基于传递矩阵的柔性精密定位平台刚度建模方法

The Method for Stiffness Modeling of Flexure Precision Positioning Platform Based on Transfer Matrix

刚度是柔性结构的重要性能指标,间接影响着柔性精密定位系统的分辨率、工作空间和承载能力等性能。针对传统刚度建模方法在精确性、简便性和通用性等综合性能上的不足,充分以矩阵为工具,结合传递矩阵、力平衡方程和位移协调方程,得到了综合性能较好的刚度建模方法。应用该方法求解了二维精密定位平台的刚度参数模型,并与有限元方法求解结果对比,两者误差在8%以内,表明了该方法的精确性,又由于传递矩阵良好的递推性,保证了该方法求解上的简便性。这些特性最终保证了该方法能够更好的为柔性精密定位系统的设计与分析提供可靠的理论依据。

Stiffness is an important performance index of flexure structure,which indirectly affects the resolution ratio,working space and carrying capacity of flexure precision positioning system.In view of the shortcomings of the traditional stiffness modeling method in the colligation of accuracy,simplicity and versatility,using fully the matrix as the tool,a stiffness modeling method with better comprehensive performance was obtained by combining the transfer matrix,the force balance equation and the displacement coordination equation.The parameter model of the stiffness of a precision positioning platform with two dimension was solved by this method,and the result of this model was compared with the one of the finite element method,which showed that the error of the two results was under 8%,proving the accuracy of the model.Because of the good recurrence of transfer matrix,the simplicity of the solving of the method is guaranteed.These characteristics of the method ultimately guarantee that it can provide a reliable theoretical basis for the design and analysis of flexure precision positioning system.