面向纳米压印光刻设备的精密定位工作台的设计方法与实验
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摘要
本文以用于纳米压印光刻技术的精密定位工作台的开发为目标,深入系统地研究了一种具有3平动自由度的空间柔性并联定位机构的创新结构设计、运动学分析、刚度分析、静动力学分析、误差建模等关键技术,并建造了由压电陶瓷驱动器驱动的精密定位工作台样机。取得了如下主要研究成果:
以改进的DELTA并联机构为基础,将机构中的转动副用单自由度柔性铰链代替,研制了一台具有3平动自由度的精密定位工作台。该定位工作台采用多个压电陶瓷驱动器驱动方式,可实现末端位置的主动调整。
采用“伪刚体模型”方法将该精密定位工作台分别等效为偏置式伪刚体模型和非偏置式伪刚体模型,并利用齐次坐标变换方法和矢量闭环方法构建其正、逆运动学模型,结合有限元分析比较两种模型的优劣,并以非偏置式伪刚体模型作为后续分析的依据,以柔性铰链允许转角范围为约束条件分析工作台可达工作空间,并以工作空间最大为目标进行机构参数的优化设计。
考虑工作台重力势能和柔性铰链的弹性应变能,建立支链驱动刚度模型,为压电陶瓷驱动器的选择提供依据。针对从动臂平行四边形结构,讨论不同约束方式下,上下端连接横梁柔度特性对其输出刚度的影响。利用柔度矩阵和位置变换矩阵相结合的方法,建立定位工作台输出刚度模型,分别讨论了杆长、柔性铰链切口半径等几何参数的影响规律,并利用有限元仿真加以验证。
利用虚功原理方法建立了机构的静力学模型,讨论了各构件质量、柔性铰链刚度对动平台位置的影响作用。利用虚功原理方法和拉格朗日方程方法建立机构的动力学模型,讨论了构件质量、柔性铰链刚度对驱动力矩的影响规律,并结合不同的运动轨迹,将根据两种方法得到的动力学逆解模型进行对比,说明其有效性。讨论了几何参数、柔性铰链刚度对系统固有频率的影响。
综合考虑包括理论建模误差、杆长误差、柔性铰链加工误差、装配误差等多种误差源形式,并以采用递推方式得到的运动学模型为基础,建立了定位工作台全参数误差辨识模型,并进行了计算机仿真。
最后,利用所建造的精密定位工作台样机,进行了运动学、静态刚度以及固有频率试验,将试验结果与理论模型以及有限元仿真模型结果进行比较表明所建立的理论模型以及所进行的相关理论分析是合理且有效的。
In order to develop a precision positioning stage for nanoimprint lithography, this dissertation deals with the key issues relevant to mechanical design, kinematic modeling, stiffness analysis, static and dynamic modeling and kinematic calibration. As a result, a prototype machine of 3-DOF piezo-driven compliant stage has been developed. The following research achievements have been completed. Replacing the revolute joints of the modified DELTA mechanism with single-axis flexure hinges and adjusting the length of the links, a new-type precision positioning stage with three translation degrees of freedom has been achieved. Three piezoelectric actuators are used to carry out the passive position adjustment of the platform.
The Pseudo-Rigid-Body (PRB) Model methodology is utilized to investigate the kinematical characteristics of the stage, and two kinds of PRB models with effsets and non-effsets are developed. By the homogeneous coordinate transformation methodology and the vector-loop equation respectively, the forward and inverse kinematics modeling are achieved. The comparison of the two PRB model is done by the finite element simulation and the PRB model with non-effsets is adopted for the subsequent works. The workspace of the stage is evaluated in term of the constraints due to the allowable rotation range at the flexure hinges. And in order to achieve a maximum workspace subjected to the given dexterity indices, kinematic optimization of the design parameters is carried out, which results in a stage satisfying the operational requirements.
Considering the energy stored as elastic deformation of the flexure hinges and the gravitational potential of the platform and the links, the stiffness at driving point of the active arm is modeled based on the Castigliano’s first theorem. For the influence of the stiffness of the compliant prismatic pair, that constructed as a planar four-bar parallelogram, in the flexure-based precision positioning stage, the mathematics model of the stiffness matrix of the compliant prismatic pair is established using the compliant matrix and matrix transformation method. Discussions are developed about the influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair, the geometric parameters are changed to show the variation of stiffness. After that, the system stiffness of the flexure-based stage is analytically modeled on the same methodology, and the influence of the geometry parameters on three stiffness factors has been graphically evaluated as well. Furthermore, the finite-element simulation has been undertaken to validate the analytical model.
The static analysis of the compliant stage has been studied on the principle of virtue work, the influence of the mass of the platform and the links and the stiffness of the flexure hinges on the position of the platform are discussed. The dynamic modeling has been performed on the principle of virtue work and the Lagrangian equation respectively. The influences of the mass of the platform and the links and the stiffness of the flexure hinges on the driving torques are analyzed, and the numerical simulations with different movement modes are presented to verify the validity of both models. The natural frequencies are analyzed with the variation of the geometry parameters and the stiffness of the flexure hinges.
The imperfect error characteristics of the stage such as the modeling and calculating errors, geometric errors of flexure hinges and links caused by machining imperfections, assembling errors, gravity’s effect are analyzed and discussed on the kinematic model deduced by the recursive matrix methodology, The all-parameter-error-identification model of the compliant stage is setup, and the computer simulation is made.
Experiments results about the kinematics, the static compliance characteristics and the natural frequency confirmed that the mathematic modeling and the relative theoretic analysis is creditable.
以改进的DELTA并联机构为基础,将机构中的转动副用单自由度柔性铰链代替,研制了一台具有3平动自由度的精密定位工作台。该定位工作台采用多个压电陶瓷驱动器驱动方式,可实现末端位置的主动调整。
采用“伪刚体模型”方法将该精密定位工作台分别等效为偏置式伪刚体模型和非偏置式伪刚体模型,并利用齐次坐标变换方法和矢量闭环方法构建其正、逆运动学模型,结合有限元分析比较两种模型的优劣,并以非偏置式伪刚体模型作为后续分析的依据,以柔性铰链允许转角范围为约束条件分析工作台可达工作空间,并以工作空间最大为目标进行机构参数的优化设计。
考虑工作台重力势能和柔性铰链的弹性应变能,建立支链驱动刚度模型,为压电陶瓷驱动器的选择提供依据。针对从动臂平行四边形结构,讨论不同约束方式下,上下端连接横梁柔度特性对其输出刚度的影响。利用柔度矩阵和位置变换矩阵相结合的方法,建立定位工作台输出刚度模型,分别讨论了杆长、柔性铰链切口半径等几何参数的影响规律,并利用有限元仿真加以验证。
利用虚功原理方法建立了机构的静力学模型,讨论了各构件质量、柔性铰链刚度对动平台位置的影响作用。利用虚功原理方法和拉格朗日方程方法建立机构的动力学模型,讨论了构件质量、柔性铰链刚度对驱动力矩的影响规律,并结合不同的运动轨迹,将根据两种方法得到的动力学逆解模型进行对比,说明其有效性。讨论了几何参数、柔性铰链刚度对系统固有频率的影响。
综合考虑包括理论建模误差、杆长误差、柔性铰链加工误差、装配误差等多种误差源形式,并以采用递推方式得到的运动学模型为基础,建立了定位工作台全参数误差辨识模型,并进行了计算机仿真。
最后,利用所建造的精密定位工作台样机,进行了运动学、静态刚度以及固有频率试验,将试验结果与理论模型以及有限元仿真模型结果进行比较表明所建立的理论模型以及所进行的相关理论分析是合理且有效的。
In order to develop a precision positioning stage for nanoimprint lithography, this dissertation deals with the key issues relevant to mechanical design, kinematic modeling, stiffness analysis, static and dynamic modeling and kinematic calibration. As a result, a prototype machine of 3-DOF piezo-driven compliant stage has been developed. The following research achievements have been completed. Replacing the revolute joints of the modified DELTA mechanism with single-axis flexure hinges and adjusting the length of the links, a new-type precision positioning stage with three translation degrees of freedom has been achieved. Three piezoelectric actuators are used to carry out the passive position adjustment of the platform.
The Pseudo-Rigid-Body (PRB) Model methodology is utilized to investigate the kinematical characteristics of the stage, and two kinds of PRB models with effsets and non-effsets are developed. By the homogeneous coordinate transformation methodology and the vector-loop equation respectively, the forward and inverse kinematics modeling are achieved. The comparison of the two PRB model is done by the finite element simulation and the PRB model with non-effsets is adopted for the subsequent works. The workspace of the stage is evaluated in term of the constraints due to the allowable rotation range at the flexure hinges. And in order to achieve a maximum workspace subjected to the given dexterity indices, kinematic optimization of the design parameters is carried out, which results in a stage satisfying the operational requirements.
Considering the energy stored as elastic deformation of the flexure hinges and the gravitational potential of the platform and the links, the stiffness at driving point of the active arm is modeled based on the Castigliano’s first theorem. For the influence of the stiffness of the compliant prismatic pair, that constructed as a planar four-bar parallelogram, in the flexure-based precision positioning stage, the mathematics model of the stiffness matrix of the compliant prismatic pair is established using the compliant matrix and matrix transformation method. Discussions are developed about the influences of the constraints and the compliance of the connecting rods on the flexibility characteristics of the prismatic pair, the geometric parameters are changed to show the variation of stiffness. After that, the system stiffness of the flexure-based stage is analytically modeled on the same methodology, and the influence of the geometry parameters on three stiffness factors has been graphically evaluated as well. Furthermore, the finite-element simulation has been undertaken to validate the analytical model.
The static analysis of the compliant stage has been studied on the principle of virtue work, the influence of the mass of the platform and the links and the stiffness of the flexure hinges on the position of the platform are discussed. The dynamic modeling has been performed on the principle of virtue work and the Lagrangian equation respectively. The influences of the mass of the platform and the links and the stiffness of the flexure hinges on the driving torques are analyzed, and the numerical simulations with different movement modes are presented to verify the validity of both models. The natural frequencies are analyzed with the variation of the geometry parameters and the stiffness of the flexure hinges.
The imperfect error characteristics of the stage such as the modeling and calculating errors, geometric errors of flexure hinges and links caused by machining imperfections, assembling errors, gravity’s effect are analyzed and discussed on the kinematic model deduced by the recursive matrix methodology, The all-parameter-error-identification model of the compliant stage is setup, and the computer simulation is made.
Experiments results about the kinematics, the static compliance characteristics and the natural frequency confirmed that the mathematic modeling and the relative theoretic analysis is creditable.
引文
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