T Shinshi, C jima, et al. Compensation of rotor imbance for precision rotation of a planar magnetic bearing rotor[J]. Precision Engineering, 2003, 27:140-150.
[53] Samir Mekid, Marc Bonis. Conceptual design and study of high precision translational stages: application to an optical delay line[J]. Precision Engineering, 1997, 21:29-35.
[54] G Belforte, T Raparelli, V Viktorov, et al. Discharge coefficient of orifice-type restrictor for aerostatic bearings[J]. Tribology International, 2007, 40:512-521.
[55] S Yoshimoto, J Tamura, T Nakamura. Dynamic tile characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors[J]. Tribology International, 1999, 32:731-738.
[56] Yusaku Fujii. Frictional characteristics of an aerostatic linear bearing[J]. Tribology International, 2006, 39:888-896.
[57] Yuantang Li, Han Ding. Influences of the geometrical parameters of aerostatic thrust bearing with pocketed orifice-type restrictor on its performace[J]. Tribology International, 2007, 40:1120-1126.
[58] Alexander Slocum, Murat Basaran, Roger Cortesi, et al. Linear motion carriage with aerostatic bearings preloaded by inclined iron core linear electric motor[J]. Precision Engineering, 2003, 27:382-394.
[59] Shigeka Yoshimoto, Makoto Yamamoto, Kazuyuki Toda. Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet[J]. Transaction of the ASME, 2007, 129:384-390.
[60] Cheng-Ying Lo, Cheng-Chi Wang, Yu-Han Lee. Performance analysis of high-speed spindle aerostatic bearings[J]. Tribology International, 2005, 38:5-14.
[61] Yim-Bun Patricl Kwan, Justus B. Post. A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings[J]. Tribology International, 2000, 33:581-585.
[62] Mohamed Fourka, Marc Bonis. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems[J]. Wear, 1997:311-317.
[63] Sadek Z Kassab, Elsayed M Noureldeen, Medhat A Shawky. Effects of operating conditions and supply hole diameter on the performance of a rectangular aerostatic bearing[J]. Tribology International, 1997, 30(7):533-545.
[64] Jyh-Chyang Renn, Chih-Hung Hsiao. Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings[J]. Tribology International, 2004, 37:309-315.
[65] M F Chen, Y T Lin. Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method[J]. Tribology International, 2002, 35:329-338.
[66] T S Giam, K K Tan, S Huang. Precision coordinated control of multi-axis gantry stages[J]. ISA Transactions, 2007, 46(3):399-409.
[67] Wen-Ruey Chang. The effect of surface roughness and contaminant on the dynamic friction of porcelain tile[J]. Applied Ergonomics, 2001, 32:183-184.
[68]叶云岳.直线电机原理与应用北京[M].北京:机械工业出版社, 2000.
[69] S Yoshimoto, K Kohno. 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):501-508.
[70] J P Khatait, W Lin, W J Lin. Design and development of orifice-type aerostatic thrust bearing[J]. SIMTech technical reports, 2006, 6:7-12.
[71]何学明.超精密气浮定位工作台的动力学研究[D].武汉:华中科技大学, 2007.
[72]徐月同.高速精密永磁直线同步电机进给系统及控制技术研究[D].杭州:浙江大学, 2004.
[73]夏家宽.高精度永磁直线电机端部效应推力波动及补偿策略研究[D].沈阳:沈阳工业大学, 2006.
[74] K K Tan, T H Lee, H Dou, S Zhao, Force ripple suppression in iron-core permanent magnet linear motors using an adaptive dither[J]. Journal of the Franklin Institute, 2004, 341:375-390.
[75] Mike Holmes, Robert Hocken, David Trumper. The long–range scanning stage: a novel platform for scanned-probe microscopy[J]. Journal of the International Societies for Precision Engineering and Nanotechnology, 2000, 24:191-209.
[76] Shuichi Dejima, Wei Gao, Hiroki Shimizu, Satoshi Kiyono, Yoshiyuki Tomita. Precision positioning of a five degree-of-freedom planar motion stage[J]. Mechatronics, 2005 ,15:969-987.
[77]陈丽萍.精密隔振平台微振动的H∞控制[J].中国工程机械学报, 2004, 2(4):494-498.
[78]石亦平,周玉蓉. ABAQUS有限元分析实例详解[M],北京:机械工业出版社, 2007, 7.
[79]赵腾伦,姚新军. ABAQUS 6.6在机械工程中的应用[M].北京,中国水利水电出版社, 2007, 5.
[80]李裕春,时党勇,赵远. ANSYS10.0/LS-DYNA基础理论裕工程实践[M].北京:中国水利水电出版社, 2006, 4.
[81]隋允康,杜家政,彭细荣. MSC.Nastran有限元动力分析与优化设计实用教程[M],北京:科学出版社, 2004.
[82] O C Zienkiewicz, R L Taylor. The finite element method Volume 1:The Basis(第5版)[M], Singapore:Elseview Pte Itd,北京:世界图书出版社公司, 2005.
[83] O C Zienkiewicz, R L Taylor. The finite element method Volume 2:Solid Mechanics(第5版)[M], Singapore:Elseview Pte Itd,北京:世界图书出版社公司, 2005.
[84] O C Zienkiewicz, R L Taylor. The finite element method Volume 3:Fluid dynamics(第5版)[M], Singapore:Elseview Pte Itd,北京:世界图书出版社公司, 2005.
[85] John O Hallquist. LS-DYNA theory manual [M], March 2006.
[86]王勖成,绍敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,2003,5.
[87]马爱军,周传月,王旭. Patran和Nastran有限元分析[M].北京:清华大学出版社, 2005.
[88] Ted Belytschko, Wing kan Liu, Brian Moran著,庄茁译.连续体和结构体的非线性有限元[M].北京:清华大学出版社, 2002.
[89]陈火红,杨剑,薛小香等. Marc有限元实例教程[M].北京:机械工业出版社,2007.
[90] Sung-Q Lee, Dae-Gab Gweon. A new 3-DOF Z-tilts micropositioning system using electromagnetic actuators and air bearings[J]. Precision Engineering, 2000, 24(1):24–31.
[91] K S Chen, D L Trumper, S T Smith. Design and control for an electromagnetically driven X–Y–θstage[J]. Journal of the International Societies for Precision Engineering and Nanotechnology, 2002, 26(2): 355–369.
[92] Gross W A etc. Fluid film lubrication [M]. New York: John Wiley&Sons, 1980:1-200.
[93]刘暾等著.静压气体润滑[M].哈尔滨:哈尔滨工业大学出版社,1990:1-200.
[94] Mohamed Fourka, Marc Bonis. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems[J]. Wear, 1997, 210(2):311-317.
[95] Sadek Z Kassab. Empirical correlations for the pressure depression in externally pressurized gas bearings[J]. Tribology International, 1997, 30(1):59-67.
[96] S Yoshimoto, J Tamura, T Nakamura. Dynamic tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors[J]. Tribology International, 1999, 32(5):731–738.
[97] C W Wu, G J Ma. Abnormal behavior of a hydrodynamic lubrication journal bearing caused by wall slip[J]. Tribology International, 2005, 38(3): 492–499.
[98] Jong Soo Kim, Kyung-Woong Kim. Effects of distance between pads on the inlet pressure build-up on pad bearings[J]. ASME Journal of Tribology, 2002, 124(7):506-514.
[99] Yim-Bun Patrick Kwan, Justus B Post. A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings[J]. Tribology International, 2000, 33(3):581–585.
[100] Mansour Karkoub, Ali Elkamel. Modelling pressure distribution in a rectangular gas bearing using neural networks[J]. Tribology International, 1997, 30(2):139-150.
[101]董卫华.几何加工精度对气体动压径向轴承性能的影响[J].南京航空航天大学学报, 1994, 26(5):635-641.
[102]里见忠笃,章亚男.节流孔特性对抑制气浮工作台自激振动的效果研究[J].光学精密工程, 1998, 6(5):33-38.
[103]边新孝,李谋渭.静压空气轴承的动刚度和阻尼分析[J].轴承, 2004, 12(1):1-3.
[104]薛贵侠.静压空气轴承的气膜刚度[J],计量技术, 2003, 36(6):24-25.
[105]景岗,杨清好,王元勋等.锯齿形多槽式动静压气体润滑轴承稳定性研究[J].华中理工大学学报, 1994, 22(2):74-77.
[106]景岗,杨清好,陈尔昌等.锯齿形多槽式动静压气体润滑轴承稳态和动态特性的研究[J].华中理工大学学报, 1994, 22(2):69-73.
[107]孙西芝,陈时锦,程凯.空气静压导轨静态性能的解析计算及分析[J].机械设计与制造, 2005, 55(1):40-42.
[108]李兴华.空气静压轴承的静特性计算及其实际应用[J].同济大学学报, 1999, 27(1):69-73.
[109]陈海斌,钟先信,程雪梅.空气静压轴承的优化设计[J].重庆大学学报, 1997, 20(1):21-26.
[110]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, 39(6):4-8.
[111] 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[J]. Tribology International, 2004, 37(7):825–832.
[112] Y B P Kwan, J Corbett. A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings[J]. Tribology International, 1998, 31(12):779–786.
[113] Y B P Kwan1, J Corbett, Porous aerostatic bearings–an updated review [J]. Wear, 1998, 222(1):69–73.
[114] Yong Tian. Static study of the porous bearings by the simplified finite element analysis [J]. Wear, 1998, 218(2):203-209.
[115] M Weck, P Kruger, C Brecher. Limits for controller settings with electric linear direct drives [J]. International Journal of Machine Tools & Manufacture, 2001, 41(1):65–88.
[116]朱益民,龚建伟,沙小红.磁悬浮实验系统的设计与分析[J].南通大学学报(自然科学版), 2005, 4(4):18-18.
[117]张钢,白华,王春兰,周罡.磁悬浮支承技术在机床中的应用[J].机械工程师, 2005, 8(1):15-20.
[118]李敏花,刘淑琴.磁悬浮轴承的模糊PID控制[J].控制工程, 2004, 11(5):409-412.
[119]于国飞,宋文荣,陈阳.磁悬浮轴承结构移动平台的设计与控制仿真[J].机械设计与研究, 2004, 20(5):47-51.
[120]居冰峰,陈子辰,邱忠宇.空气静压轴承主动控制技术的研究[J].机电工程机电一体化论文集, 1997, 1(1):144-145.
[121]葛卫平,齐乃明,刘暾.自主静压气体轴承参数优化与静态性能分析[J].南京理工大学学报, 2007, 31(3):308-311.
[122]杨国哲,王立平,郁鼎文等.三坐标精密运动平台的设计[J].机床与液压, 2006, 6:1-3.
[123]冯康,秦孟兆.哈密尔顿系统的辛几何算法[M],浙江:浙江科学技术出版社, 2003.
[124]程耿东.关于桁架结构拓扑优化中的奇异最优解[J].大连理工大学学报, 2000, 40(4):379-383.
[125]唐文艳,顾元宪,郭旭.求解具有奇异性的桁架拓扑优化的遗传算法[J].计算力学学报, 2004, 21(2):191-196.
[126] Yulu Wang. A study on microstructures of homogenization for topology optimization [D]. Australia, Melbourne, Victoria Universitu of Technology, 2003.
[127] N Ohno, T Marsuda, X Wu. A homogenization theory for elastic-viscoplastic composites with point symmetry of internal distributions[J]. International Journal of Solids and Structures, 2001, 38:2867-2878.
[128] Shinji Nishiwaki, Mary I Frechker, Seungjae Min, Noboru Kikychi. Topology optimization of compliant mechanisms using the homogenization method[J]. Int J Numer Meth Engng, 1998, 42:535-559.
[129] B Hassani, E Hinton. A review of homogenization and topology optimization I-homogenization theory for media with periodic structure[J]. Computers and Structures, 1998(69):707-717.
[130] B Hassani, E Hinton. A review of homogenization and topology optimization II-analytical and numerical solution of homogenization equations[J]. Computers and Structures, 1998(69):719-738.
[131] B Hassani, E Hinton. A review of homogenization and topology optimization III-topology optimization using optimality criteria [J]. Computers and Structures, 1998(69):739-756.
[132] Z Dimitrovova. A new methodology to establish upper bounds on open-cell foam homogenized moduli[J]. Struct Multidisc Optim, 2004(10).
[133] Sung Kie Koun, Sang-Hoon Park. A study on the shape extraction process in the structural topology optimization using homogenization material[J]. Computers & Structures, 1997(62):527-538.
[134] G Allaire, F Jouve, H Maillot. Topology optimization for minimum stress design with the homogenization method[J]. Struct Multidisc Optim, 2003(10).
[135] Greogire Allaire, Francois Jouve, Anca-Maria Toader. A level-set method for shape optimization[J]. Numerical Analysis, 2002(334):1125-1130.
[136] J Sethian, A Wiegmann. Structural boundary design via level set and immersed interface methods[J]. J. Comput. Phys. 2000, 163:489-528.
[137] S Osher, F Santosa. Level set methods for optiomization problems involving geometry and constraints: Frequencies of a two-density inhomogeneous drum[J]. J. Comput. Phys, 2001(171):272-288.
[138] Michael Yu Wang, Xiaoming Wang, Dongming Guo. A level set method for structural topology optimization[J], Comput. Methods Appl. Mech. Engrg. 2003(192):227-246.
[139] Mei Yulin, Wang Xiaoming. A level set method for structural topology optimization and its applications[J]. Advanced in Engineering Software, 2004(35):415-441.
[140] Michael Yu Wang, Xiaoming Wang. A level-set based varitional method for design and optimization of heterogeneous objects[J]. Computer-Aided Design, 2005(37):321-337.
[141] Gregoire Allaire, Francois Jouve. A level-set method for vibration and multiple loads structural optimization[J]. Comput. Methods Appl. Mech. Engrg., 2005(194):3269-3290.
[142] Oleg Alexandrov, Fadil Santosa. A topology-preserving level set method for shape optimization[J]. Journal of Computational physics, 2005(204):121-130.
[143] Michael Yu Wang, Xiaoming Wang.“Color”level sets: a multi-phase method for structural topology optimization with multiple materials[J]. Comput, Methods Appl. Mech. Engrg, 2004(193):469-496.
[144] Yoshifumi Okamoto, Norio Takahashi. Minimization of driving force ripple of linear motor for rope-less elevator using topology optimization technique[J]. Journal of Materials Processing Technology, 2007(181):131-135.
[145] Won-jong Kim, David L. Trumper. High-precision magnetic levitation stage forphotolithography[J]. Precision Engineering, 1998, 22(1):66–77.
[146]哈尔滨工业大学理论力学教研室.理论力学(I)[M].北京:高等教育出版社, 2005, 9.
[147] John O. Hallquist. LS-DYNA theory manual. 2006 March.
[148]王福军.计算流体动力学分析-CFD软件原理与应用[M].北京:清华大学出版社, 2004:1-55.
[149]张从鹏,刘强.直线电机气浮精密定位平台设计与控制[J].北京航空航天大学学报, 2008, 34(2):224-228.
[150]韩占忠,王敬,兰小平. FLUENT流体工程仿真计算[M].北京:北京理工大学出版社, 2004:1-46.
[151]张大卫,田延岭,王杏华,高咏生.超精密磨削辅助工作台及结构金币动态特性研究[J].天津大学学报, 2002, 35(4):506-510.
[152] Shane Woody, Stuar Smith. Design and performance of a dual drive system for tip-tilt angular control of a 300mm diameter mirror[J]. Mechatronics, 2006(16):389-397.
[153] Kato S. Theoretical analysis of damping characteristics of air-lubricated slideways [J]. Int J JSPE 1996(30):77-82.
[154]孙靖民,米成秋.机械结构优化设计[M].哈尔滨:哈尔滨工业大学出版社, 1985, 5.
[155] Kim J K, Joo S W, Hahn S C. Static characteristics of linear BLDC motor using equivalent circuit and finite element method [J]. IEEE Transactions on Magnetic, 2004, 40(2):742-745.
[156] Jang S M, Choi J Y, Cho H W. Dynamic characteristic analysis and experiments of moving-magnet linear actuator with cylindrical Halbach array[J]. IEEE Transactions on Magnetic, 2005, 41(10):3814-3816.
[157] Lu C, Eastham T R, Dawson G E. Transient and dynamics performance of a linear induction motor[J]. Industry Application Society Annual Meeting, 1993, 1:266-273.
[158] Kato S. Theoretical analysis of damping characteristics of air-lubricated slideways[J]. Int J JSPE 1996(30):77-82.
[159] Castillo J E, Otto J S. A practical guide to direct optimization for planar grid-generation[J]. Computers and Mathematics with Applications, 1999(37):123-156.
[160] Valliappan S, Tandjiria V, Khalili N. Design of raft-pile foundation using combined optimization and finite element approach[J]. Int J Numer and Meth Geomech, 1999(23):1043-1065.
[161] Lee D H, Hwang W S, Kim C M, Design sensitivity analysis and optimization of an engine mount system using an FRF-Based substructuring method[J]. Journal of Sound and Vibration, 2002, 255(2):383-397.
[162] Kirsch U. Combined approximations-a general reanalysis approach for structural optimization[J]. Struct Multidisc Optim, 2000(20):97-106.
[2] H Shinno, H Yoshioka, K Taniguchi. A newly developed linear motor-driven aerostatic X-Y planar motion table system for nano-machining[J]. CIRP Annals - Manufacturing Technology, 2007, 56(1):369-372.
[3] Jan Holterman, Theo J.A. de Vries, Frank, Auer. Active damping based on decoupled collocated control[J]. Proc. International Symposium on Active Control of Sound and Vibration Active 2002:827-838.
[4] T Kawai, K Ebihara, Y Takeuchi. Improvement of machining accuracy of 5-axis control ultraprecision machining by means of laminarization and mirror surface finishing[J]. CIRP Annals - Manufacturing Technology, 2005, 54(1): 329-332.
[5] Lee S Q, Gweon D G. A new 3-DOF Z-tilts micropositioning system using electromagnetic actuators and air bearings[J]. Precision Engineering, 2004(24):24-31.
[6] Chen X D, Yu X Z, He X M, et al. Dynamic characteristic analysis of precision long stroke linear motor with air-bearing in optical lithography[J]. Chinese Journal of Mechanical Engineering, 20008, 21(2):17-22.
[7]朱煜,尹文生,段广洪.光刻机超精密工件台研究.电子工业专用设备[J], 2004, 109(2):25-27.
[8]嵇钧生. X射线光刻机中应用的精密定位工作台[J].航空精密制造技术, 1998, 34(3):10-12.
[9]赵文宏,文东辉,戴勇等. IC硅片纳米级抛光专家控制技术的研究[J].金刚石与磨料磨具工程, 2006, 155(5):90-92.
[10]张从鹏,刘强.基于静压气浮导轨的直线电机高性能工作台的研制[J].机械科学与技术, 2006, 25(10):1212-1216.
[11]王文,李欣欣.超精密定位平台的测量系统研究[J],机电工程, 2006, 23(4):13-16.
[12] Mekid Samir. High precision linear slide part I: design and construction[J]. International Journal of Machine Tools & Manufacture, 2000, 40(3): 1039-1050.
[13] Akihisa Amada, Michio Tsunoda. High straightness positioning stage implementing real-time position compensation[J]. Motion & control, 2003, 12(5): 29-32.
[14] Mao Junhong, Tachikawa Hiroyuki, Shimokohbe Akira. Precision positioning of a DC-motor-driven aerostatic slide system[J]. Precision Engineering, 2003, 27(1): 32–41.
[15] Chen C L, Jang M J, Lin K C. Modeling and high-precision control of a ball-screw-driven stage[J]. Precision Engineering, 2004, 28(8): 483–495.
[16] Stout K J, Barrans S M. The design of aerostatic bearings for application to nanometer resolution manufacturing machine systems[J]. Tribology International, 2000, 33(10):803~809.
[17]冯伯儒,张锦,侯得胜等.微光刻技术的发展[J].微细加工技术, 2000, 36(l):1-9.
[18]陈开盛.亚微米光刻与光掩模新技术现状与研发前景[J].半导体技术, 2000, 25(5):18-21.
[19]苏雪莲.新世纪光刻技术及光刻设备的发展趋势[J].微电子技术, 2001, 29(2):8-17.
[20]王波,董申,赵万生.超精密定位中的几项相关关键技术[J].航空精密制造技术, 1998, 34(3):13-16.
[21]黄练伟,胡基士.直线感应电机推力及法向力的计算[J].机车电传动, 2005(1):36-39.
[22]李庆雷,王先奎,吴丹等.永磁同步直线电机推力及垂直力的有限元计算[J].清华大学学报(自然科学版), 2000, 40(5):20-23.
[23]张从鹏,刘强. H型直线电机工作台控制技术研究[J].机床与液压, 20007, 35(10):130-132.
[24]董吉洪,田兴志,李志来等. 100nm步进扫描投影光刻机工件台、掩模台的发展[J].微纳科学与技术, 2004,11(5):20-24.
[25]王继红,唐小平. 0.35微米分步重复投影光刻气浮工件台研究[J].微细加工技术, 1998, 13(3):20-24.
[26] Bert Vleeming, Barbra Heskamp, Hans Bakker. ArF step & scan with 0.75NA for the 0 .10μm node[J]. Proc. SPIE, 2001, 4346(4):634-652.
[27] Sluijk, Boudewijn, Castenmiller, Tom. Performance results of a new generation of 300mm lithography systems[J]. Proc. SPIE, 2001, 4346(3):544-557.
[28] Chensong Dong, Chuck Zhang, Ben Wang, et al. Reducing the dynamic errors of coordinate measuring machines[J]. Journal of Mechanical Design ASME, 2003, 125(7): 831-839.
[29]刘丹,程兆谷,高海军等.步进扫描投影工件台和掩膜台的进展[J].激光与光电子学进展, 2003, 40(5):14-20.
[30] H. Shinno, H. Hashizume, H. Yoshioka, et al. X-Y-θnano-positioning table system for a mother machine[J]. CIRP Annals-Manufacturing Technology, 2004, 53(1):337-340.
[31] Shigeki Goka, Seiji Hashimoto, Kiyoshi Ohishi, et al. Variable forgetting factor-based friction compensation method of precision stages[J]. SICE-ICASE International Joint Conference 2006, 10:18-21.
[32] Seiji Hashimoto, Kiyoshi Ohishi, Takuya Ohishi,et al. Ultra-precision stage control based on friction model of non-resonant ultrasonic motor[J]. AMC 2004, 1 (4):559-564.
[33] Heui Jae Pahk, Dong Sung Lee, Jong Ho Park. Ultra precision positioning system for servo motor–piezo actuator using the dual servo loop and digital filter implementation[J]. International Journal of Machine Tools and Manufacture, 2001, 41(1): 51-63.
[34] Z. Z Liu, F. L. Luo, M. H. Rashid. Robust high speed and high precision linear motor direct-drive XY-table motion system[J]. IEE Proc.–Control Appl. 2004, 151(2):166-173.
[35] Hongbo Lan, Yucheng Ding, Hongzhong Liu, et al. Review of the wafer stage for nanoimprint lithography[J]. Microelectronic Engineering, 2007,84(4):684-688
[36] Shuichi Dejima, Wei Gao, Hiroki Shimizu, et al. Precision positioning of a five degree-of-freedom planar motion stage[J]. Mechatronics, 2005, 15(8):969-987.
[37] Yung-Tien Liu, Rong-Fong Fung, Chun-Chao Wang. Precision position control using combined piezo-VCM actuators[J]. Precision Engineering, 2005, 29(4):411-422.
[38] H Shinno, H Yoshioka, K Taniguchi. A newly developed linear motor-driven aerostatic X-Y planar motion table system for nano-machining[J]. CIRP Annals-Manufacturing Technology, 2007, 56(1): 369-372.
[39] Chih-Liang Chu, Sheng-Hao Fan. A novel long-travel piezoelectric-driven linear nanopositioning stage[J]. Precision Engineering, 2006, 30(1):85-95.
[40] Wei Gao, Shuichi Dejima, Hiroaki Yanai, et al. A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning[J]. Precision Engineering, 2004, 28 (3):329-337.
[41] Shuichi Dejima, Wei Gao, Kei Katakura, et al. Dynamic modeling, controller design and experimental validation of a planar motion stage for precision positioning[J]. Precision Engineering, 2005, 29(3):263-271.
[42] Jooho Hwang, Chun-Hong Park, Chan-Hong Lee, et al. Estimation and correction method for the two-dimensional positionerrors of a planar XY stage based on motion error measurements[J]. International Journal of Machine Tools and Manufacture, 2006, 46(1):801-810.
[43] Wei Gao, Yoshikazu Arai, Atsushi Shibuya, et al. Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage[J]. Precision Engineering, 2006, 30(1):96-103.
[44] Mike Holmes, Robert Hocken, David Trumper. The long-range scanning stage: a novel platform for scanned-probe microscopy[J]. Precision Engineering, 2000, 24(3):191-209.
[45] Mike Holmes, David Trumper. Magnetic/fluid-bearing stage for atomic-scale motion control (the angstrom stage)[J]. Precision Engineering, 1996, 18(1):38-49.
[46] Won-Jong Kim, David L Trumper, James B Bryan. Linear motor-leviated stage for photolithography[J]. CIRP Annals-Manufacturing Technology, 1997, 46(1):447-450.
[47] Won-Jong Kim, David L Trumper. High-precision magnetic levitation stage for photolithography[J]. Precision Engineering, 1998, 22(2):66-77.
[48]何惠阳.微电子制芯领域中磁悬浮精密定位平台的研究[D].长春:中国科学院长春光学精密机械与物理研究所, 2004.
[49]黄欢,郁鼎文,刘向阳.超精密运动平台隔振系统性能分析与试验研究[J].科学技术与工程, 2006, 6(1):23-27.
[50]侯予,熊联友,林明峰等.多数供气孔静压环形止推气体轴承的研究[J].机械设计, 1999, 3:38-40.
[51] Y B P Kwan, J Corbett. A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings[J]. Tribology International, 1998, 31(12):779-786.
[52] L Li, T Shinshi, C jima, et al. Compensation of rotor imbance for precision rotation of a planar magnetic bearing rotor[J]. Precision Engineering, 2003, 27:140-150.
[53] Samir Mekid, Marc Bonis. Conceptual design and study of high precision translational stages: application to an optical delay line[J]. Precision Engineering, 1997, 21:29-35.
[54] G Belforte, T Raparelli, V Viktorov, et al. Discharge coefficient of orifice-type restrictor for aerostatic bearings[J]. Tribology International, 2007, 40:512-521.
[55] S Yoshimoto, J Tamura, T Nakamura. Dynamic tile characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors[J]. Tribology International, 1999, 32:731-738.
[56] Yusaku Fujii. Frictional characteristics of an aerostatic linear bearing[J]. Tribology International, 2006, 39:888-896.
[57] Yuantang Li, Han Ding. Influences of the geometrical parameters of aerostatic thrust bearing with pocketed orifice-type restrictor on its performace[J]. Tribology International, 2007, 40:1120-1126.
[58] Alexander Slocum, Murat Basaran, Roger Cortesi, et al. Linear motion carriage with aerostatic bearings preloaded by inclined iron core linear electric motor[J]. Precision Engineering, 2003, 27:382-394.
[59] Shigeka Yoshimoto, Makoto Yamamoto, Kazuyuki Toda. Numerical calculations of pressure distribution in the bearing clearance of circular aerostatic thrust bearings with a single air supply inlet[J]. Transaction of the ASME, 2007, 129:384-390.
[60] Cheng-Ying Lo, Cheng-Chi Wang, Yu-Han Lee. Performance analysis of high-speed spindle aerostatic bearings[J]. Tribology International, 2005, 38:5-14.
[61] Yim-Bun Patricl Kwan, Justus B. Post. A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings[J]. Tribology International, 2000, 33:581-585.
[62] Mohamed Fourka, Marc Bonis. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems[J]. Wear, 1997:311-317.
[63] Sadek Z Kassab, Elsayed M Noureldeen, Medhat A Shawky. Effects of operating conditions and supply hole diameter on the performance of a rectangular aerostatic bearing[J]. Tribology International, 1997, 30(7):533-545.
[64] Jyh-Chyang Renn, Chih-Hung Hsiao. Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings[J]. Tribology International, 2004, 37:309-315.
[65] M F Chen, Y T Lin. Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method[J]. Tribology International, 2002, 35:329-338.
[66] T S Giam, K K Tan, S Huang. Precision coordinated control of multi-axis gantry stages[J]. ISA Transactions, 2007, 46(3):399-409.
[67] Wen-Ruey Chang. The effect of surface roughness and contaminant on the dynamic friction of porcelain tile[J]. Applied Ergonomics, 2001, 32:183-184.
[68]叶云岳.直线电机原理与应用北京[M].北京:机械工业出版社, 2000.
[69] S Yoshimoto, K Kohno. 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):501-508.
[70] J P Khatait, W Lin, W J Lin. Design and development of orifice-type aerostatic thrust bearing[J]. SIMTech technical reports, 2006, 6:7-12.
[71]何学明.超精密气浮定位工作台的动力学研究[D].武汉:华中科技大学, 2007.
[72]徐月同.高速精密永磁直线同步电机进给系统及控制技术研究[D].杭州:浙江大学, 2004.
[73]夏家宽.高精度永磁直线电机端部效应推力波动及补偿策略研究[D].沈阳:沈阳工业大学, 2006.
[74] K K Tan, T H Lee, H Dou, S Zhao, Force ripple suppression in iron-core permanent magnet linear motors using an adaptive dither[J]. Journal of the Franklin Institute, 2004, 341:375-390.
[75] Mike Holmes, Robert Hocken, David Trumper. The long–range scanning stage: a novel platform for scanned-probe microscopy[J]. Journal of the International Societies for Precision Engineering and Nanotechnology, 2000, 24:191-209.
[76] Shuichi Dejima, Wei Gao, Hiroki Shimizu, Satoshi Kiyono, Yoshiyuki Tomita. Precision positioning of a five degree-of-freedom planar motion stage[J]. Mechatronics, 2005 ,15:969-987.
[77]陈丽萍.精密隔振平台微振动的H∞控制[J].中国工程机械学报, 2004, 2(4):494-498.
[78]石亦平,周玉蓉. ABAQUS有限元分析实例详解[M],北京:机械工业出版社, 2007, 7.
[79]赵腾伦,姚新军. ABAQUS 6.6在机械工程中的应用[M].北京,中国水利水电出版社, 2007, 5.
[80]李裕春,时党勇,赵远. ANSYS10.0/LS-DYNA基础理论裕工程实践[M].北京:中国水利水电出版社, 2006, 4.
[81]隋允康,杜家政,彭细荣. MSC.Nastran有限元动力分析与优化设计实用教程[M],北京:科学出版社, 2004.
[82] O C Zienkiewicz, R L Taylor. The finite element method Volume 1:The Basis(第5版)[M], Singapore:Elseview Pte Itd,北京:世界图书出版社公司, 2005.
[83] O C Zienkiewicz, R L Taylor. The finite element method Volume 2:Solid Mechanics(第5版)[M], Singapore:Elseview Pte Itd,北京:世界图书出版社公司, 2005.
[84] O C Zienkiewicz, R L Taylor. The finite element method Volume 3:Fluid dynamics(第5版)[M], Singapore:Elseview Pte Itd,北京:世界图书出版社公司, 2005.
[85] John O Hallquist. LS-DYNA theory manual [M], March 2006.
[86]王勖成,绍敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,2003,5.
[87]马爱军,周传月,王旭. Patran和Nastran有限元分析[M].北京:清华大学出版社, 2005.
[88] Ted Belytschko, Wing kan Liu, Brian Moran著,庄茁译.连续体和结构体的非线性有限元[M].北京:清华大学出版社, 2002.
[89]陈火红,杨剑,薛小香等. Marc有限元实例教程[M].北京:机械工业出版社,2007.
[90] Sung-Q Lee, Dae-Gab Gweon. A new 3-DOF Z-tilts micropositioning system using electromagnetic actuators and air bearings[J]. Precision Engineering, 2000, 24(1):24–31.
[91] K S Chen, D L Trumper, S T Smith. Design and control for an electromagnetically driven X–Y–θstage[J]. Journal of the International Societies for Precision Engineering and Nanotechnology, 2002, 26(2): 355–369.
[92] Gross W A etc. Fluid film lubrication [M]. New York: John Wiley&Sons, 1980:1-200.
[93]刘暾等著.静压气体润滑[M].哈尔滨:哈尔滨工业大学出版社,1990:1-200.
[94] Mohamed Fourka, Marc Bonis. Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems[J]. Wear, 1997, 210(2):311-317.
[95] Sadek Z Kassab. Empirical correlations for the pressure depression in externally pressurized gas bearings[J]. Tribology International, 1997, 30(1):59-67.
[96] S Yoshimoto, J Tamura, T Nakamura. Dynamic tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors[J]. Tribology International, 1999, 32(5):731–738.
[97] C W Wu, G J Ma. Abnormal behavior of a hydrodynamic lubrication journal bearing caused by wall slip[J]. Tribology International, 2005, 38(3): 492–499.
[98] Jong Soo Kim, Kyung-Woong Kim. Effects of distance between pads on the inlet pressure build-up on pad bearings[J]. ASME Journal of Tribology, 2002, 124(7):506-514.
[99] Yim-Bun Patrick Kwan, Justus B Post. A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings[J]. Tribology International, 2000, 33(3):581–585.
[100] Mansour Karkoub, Ali Elkamel. Modelling pressure distribution in a rectangular gas bearing using neural networks[J]. Tribology International, 1997, 30(2):139-150.
[101]董卫华.几何加工精度对气体动压径向轴承性能的影响[J].南京航空航天大学学报, 1994, 26(5):635-641.
[102]里见忠笃,章亚男.节流孔特性对抑制气浮工作台自激振动的效果研究[J].光学精密工程, 1998, 6(5):33-38.
[103]边新孝,李谋渭.静压空气轴承的动刚度和阻尼分析[J].轴承, 2004, 12(1):1-3.
[104]薛贵侠.静压空气轴承的气膜刚度[J],计量技术, 2003, 36(6):24-25.
[105]景岗,杨清好,王元勋等.锯齿形多槽式动静压气体润滑轴承稳定性研究[J].华中理工大学学报, 1994, 22(2):74-77.
[106]景岗,杨清好,陈尔昌等.锯齿形多槽式动静压气体润滑轴承稳态和动态特性的研究[J].华中理工大学学报, 1994, 22(2):69-73.
[107]孙西芝,陈时锦,程凯.空气静压导轨静态性能的解析计算及分析[J].机械设计与制造, 2005, 55(1):40-42.
[108]李兴华.空气静压轴承的静特性计算及其实际应用[J].同济大学学报, 1999, 27(1):69-73.
[109]陈海斌,钟先信,程雪梅.空气静压轴承的优化设计[J].重庆大学学报, 1997, 20(1):21-26.
[110]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, 39(6):4-8.
[111] 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[J]. Tribology International, 2004, 37(7):825–832.
[112] Y B P Kwan, J Corbett. A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings[J]. Tribology International, 1998, 31(12):779–786.
[113] Y B P Kwan1, J Corbett, Porous aerostatic bearings–an updated review [J]. Wear, 1998, 222(1):69–73.
[114] Yong Tian. Static study of the porous bearings by the simplified finite element analysis [J]. Wear, 1998, 218(2):203-209.
[115] M Weck, P Kruger, C Brecher. Limits for controller settings with electric linear direct drives [J]. International Journal of Machine Tools & Manufacture, 2001, 41(1):65–88.
[116]朱益民,龚建伟,沙小红.磁悬浮实验系统的设计与分析[J].南通大学学报(自然科学版), 2005, 4(4):18-18.
[117]张钢,白华,王春兰,周罡.磁悬浮支承技术在机床中的应用[J].机械工程师, 2005, 8(1):15-20.
[118]李敏花,刘淑琴.磁悬浮轴承的模糊PID控制[J].控制工程, 2004, 11(5):409-412.
[119]于国飞,宋文荣,陈阳.磁悬浮轴承结构移动平台的设计与控制仿真[J].机械设计与研究, 2004, 20(5):47-51.
[120]居冰峰,陈子辰,邱忠宇.空气静压轴承主动控制技术的研究[J].机电工程机电一体化论文集, 1997, 1(1):144-145.
[121]葛卫平,齐乃明,刘暾.自主静压气体轴承参数优化与静态性能分析[J].南京理工大学学报, 2007, 31(3):308-311.
[122]杨国哲,王立平,郁鼎文等.三坐标精密运动平台的设计[J].机床与液压, 2006, 6:1-3.
[123]冯康,秦孟兆.哈密尔顿系统的辛几何算法[M],浙江:浙江科学技术出版社, 2003.
[124]程耿东.关于桁架结构拓扑优化中的奇异最优解[J].大连理工大学学报, 2000, 40(4):379-383.
[125]唐文艳,顾元宪,郭旭.求解具有奇异性的桁架拓扑优化的遗传算法[J].计算力学学报, 2004, 21(2):191-196.
[126] Yulu Wang. A study on microstructures of homogenization for topology optimization [D]. Australia, Melbourne, Victoria Universitu of Technology, 2003.
[127] N Ohno, T Marsuda, X Wu. A homogenization theory for elastic-viscoplastic composites with point symmetry of internal distributions[J]. International Journal of Solids and Structures, 2001, 38:2867-2878.
[128] Shinji Nishiwaki, Mary I Frechker, Seungjae Min, Noboru Kikychi. Topology optimization of compliant mechanisms using the homogenization method[J]. Int J Numer Meth Engng, 1998, 42:535-559.
[129] B Hassani, E Hinton. A review of homogenization and topology optimization I-homogenization theory for media with periodic structure[J]. Computers and Structures, 1998(69):707-717.
[130] B Hassani, E Hinton. A review of homogenization and topology optimization II-analytical and numerical solution of homogenization equations[J]. Computers and Structures, 1998(69):719-738.
[131] B Hassani, E Hinton. A review of homogenization and topology optimization III-topology optimization using optimality criteria [J]. Computers and Structures, 1998(69):739-756.
[132] Z Dimitrovova. A new methodology to establish upper bounds on open-cell foam homogenized moduli[J]. Struct Multidisc Optim, 2004(10).
[133] Sung Kie Koun, Sang-Hoon Park. A study on the shape extraction process in the structural topology optimization using homogenization material[J]. Computers & Structures, 1997(62):527-538.
[134] G Allaire, F Jouve, H Maillot. Topology optimization for minimum stress design with the homogenization method[J]. Struct Multidisc Optim, 2003(10).
[135] Greogire Allaire, Francois Jouve, Anca-Maria Toader. A level-set method for shape optimization[J]. Numerical Analysis, 2002(334):1125-1130.
[136] J Sethian, A Wiegmann. Structural boundary design via level set and immersed interface methods[J]. J. Comput. Phys. 2000, 163:489-528.
[137] S Osher, F Santosa. Level set methods for optiomization problems involving geometry and constraints: Frequencies of a two-density inhomogeneous drum[J]. J. Comput. Phys, 2001(171):272-288.
[138] Michael Yu Wang, Xiaoming Wang, Dongming Guo. A level set method for structural topology optimization[J], Comput. Methods Appl. Mech. Engrg. 2003(192):227-246.
[139] Mei Yulin, Wang Xiaoming. A level set method for structural topology optimization and its applications[J]. Advanced in Engineering Software, 2004(35):415-441.
[140] Michael Yu Wang, Xiaoming Wang. A level-set based varitional method for design and optimization of heterogeneous objects[J]. Computer-Aided Design, 2005(37):321-337.
[141] Gregoire Allaire, Francois Jouve. A level-set method for vibration and multiple loads structural optimization[J]. Comput. Methods Appl. Mech. Engrg., 2005(194):3269-3290.
[142] Oleg Alexandrov, Fadil Santosa. A topology-preserving level set method for shape optimization[J]. Journal of Computational physics, 2005(204):121-130.
[143] Michael Yu Wang, Xiaoming Wang.“Color”level sets: a multi-phase method for structural topology optimization with multiple materials[J]. Comput, Methods Appl. Mech. Engrg, 2004(193):469-496.
[144] Yoshifumi Okamoto, Norio Takahashi. Minimization of driving force ripple of linear motor for rope-less elevator using topology optimization technique[J]. Journal of Materials Processing Technology, 2007(181):131-135.
[145] Won-jong Kim, David L. Trumper. High-precision magnetic levitation stage forphotolithography[J]. Precision Engineering, 1998, 22(1):66–77.
[146]哈尔滨工业大学理论力学教研室.理论力学(I)[M].北京:高等教育出版社, 2005, 9.
[147] John O. Hallquist. LS-DYNA theory manual. 2006 March.
[148]王福军.计算流体动力学分析-CFD软件原理与应用[M].北京:清华大学出版社, 2004:1-55.
[149]张从鹏,刘强.直线电机气浮精密定位平台设计与控制[J].北京航空航天大学学报, 2008, 34(2):224-228.
[150]韩占忠,王敬,兰小平. FLUENT流体工程仿真计算[M].北京:北京理工大学出版社, 2004:1-46.
[151]张大卫,田延岭,王杏华,高咏生.超精密磨削辅助工作台及结构金币动态特性研究[J].天津大学学报, 2002, 35(4):506-510.
[152] Shane Woody, Stuar Smith. Design and performance of a dual drive system for tip-tilt angular control of a 300mm diameter mirror[J]. Mechatronics, 2006(16):389-397.
[153] Kato S. Theoretical analysis of damping characteristics of air-lubricated slideways [J]. Int J JSPE 1996(30):77-82.
[154]孙靖民,米成秋.机械结构优化设计[M].哈尔滨:哈尔滨工业大学出版社, 1985, 5.
[155] Kim J K, Joo S W, Hahn S C. Static characteristics of linear BLDC motor using equivalent circuit and finite element method [J]. IEEE Transactions on Magnetic, 2004, 40(2):742-745.
[156] Jang S M, Choi J Y, Cho H W. Dynamic characteristic analysis and experiments of moving-magnet linear actuator with cylindrical Halbach array[J]. IEEE Transactions on Magnetic, 2005, 41(10):3814-3816.
[157] Lu C, Eastham T R, Dawson G E. Transient and dynamics performance of a linear induction motor[J]. Industry Application Society Annual Meeting, 1993, 1:266-273.
[158] Kato S. Theoretical analysis of damping characteristics of air-lubricated slideways[J]. Int J JSPE 1996(30):77-82.
[159] Castillo J E, Otto J S. A practical guide to direct optimization for planar grid-generation[J]. Computers and Mathematics with Applications, 1999(37):123-156.
[160] Valliappan S, Tandjiria V, Khalili N. Design of raft-pile foundation using combined optimization and finite element approach[J]. Int J Numer and Meth Geomech, 1999(23):1043-1065.
[161] Lee D H, Hwang W S, Kim C M, Design sensitivity analysis and optimization of an engine mount system using an FRF-Based substructuring method[J]. Journal of Sound and Vibration, 2002, 255(2):383-397.
[162] Kirsch U. Combined approximations-a general reanalysis approach for structural optimization[J]. Struct Multidisc Optim, 2000(20):97-106.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |