This paper focuses on the configuration design of flexure hinges with a prescribed compliance matrix and preset rotational center position. A new method for the topology optimization of flexure hinges is proposed based on the adaptive spring model and stress constraint. The hinge optimization model is formulated by maximizing the bending displacement with a spring while optimizing the compliance matrix to a prescribed value. To avoid numerical instability, an artificial spring is used as an auxiliary calculation, and a new strategy is developed for adaptively adjusting the spring stiffness according to the prescribed compliance matrix. The maximum stress of flexure hinge is limited by using a normalized P-norm of the effective von Mises stress, and a position constraint of rotational center is proposed to predetermine the position of the rotational center. In addition, to reduce the error of the stress measurement, a simple but effective filtering method is presented to obtain a complete black-and-white design. Numerical examples are used to verify the proposed method. Topology results show that the obtained flexure hinges have the prescribed compliance matrix and preset rotational center position while also meeting the stress requirements.

本文重点研究具有规定柔度矩阵和预设旋转中心位置的挠性铰链的配置设计。提出了一种基于自适应弹簧模型和应力约束的柔性铰链拓扑优化新方法。铰链优化模型是通过使用弹簧最大化弯曲位移同时将柔量矩阵优化到规定值来制定的。为了避免数值不稳定，使用人工弹簧作为辅助计算，并开发了一种新策略，根据规定的柔量矩阵自适应调整弹簧刚度。挠性铰链的最大应力通过使用归一化的 P范数来限制的有效 von Mises 应力，并提出了旋转中心的位置约束来预先确定旋转中心的位置。此外，为了减少应力测量的误差，提出了一种简单而有效的滤波方法，以获得完整的黑白设计。数值例子用于验证所提出的方法。拓扑结果表明，获得的挠性铰链具有规定的柔量矩阵和预设的旋转中心位置，同时也满足应力要求。