Research On Vibration Characteristics Of Non-uniform Ring Structure

Ring is a typical structure in engineering,which is widely used in motor,planetary gear systems,ring-vibrating gyroscopes,and other systems.Due to the existence of machining errors,the geometric shape and physical parameters of the ring structure will inevitably change,affecting its dynamic characteristics.In this thesis,the effects of periodic changes in thickness and radius on the in-plane vibration of the ring are studied through analytical analysis,finite element simulation,and vibration measurement experiments.The main contents of the thesis are as follows:(1)The influence of periodic change of normal thickness on the free vibration characteristics of the ring is studied.The ring’s dynamic model is established by the Hamilton principle,and the analytical analysis is carried out by using the direct perturbation method.The expressions of the natural frequency and coupling coefficient of the ring are obtained.The finite element simulation is used to calculate several groups of rings,which is verified with the analytical results obtained.The natural frequency splitting law and thickness variation amplitude of the ring are obtained to influence frequency.(2)Taking the rotating thin circular ring with variable thickness as the research object.The balance equation of the circular ring is obtained by the Hamilton principle,and the equation is solved by using the direct perturbation method.The deformation components of the circular ring in the vibration process are analyzed,the expressions of the natural frequency and mode coupling coefficient of the circular ring are solved.The variation rules of the tnatural frequency the circular ring are obtained.(3)The thin ring with the periodic change of the radius of the neutral line is studied.The ring’s dynamic model is established through the Hamilton principle,and its analytical analysis is carried out using the direct mode perturbation method.The expression of the natural frequency of the ring is solved.The splitting law of the natural frequency of the ring is obtained through the finite element simulation and analytical results.(4)An experimental method for the free vibration of circular rings is presented.Taking a ring with periodically changing neutral wire radius as an example,using laser LMS vibration measurement experiment and finite element simulation,the natural frequencies and vibration modes of the first eight orders of vibration of the variable radius ring are obtained,which verifies the feasibility of the experimental method,and summarizes the natural frequency splitting law of the variable radius ring under the different relationship between the radius change period q and the mode order n.Through the research on two kinds of non-uniform rings with variable thickness and variable radius,the effects of periodic changes in geometric shape on the natural frequency,natural frequency splitting,and mode coupling of the ring are obtained.The conclusions have been compared with the existing literature and verified by simulation and experimental analysis.The research on the dynamic characteristics of non-uniform rings was improved.