面向单向输入力的柔顺正交位移放大机构拓扑构型设计

Topological design of compliant orthogonal displacement amplification mechanism under the unidirectional input force

正交位移放大机构用以输出且放大垂直于输入力方向的位移,其构型常采用典型的桥式结构.但是桥式放大机构要实现正交位移转换必须输入双向对称力,否则输出端会产生寄生位移.针对此问题,采用连续体结构拓扑优化技术寻找新构型的柔顺位移放大机构,使之在单向输入力条件下,依然可以实现正交位移转换.基于固体各向同性材料惩罚模型(SIMP)拓扑描述方法,以输出位移与输入位移比最大化作为目标函数,以相对寄生位移,即输出端寄生位移与输出位移之比作为其中一个约束函数,建立了面向单向输入力的柔顺正交位移放大机构的拓扑优化数学模型.采用伴随法详细推导了目标函数和约束函数的敏度信息,并采用移动渐近线算法(MMA)进行了优化问题的求解.通过数值算例,给出了正交位移放大机构的拓扑优化结果,并探讨了弹簧刚度对拓扑优化结果的影响.最后,通过有限元仿真和实验,研究了拓扑优化得到的新型正交位移放大机构和桥式位移放大机构的相对寄生位移.仿真和实验都验证了所提方法的正确性和有效性.

The orthogonal displacement amplification mechanism is used to output and amplify the displacement perpendicular to the direction of the in put force,and its configuration often uses a typical bridge-type.However,the bridge-type amplifier to achieve orthogonal shift conversion must enter the bidirectional symmetric input forces,otherwise the output will produce parasitic displacement.In view of this problem,the topology optimization method is used to find the new configuration of the displacement amplification mechanism,so that it can still realize the orthogonal displacement transformation under the unidirectional input force condition.Based on the solid isotropic material with penalization (SIMP) topological description method,the ratio of output and in put displacements is maximized as the objective function,the ratio of parasitic displacement and output displacement as one of constraint functions,and the topological optimization mathematical model of the compliant orthogonal displacement amplifier is established under the unidirectional input force.The sensitivity information of the objective and constraint functions is deduced by the adjoint matrix method,and the optimization problem is solved by the method of moving asymptotes (MMA).The topology optimization results of orthogonal displacement amplifier are given through numerical examples,and the effect of spring stiffness on the topology optimization result is also discussed.Fin ally,the parasitic motions of the displacement amplification mechanism obtained from topology optimization and the bridge-type amplification mechanism are compared through the finite element analysis and experiment.Finite element simulation and experiment confirm the correctness and validity of the proposed method.