Modeling And Optimizing Of Pseudo-elastic Flexure Hinges

As monolithic kinematic pairs, flexure hinges are widely employed in applications where high precision is required, such as micro-positioning stages, piezoelectric actuators, the displacement amplification mechanisms, antenna pointing, etc. Compared with traditional rigid mechanical joints, flexure hinges effectively avoid the clearance in mechanical assemblies as well as the friction and wear during use, which highly improves the accuracy and resolution. Due to the limited strains, the motion range of flexure hinges made of conventional metallic materials is greatly restricted. This problem can be addressed by employing shape memory alloys depending on the pseudo-elasticity of this material. Modeling and optimizing of pseudo-elastic flexure hinges are mainly discussed in this thesis.First of all, based on Brinson’s constitutive law, a piecewise linear model for the finite element analysis is proposed to describe the pseudo-elasticity of shape memory alloys. By combining with this model, the static model of pseudo-elastic flexure hinges is established in the co-rotational framework, considering the material nonlinearity and the geometrical nonlinearity caused by large rotational angles and large strains respectively. Three evaluation indexes are defined, i.e. rotation capacity, rotation error and flexibility, which are used to assess the quality of pseudo-elastic flexure hinges. Compared with various longitudinal sections(elliptic, parabolic, and hyperbolic etc.) under the same key parameters, elliptic flexure hinge is considered as the best candidate to be further optimized. The proposed method is verified by ABAQUS simulation within a 3% margin of error.Secondly, Lagrange’s Equations are implemented to establish the motion equations of pseudo-elastic flexure hinges by combining with the stiffness model. Newton-Raphson method along with the Newmark time integration method is employed to solve the highly nonlinear equations. Simulation results validate the effectiveness of the proposed model, with which the damping effect, the pseudoelastic deformation and the resonant response are analyzed. It can be seen that, compared with the flexure hinges made of conventional metallic materials, pseudo-elastic flexure hinges are superior in motion range, vibration suppression and resonance avoidance.Thirdly, the parameters of the elliptic flexure hinge are optimized by multi-objective optimization based on the established models. The optimization model is built by using dominated elitist genetic algorithms and employing rotation capacity, rotation error, flexibility and the first natural frequency for bending vibration as optimization objectives. The global optimized solution is selected eventually in terms of the design goals.Finally, three different cross-section flexure hinges using nitinol are fabricated and the experimental test is carried out. Based on MATLAB image processing, the static deformation of pseudo-elastic flexure hinges is measured by a CCD industrial camera. A high-precision Laser Doppler Vibrometer is used for the vibration measurement and the experimental data are recorded and stored by a digital storage oscilloscope. Experimental results show the effectiveness of the presented theory.