基于有限元法的桥式柔顺机构动态性能分析

为了精确描述桥式柔顺机构的动态性能,采用有限元方法建立其动力学模型,并基于该模型分析其动态性能。采用欧拉-伯努利梁模拟柔性铰链和杆件的力学行为,采用最小势能原理得到桥式机构的刚度矩阵,采用拉格郎日方程建立机构的质量矩阵和动力学方程。基于桥式机构的有限元模型,分别进行铰链尺寸参数对固有频率的灵敏度分析、动刚度和动应力分析。分析结果表明:增大铰链厚度与长度之比可提高机构的响应快速性;在机构工作运动方向有较大的振动,而且在接近于固有频率处发生较大的超调;靠近驱动端的铰链所受的动应力较大,容易疲劳破坏。     

4种柔性铰链的温度效应比较分析

为了减小温度效应对柔顺机构的影响,比较分析直梁、直圆、椭圆和抛物线型4种典型柔性铰链的温度效应,以便合理选取柔性铰链设计柔顺机构。将柔性铰链划分为2个变截面梁单元,计入温度变化产生的初应变,采用最小势能原理推导出4种柔性铰链的热载荷向量和刚度矩阵,采用拉格郎日方程得出其质量矩阵,得出铰链的力学模型。基于柔性铰链的有限元模型,并以柔顺四杆机构为算例,分别对基于4种柔性铰链的柔顺机构的精度、热应力和热振动进行比较分析,分析结果表明:直圆型铰链的热误差最大,抛物线型次之,椭圆型和直梁型最小;所受热应力由大到小的顺序为直圆、椭圆、抛物线和直梁型铰链;直梁型柔性铰链的热振动谐振频率最小,直圆型和椭圆型次之,抛物线型最大,说明直梁型柔性铰链更容易受动态温度变化影响,但抛物线型在谐振频率处的幅值最大,抛物线型铰链热振动更大。     

传递矩阵法分析FBG加速度计的动态性能

为了分析基于柔性铰链的FBG(fiber Bragg grating)加速度计的力学传递关系和动态性能,建立了加速度计的传递矩阵法力学模型。柔性铰链主要考虑其变形而忽略质量影响,应用材料力学相关理论建立其传递矩阵。质量块主要考虑其刚体运动而忽略变形,应用理论力学相关理论建立其传递矩阵。通过分析计算,设计了一种灵敏度高于29pm/g,固有频率约为1950Hz的加速度计。测试结果表明该加速度计的灵敏度高于26pm/g,固有频率约为1850Hz。实验结果表明了所建模型的正确性。     

基于伪刚体模型法的柔顺机构驱动特性研究

本文对不同载荷下大变形柔性杆件的末端轨迹进行了分析,给出不同情况下柔性杆件伪刚体模型中各参数的确定方法.在此基础上,对一个大变形曲柄滑块机构分析了已知从动件规律,如何用伪刚体模型法求解主动件的驱动问题,其结果证明了伪刚体模型法在柔顺机构研究中的有效性.     

基于伪刚体模型的柔顺簧片性能分析

柔顺簧片的性能对微动机构运动精度具有较大影响,因其具有非线性、大变形等特点,根据Bernoulli-Euler方程,结合伪刚体模型,建立柔性簧片力学特性分析模型。研究载荷、位移,曲率等与柔顺簧片几何参数之间的关系,并求得系统的力学方程。最后通过算例分析柔顺簧片在精密导向机构中的应用,其为精密微动装置的设计提供一定的理论依据。     

基于有限元法的柔顺机构动力学分析

为描述柔顺机构动力学特性,需要建立其动力学模型。基于有限元法,根据Lagrange方程建立柔顺机构的动力学方程。在此基础上,得到机构各阶固有频率和模态,并给出固有频率和模态对各项设计变量的灵敏度计算方法。推导出柔顺机构中柔性杆件上任意一点应变的算法,计入应变中的非线性项。求解柔性杆件上任意位置的动应力,并计算杆件在各个时刻的最大应力及出现的位置。以平面柔顺四杆机构为例进行分析,说明基于有限元法对柔顺机构的动力学特性分析的可行性和有效性,并且指出柔顺机构杆件的动应力和应变分析对柔顺机构的优化设计具有重要意义。     

一种柔顺五杆机构的动力学建模与仿真

以一种柔顺五杆机构为模型,该机构包含柔性铰链与柔性杆。通过伪刚体模型法建立了伪刚体模型,并进行了动力学分析。随后,进行了该机构的频率特性分析以及受力分析,为下一步该机构的设计奠定了的理论基础。     

椭圆形柔性铰链的频率特性分析

建立了平行导向柔顺机构的模型,分析了由椭圆形柔性铰链构成的平面柔顺机构的参数特性.讨论了椭圆形柔性铰链最小厚度、切口几何参数、机构厚度与系统固有频率的关系,并通过数值算例得到一些规律性结论,为椭圆形柔性铰链的设计与应用提供了理论依据,也为柔顺机构的动力学研究提供了参考.     

集中柔度全柔性机构变形分析及仿真

柔性铰链四杆机构在精密机械中的应用日益广泛.采用伪刚体模型法对具有集中柔度的全柔性铰链四杆机构进行了分析,利用MATLAB编写了外载荷与杆件转角关系的Newton迭代法程序.同时用有限元方法建立了全柔性铰链四杆机构模型,并用ANSYS进行了仿真.给出了两种方法的计算实例,对所得结果进行了讨论,分析了误差产生的原因.     

基于2R伪刚体模型的柔顺机构动力学建模及特性分析

柔顺机构是利用机构中柔性构件的自身变形来实现运动、力和能量的传递和转换的一种新型机构,是机构学研究领域的前沿课题之一。以柔顺机构中的柔顺杆为研究对象,基于2R伪刚体模型(Pseudo-rigid-body model,PRBM)提出末端受不同载荷形式(力矩或垂直力)作用下的动力学新模型,分析其动能和变形能,应用拉格朗日方程推导其动力学方程。通过与1R伪刚体动力学模型(Pseudo-rigid-body dynamic model,PRBDM)对比,从方程特征、响应曲线等方面分析各动力学模型的特点,从而展示基于2R伪刚体模型的动力学模型优越性,并以平行导向柔顺机构为例验证了模型的有效性。分析结果表明,基于2R伪刚体模型的动力学模型不仅可以反映柔顺杆整体大范围变形状况,而且描述出杆件内部局部变形状况,可以更真实地体现柔顺机构的动力学特性,更加适合于柔顺机构的动力学分析与设计。*     

Analytical Compliance Modeling of Serial Flexure-Based Compliant Mechanism Under Arbitrary Applied Load

Analytical compliance model is vital to the flexure- based compliant mechanism in its mechanical design and motion control. The matrix is a common and effective approach in the compliance modeling while it is not well developed for the closed-loop serial and parallel compliant mechanisms and is not applicable to the situation when the external loads are applied on the flexure members. Concise and explicit analytical compliance models of the serial flexure-based compliant mechanisms under arbitrary loads are derived by using the matrix method. An equivalent method is proposed to deal with the situation when the external loads are applied on the flexure members. The external loads are transformed to concentrated forces applied on the rigid links, which satisfy the equations of static equilibrium and also guarantee that the deformations at the displacement output point remain unchanged. Then the matrix method can be still adopted for the compliance analysis of the compliant mechanism. Finally, several specific examples and an experimental test are given to verify the effectiveness of the compliance models and the force equivalent method. The research enriches the matrix method and provides concise analytical compliance models for the serial compliant mechanism.     

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.     

剪切型阻尼U型柔性铰链设计与实验分析

根据柔性铰链的无阻尼结构特点,并利用黏弹性阻尼材料的剪切损耗特性,提出一种剪切型阻尼U型柔性铰链的结构模型,并结合GHM(Goulla-Hughes-MacTavish,简称GHM)黏弹性理论模型建立带阻尼铰链动力学方程。该铰链通过提高外加黏弹性阻尼层材料的剪切效应,达到增强结构阻尼目的。为了测试剪切型阻尼结构对该U型铰链的振动抑制效果,对其进行自由振动信号测试和动态力学分析(dynamic mechanical analysis,简称DMA)实验。结果显示,该阻尼结构能使铰链结构在120~150Hz的共振频段内因振幅增大,阻尼层剪切效应加剧,出现明显的阻尼损耗峰值,有效增强了铰链的结构阻尼。     

Constraint-force-based approach of modelling compliant mechanisms: Principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.     

Spatial force-based non-prismatic beam element for static and dynamic analyses of circular flexure hinges in compliant mechanisms

This paper presents a spatial force-based non-prismatic beam element modeling approach for circular flexure hinges, which is capable of accurate and efficient modeling of both static and dynamic characteristics of flexure-based compliant mechanisms. The spatial force-based non-prismatic beam element is an improvement and extension of the existing beam elements by considering shear and torsional effects of circular flexure hinge. The new consistent mass matrix formulation was derived using the Unit Load method. A parallel-guided compliant mechanism was taken as an example to validate the efficiency and accuracy of the proposed approach through static and modal analyses with fewer non-prismatic beam elements, and the results are well agreed with ANSYS simulation results with massive 3D solid or 2D shell elements. The developed approach is also available to model arbitrarily shaped flexure hinges in compliant mechanisms.     

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.     

高性能主轴偏心状态传递矩阵法的研究

分析电主轴的结构组成并进行简化建模,针对电主轴的偏心状态,采用电磁学对其进行力学分析;基于传递矩阵法对分段电主轴的简化模型进行机械动力学分析,对轴系的典型单元的状态进行了数学描述,递推出整个轴系的传递矩阵;综合电磁学与机械动力学的分析结果,修改部分典型单元的状态矩阵,根据电主轴整体的边界条件,得到偏心电主轴的传递矩阵方程即轴系的频率方程。     

柔顺机构动力学建模新方法

由于柔性杆大变形所引起的几何非线性因素的影响,柔顺机构动力学模型的建立变得更加复杂、困难。基于此,在充分考虑柔性杆大变形特性的基础上,基于简化思想,提出一种柔顺机构动力学建模的新方法。该方法主要以末端受纯弯矩、垂直力以及固定—导向等3种模式下的柔性杆为研究对象,根据欧拉—伯努利方程,并结合伪刚体模型所得边界条件,利用最小二乘原理,拟合柔性杆的变形曲线方程;通过求解变形曲线对时间的导数,得到其上任意点的速度,进而推出柔性杆的动能表达。基于伪刚体模型,根据功能转换关系,推导出柔性杆的变形势能。在此基础上,建立平行导向柔顺机构的动力学模型。最后,结合具体算例,通过对几种不同模型所得系统频率比较分析,验证了该方法的有效性。     

Robust control of XYZ flexure-based micromanipulator with large motion

This article describes the development of an XYZ flexure-based micromanipulator, with the features of decoupled kinematic structure, large motion range, high positioning precision, and fast response. The large motion range of flexure mechanisms is quantified by a given definition. Based on the given definition, large motion is achieved in the mechanical design of the XYZ-flexure parallel mechanism (FPM). To ensure high positioning precision and fast dynamic response, a hybrid control algorithm with both position control and vibration control are designed, using the H_∞-theory. The controller strongly solves the three common problems of flexure mechanisms simultaneously, including unmodeled uncertainties, the external disturbances and vibration caused by inherent low damping.