摘要
利用桥式微位移放大机构的结构全对称性,建立了微位移放大机构的四分之一数学模型.采用矩阵法建立了其柔度矩阵,推导出位移放大机构的输出位移公式及位移放大比公式;基于模态分析理论,根据拉格朗日方程建立了桥式放大机构的运动微分方程,给出了计算桥式微位移放大机构固有频率的解析式.用ANSYS11.0进行有限元仿真,结果表明:在X,Y轴方向上的输出位移、位移放大比以及机构的固有频率,理论计算值与有限元仿真值的误差分别为7.05%,4.81%,2.48%和0.08%.X轴输出位移相差较大主要原因是在理论模型中采取简化分析而忽略了柔性铰链的伸长,并且假设除柔性铰链外,其它的部分为刚性.
A quarter model was proposed to analyze the characteristics of the mechanism according to the symmetrical structure.The compliance matrix was deduced using a matrix method,and formulas for calculating output displacements and displacement amplification ratio of the bridge-type amplifier were derived.The differential equation of motion was established by the Lagrange equation,and a formula of natural frequence was derived based on the modal analysis theory.The finite element simulation for verification was carried on by a software ANSYS11.0.The results show that the error of output displacements,displacement ratio and natural frequency between theoretical calculation and finite element simulation is 7.05%,4.81%,2.48% and 0.08%,respectively.The error of output displacement along X-axis is the largest,because the extension of flexure hinges are ignored in theoretical model for simplification and the other parts are rigid expect for flexure hinges.
出处
《中国矿业大学学报》
EI
CAS
CSCD
北大核心
2011年第2期310-314,共5页
Journal of China University of Mining & Technology
基金
高等学校博士学科点专项科研基金项目(20090095110012)
江苏省普通高校研究生科研创新计划项目(CX09B_109Z)
关键词
桥式放大机构
四分之一模型
有限元仿真
bridge-type amplifier
a quarter model
finite element simulation
