椭圆柔性铰链柔顺机构的动力学建模与分析

以椭圆的离心角为积分变量,得到椭圆柔性铰链的转角计算的积分公式,推导出椭圆柔性铰链的刚度表达式.在此基础上针对一种应用广泛的含椭圆柔性铰链的柔顺机构,建立其动力学模型,得到该机构系统的固有频率计算公式.通过算例分析了该机构的各种参量对系统固有频率以及柔性铰链刚度的影响.     

基于动力学性能的全柔性机构优化设计

全柔性机构是一种新型机构,多应用在精密定位场合。为保证该机构具有很高的定位精度和较强的抗环境干扰能力,仅以静力学性能作为指标进行机构的优化设计是不足以满足要求的,还需要对机构的动力学性能进行优化。研究以一具体的全柔性机构为例,给出一种基于机构动力学性能的结构优化设计方法。为此首先建立了该机构的动力学理论模型,为保证结果的准确性,还进行了有限元模拟;在设计过程中,同时考虑到了机构的静态特性与动态特性。该方法可有效地完成机构的尺度综合。     

Analysis of frequency characteristics and sensitivity of compliant mechanisms

Based on a modified pseudo-rigid-body model, the frequency characteristics and sensitivity of the large-deformation compliant mechanism are studied. Firstly, the pseudo-rigid-body model under the static and kinetic conditions is modified to enable the modified pseudo-rigid-body model to be more suitable for the dynamic analysis of the compliant mechanism. Subsequently, based on the modified pseudo-rigid-body model, the dynamic equations of the ordinary compliant four-bar mechanism are established using the analytical mechanics. Finally, in combination with the finite element analysis software ANSYS, the frequency characteristics and sensitivity of the compliant mechanism are analyzed by taking the compliant parallel-guiding mechanism and the compliant bistable mechanism as examples. From the simulation results, the dynamic characteristics of compliant mechanism are relatively sensitive to the structure size, section parameter, and characteristic parameter of material on mechanisms. The results could provide great theoretical significance and application values for the structural optimization of compliant mechanisms, the improvement of their dynamic properties and the expansion of their application range.     

传递矩阵法分析平面柔顺机构的振动特性

为了分析柔顺机构的动态性能和力学传递关系,提出一种新型的基于传递矩阵法的振动力学模型。柔顺机构由若干个柔性铰链与杆件顺序联接而成,采用传递矩阵法描述其力学状态量的传递关系。将柔性铰链视为拉伸和弯曲变形的弹性梁,应用材料力学理论建立反映其自振性能的传递矩阵。将杆件视为刚体,采用动量矩定理建立其动力学模型,得到描述振动刚体的传递矩阵。按照柔顺机构的联接形式,将每个元件的传递矩阵进行拼装,得到系统总传递矩阵。总传递方程以柔顺机构的边界点状态矢量为未知变量,矩阵中的元素为机构结构参数和频率的函数。应用边界条件,可得柔顺机构的特征方程,通过求解方程可得系统的固有频率和振型。将外力纳入传递矩阵,建立反映外力激励与系统的关系的扩展传递矩阵以求解系统的频率响应。通过2种常用平面柔顺机构的动态性能分析,结果表明所建立模型的正确性,能精确描述柔顺机构力学传递关系。     

区间参数柔性机构设计的混合元胞自动机方法

进行柔性机构设计时,应考虑不确定性参数对机构性能的影响。基于此,将柔性机构物理参数及其外载荷视为区间变量,基于柔性机构的刚性测度和柔性测度,建立在连续域中利用结构拓扑优化设计柔性机构的数学模型。采用固体各向同性惩罚方法进行设计域材料的参数化,将材料相对密度作为设计变量,结构受载时的应变能和交互势能线性加权的极大化作为目标函数,结构体积作为约束。优化设计求解策略采用混合元胞自动机方法,用区间有限元法进行结构总体分析以获取优化过程中的每次迭代信息,设计变量中的局部改变由基于比例—积分—微分控制律的局部设计规则来确定。数值算例证明了所建模型及其解法的有效性。按照数值算例结果之一进行等比例尺寸放大后的实物制造,并进行简单试验验证。     

基于多刚体离散元模型的柔顺机构动力分析新方法

柔顺机构是部分或者全部由其构件的预期弹性变形来传递运动和力,这使得构件的弹性变形一般都较大。它的分析一般属于几何非线性问题。基于弹性体的多刚体离散元模型,研究了柔顺段和柔顺机构的多刚体离散元建模方法,推导了柔顺机构系统的一般控制方程,该方程可以解决柔顺机构的特征频率和几何非线性变形问题。并给出了算例,计算结果表明多刚体离散元方法能较好解决柔顺机构的几何非线性静力学和动力学分析。     

集中式柔性机构动力学等效分析方法研究

基于伪刚体模型与功能守恒定律,建立了集中式柔性机构动力学等效分析方法。在忽略杆件弹性变形的基础上,借助Paros给出的圆弧形柔性铰链扭转刚度计算公式,形成集中式柔性机构的伪刚体模型;依据动能不变及功率不变的原则,将柔性机构的伪刚体模型进行等效处理,建立了集中式柔性机构动力学等效分析方法。采用该方法,分别对单自由度和双自由度柔性机构进行了动力学等效分析,并将获得的解析解与ANSYS软件获得的数值结果进行了对比,证实了本文提出的动力学等效分析方法是十分有效的,该方法为柔性机构的动态优化设计提供了有力工具。     

动平台惯性参数对柔性并联机构 动力学特性的影响及优化设计

利用柔性并联机构的动力学模型,定性地分析了动平台质量、转动惯量对柔性并联机构的动态响应、动态应力及固有频率的影响。以动平台惯性参数边界条件、运动误差、固有频率、动态应力、驱动力矩等限制条件作为约束方程,将机构总质量函数和弹性变形能函数采用线性加权组合成多目标函数,进行多目标优化设计,确定了动平台的最佳惯性参数。通过对平面3- R RR柔性并联机构算例的分析和讨论,说明了动平台惯性参数在柔性并联机构的动力学分析和设计中的重要作用。     

垂直型多级位移放大机构设计与力学解析建模

针对压电位移放大机构在垂直方向较难实现大行程、高频带宽度的问题,结合两个复合菱形机构、两个杠杆机构以及一个普通菱形机构,提出了一种垂直型多级位移放大机构。基于能量守恒方法和弹性梁理论建立了位移放大比和输入/输出刚度解析模型,根据拉格朗日方程推导了固有频率解析模型。通过有限元法对解析模型进行了验证,所建立的位移放大比解析模型有较高的预测精度,可为大行程垂直型柔顺平台的优化设计提供参考。与文献中的位移放大机构性能对比结果表明,提出的垂直型位移放大机构具有更好的静动态平衡性能,其位移放大比可达43.29,同时保持一个较高的固有频率561.28 Hz。     

基于多目标拓扑优化的全柔顺并联机构构型固有振动频率研究

为有效抑制随机振动对超精密定位与加工装备性能的影响,提高本体机构的固有响应频率,提出了基于多目标拓扑优化的全柔顺并联机构构型设计方法。基于折衷规划法和平均频率法定义了多目标优化函数,并以体积分数为约束条件,建立了全柔顺并联机构SIMP拓扑优化模型。基于Optistruct软件及优化准则算法,并结合微分矢量同构映射雅可比矩阵,实现了全柔顺并联机构构型多目标拓扑优化设计。研究结果表明：所设计出的3-PRR型全柔顺并联机构与并联原型机构具有微分运动一致性,且优化过程中的频率交叉振荡明显减弱并趋于收敛。     

Manufacturing of multi-material compliant mechanisms using multi-material molding

Multi-material compliant mechanisms enable many new design possibilities. Significant progress has been made in the area of design and analysis of multi-material compliant mechanisms. What is now needed is a method to mass-produce such mechanisms economically. A feasible and practical way of producing such mechanisms is through multi-material molding. Devices based on compliant mechanisms usually consist of compliant joints. Compliant joints in turn are created by carefully engineering interfaces between a compliant and a rigid material. This paper presents an overview of multi-material molding technology and describes feasible mold designs for creating different types of compliant joints found in multi-material compliant mechanisms. It also describes guidelines essential to successfully utilizing the multi-material molding process for creating compliant mechanisms. Finally, practical applications for the use of multi-material molding to create compliant mechanisms are demonstrated.     

分布式柔性机构拓扑优化设计的理论和算法

将连续体结构的拓扑优化技术应用到分布式柔性机构的设计中,基于变密度法和优化准则法推导并建立柔性机构拓扑优化的一种显式的设计变量收敛格式。结合分布式柔性机构优化设计的人工弹簧模型和虚拟载荷法,提出一种新型的分布式柔性机构拓扑优化设计的多准则优化模型,同时综合考虑柔性机构设计的机械效率要求和结构的刚度要求,并利用伴随敏度分析法进行敏度分析。数值算例证明研究方法的有效性,并分析和讨论优化模型和收敛格式中有关优化设计参数对柔性机构优化设计结果的影响。用激光快速成形技术验证柔性机构概念设计的合理性。     

Spring-joint method for topology optimization of planar passive compliant mechanisms

There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms. The most commonly-used approaches, which start with an existing rigid-body mechanism, do not consider the performances between different topologies. Moreover, they rely heavily on the rigid-body topology, therefore limit the diversity of compliant mechanisms topology. To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies, a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms, which are the building blocks of parallel compliant mechanisms. The topology of the compliant mechanisms is represented by a serial spring-joint mechanism（SSJM） that is a traditional rigid-body mechanism with a torsional spring acting on each joint, and is described by position vectors of the spring-joints. A simplified compliance matrix, determined by the position vectors, is used to characterize the tip of the SSJM kinematically, and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization. The topology optimization problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix. In design examples, syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to illustrate the proposed method. The proposed method provides a new way for the initial design of flexure-based compliant mechanisms.     

全柔性机构与MEMS

柔性机构是一种新型机构。首先描述了柔性机构和全柔性机构的概念及特点,论述了它们与MEMS之间的关系。然后详细介绍了全柔性机构在MEMS领域内包括微装配、微操作等应用背景下的状况及前景。最后就对全柔性机构研究中的几个关键技术问题如机构的分析、设计及加工,柔性铰链的选择与设计,驱动器的选择及设计等进行了探讨。     

三自由度微扰下箔片端面气膜密封动态特性分析

提出一种新型箔片端面气膜密封方式,基于气体润滑与弹性力学理论,应用小扰动法建立箔片端面气膜密封的微扰膜压控制方程。对比分析了不同箔片变形力学模型下的动态特性系数变化规律,探究了不同工况及结构参数对气膜动态特性的影响规律,以最大动态主刚度和阻尼作为综合优化目标,确定了结构参数的优选范围。结果表明：随着激振频率、转轴转速的提高,气膜动态主刚度与动态主阻尼的动态互补变化,抑制了润滑膜厚的激变,同时作为气膜不稳定诱因的动态交叉系数的变化放缓,降低了因工况突变引起气膜振荡、失稳的风险;此外,介质压力的增大能够显著提升密封维稳、抗振性能。当楔形高度取5～8 μm,节距比取0.2～0.4,箔坝比取0.5～1.1,箔片数取4～6,箔片结构阻尼取5×107～8×107 Pa·s/m时,箔片端面气膜密封综合动态抗扰性能较优。     

Three flexure hinges for compliant mechanism designs based on dimensionless graph analysis

This paper presents the dimensionless empirical equations and graph expressions of three flexure hinges for compliant mechanism designs. The in-plane and out-of-plane stiffnesses of the flexure hinges are developed. The rotational precision, denoted by the midpoint stiffness, is derived for the purpose of optimized geometric design. Based on the developed methodologies, the influences of the geometric parameters on the performance of the flexure hinges are investigated, and the performance comparisons among the flexure hinges are conducted to further understand the characteristics of these kinds of compliant mechanisms.     

Conceptual design of compliant mechanisms using level set method

We propose a level set method-based framework for the conceptual design of compliant mechanisms. In this method, the compliant mechanism design problem is recast as an infinite dimensional optimization problem, where the design variable is the geometric shape of the compliant mechanism and the goal is to find a suitable shape in the admissible design space so that the objective functional can reach a minimum. The geometric shape of the compliant mechanism is represented as the zero level set of a one-higher dimensional level set function, and the dynamic variations of the shape are governed by the Hamilton-Jacobi partial differential equation. The application of level set methods endows the optimization process with the particular quality that topological changes of the boundary, such as merging or splitting, can be handled in a natural fashion. By making a connection between the velocity field in the Hamilton-Jacobi partial differential equation with the shape gradient of the objective functional, we go further to transform the optimization problem into that of finding a steady-state solution of the partial differential equation. Besides the above-mentioned methodological issues, some numerical examples together with prototypes are presented to validate the performance of the method.     

基于最大应力约束的柔顺机构拓扑优化设计

采用拓扑优化方法获得柔顺机构构型容易出现类铰链结构,导致应力集中、疲劳可靠性差。为了抑制类铰链结构,提出了一种基于最大应力约束的柔顺机构拓扑优化设计方法。采用改进的固体各向同性材料惩罚模型（Solid isotropic material with penalization,SIMP）,以柔顺机构的互应变能最大化作为目标函数,采用P范数方法对所有单元的局部应力凝聚化成一个全局化应力约束,利用自适应约束缩放法使得P范数应力更加接近最大应力,以机构的最大应力和体积作为约束,建立柔顺机构最大应力约束拓扑优化模型,采用全局收敛移动渐近线算法求解柔顺机构最大应力约束拓扑优化问题。结果表明,采用P范数方法进行柔顺机构最大应力约束拓扑优化设计,能够有效抑制类铰链结构。随着应力约束极限值减少,获得机构构型由集中式柔顺机构逐渐转变为分布式柔顺机构,应力分布更加均匀,但机构的互应变能逐渐减小。     

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.     

基于基础结构法的柔顺机构动力学拓扑优化

提出一种新的在简谐激励作用下,基于基础结构法的柔顺机构动力学拓扑优化方法.框架单元能够包含弯曲模式,因此采用它的集合表示设计域.以动力放大系数最大化与应变能的最小化加权函数为目标,满足在动态条件下柔顺机构具有足够柔度和刚度;并且规一化目标函数避免不同性质目标函数的量级差异.目标函数的敏度采用伴随矩阵法求解,用移动近似算法对优化问题进行迭代求解.通过数值算例对不同外激励频率和不同输出刚度的拓扑优化结构进行分析讨论.结果表明,该方法在柔顺机构动力学拓扑优化设计中是正确的和有效的.