二维微动工作台分析及其优化设计方法

设计了一种压电陶瓷驱动的二维微动工作台,采用结构力学理论建立了工作台的简化模型,并推导出工作台沿x、y方向刚度计算表达式。将工作台简化为2自由度弹簧一质点系统,得出其前二阶固有频率计算表达式。通过微动工作台固有频率及沿x、y方向刚度的试验测试,验证了解析法和有限元法用于微动工作台设计分析的可行性。采用有限元法,研究了微动工作台的直角平板柔性铰链特征参数对微动工作台性能的影响。有限元分析结果表明:当平板柔性铰链长度较小或铰链宽度较大时,其刚度、频率及驱动力较高,然而铰链根部应力集中也较严重。通过改变柔性铰链的特征参数,可达到控制和优化工作台固有频率、输出位移、应力分布及驱动力响应的目的,并提出一种优化设计微动工作台柔性铰链的简易方法。     

一种低成本微定位平台的设计与仿真

针对半导体及微纳制造等领域对微定位系统低成本高精度的要求,根据以宏观的输入获得微观的输出、低精度驱动器输入获得高精度输出的设计思想,设计了一种基于柔性铰链差式杠杆机构的低成本微定位平台。在该平台中,通过设计位移缩放机构,将驱动器的宏观输入位移进行比例缩小,实现平台的微观输出,降低微定位平台的成本。分析了微定位平台的刚度,并根据该平台定位机构所受载荷的不同,设计了两种不同的柔性铰链。在此基础上,建立了该平台的有限元分析模型,采用ANSYS对该平台的应力进行了分析,并对该平台的输出位移进行了仿真。仿真结果证明了该微定位平台的可行性。     

Optimal design of a flexure-hinge precision stage with a lever

Lever mechanisms are usually used to enlarge output displacements in precision stages. A precision stage employing a lever mechanism and flexure hinges is analyzed theoretically, with bending in the lever considered. Relations between design parameters and magnification ratio, and the optimal values for the parameters to achieve a longer stage displacement are presented. Finite element analysis is used to verify the theoretical analysis. It is found that adjustment of lever dimensions and hinge stiffnesses can increase the stage travel range significantly.     

Development of 2-axis hybrid positioning system for precision contouring on micro-milling operation

A 2-axis hybrid positioning system was developed for precision contouring on micro-milling operation. The system was developed to overcome the micro-positioning limitations of conventional linear stage positioning system on machine tools. A 2-axis flexure hinge type piezoelectric stage was added on a standard milling machine to obtain better machining results. The control method used for the hybrid system was active error compensation type, where errors from linear stages are cancelled by the piezoelectric stage motion. Positioning experiments showed an improvement of machine accuracy which was confirmed by the machining results. A micro-pillar was fabricated for the validation of long-range and high-precision contouring capability. The system was successfully implemented on micro-milling machining to achieve high-precision machining results.     

Design and analysis of a multi-notched flexure hinge for compliant mechanisms

This article presents a new multi-notched flexure hinge, which consists of two right circular and two parabolic notches, for positioning stages based on compliant mechanisms. First, the configuration of the presented multi-notched hinge is obtained using topology optimization, and the final shape is proposed based on post-processing. Second, the dimensionless empirical equations for the stiffness, rotational precision and stress levels of the flexure hinges are developed using finite element analysis (FEA). Third, based on the established equations, the influences of the geometric parameters on the performance of the flexure hinge are investigated. Finally, to further understand the characteristics of this type of flexure hinge, comparisons with flexure hinges of various shapes are performed in terms of stiffness, rotational precision and stress levels.     

低成本柔顺板式精密定位平台的理论与试验

基于柔顺薄板的弹性变形原理,提出一种低成本、整体式柔顺精密定位平台的设计方法。设计一种平板弹簧机构,使平台能够在较低精度驱动器的驱动下获得高精度的位移输出,从而大幅度降低精密定位平台的成本。建立平台的刚度模型,分析驱动器的精度与平台的定位精度之间的相互关系。最后,分析加工误差对平台定位精度的影响,得出影响定位精度的关键结构参数。通过试验测试,得出驱动器的输入位移和精度分别为4 mm和10m,平台的输出位移和精度分别为9 m和40 nm,线性度为0.33,从而验证了该设计方法的正确性。该平台结构紧凑,成本低,具有很好的性价比,应用前景广阔。     

A novel analytical model for flexure-based proportion compliant mechanisms

This paper proposes a novel analytical model for flexure-based proportion compliant mechanisms. The displacement and stiffness calculations of such flexure-based compliant mechanisms are formulated based on the principle of virtual work and pseudo rigid body model (PRBM). According to the theory and method, a set of closed-form equations are deduced in this paper, which incorporate the stiffness characteristics of each flexure hinge, together with the other geometric and material properties of the compliant mechanism. The rotation center point for a corner-filleted flexure hinge is investigated based on the finite element analysis (FEA) and PRBM. An empirical equation for the rotational angle is fitted in this paper in order to calculate accurately the position of the end-point of the flexure hinge. The displacement proportion equation for such mechanisms is derived according to the new approach. Combining the new proposed design equation and the existed stiffness equation, a new proportion compliant mechanism with corner-filleted flexure hinges is designed by means of the least squares optimization. The designed models are verified by finite element analysis.     

三维纳米级微动工作台的设计与分析

研究开发了一种新型精密三维微动工作台。采用呈等边三角形分布的三个压电陶瓷和环形平板铰链机构 ,保证了运动传递的连续性、无洄滞、无摩擦、高精度。建立了工作台的简化模型,并利用结构力学理论推导出工作台沿z方向平动刚度、绕x、y方向转动刚度以及前三阶固有频率解析式。进行了微动工作台沿z方向平动刚度、绕x、y方向转动刚度以及固有频率试验测试,验证了解析方法和有限元方法进行三维工作台刚度及动力特性分析的正确性。有限元分析表明:当工作台的环形平板铰链半径较小而铰链厚度较大时,其刚度、频率及驱动力较高,其铰链根部应力集中也较严重。通过改变环形平板铰链的特征参数,可达到控制和优化工作台固有频率、输出位移、应力分布及驱动力响应的目的,并提出了一种优选微动工作台环形平板铰链参数的简易方法。     

基于柔顺机构的两自由度微动精密定位平台的分析与设计

基于柔性铰链变形原理设计了一种压电驱动的两自由度柔顺机构微动精密定位平台.首先建立了平台的刚度、固有频率和强度的分析模型,通过优化设计得出了平台的最优结构尺寸.利用有限元软件仿真分析验证了设计模型和优化结果的正确性.最后制造了原型样机,进行了实验,对平台进行了标定并分析了平台的定位误差.     

二自由度微定位平台的研制

研制了一台压电陶瓷驱动和弹性铰链导向的一体化微定位平台,该微定位平台具有高刚度、高响应速度和高分辨率等优点。为了克服压电陶瓷驱动器伸长量较小的不足,采用杠杆放大机构增加微定位平台的位移输出。考虑驱动电路的影响,建立了微定位平台的机电耦合模型。通过试验研究了微定位平台的静动态特性,试验结果表明微定位平台的分辨率为5 nm,固有频率分别为143 Hz和180 Hz。该微定位平台可应用于纳米级的微定位。     

基于单元刚度矩阵法的二维微动平台刚度分析

刚度作为设计和评价全柔性机构的一个重要指标,在很大程度上影响着全柔性机构的动态性能和定位精度。利用材料力学中的单元刚度矩阵原理,根据柔性机构的结构特点进行单元划分。然后全面考虑机构中各单元的复杂变形,建立单元间的位移、力平衡方程,得到便于进行递推运算的刚度表达形式。以一种二维微动平台为例,给出了应用该方法的刚度分析过程,结果表明理论计算接近有限元分析数据。     

超磁致伸缩二维精密工作台研究

在超磁致伸缩驱动器的基础上,以柔性铰链机构作为传动部件,设计了创新结构的二维精密工作台。应用ANSYS软件对所设计的柔性铰链机构进行了应力和位移分析。设计了闭环控制系统来控制工作台的输出精密和响应速度。经分析,X和Y方向的最大位移量可达0．2mm。     

Modeling and analysis of an over-constrained flexure-based compliant mechanism

Bridge-type micro-displacement amplifier with flexure hinges is a classic displacement amplification mechanism. Existing theoretic models cannot predict its amplification ratio and input stiffness accurately and make it very difficult to confirm the amplifier’s performance and error compensation by means of these models, which is very significant in ultra-precision positioning. This paper focuses on the development of design equations that can accurately calculate the ideal displacement amplification ratio and input stiffness of the amplifier based on the thought of statically indeterminate structure. Force Method, Maxwell–Mohr Method, principle of superposition and deformation compatibility are used together to establish uncanonical linear homogeneous equations. The analytical results are verified by FEA simulations. The influence of the geometric parameters on the amplifier performance is investigated. It is noted that amplifier performance is more sensitive to the longitudinal distance of flexure hinges. Besides, two same-sized amplifiers with the opposite output directions can be clearly differentiated by these equations.     

基于应力刚化效应的动态特性可调微动平台设计新方法

针对现有基于柔性铰链的微动平台动态特性受材料特性、设计制造等误差影响,难以满足精密微动平台对动态响应（特别是可变频率操作）的高要求,基于应力刚化效应,提出了动态特性可调的微动平台设计新方法,推导预应力作用下一端固定一端导向梁的等效刚度和质量公式;基于对称布置假设,建立含有弹片式柔性铰链(下面简称弹片)组数(离散变量)和截面尺寸(连续变量)的离散连续变量复合优化模型,释放承载刚度约束,获得截面尺寸含有弹片组数变量的精确解系列,分析了给定预应力下不同弹片组数微动平台的承载刚度和频率调节范围,从而通过承载刚度约束和频率调节范围要求确定弹片组数。通过数值算例,验证了推导计算模型求解精度和所提设计方法的应用有效性。计算结果表明,与有限元分析结果相比,本模型的计算结果相对误差小于2%,实现了给定工作刚度、频率和承载刚度约束的微动平台最优结构设计。所提方法实现了刚度和频率大范围的调整,不但降低了加工精度要求,还为动态特性自适应匹配的智能微动平台提供一种实现途径。     

Detachment modeling of a novel workpiece micro-positioning table under preloaded hertz contact

A micro-positioning table for precision machining applications is developed utilizing a piezoelectric translator to generate high speed precision motions with accelerations up to 33.51 g. The piezoelectric translator is preloaded by four springs such that the moving part in the table keeps contact with the translator. The contact between the translator and the moving part is of the hertz contact type. It is a typical design for high performance micro-positioning devices. It is found that the hertz contact may not be maintained and detachment occurs when implementing large step motions. The detachment phenomenon is analyzed and the models to determine the separation time and the maximum overshoot are established. It is found that the stiffness of the preloading springs and the distance of compression for preloading are the key parameters of the detachment. A pseudo-step command signal design is proposed to use as a solution in order to conveniently reduce the overshoot without compromising the settling time. Experimental tests have been carried out, verifying the established models for the micro-positioning device.     

Development of nanopositioning mechanism with real-time compensation algorithm to improve the positional accuracy of a linear stage

A compensation mechanism with six degrees of freedom (DOF) was developed to enable precise control of a linear stage. Geometric, thermally induced, and dynamic errors in the linear stage were compensated for in real time by the nanopositioning stage. A stage-based hinge with high structural stiffness and rapid response characteristics was modified for parallel operation. The stage’s full range of motion was measured and kinematics was used to calculate the displacement required by each actuator to compensate for the errors. Except for the displacement error of the linear stage, the contribution of each error source was measured by a reference mirror and five capacitive sensors. A compensation algorithm, based on a recursive method, was used to improve the positioning accuracy of the system. The performance of the stage presented here was investigated by measuring, and compensating for, the five-DOF linear stage errors in real time. In practice, the peak-to-valley errors of the translational and rotational errors were reduced by 89% and 93%, respectively.     

压电驱动超精密加工微定位工作台的设计与研究

设计开发了一种用于超精密加工的新型压电驱动微定位工作台(PBMPM-PZT Based M icro-position ing P lat-form forM ach in ing)。利用力学理论,对柔性铰链和平行铰链运动副进行建模,推导出其刚度理论计算公式。同时,用有限元方法分析了由柔性铰链构建的微定位工作台静、动态特性和振动特性。理论分析、有限元计算和实验结果的一致性说明了理论分析的正确性和数值分析的可靠性。     

一种纳米级二维微定位工作台的设计与分析

研究开发了一种采用柔性铰链导向的二维光学调整微定位工作台,建立了工作台的简化模型,并利用结构力学理论推导出工作台沿x、y方向刚度及前二阶固有频率解析式。进行了微定位工作台固有频率及沿x、y方向刚度的试验测试,并结合解析方法和有限元方法对微定位工作台设计刚度及动力特性进行分析验证。有限元分析表明:当工作台的直角平板柔性铰链长度较小而铰链宽度较大时,其刚度、频率及驱动力较高,铰链根部应力集中也较严重。通过改变柔性铰链的特征参数,可达到控制和优化工作台固有频率、输出位移、应力分布及驱动力响应的目的,并提出了一种优选微定位工作台柔性铰链参数的简易方法。     

3K-Ⅱ型直齿行星齿轮传动的固有特性

为揭示3K-Ⅱ型直齿行星齿轮传动的固有特性,建立该类传动系统在系杆随动参考坐标系下的平移-扭转耦合动力学模型.模型设定系统中每个构件均拥有3自由度,并计入各构件的支承刚度、轮齿时变啮合刚度和陀螺效应等影响因素.通过分析各构件间的相对位移关系,推导出系统的运动微分方程,进而求解其特征值问题即可获知系统的固有频率和相应振型.固有特性分析表明,3K-Ⅱ型行星齿轮传动具有与2K-H行星齿轮传动类似的三种典型振动模式,即扭转振动模式、平移振动模式和行星轮振动模式.列出三种典型振动模式下传动系统的运动特征.     

基于柔性铰链的微操作执行器的设计和分析

为了满足微型机电系统研究和测试的要求，设计了一种压电驱动的基于柔性铰链的微操作执行器。该微操作执行器采用组合杠杆原理将压电驱动器的微小位移放大。用简化方法和有限元方法分别对该柔性铰链微操作执行器进行了分析，发现简化方法可以用在初步设计中，而最终需要用有限元方法进行校验。在柔性铰链微操作执行器的设计中，加强杠杆的支点和杠杆臂的刚度，能有效地提高系统的运动放大倍数，并且使简化分析的结果和有限元分析结果更接近。