摘要
针对现有基于柔性铰链的微动平台动态特性受材料特性、设计制造等误差影响,难以满足精密微动平台对动态响应(特别是可变频率操作)的高要求,基于应力刚化效应,提出了动态特性可调的微动平台设计新方法,推导预应力作用下一端固定一端导向梁的等效刚度和质量公式;基于对称布置假设,建立含有弹片式柔性铰链(下面简称弹片)组数(离散变量)和截面尺寸(连续变量)的离散连续变量复合优化模型,释放承载刚度约束,获得截面尺寸含有弹片组数变量的精确解系列,分析了给定预应力下不同弹片组数微动平台的承载刚度和频率调节范围,从而通过承载刚度约束和频率调节范围要求确定弹片组数。通过数值算例,验证了推导计算模型求解精度和所提设计方法的应用有效性。计算结果表明,与有限元分析结果相比,本模型的计算结果相对误差小于2%,实现了给定工作刚度、频率和承载刚度约束的微动平台最优结构设计。所提方法实现了刚度和频率大范围的调整,不但降低了加工精度要求,还为动态特性自适应匹配的智能微动平台提供一种实现途径。
Since the dynamic characteristics of existing micro motion stage based on flexible hinge apt to be influenced by material properties, designing and manufacturing errors, it is difficult to meet the high demands of dynamic response for the precision micro motion （especially frequency variable operation）. A new method is proposed to design the dynamic characteristics adjustable micro motion stage based on tension stiffening effect. In the procedure, formulas of the equivalent stiffness and mass of the one end clamped and one end guided beam under preload are deduced, and the discrete-continuous optimization model of the number of spring leaf type flexure hinge groups（discrete variables） and cross-section size（continuous variables） is established based on the assumption of symmetric layout, by release the payload stiffness constraint, the model is transformed to the analytic solution series of cross-section size with the function of the number of spring leaf type flexure hinge groups. The payload stiffness and frequency adjustment range of different number of spring leaf type of flexure hinge groups at a given preload are analyzed, and the number of spring leaf type flexure hinge groups is determined by the demands of payload stiffness and frequency adjustment range. Application cases show the accuracy and the effectiveness of the presented method. Compared with finite element analysis, the relative error is less than 2%, realizing the optimal design of micro motion stage at given working stiffness, frequency and payload stiffness. The proposed method achieves a wide adjustment range of the stiffness and frequency, not only reduces the machining precision requirements, but also provides an implementation of the intelligent micro motion stage with the dynamic characteristics adaptive matched.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2015年第23期153-159,共7页
Journal of Mechanical Engineering
基金
国家自然科学基金(U1134004
50905033)
国家重点基础研究发展计划(973计划
2011CB013104)
广东省自然科学基金(2015A030312008)
广州市科技计划(201510010281)
广东省科技计划(2013B010402014
2012CXZD0020)资助项目
关键词
微动平台
柔性铰链
柔顺机构
应力刚化
智能平台
micro motion stage
flexible hinge
complaint mechanism
tension stiffening
intelligent motion stage
作者简介
杨志军，男，1977年出生，教授。主要研究方向为机械系统动力学。E-mail：yangxj@gdut．edu．cn
陈新（通信作者），男，1960年出生，博士，教授，博士研究生导师。主要研究方向为结构优化设计。E-mini：chenx@gdut．edu．cn
