Design Calculation And Performance Analysis Of Exponential Hybrid Flexure Hinge

Compliant mechanism has important applications in the fields of precision machinery,micro-manufacturing,micro-electromechanical,micro-robot and so on,and has become a research hotspot in the field of machinery.As the main component of the compliant mechanism,flexure hinge has been widely studied by researchers.The gap of flexible hinge form determines the precision and flexibility,many scholars put forward different gap in the shape of the flexible hinge,in order to enrich the shape of the flexure hinge and variety,explore the mechanical properties of new type of flexible hinge,this paper designed a six to and six kinds of longitudinal asymmetry of flexure hinge,concrete research content is as follows:The shape of the lateral exponential-semicircle asymmetrical flexure hinge was designed,and the form function expression of the flexure hinge was deduced.The general flexibility matrix model and precision matrix model of the flexure hinge were calculated by Cartesian second theorem and energy method.According to the stress concentration coefficient,the maximum stress of the hinge is calculated by the maximum stress formula.Adopt the method of correction coefficient,calculate each coefficient by consulting the data,and analyze the fatigue strength.The results show that Each flexibility coefficient and precision coefficient increase with the increase of flexure hinge length L,decreases with the increase of the minimum thickness of flexure hinge,decreases with the increase of flexure hinge index base a.The maximum stress increases with the increase of hinge length L,decreases with the increase of minimum thickness t of flexure hinge,and does not change with the change of index base number of hinge.The minimum thickness t of flexure hinge has a greater effect on the flexibility.Six kinds of flexible hinges are designed,which are: transverse index semicircular mixed type,transverse index parabola mixed type,transverse index hyperbolic mixed type,transverse index ellipsoid mixed type,transverse index power function mixed type,transverse index chamfering mixed type,etc.Their shape function,flexibility matrix and precision matrix are obtained.The influence of hinge parameters on the flexibility,accuracy and maximum stress of hinges with different shapes is analyzed by using MATLAB.The results show that under the premise of equal hinge parameters L,t and a,the flexibility of transverse exponential linear flexure hinge is higher than that of other hinges,and the flexibility of exponential power function flexure hinge is the smallest;the accuracy of transverse exponential power function flexure hinge is the highest,and the accuracy of transverse exponential linear flexure hinge is the lowest The maximum stress of exponential hyperbolic type is the largest and that of exponential symmetric type is the smallest.The shape of the longitudinal index semicircular hybrid flexure hinge is designed.The form function expression of the hinge is written.By the second theorem of karschner and the energy method,the general flexibility matrix model and precision matrix model of the flexure hinge are calculated.Six kinds of flexure hinges with longitudinal asymmetric shape are designed.Their shape function,flexibility matrix model and accuracy matrix model are obtained respectively,and their flexibility matrix and accuracy matrix are obtained.The correctness of the formula of maximum stress is verified by ANSYS.The influence of hinge parameters on the flexibility,accuracy and maximum stress of hinges with different shapes is analyzed by using MATLAB.The results show that the accuracy of longitudinal exponential symmetry type is the highest,and that of transverse exponential linear type is the lowest;the maximum stress of exponential hyperbolic type is the highest,and that of exponential symmetry type is the lowest.Four kinds of representative longitudinal asymmetric flexure hinges are selected as experimental samples for displacement test.A non-contact single point laser vibrometer is used to test the output displacement of the flexure hinge after applying equal reverse force,and the bidirectional unequal stiffness of the longitudinal asymmetric flexure hinge is verified.The experimental value is compared with the theoretical value,and the correctness of the theory is verified.