摘要
为了分析平面串并联椭圆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。将平面椭圆柔顺机构分解成许多易于用矩阵形式表达的简单力学特征元件,采用传递矩阵法描述其力学状态量的传递关系。将椭圆型柔性铰链视为拉伸和弯曲变形的变截面梁,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,运用动量矩定理建立其动力学模型,得到描述平面振动刚体的传递矩阵。依据柔顺机构特征元件的联接特点,将结构元件的传递矩阵进行拼装并得到总体传递矩阵。总传递方程以椭圆柔顺机构的输入、输出端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,可得平面串并联柔顺机构的特征方程,通过求解齐次方程可得系统的固有频率。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。通过平面串联椭圆柔性铰链机构及3RRR并联柔顺机构的动态性能分析,结果表明所建立模型的正确性,能精确描述平面椭圆柔顺机构力学性能。
In order to analyze the dynamic performance and mechanical transfer relationship of planar series-parallel elliptical compliant mechanisms,a new vibration mechanical model based on transfer matrix method is proposed.The plane elliptic compli-ant mechanism is decomposed into many simple mechanical characteristic elements which are easy to express in matrix form.An elliptic flexure hinge is considered as a beam of variable section with tensile and bending deformation.The bar is regarded as a rigid body,and its dynamic model is established by using the moment of momentum theorem,and the transfer matrix describing the plane vibrating rigid body is obtained.According to the connection form of the characteristic elements of the flexible mecha-nism,the transfer matrix of each element is assembled to obtain the overall transfer matrix of the planar serial and parallel sys-tems.The general transfer equation takes the state vectors of the input and output ends of the elliptic compliant mechanism as un-known variables,and the elements in the matrix as functions of the structural parameters and frequencies of the mechanism.An ex-tended transfer matrix reflecting the relationship between external force excitation and the system is established to solve the fre-quency response of the system.Through the analysis of the dynamic performance of the plane series elliptic flexible hinge mecha-nism and the 3RRR parallel compliant mechanism the results show that the model is correct and can accurately describe the dy-namic performance and mechanical transfer relationship of plane elliptic flexure hinge mechanism.
作者
胡俊峰
廖弘
徐旺
张俊
HU Junfeng;LIAO Hong;XU Wang;ZHANG Jun(School of Mechanical&Electrical Engineering,Jiangxi University of Science and Technology,Jiangxi Ganzhou 341000,China;Ningde Liyuanheng Intelligent Equipment Co.,Ltd.,Fujian Ningde 352100,China)
出处
《机械设计与制造》
北大核心
2025年第11期215-221,共7页
Machinery Design & Manufacture
基金
国家自然科学基金资助项目(52165011)。
关键词
传递矩阵法
椭圆柔顺机构
固有频率
频率响应
Transfer Matrix Method
Oval Supple Mechanism
Natural Frequency
Frequency Response
