Study On The Dynamics Of Eccentrically Rotating Beam And Axially Moving Cantilever Beam

The dynamics of eccentrically rotating flexible beam and axially moving cantilever beam have wide applications in engineering,such as robot manipulators,machine barrel,machine tools and radar antenna,et.al.With the lightweight design of mechanical system,there always exist some flexible structures with poor stiffness in the mechanical system.These flexible structures may produce large elastic vibration when the mechanism work with high-speed or subjected to external impact excitation,which will in turn affect the performance of the system.Computing the dynamic response of the flexible beam structure is an important method to evaluate the dynamic performance to guide the structure design,to explore the vibration reduction technique and to design the control law of the motion.Some effective and reliable dynamic modeling and computational techniques are presented for the eccentrically rotating beam and axially moving cantilever beam systems in this paper.And a feasible vibration reduction technique for the slender beam structure is discussed by introducing a novel "DVA-Beam element".The main research work and achievements are as follows:(1)The dynamic modeling and periodic motion characteristics of a eccentrically rotating beam subject external pulse excitation are studied.The nonlinear rigid-flexible coupling motion equations are derived by using the Lagrange equation and assumed mode method.The post-processing formulations of the beam tip dynamic responses in inertial system is given.Through some numerical examples,the dynamic responses are analyzed and compared with those simulated by Adams software,good agreement is achieved.And the periodic motion characteristic of the system subjected to a continuous half-sine excitation is studied.The effects of rotating radius,beam length,torsion damping and torsion stiffness on beam periodic motion are investigated.According to the dynamic characteristics of the eccentrically rotating beam,a feasible firing accuracy improvement method is presented for the demonstrated 12.7 mm machine gun system.(2)An efficient dynamic modeling and analysis method for the axially moving cantilever beam problem is presented.That is,the assumed mode method with fitted and scalable basis functions.Based on the Euler beam theory,the time-varying dynamic equations of the axially moving beam are derived using the Rayleigh-Ritz method,Lagrange equation as well as the presented method.The accuracy of the presented method and the motion equations are investigated by comparing the dynamic responses with those from previous literatures.The results show that the presented method and the motion equations are accurate and reliable.Then,the computational convergence of the method is discussed.The frequency response characteristics of the axially moving system are studied,and an interesting anti resonance phenomenon is observed which may provide a new approach for the vibration reduction of the axially moving system.And the influence of the axial motion velocity and acceleration on the beam dynamic stability is studied by using the eigenvalue theory.(3)The dynamic behavior of an axially moving cantilever beam with a tip mass is investigated.The moving mesh tecevaluate the dynamic performance to guide the structure design,to explore the vibration hnique,which based on the finite element method,is adopted to solve the problem.Based on the derived motion equations the effects of tip mass on frequence response characteristic and stability of the axially motion is investigated.Some dimensionless parameters of the axially moving system are introduced and their critical stable values are analyzed.According to the dynamic characteristics of the axially moving system,a feasible firing accuracy improvement method by dynamic matching of gun barrel is presented for the demonstrated 12.7 mm machine gun system.And the effectiveness of the method is discussed.(4)A feasible vibration suppression technique for slender beam structure under pulse excitation is explored,that is dynamic vibration absorber(DVA).A DVA-beam element for DVA optimization is proposed first,the dynamic motion equations of the DVA-beam element are then derived.An element birth and death technique for the DVA-beam element is proposed.In this way,a DVA-beam system can be simulated in a much simpler way.Using the proposed element birth and death technique,it will make the global dynamic equation assembling and results post-processing more convenient.The accuracy of the dynamic model is validated by comparing the dynamic responses with those simulated by Adams software,good agreement is achieved.The random optimization and particle swarm optimization techniques are applied to the DVA-beam parameters optimization design.The DVA-beam optimization in four kinds of loading conditions are carried out,that is free vibration,beam subjected to harmonic excitation,beam subjected to a single pulse excitation and beam subjected to multi pulse excitation.The efficiency and reliability of the random optimization method and particle swarm optimization method are investigated.