【作者】 谢祖强；

【导师】 沈健；

【作者基本信息】 合肥工业大学 ， 环保装备及环境监测工程， 2007， 硕士

【摘要】 本文针对应用于空间多自由度微位移工作台的双轴柔性铰链机构进行研究，推导柔性铰链柔度计算公式。在此基础上对柔性铰链微位移工作台进行研究，建立工作台的理论数学模型。本文针对柔性铰链微位移工作台的分析与设计方法进行如下研究：1．利用力学和微积分基本方程推导了双轴柔性铰链转动柔度的一般设计计算公式，并给出了θ_m=π／2时常用直圆型柔性铰链转动柔度。公式是精确推导的结果，表达式较J．M．Paros给出的公式简洁。通过得到的公式定量地分析了铰链参数对转动柔度的影响。同时针对多个不同尺寸柔性铰链，采用推出的计算公式、J．M．Paros公式和有限元法进行计算，三种计算方法的结果吻合很好，说明推出的计算公式的正确性和简洁性。2．利用能量法推导了双轴柔性铰链柔度的系列设计计算公式。在此基础上得到了常用的直圆双轴柔性铰链柔度的设计计算公式。并指出了应用柔度计算公式应注意的问题。3．根据有限单元法基本原理，把柔性铰链单元视为变截面梁单元，建立了柔性铰链单元的刚度矩阵。在此基础上，建立了单自由度微位移工作台的有限元数学模型，得到了微位移工作台的位移输出特性。同时，用有限元分析软件对微位移工作台进行实体建模和分析计算并与理论模型进行比较，计算结果表明两种方法计算的结果吻合很好，相对误差很小，验证了理论模型的正确性。4．设计了一种新型压电式双自由度微位移工作台，提出了一种采用直角双杆机构代替平行四杆机构实现双自由度运动的方法。5．基于卡氏第二定理推导了新型工作台在不同方向上的输出刚度解析表达式，在此基础上推导出了工作台的前两阶固有频率。根据得到的输出刚度表达式，定量地分析了柔性铰链参数及连杆长度对工作台输出刚度的影响。同时针对三组不同尺寸参数的工作台，采用有限元法对其进行数值计算，并与理论计算比较，结果表明两种方法计算结果吻合很好，说明了理论模型的正确性。更多还原

【Abstract】 This thesis researches on the double-axis flexure hinges which widely used in the space multi-DOF micro-displacement work stage, and presents the compliance equations for double-axis flexure hinges. Based on the compliance equations, this thesis researches on the flexure hinges micro-displacement stage, and creates the theoretical modal of the stage. Therefore, in this thesis, the analysis and design methodology for flexure hinges micro-displacement stage are presented and the following studies are completed:1. Based on the basic equation of mechanics and calculus, this paper presents the deduction process of design equation for calculating the rotation compliance of double-axis flexure hinge. And this paper also presents the rotation compliance equation of right circular double-axis flexure hinge (θ_m=π/2). The equation isexact and more concise in expression than J.M.Paros’s. The analytical equation is built to quantitatively analyze the influence of parameters of flexure hinge of rotation compliance. Simultaneously, a number of right circular double-axis flexure hinges with different shapes are analyzed with finite element analysis method. And comparison is made between the present equation and those of widely used J.M.Paros’ equations. The results of three methods to calculate the rotation compliance are in good agreement, which indicates that the analytical equations are correct and concise.2. Based on the energy method, this paper presents the compliance equations for double-axis flexure hinges and right circular double-axis flexure hinges. Some suggestions are made in regard to the design of flexure hinges.3. By applying the basics principles of the finite element methods, a finite element modal of flexure hinge which is looked as non-uniform beam. Based on the stiffness matrix, the finite element modal of a single direction translation micro-displacement is created. The characteristic in the displacement output of the stage is gained by the modal. Simultaneously, a finite element simulation modal of the stage is constructed by finite element analysis software. And comparison is made between the theoretical modal and the simulation modal. The results of two methods to calculate the output displacement are in good agreement, which indicates that the theoretical modal is correct.4. A novel two degree of freedom micro-displacement work stage derived by PZT was developed. And a vertical two-bar mechanism was designed to replace four-bar parallel mechanism to realize two degree of freedom motions.5. Castigliano’s second theorem was used to derive a series of analytical equations for computing the output stiffness and resonant frequency for different directions of the stage. The analytical equations were built to quantitatively analyze the influence of parameters of flexure hinge and length of link bar of output stiffness. Simultaneously, three group different dimensions of the stages were analyzed with finite element analysis method. And comparison was made between the theoretical modal and finite element modal. The results of the two methods were in good agreement, which indicated that the analytical equations were correct.更多还原