Optimization Design and Experiment of XY Compliant Platform with Local Resonance Damping

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.