Abstract:

：The circular-axis flexure hinge has been widely used in various fields. In order to solve the problem of optimizing material and geometrical configuration of flexure hinge simultaneously, the mechanical modeling method and optimization algorithm is investigated. According to the structural property of the flexure hinge, which consists of several flexural elements, the flexure hinge is simplified to indeterminate beam. The radical and tangential stiffness is derived by using virtual work principle. The whole stiffness of the flexure hinge, which is the function of material, geometrical parameters and its configuration, is obtained based on force equilibrium condition and compatible deformation. The optimization model for flexure hinge design is established. By introducing the SIMP/RAMP based model, the material parameter is expressed as the combination of artificial variables and candidate material parameters and the stiffness of flexure hinge is expressed as the combination of artificial variables and stiffness parameter corresponding to different geometrical configuration. The discrete integer programming problem can be transformed into continuous parameters optimization problem, then the gradient based method can be used to solve the optimization problem, which decreases the complexity of optimization model and improves the computational efficiency. The stiffness model of flexure hinge is verified by experiment, and the theoretical results are in good agreement with experimental results. In addition, the example of spherical mirror is given to verify the optimization model and algorithm. The obtained results show that the solving scheme guarantees the enough solution space in the beginning and finally drives the artificial variables to 0-1 values as the penal factor increasing. The surface precision of the mirror is increased by 15% after optimization design.

Key words: continuous optimization, discrete optimization, geometrical configuration, virtual work principle, flexure hinge