超精密气浮定位工作台的动力学研究
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摘要
基于气浮支承和电磁直接驱动的定位工作台,是一种新型的超精密运动机构,它克服了传统的以旋转电机和滚动丝杠驱动的定位工作台传动环节多、响应滞后大、存在摩擦等缺点,在半导体光刻设备、精密测量和生物医学等领域具有十分广泛的应用前景。由于该定位工作台存在复杂的气浮非线性效应,传统的理论建模和分析方法不能解决这类超精密运动机构的系统动力学及定位控制的难题。
利用气浮支承润滑变分方法和有限元数值分析方法,计算并获得精密气浮轴承的动静特性的变化规律、气体流场和压力场的分布,揭示了气腔形状和气浮轴承内表面形状对轴承特性的影响规律,分析并辨识了气浮支承的特征参数,从而求得了不同气膜厚度下的轴承承载力和刚度,提出了气浮轴承的最佳结构形式。
运用理论分析和实验研究相结合的方法,探明了精密气浮定位工作台幅频响应受气浮支承参数非线性的影响特征,阐明了系统动力学性能随气浮轴承特征参数的变化规律。建立了气浮定位工作台定位运动的数学模型,提出了混合趋近律滑模控制新策略(MTSMC),进而建立了气浮定位工作台运动的混合趋近滑模控制的位置反馈控制模型,并进行了气浮参数的分析试验。结果表明气浮定位工作台在混合趋近滑模控制下,能消除气浮轴承非线性及定位平台存在未建模现象的影响,实现纳米级的定位控制精度。
完成了超精密气浮平台的动力学特性和定位精度测试实验,结果表明:在非气浮状态下,定位平台的运动部件间存在间隙和摩擦力,严重影响了平台运动的定位精度;而在气浮状态下,平台的运动部件间充满了压缩空气,虽然运动部件间仍然存在间隙,但是气浮支承所产生的气浮刚度使运动部件间具有了可靠的柔性连接,维持了较好的运动平稳性和良好的试验重复性;同时运动部件间不存在直接接触性摩擦,由于气体粘度小,其摩擦阻力可以忽略,平台的定位精度得到了极大的改善;气浮平台在Y方向和Z方向的最大直线度误差(3σ)为9.8256 nm,最大偏转误差(3σ)为3.8238×10-8 rad,平台的定位误差不超过±10 nm,验证了本文前面所述的理论和仿真结果的正确性。
The positioning stage with air bearings, which based on the air-supported bearing and direct electromagnetic-drive technology, is the new-typical machine of the precision motion which can overcome the shortages of the traditional positioning stage (The traditional positioning stage usually contains rotary motor, ball-screw and oil-lubricated bearings), such as more driving taches, big lag of response, and existed friction between the moving parts etc, therefore it has a prosperous application in the fields of semiconductor lithography equipment, precision measurement and biomedicine etc. For the existence of nonlinear effect caused by the air-supported bearing, the traditional modeling theory and analyse method couldn’t solve the problems on the system dynamics and positioning control of this kinds of ultra-precision moving machine.
The methods of the partial differential and the numerical analysis with limited elements are used to research the characteristic of the precision air bearing, and the changing regulation of the dynamic and static characteristic of the ultra-precision air bearing, as well as the models of the gas flow field, the pressure distribution, and characteristic parameters of the air bearing is obtained. Especially the effect rules of the recess shape and inner planar shape of the air lubricated bearings on the characteristic of the bearings are firstly opened out in the world, and the characteristic parameters of the air beanring are identified and the load capacity and the stiffness of the air bearing are obtained. Therefore, based on the researches mentioned above, the optimal structure of the air bearing is presented for the ultra-precision stage.
Through the theoretical and experimental studies, the effects of the nonlinearity caused by the air supported-bearing on the frequency characteristic of the precision positioning stage are proved up, and the researches on the dynamic performance of the ultra-precion positioning stage varied with the characteristic parameters of the air-supported bearings are carried out. The mathematical model of the positioning stage with air supported bearing is established, and a novel control tactic which based on the mixture trending slide mode control (MTSMC) is presented and the control model based on the MTSMC position feedback controller is established accordingly. The parameter sensitive analysis of the positioning stage is carried out. The results show that the effects the nonlinearity and unmodel factors can be eliminated and the positioning accuracy of the stage with air supported bearings can reach nanometer class when the MTSMC controller is used.
The dynamical experiment and positioning experiment of the stage are carried out too. The results show as follows: In the positioning stage without air supported bearings, the existence of the gap and the friction between the moving parts decrease the position accuracy of the stage seriously. Whereas, in the positioning stage with air supported bearings, though the gap between the moving parts exists yet, but there is pressured air in the gap, the stiffness of the air bearings play the role of the flexable connection between the moving parts, which makes the stage possess excellent repeatable positioning accuracy and smooth motion. Furthermore, the air-supported bearings eliminate friction between the moving parts, the positioning accuracy of stage is improved extremely, the maximum error of linearity(3σ) can reach 9.8256 nm in Y direction or Z direction, and the maximum error of pitch(3σ) can reach 3.8238×10-8 rad and the maximum error of positioning can reach not more than±10 nm , which means that the theoretical and simulating results above are correct.
利用气浮支承润滑变分方法和有限元数值分析方法,计算并获得精密气浮轴承的动静特性的变化规律、气体流场和压力场的分布,揭示了气腔形状和气浮轴承内表面形状对轴承特性的影响规律,分析并辨识了气浮支承的特征参数,从而求得了不同气膜厚度下的轴承承载力和刚度,提出了气浮轴承的最佳结构形式。
运用理论分析和实验研究相结合的方法,探明了精密气浮定位工作台幅频响应受气浮支承参数非线性的影响特征,阐明了系统动力学性能随气浮轴承特征参数的变化规律。建立了气浮定位工作台定位运动的数学模型,提出了混合趋近律滑模控制新策略(MTSMC),进而建立了气浮定位工作台运动的混合趋近滑模控制的位置反馈控制模型,并进行了气浮参数的分析试验。结果表明气浮定位工作台在混合趋近滑模控制下,能消除气浮轴承非线性及定位平台存在未建模现象的影响,实现纳米级的定位控制精度。
完成了超精密气浮平台的动力学特性和定位精度测试实验,结果表明:在非气浮状态下,定位平台的运动部件间存在间隙和摩擦力,严重影响了平台运动的定位精度;而在气浮状态下,平台的运动部件间充满了压缩空气,虽然运动部件间仍然存在间隙,但是气浮支承所产生的气浮刚度使运动部件间具有了可靠的柔性连接,维持了较好的运动平稳性和良好的试验重复性;同时运动部件间不存在直接接触性摩擦,由于气体粘度小,其摩擦阻力可以忽略,平台的定位精度得到了极大的改善;气浮平台在Y方向和Z方向的最大直线度误差(3σ)为9.8256 nm,最大偏转误差(3σ)为3.8238×10-8 rad,平台的定位误差不超过±10 nm,验证了本文前面所述的理论和仿真结果的正确性。
The positioning stage with air bearings, which based on the air-supported bearing and direct electromagnetic-drive technology, is the new-typical machine of the precision motion which can overcome the shortages of the traditional positioning stage (The traditional positioning stage usually contains rotary motor, ball-screw and oil-lubricated bearings), such as more driving taches, big lag of response, and existed friction between the moving parts etc, therefore it has a prosperous application in the fields of semiconductor lithography equipment, precision measurement and biomedicine etc. For the existence of nonlinear effect caused by the air-supported bearing, the traditional modeling theory and analyse method couldn’t solve the problems on the system dynamics and positioning control of this kinds of ultra-precision moving machine.
The methods of the partial differential and the numerical analysis with limited elements are used to research the characteristic of the precision air bearing, and the changing regulation of the dynamic and static characteristic of the ultra-precision air bearing, as well as the models of the gas flow field, the pressure distribution, and characteristic parameters of the air bearing is obtained. Especially the effect rules of the recess shape and inner planar shape of the air lubricated bearings on the characteristic of the bearings are firstly opened out in the world, and the characteristic parameters of the air beanring are identified and the load capacity and the stiffness of the air bearing are obtained. Therefore, based on the researches mentioned above, the optimal structure of the air bearing is presented for the ultra-precision stage.
Through the theoretical and experimental studies, the effects of the nonlinearity caused by the air supported-bearing on the frequency characteristic of the precision positioning stage are proved up, and the researches on the dynamic performance of the ultra-precion positioning stage varied with the characteristic parameters of the air-supported bearings are carried out. The mathematical model of the positioning stage with air supported bearing is established, and a novel control tactic which based on the mixture trending slide mode control (MTSMC) is presented and the control model based on the MTSMC position feedback controller is established accordingly. The parameter sensitive analysis of the positioning stage is carried out. The results show that the effects the nonlinearity and unmodel factors can be eliminated and the positioning accuracy of the stage with air supported bearings can reach nanometer class when the MTSMC controller is used.
The dynamical experiment and positioning experiment of the stage are carried out too. The results show as follows: In the positioning stage without air supported bearings, the existence of the gap and the friction between the moving parts decrease the position accuracy of the stage seriously. Whereas, in the positioning stage with air supported bearings, though the gap between the moving parts exists yet, but there is pressured air in the gap, the stiffness of the air bearings play the role of the flexable connection between the moving parts, which makes the stage possess excellent repeatable positioning accuracy and smooth motion. Furthermore, the air-supported bearings eliminate friction between the moving parts, the positioning accuracy of stage is improved extremely, the maximum error of linearity(3σ) can reach 9.8256 nm in Y direction or Z direction, and the maximum error of pitch(3σ) can reach 3.8238×10-8 rad and the maximum error of positioning can reach not more than±10 nm , which means that the theoretical and simulating results above are correct.
引文
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