【作者】 刘小院；

【导师】 贾建援； 陈贵敏；

【作者基本信息】 西安电子科技大学 ， 机械电子工程， 2014， 博士

【摘要】 作为柔性铰链机构的核心单元,柔性铰链的选型与参数设计直接关系到机构的整体性能。由于对各种切口型式的柔性铰链的研究是独立完成的,每种铰链都对应一套十分复杂的设计计算公式,这使得柔性铰链机构的设计者在选择铰链型式时难度很大。在进行柔性铰链参数设计之前,设计者主要根据经验来完成柔性铰链的选型,这样难以保证所选择的铰链切口型式最佳。柔性铰链的通用模型方法,通过通用的解析模型将多种切口形状的柔性铰链统一起来,从而将柔性铰链切口型式的选择和参数设计两个过程合二为一。论文基于圆锥曲线类柔性铰链的通用模型,以桥式柔性位移放大机构为研究对象,研究柔性位移放大机构的运动静力学和动力学建模、应力分析以及涉及柔性铰链切口选型和机构几何参数(包括柔性铰链的几何参数)的多目标优化设计。论文完成的主要工作有:(1)利用圆锥曲线的统一极坐标方程,提出了一种圆锥曲线类柔性铰链的通用模型,并基于小变形梁假设,推导了柔性铰链沿各个方向柔度的解析表达式;基于圆锥曲线类柔性铰链的通用模型,综合考虑机构中柔性铰链的切口形状及几何参数、机构中刚性杆的几何参数,建立了柔性位移放大机构的静力学分析模型;基于该模型分析了柔性铰链切口形状及机构几何参数对机构静力学性能的影响,以及柔性铰链几何参数加工误差对机构静力学性能的影响。(2)基于力插值的有限元法,采用单位载荷法推导了柔性铰链的通用位移插值函数,并利用位移插值函数给出了圆锥曲线类柔性铰链的一致质量矩阵表达式。基于圆锥曲线类柔性铰链的通用模型,建立了单个柔性铰链的动力学方程,并分析了柔性铰链切口形状及几何参数对其基频的影响。(3)分别基于伪刚体模型和多柔体系统动力学理论,建立了柔性位移放大机构的动力学分析模型;基于圆锥曲线类柔性铰链的通用模型,分析了机构中柔性铰链的切口形状及机构几何参数对放大机构最低阶固有频率的影响。(4)基于圆锥曲线类柔性铰链的通用模型,研究了平面载荷作用下柔性铰链中的应力分布,并根据畸变能密度屈服准则,给出了柔性铰链最大名义应力的计算公式及强度校核条件;基于有限元仿真分析数据,采用数值拟合法,得到了圆锥曲线类柔性铰链的拉伸应力集中系数和弯曲应力集中系数的经验计算公式,并考虑应力集中影响给出了平面载荷作用下柔性铰链及位移放大机构最大应力的计算公式。(5)根据使用性能原则,在保证机构固有频率的前提下,以柔性铰链的失效抗力指标为材料选择原则,基于Ashby图法分析了柔性铰链的材料选择,给出了几种适合加工柔性铰链机构的材料。(6)在综合考虑静力学、动力学性能及应力条件下,给出了位移放大机构的综合评价函数,并进行了位移放大机构的参数优化设计。根据优化结果加工样机,并搭建样机实验平台,通过实验测试了位移放大机构样机的位移放大比,有限元仿真结果和实验结果验证了理论模型的正确性。更多还原

【Abstract】 The performance of flexure-based mechanisms is highly dependent on the characteristics of flexure hinges; therefore, the design of flexure hinges is of practical importance. There are two chief aspects to consider when designing flexure hinges for a flexure-based mechanism, namely, the cutout profile selection and the parameter design of flexure hinges. Because the two aspects are theoretically independent, and there are no clear-cut guidelines for selection of the cutout profile, flexure hinge design is always performed first by selecting a certain type of flexure hinge based on the designer’s experience, and then designing the parameters using the corresponding design equations. This situation prohibits designers from confidently and consistently finding the most suitable hinge designs. The generalized flexure hinge model, with one set of design equations which includes multiple types of conic flexure hinges, effectively combines the aspects of cutout profile selection and parameter design into one.Based on a generalized model for conic flexure hinges, this dissertation investigates the kinetostatics and dynamics modeling, stress and multi-objective optimization of the bridge-type displacement amplifier, considering the cutout profile and parameters of flexure hinges, and other parameters of the mechanism. The main works include:(1) By utilizing the generalized equation for conic curves in polar coordinates, a generalized model for conic flexure hinges is proposed, and it brings elliptical arc, parabolic, and hyperbolic profiles together. Based on the hypothesis of the small deflection beam, all the elements in the compliance matrices for conic flexure hinges are deduced. The kinetostatics model of the bridge-type displacement amplifier, comprehensively considering the cutout profile and parameters of flexure hinges, and other parameters of the mechanism, is established. On the basis of the generalized conic flexure hinge model, effects of the cutout profile of flexure hinges and geometric parameters of the mechanism on the performance of the mechanism are manifested.(2) Based on the force-based finite element method, the derivation of the exact displacement shape function of flexure hinges is developed by using the Unit Load method, and equations of the consistant mass matrix are derived. The dynamical equations of conic flexure hinges are established, and the effect of the cutout profile and geometric parameters of flexure hinges on the natural frequency is analyzed, based on the generalized conic flexure hinge model.(3) Dynamic models of the bridge-type displacement amplifier are derived by employing Lagrange’s equation, respectively based on the pseudo-rigid-body-model(PRBM) method and the flexible multibody dynamic(FMD) model method. The research, concerning the effect of the cutout profile of flexure hinges and geometric parameters of the mechanism on the natural frequency of the mechanism, is carried out.(4)The stress distribution in conic flexure hinges under loads in plane is investigated, and the equation of the maximum nominal stress is provided. According to the distortion energy theory, the strength criterion of flexure hinges is given. Using the ratio of the radius of curvature of the stress concentrating feature to the minimum thickness as the only fitting variable, generalized equations for both the bending and tension stress concentration factors are obtained for conic flexure hinges, through fitting the finite element results. And equations for the maximum stress of conic flexure hinges and the displacement amplifier are derived, with the stress concentration in consideration.(5) According to the usability principle, the materials selection criterion is the failure resisting force indexes of flexure hinges on the premise of the natural frequency. Material selections of flexure hinges are analysed based on the Ashby charts, and some kinds of materials which suitable for manufacturing flexure hinges are provided.(6) Comprehensively considering static and dynamic performances and the stress condition, the evaluation function of the amplification mechanism is constructed and parameters optimizations of the mechanism are carried out. The prototype, according to the optimized results, is manufactured. The experiment platform is set up, and the amplification ratio of the prototype is tested. Results of the experiment and the finite element simulation verify the correctness of the theoretical model.更多还原