考虑疲劳性能的柔顺机构拓扑优化设计

Topological Design of Compliant Mechanisms Considering Fatigue Constraints

柔顺机构需要承受多次往复运动,交变应力导致机构容易发生疲劳损伤及失效。为了满足疲劳性能要求,提出一种考虑疲劳性能的柔顺机构拓扑优化设计方法。考虑恒定振幅的比例载荷作用,采用修正的Goodman疲劳准则评定柔顺机构的疲劳强度,以柔顺机构的输出位移最大化为目标函数,以疲劳性能和结构体积作为约束,采用改进的P范数方法进行疲劳约束凝聚,建立基于疲劳性能约束的柔顺机构拓扑优化模型,利用映射过滤方法避免数值不稳定性现象,采用移动渐近优化算法求解柔顺机构疲劳约束拓扑优化的多约束优化问题。数值算例结果表明基于疲劳约束拓扑优化获得的柔顺机构能够满足疲劳要求,机构的von Mises等效应力分布更加均匀;并且分析不同的作用载荷条件对柔顺机构构型及其性能的影响规律。

Compliant mechanisms need to withstand multiple reciprocating motions, and the alternating stress causes the mechanism to be prone to fatigue damage and failure. In order to meet the fatigue performance, a method for topology optimization of compliant mechanisms considering fatigue constraints is proposed. The proportional loadings with constant amplitude is considered in fatigue analysis. The modified Goodman fatigue criterion are applied to evaluate the fatigue strength. The maximum of the output displacement of the compliant mechanisms is developed as the objective function, and the fatigue performance and structural volume are used as the constraints. Fatigue constraints are aggregated into a constraint using the improved P-norm method. The model for topology optimization of compliant mechanisms considering fatigue constraints is established. The projection filter is applied to avoid the phenomenon of numerical instabilities. The method of moving asymptotes is applied to solve the multi-constrained optimization problem. The results of several numerical examples show the compliant mechanisms obtained by fatigue constrained topology optimization can meet the fatigue strength requirement, and the stress is more uniformly distributed. The effect of different loading conditions on the configuration and performance of the compliant mechanisms is analyzed.