Research On Vibration Analysis And Intelligent Control Of High-Speed Spinning Flexible Beam

Over the last few decades,spinning structures were present in large numbers and used widely in the fields of aeronautics and astronautics.For instance,cyclogyro,satellite booms,shafts of combustion engines,DC and AC electric motors,turbine blades,rotating shafts,propellers and so on.The vibrationcaused by the uneven mass distribution or external excitation may result in safety problem,such as structural fatigue and weakening of the function.Thus,it has an extremely important meaning in the investigation of the dynamic analysis and vibration suppression of such kind of spinning structures.Dynamic equations and finite element model of spinning flexible beam with simply-supported ends are studied in the article.The work comprehended on the key issues of the dynamic analysis and control of spinningflexible beams,which include the dynamic equations,finite element modelling,model reduction,intelligent vibration control and thermal shock investigation.The main points of the contents are organized as follows.(1)It was observed the control authority of the piezoelectric bender varied significantly between DC and AC excitation fields.The compliance of clamped piezoelectric bender remains almost the same in DC electric field,while it increased with the increasing AC electric field.Experiments conducted showed that the change of stiffness is the main reason.The excitation field has a major effect on the stiffness,while excitation frequency not.To verify this hypothesis,theoretical model was established to predict such change.The simulation results showed that the stiffness of clamped bimorph decreased about 55% with an AC excitation of 3.94kV/cm.Thetheoretical model could predict the change of stiffness well and anastomosedthe experimental results pretty well.(2)The rigid-flexible coupling dynamic properties of a high-speed spinning flexible beam by its ownlongitudinalaxisare studied.Using a first-order approximation model,the coupling effect of the axial and transverse vibration is considered,besides,the centrifugal forces caused by eccentricity are considered.The beam's governing coupledpartial differential equationsof motion are derivedusing Hamilton's principle,while assumed mode methodand finite element methodare used for discretization,respectively.For different rotating speeds,the transverse vibration response of zero-order approximate model is compared with that of a first-order approximation model.The simulation results indicate that a zero-order approximate model is valid for dynamic description of flexible beam spinning at a low speed for that the effect of the rigid-flexible coupling terms is small and can be neglected,but not at a high speed.And first-order approximate coupling modelaccounting for the effect of the rigid-flexible coupling is a key factor to obtain a more accurate dynamic response.(3)Piezoelectric shunt damping system was investigated to reduce the vibration of spinning beam and simulated-annealing(SA)algorithm was used for optimization of the values of R and L in piezoelectric shunt circuit to achieve the maximum suppression effect.Hamilton'sprinciple with the Rayleigh-Ritz method was used for the dynamic equations of the beam motion.Besides,the the transfer function between displacementresponse and force was presented.Anoptimization model of the transfer function was built and SA algorithm was employed to minimize the objective functions in the appropriately defined optimization problems.The simulation results prove that the SA algorithm obtained a better optimizationeffect and a much higher efficiency compared with Genetic algorithm.The results have also shown that piezoelectric shunt damping system could suppress the vibration of spinning beam markedly.(4)Model reduction and intelligent vibration control for a high-speed spinning flexible beam by its ownlongitudinalaxis is investigated.The internal balance method was studied,andfurthera fuzzy self-adaptive PID controller based on the reduction model was designed.The results show that the reduction model derived by the internal balance method is a good approximation of the original system,besides,theproposed controller is effective in suppressing the vibration and can achieve perfect dynamic and static performance comparing with the traditional PID controller.(5)Vibration suppression of such spinning structures is necessary and challenging for the arrangement of actuators.To suppress the vibration of spinning beam effectively,piezoelectric stack in a varying magnet filed based onadaptive fuzzy sliding mode control is investigated.The voltage to the actuator is generated by the motion of the wires in magnetic field,while the induced moment by piezoelectric stack is formulated and applied as control force of the spinning structure.Slide mode controller with universal fuzzy sets is designed.The finite element method simulation results show that the adaptive fuzzy sliding mode controller could suppress the vibration of spinning beam effectively.(6)The dynamic responses and control of high-speed spinning flexible beam with simply-supported ends subjected to the thermal shock is investigated.Taken the thermal shock and thermal force into consideration,the dynamic equations of the spinning flexible beam are formulated using Hamilton Principle.Central difference method is used to get an approximate solution of dynamic response.Thermal mode and frequency arestudied.An intelligent controller is designed to suppress the vibration induced by thermal shock.