多输入多输出柔顺机构几何非线性拓扑优化

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,柔顺机构拓扑实际上是一个几何非线性问题,因而研究多自由度柔顺机构几何非线性拓扑优化就显得十分必要.基于此,给出一种多输入多输出柔顺机构几何非线性拓扑优化设计的新方法.首先,建立增量形式平衡方程,采用Total-Lagrange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应.其次,推导描述多输入多输出柔顺机构柔性的几何增益公式和描述机构刚性的应变能公式,研究抑制耦合输出策略,给出描述输出耦合效应的计算公式,在此基础上建立考虑抑制输出耦合效应时多输入多输出柔顺机构的多目标几何非线性拓扑优化数学模型.目标函数敏度分析采用伴随求解技术,拓扑优化采用固体各向同性材料插值方法,并用移动近似算法进行迭代求解.最后,通过算例说明以上方法的正确性和有效性.研究结果表明,拓扑优化后柔顺机构可以按照预定要求运动,输出耦合现象得到了有效抑制,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性.     

多输入多输出柔顺机构拓扑优化及输出耦合的抑制

多自由度柔顺机构在微动精密定位和精密操作等领域有广泛的应用,因而研究多自由度柔顺机构的拓扑优化方法就显得十分必要。给出了一种多输入多输出柔顺机构拓扑优化设计的新方法。首先,推导了描述多输入多输出柔顺机构柔性的互应变能公式和描述机构刚性的应变能公式,研究了抑制耦合输出的策略,进一步给出了描述输出耦合效应的计算公式,在此基础上建立了考虑抑制输入输出耦合效应时柔顺机构的多目标拓扑优化设计模型。其次,基于改进的优化准则法给出了优化模型的有效求解算法。最后,通过算例说明了该方法的正确性和有效性,研究结果表明,拓扑优化后柔顺机构可以按照预定的要求运动,其输出耦合现象得到了有效抑制。     

柔顺机构几何非线性多目标拓扑优化设计

给出一种柔顺机构几何非线性多目标拓扑优化设计的新方法.首先,建立增量形式平衡方程,采用Total-La-grange描述方法和Newton- Raphson载荷增量求解技术获得几何非线性的结构响应.其次,建立适合求解几何非线性的多目标拓扑优化数学模型,目标函数以平均柔度最小和几何增益最大来满足机构的刚度和柔度需求,提出用标准化方法建立多目标函数,利用决定函数得到最优妥协解.目标函数敏度分析采用伴随求解技术,拓扑优化采用固体各向同性材料插值方法,并用移动近似算法进行迭代求解.最后,通过算例说明以上方法的正确性和有效性.研究结果表明,运用该柔顺机构几何非线性多目标拓扑优化方法能够在刚度和柔度之间找到最优妥协解,不但提高机构柔度,而且提高机构刚度,同时也说明对柔顺机构进行几何非线性拓扑优化的必要性.     

柔顺机构拓扑图提取

柔顺机构拓扑优化所得机构是非光滑锯齿状跳跃边界的几何图像,不能直接应用于工程实际,因而研究柔顺机构拓扑图提取就显得十分必要。基于此,给出了一种柔顺机构拓扑图提取的新方法。首先,对柔顺机构拓扑所得灰度图像进行二值化处理,找到满足目标函数的罚值,得到只有0和1密度分布的锯齿跳跃边界图像。然后,采用密度等值线方法,求节点密度,对锯齿跳跃边界进行光滑近似。第三,针对柔顺机构性能特点,选择适合形状优化的变量参数,用样条曲线对光滑边界进行曲线重构,得到CAD系统可以识别的参数化模型。最后,通过算例说明以上方法的正确性和有效性。     

基于等几何分析的电热驱动柔顺机构拓扑优化设计

为了提高计算效率,提出一种基于等几何分析(Isogeometricanalysis, IGA)的电热驱动柔顺机构拓扑优化设计方法。采用NURBS曲线表达几何模型和分析模型,利用改进的固体各向同性材料惩罚法和密度分布函数描述材料分布,采用顺序耦合方法进行电-热-结构多物理场耦合有限元分析,以电热驱动柔顺机构的输出位移最大化为目标函数,以机构的体积为约束,建立基于等几何分析的电热驱动柔顺机构拓扑优化数学模型,利用移动渐近线算法求解拓扑优化问题。数值算例验证了提出的设计方法的有效性。与基于有限元分析的优化结果相比,基于等几何分析获得的电热驱动柔顺机构拓扑构型有所不同,边界更加光滑,机构的输出位移更大;并且等几何分析能够有效地减少迭代步数,显著地提高了计算效率。分析不同的输出刚度对电热驱动柔顺机构拓扑构型和机构性能的影响规律。     

柔顺机构几何非线性拓扑优化设计

对柔顺机构几何非线性拓扑优化设计理论进行了深入研究。首先,建立增量形式平衡方程,采用Total-Lagrange描述方法和Newton-Raphson载荷增量求解技术获得几何非线性的结构响应。其次,基于固体各向同性材料插值方法,建立体积约束下,输出位移最大为目标函数的柔顺机构几何非线性拓扑优化数学模型,目标函数敏度分析采用伴随求解技术,并用移动近似算法进行迭代求解。最后,通过算例说明以上方法的正确性和有效性。研究结果表明,应用上述方法对柔顺机构进行几何非线性拓扑优化设计能够得到合理拓扑图,并比线性分析所得机构的稳定性更高,同时也说明了对柔顺机构进行几何非线性拓扑优化的必要性。     

平面三自由度柔顺机构构型设计与性能分析

采用并联原型机构微分雅克比矩阵与实体各向同性材料惩罚函数法(Solid isotropic material with penalization, SIMP)相结合的拓扑优化方法,以柔度最小和低阶模态频率最大为多设计目标,建立平面三自由度柔顺机构拓扑优化模型实现拓扑优化。以拓扑优化得到的模型边界为形状优化为设计变量,对拓扑优化模型应力与末端位移约束为优化目标进行二次优化。采用增材制造方法3D打印技术对平面三自由度柔顺机构拓扑构型进行加工,并采用雷尼绍双频激光干涉仪进行测量与数据采集。实验与有限元仿真对比结果表明:采用多目标拓扑优化和形状优化组合形成二次优化,运用二次优化方法设计得到的平面三自由度柔顺并联机构,在满足机构具有很好的整体刚度要求下,拥有很高的低阶模态频率实现振动拟制,而且能够实现微纳尺度位移运动特性。     

基于节点密度插值的多材料柔顺机构拓扑优化

基于弹簧模型和节点密度插值的固体各向同性材料惩罚模型(Solid isotropic material with penalization,SIMP)方法,给出了一种用于多材料柔顺机构拓扑优化设计的分层优化方法.首先,以输出端位移最大化为目标以各种材料相应的体积占比为约束,建立了多材料柔顺机构拓扑优化模型;其次,采用节点密度插值,构造了设计区域内具有C0连续性的密度场函数,给出了目标函数和约束的敏度解析表达式,使用过滤半径自适应迭代的敏度过滤方案,消除了节点密度插值法中的层化现象;再次,给出了一种分层优化策略用于求解多材料柔顺机构拓扑优化问题;最后,分别用典型的二维和三维柔顺机构拓扑优化问题验证了所提出方法的有效性,并分析了设计参数对优化结果的影响机制.     

基于转动约束策略的柔顺机构拓扑优化

柔顺机构在航天航空、生物医疗、及仿生机器人等高新科技领域的精密微机械系统中拥有巨大的应用潜力。目前,拓扑优化是柔顺机构构型设计的主要方法之一。为了解决传统柔顺机构拓扑优化设计中存在虚铰的问题,首先,将旋转角引入柔顺机构构型设计中,以旋转角为观测指标,分析拓扑优化结果中存在虚铰的原因。其次,通过约束设计域内的旋转角平方的平均值不超过许用值,建立无铰链式柔顺机构拓扑优化模型,并且利用伴随法推导与之相应的灵敏度分析列式。最后,采用反向位移机构与柔性夹钳这两个经典算例的拓扑优化设计验证了所提优化模型的可行性和有效性。研究结果表明：基于转动约束策略获得的具有类桁架构型无铰链式柔顺机构,虽然在输入位移与输出位移方面表现出一定程度的减少,但避免了局部应变过大、应力集中问题的出现。     

考虑疲劳性能的柔顺机构拓扑优化设计

柔顺机构需要承受多次往复运动,交变应力导致机构容易发生疲劳损伤及失效.为了满足疲劳性能要求,提出一种考虑疲劳性能的柔顺机构拓扑优化设计方法.考虑恒定振幅的比例载荷作用,采用修正的Goodman疲劳准则评定柔顺机构的疲劳强度,以柔顺机构的输出位移最大化为目标函数,以疲劳性能和结构体积作为约束,采用改进的P范数方法进行疲劳约束凝聚,建立基于疲劳性能约束的柔顺机构拓扑优化模型,利用映射过滤方法避免数值不稳定性现象,采用移动渐近优化算法求解柔顺机构疲劳约束拓扑优化的多约束优化问题.数值算例结果表明基于疲劳约束拓扑优化获得的柔顺机构能够满足疲劳要求,机构的von Mises等效应力分布更加均匀;并且分析不同的作用载荷条件对柔顺机构构型及其性能的影响规律.     

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.     

Modeling of large-deflection links for compliant mechanisms

The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.     

Modeling of large-deflection links for compliant mechanisms

The traditional pseudo-rigid-body model (PRBM) has one degree of freedom (DOF) and performs a good simulation to the tip locus of flexible links for compliant mechanisms on the basis of a parametric approximation method. In this study, a new approach of a two-DOF PRBM is proposed to simulate both the tip locus and tip deflection angle of large-deflection links for compliant mechanisms on the basis of the angular deflection approximation technique. A linear regression for the spring stiffness coefficient of the 2R PRBM using the optimization technique is presented. The advantage of the new model is well illustrated through a numerical comparison between the 1R and the 2R PRBM.     

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。     

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。     

基于均匀化方法的柔顺机构的拓扑优化设计

基于柔顺机构拓扑优化设计的均匀化方法,给出了柔顺机构应变能和互应变能的算法,建立了柔顺机构多目标优化设计的模型并给出了相应的求解方法。最后通过算例说明了方法的可行性。     

柔性机构拓扑优化设计研究

介绍了柔性机构拓扑设计现状,讨论了柔性拓扑优化设计模型的建立,非线性求解技术和伴随矩阵敏度分析技术,并给出简单的算例说明算法的可行性.最后指出了机构拓扑优化设计的发展方向、需要解决的问题以及可能解决的方案等.     

Integrating mechanism synthesis and topological optimization technique for stiffness-oriented design of a three degrees-of-freedom flexure-based parallel mechanism

This paper introduces a new design approach to synthesize multiple degrees-of-freedom (DOF) flexure-based parallel mechanism (FPM). Termed as an integrated design approach, it is a systematic design methodology, which integrates both classical mechanism synthesis and modern topology optimization technique, to deliver an optimized multi-DOF FPM. This design approach is separated into two levels. At sub-chain level, a novel topology optimization technique, which uses the classical linkage mechanisms as DNA seeds, is used to synthesize the compliant joints or limbs. At configuration level, the optimal compliant joints are used to form the parallel limbs of the multi-DOF FPM and another stage of optimization was conducted to determine the optimal space distribution between these compliant joints so as to generate a multi-DOF FPM with optimized stiffness characteristic. In this paper, the design of a 3-DOF planar motion FPM was used to demonstrate the effectiveness and accuracy of this proposed design approach.     

Mechanical and geometric advantages in compliant mechanism optimization

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism’s structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.