针对目前用于原子力显微镜的扫描定位平台带宽低、行程小、耦合性能差等问题, 提出了一种基于柔性梁的高带宽两自由度精密定位平台并对该平台进行了优化设计、仿真验证与实验分析。首先, 提出了以双端固定梁与平行杂交梁为基础的并联柔顺平台, 分别运用卡式第二定理和拉格朗日方程建立了平台刚度和固有频率的数学模型; 然后, 通过最优化理论获取了平台的最高固有频率及最优设计尺寸, 并运用有限元方法验证了优化结果的可靠性; 最后, 搭建了实验系统, 对平台进行了实验研究。实验结果表明: 所设计平台的最大行程为12.950 μm×13.517 μm, 耦合误差小于1.77%, X, Y方向的固有频率分别为12.21和13.50 kHz, 在开环条件下可良好地追踪频率小于1 kHz的三角波, 有效改善了传统扫描定位平台响应慢、行程小、耦合性能差等问题。

A high-bandwidth, two-degree-of-freedom nanopositioning stage based on the optimization of a flexible beam is proposed with the aim of improving the low-bandwidth performance, relative low-travel range, and poor coupling performance of the scanning positioning stage of Atomic Force Microscopy. Design optimization, simulation verification, and experimental analysis of the proposed stage are conducted as part of this process. Firstly, a parallel compliant moving stage composed of a doubly clamped beam and parallel hybrid beam is presented, while Castiglianos second theorem and Lagranges equation are applied to establish the mathematical model of its stiffness and natural frequency. Then, the maximum natural frequency and optimal size of the stage are obtained using optimization theory, while the optimization result reliability is verified using finite element method software. Finally, an experimental system is built and experiments are conducted on the developed stage. The experimental results indicate that the travel range of the proposed stage is 12.950 μm×13.517 μm, with a coupling error of less than 1.77%. The natural frequencies in the X and Y directions are 12.21 kHz and 13.50 kHz, respectively. In open loop, triangular waves with frequencies less than 1 kHz can be tracked well, effectively addressing the problems of slow response, small stroke, and poor coupling performance of the traditional scanning nanopositioning stage.