Treffer: 含局部谐振阻尼的 XY 柔顺平台优化设计与实验.

A compliant precision positioning platform is a core component of precision equipment. The high-speed and high-precision positioning operation requires the platform to possess high response speed and good regulation capabilities. Passive damping can effectively enhance the platform’s rapid response capabilities. To improve the rapid response capability of an XY compliant positioning platform with local resonance damping, this paper proposes an optimization design method that comprehensively enhances modal damping and natural frequency. In the investigation, firstly, based on elasticity theory and Castigliano’s second theorem, the platform stiffness is analytically modeled and synthesized, and the expression for the platform’s natural frequency is derived. Subsequently, aiming at the maximum control gain, a single-objective optimization function composed of natural frequency and the frequency response curve area of the resonant region is formulated, along with the mathematical expression for the platform optimization design problem and a ABAQUS-Python-Matlab joint optimization model. Then, to simplify the complexity of finite element calculations, an equivalent structure for the optimized platform based on the firstorder fixed frequency equivalence is established. Moreover, simulation analysis of the optimized platform is conducted, and the optimization design results are compared and analyzed to verify the correctness of the natural frequency analytical expression. Finally, an experimental platform is constructed to perform static, dynamic and trajectory tracking experiments on the XY compliant platform with local resonance damping. The results demonstrate that the proposed comprehensive optimization method can increase the X-axis and Y-axis control bandwidths of the platform respectively by 7. 42% and 24. 70%, and effectively enhance the trajectory tracking performance of the system. [ABSTRACT FROM AUTHOR]

柔顺精密定位平台是精密装备的核心部件, 其高速、高精度的定位操作要求 平台具有高响应速度与良好的调节能力, 被动阻尼可以有效地提升平台的快速响应能 力。为了提升含局部谐振阻尼的 XY 柔顺定位平台的快速响应能力, 该文提出了一种综 合提升模态阻尼与固有频率的柔顺平台优化设计方法。首先, 根据弹性理论以及卡氏 第二定理, 完成了平台刚度的解析建模与刚度综合, 并推导了平台固有频率的表达式。 然后, 以控制增益最大为目标, 建立了固有频率与共振区频响曲线面积构成的单目标 优化函数、平台优化设计问题的数学表达式以及ABAQUS-Python-Matlab 联合优化模型。 为简化有限元计算的复杂度, 基于平台一阶固频等效, 建立了优化后平台的等效结构。 通过对优化后的平台进行仿真分析, 验证了固有频率解析表达式的正确性。最后, 通 过搭建实验平台, 对含局部谐振阻尼的 XY 柔顺平台进行了静态、动态和轨迹追踪实 验。结果表明, 所提出的综合优化方法可使平台X轴和Y轴控制带宽分别提高 7.42%和 24. 70%, 并有效提升系统的轨迹追踪性能。 [ABSTRACT FROM AUTHOR]

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