微/纳米传动平台的模态试验及优化设计

微/纳米传动平台中，柔性机构的弹性势必导致平台高速、高加速带来的残余振动。采用拉格朗日方法，建立了平台的动力学模型，得到了平台前5阶固有频率的解析式；分析了平台固有频率与柔性板簧厚度、长度的相互关系，得到了固有频率随柔性板簧厚度、长度的变化规律。应用有限元方法，分别仿真得到了前6阶固有频率和模态阵型；以固有频率为优化目标，建立了平台的优化模型。采用动态测试系统，分别对优化前、后的平台进行了模态试验分析；通过对比分析，得到了提高平台动态性能的方法，且模态试验结果表明，调整柔性板簧厚度、长度的方法是有效的、可行的。

Modal testing and optimal design for a micro/nano-transmission platform

For a micro/nano-transmission platform,flexibility of a flexible mechanism inevitably leads to residual vibration in cases of high-speed and high acceleration.In terms of Lagrangian equation,the dynamic model of the platform was set up,the first five natural frequencies were obtained.And the relationship between the natural frequencies,the thickness and the length of a flexible leaf were analyzed.Based on finite element method,the first six natural frequencies and modal shapes were gained with simulations.The optimal model of the platform was established taking the natural frequencies as objective functions.Using a dynamic test system,modal tests were done for the platform before and after optimization.Through comparative analysis,the method to improve the dynamic performances of the platform was obtained.In addition,the results of modal testing showed that the method to adjust the thickness and the length of the flexible leaf is correct and effective.