基于动态特性的复合桥式微动平台优化设计

Optimization Design of a Compound Bridge-type Micro-platform Based on Dynamic Characteristics

为了实现复合桥式微动平台的精确运动，提出一种基于其动态特性的优化模型并对其结构参数进行优化。采用虚功原理推导出平台的运动、刚度和强度特性模型。采用伪刚体法和Lagrange方程建立平台的动态特性模型。建立的所有模型是以结构参数为变量的封闭形式，为平台优化设计提供理论模型。由理论模型与有限元分析的结果比较分析可知，两者所得的结果误差范围为6．0％-9．3％，表明所推导出的特性模型的正确性和精确性。根据固有频率和放大倍数封闭形式的模型，分析其对结构参数的灵敏度，由此选出对平台动态特性影响较大的优化设计变量。提出一种以平台的动态特性固有频率和放大倍数为目标，铰链强度、输入刚度和几何尺寸为约束的优化模型。结果表明优化后的平台能获得更大的固有频率和放大倍数，说明方案能满足其优化设计要求。

In order to achieve the precise motion of a compound bridge-type micro-platform, an optimization model based on its dynamic characteristics was presented and the optimization design of structure parameters was carried out. The kinematic, stiffness and strength characteristics of the platform were derived by using the virtual work principle. The pseudo-rigid-body method and Lagrange equation were applied to establish the dynamic model. All proposed model is based on the structural parameters as the independent variables in the closed form, and it can provide the theoretical model for the optimization design. By comparing the theoretical model and FEA, the results show that the errors are within 6.0% 9.3% , which illustrates the proposed feature models are correct and precise. According to the closed- form natural frequency and amplification ratio, the sensitivity of this model with respect to structural parameters was analyzed, and then the design variables were chosen, which have greater impact on the dynamic properties of the platform. At last, the optimal model was proposed as the maximum natural frequency and amplification factor for the objective and the hinge strength, input stiffness, and geometric dimensions for constraints. The results show that higher natural frequency and more amplification factor are obtained from the optimum platform. So the proposed optimum platform can meet the design requirement.