Study On Fatigue Reliability Of Planar Compliant Precision Positioning Mechanisms

Compliant precision positioning stage is widely used in precision machining, semiconductor manufacturing and biomedical engineering. The stage usually consists of compliant mechanism. The compliant mechanism achieves motion via elastic deformation, which may cause fatigue failure. Traditional compliant precision positioning mechanisms are usually designed based on static strength and deterministic methodology, which may cause premature fatigue failure or excessive design. The thesis mainly focuses on the fatigue reliability analysis and optimal design of planar compliant precision positioning mechanisms. At the same time, a fatigue damage model of the circular flexure hinge is established through fatigue testing. On this basis, fatigue damage characteristics of flexure mechanisms can be evaluated using the finite element method. The research contents are as follows:In order to obtain a more accurate analytical model for planar compliant precision positioning mechanisms, closed loop method based on pseudo stiffness body theory and the finite element method are studied. Stiffness matrices of three types of beam elements are derived, as well as the stiffness matrix of the right circular flexure hinge. A planar three degree of freedom(3DOF) compliant precision positioining mechanism is taken as an example. The jacobian matrix, the driving force, the natural frequency and the stress of the hinges are modelled using the finite element method. The modelling results are compared with the commercial ANSYS simulated results, which verifies the effectiveness of the method.The fatigue limit of the right circular flexure hinge is estimated considering the influence of material, dimensional parameters and surface condition, and then the stress-life curve(S-N) is established on this basis. The planar 3DOF compliant precision positioning mechanism is taken as an example. The maximum fatigue stress and the position of the cross section where the maximum stress occurs are solved using the finite element method and sequential quadratic programming(SQP). Combing the S-N curve and the maximum fatigue stress, we predict the fatigue lives of the hinges. As for the variable amplitude fatigue loading, the fatigue lives of the mechanism are predicted using the rainflow counting method. The results reveal that the mechanism designed using the statci strength theory may cause premature failure. Therefore, a novel design optimization method based on fatigue reliability is proposed. The design problem focuses on maximizing the range of motion, considering the constraints on fatigue strength, the driving force and the natural frequency. The optimized mechanism prevents the premature fatigue failure which exists in traditional mechanism.Taking account of the random scatter of the material and dimensional parameters, the variances of the fatigue stress and fatigue strength of the hinges in the mechanism are obtained using the moment function method and algebra synthesis method, respectively. And then, fatigue reliability of the hinges is calculated using the stress strength interference theory. The results show that the fatigue reliability of the mechanism based on the static strength design cannot meet the requirements. Therefore, a planar 3DOF compliant precision positioning mechanism is taken as an example, and a fatigue reliability based optimal design method is proposed. The relationship between the fatigue reliability and the size parameters and the variance of the mechanism is analyzed. Experimental and Monte-Carlo simulating results verify the effectiveness of the method.Based on fatigue testing for right circular flexure hinges, a fatigue damage stiffness degeneration model of the hinge is established based on three fatigue feature points. Fatigue damage testing for hinges with different dimensional parameters is conducted. On this basis, the relationship between feature fatigue lives and dimensional parameters is established. The equivalent fatigue stress formula for non-zero mean stress loading is established through fatigue testing. On this basis, a method using for predicting fatigue damage of the flexure mechanism is proposed. A compliant bridge mechanism is taken as an example, the fatigue damage is predicted and tested. The experimental results verify the effectiveness of the method.