华中科技大学博士学位论文超精密气浮定位平台动力学特性优化研究姓名：李志鑫申请学位级别：博士专业：机械电子工程指导教师：陈学东20080604I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/m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。 关键词：关键词：超精密气浮定位平台 动态特性分析 刚度数值优化 位置优化 拓扑优化 IIAbstract 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/m, the maximal relative error is 3.24% compared with the results from the experiment IIIand 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. Key words: Ultra-precision positioning stage with gas-lubricated bearing; Dynamic characteristics analysis; Stiffness optimization; Position optimization; Topology optimization II独创性声明独创性声明 本人声明所呈交的学位论文是我个人在导师指导下进行的研究工作及取得的研究成果。尽我所知，除文中已经标明引用的内容外，本论文不包含任何其他个人或集体已经发表或撰写过的研究成果。对本文的研究做出贡献的个人和集体，均已在文中以明确方式标明。本人完全意识到，本声明的法律结果由本人承担。 学位论文作者签名： 日期： 年 月 日 学位论文版权使用授权书学位论文版权使用授权书 本学位论文作者完全了解学校有关保留、使用学位论文的规定，即：学校有权保留并向国家有关部门或机构送交论文的复印件和电子版， 允许论文被查阅和借阅。 本人授权华中科技大学可以将本学位论文的全部或部分内容编入有关数据库进行检索， 可以采用影印、 缩印或扫描等复制手段保存和汇编本学位论文。 保密 ，在_年解密后适用本授权书。 不保密。 （请在以上方框内打“”） 学位论文作者签名： 指导教师签名： 日期： 年 月 日 日期： 年 月 日 本论文属于 11. 绪论绪论 1.1 课题来源与研究背景课题来源与研究背景 1.1.1 课题来源课题来源 本课题得到了以下科研项目的资助：