Research On Hinged Static-couple Separation Swing Frame On Fixed Vibration Center

Owing to the structure of the swing frame,the vibration center of the traditional two-plane vertical balancing machine is fluctuating and the torsional stiffness around the vibration center is also unstable,which often lead to the large error on measurement and the poor effect for static-couple separation,especially when the height-diameter ratio is large and the working speed is low.In order to solve the error source and improve the measurement accuracy,a hinged static-couple separation swing frame on the fixed vibration center is proposed.Firstly,the differential equation of motion of traditional swing frame was established,the position formula of the vibration center and the torsional stiffness formula around the vibration center were deduced,then the interfering factors and variation relations of the vibration center and torsional stiffness were researched and the error sources were analyzed,which points out the direction for the improvement of the structure of swing frame.Secondly,according to the source of error,the design idea and improvement structure of the swing frame were put forward.The separation effect was improved by the method of using a flexible hinge to stabilize the vibration center and the independent measurement of the static unbalance and the even unbalance by the spring plate.Through the analysis of the vibration characteristics of the static-couple separation swing frame,the invariance of the vibration center and the stability of the torsional stiffness were verified.The formulas of torsional stiffness and translational stiffness were derived.The relationship between the stiffness value and the geometric parameters was studied,which provides theoretical support for the optimization of the geometric size of the swing frame.At the same time,the upper and lower correction planes of the vibration system were separated and solved,which ensures the successful separation of the actual correction planes.Then,the modal analysis of the static-couple separation swing frame was carried out,and the two-order modes and their natural frequencies corresponding to translation and swing were obtained.It is found that the translation spring only transmitted the translation signal,while the flexure hinge only transmitted the swing signal.And the two-order natural frequencies were in the same order of magnitude.This new characteristic is different from the traditional swing frame,which makes sure the correctness of the theoretical modeling of the swing frame.By studying the influence of the key dimensions of the core components on the natural frequencies of translation and swing,the optimal design of the swing frame was carried out,and the preliminary optimum range of geometric parameters was obtained.Then the standard mathematical model of the vibration system was established,and the objective function,design variables and constraints were determined.The geometric dimensions of the pendulum were determined by using MATLAB optimization toolbox.At the same time,the shape and material properties of flexure hinges were compared comprehensively and determined.Finally,an experimental platform was built to evaluate the static-couple separation capability and the correction plane separation ratio.The experimental results fully verified the excellent performance of the hinged static-couple separation swing frame on the fixed vibration center,which provides a reliable vibration frame for the upgrade and optimization of the double-sided vertical dynamic balancing machine and an accurate theoretical basis for the vibration characteristics analysis of the swing frame.