Fatigue Life Prediction and Optimal Design of a Flexure Based Micro-Motion Stage

This paper presents a fatigue-based method for optimal design of a flexure based 3-RRR compliant micro-motion stage, which is driven by three piezoelectric actuators (PZT). As this compliant stage obtains motions from the deflection of its flexure hinges, fatigue failure becomes its major failure mode. The aim of this paper is to provide a method to predict the fatigue life of the stage and redesign it by considering fatigue strength. Firstly, the motion transformation matrix, which reveals the relation between output displacement vector of moving platform and three input displacements of PZT actuators, is established by using the finite element method. Then, the force vectors of all the twelve flexure elements in the stage can be derived. Secondly, the fatigue properties of circular flexure hinge are discussed by considering the effects of flexure dimension parameters, non-zero mean stress, surface conditions and et al. Combined with the material stress life curve and the fatigue strength of the flexure hinges, fatigue life prediction of the micro-motion stage can be carried out by utilizing the nominal stress approach. The aforementioned micro-motion stage, which is optimized based on maximum stress constraint, is presented as an example to illustrate the fatigue life prediction procedure. And the predicted results of fatigue lives in specified condition indicate that fatigue lives of all flexure hinges in the stage differ drastically. In this condition, the stage will fail prematurely due to the most vulnerable hinge. So, the design method based on static strength may lead to unsafe or uneconomic design of the stage. Finally, a fatigue based optimal design method is introduced to redesign the flexure based micro-motion stage. The stage dimensions and the flexure hinge geometry are considered as design variables. The maximum motion range is set as the objective function. And the fatigue strength of flexures is taken as constraint, as well as the natural frequency of the stage and the input force capacity of PZT actuators. A micro-motion stage with optimal dimension parameters is obtained at last. Numerical results show that the optimal stage has a good comprehensive properties and can endure a infinite cycles.