Nonlinear Dynamic Characterization Of The Eddy Current Damper With Permanent Magnets And Its Application In Structural Vibration Reduction

Damping devices are in great demand in the vibration control of civil engineering structures.Whether energy dissipation,seismic isolation or tuning reduction,damping devices with high performance and high reliability are required.The eddy current damper is a damping device based on the principle of electromagnetic induction.Compared with the commonly used fluid viscous damper,it has stable performance and good durability.It has been used in the field of mechanical engineering.However,due to its low energy-dissipation density,the promotion of its application in civil engineering is slow.During 2006～2010,Chen Zhengqing’s team of Hunan University invented the double-layer planar eddy current damping unit,which has solved the problem of applying eddy current damping to large-scale tuned mass damper(TMD).However,the research of eddy current dampers used for direct energy dissipation faces two major problems: further greatly increasing energy-dissipation density and solving the critical speed constraints.In this paper,based on mechanical and electromagnetic principles,combined with the demands of civil engineering structure vibration reduction,a new type of ball-screw type external rotating eddy current axial damper is developed.The equivalent energy-dissipation density can be increased by thousands of times,which solves the problem of low energy-dissipation density of eddy current itself.Through theoretical analysis,experimental testing,finite element simulation and other methods,in-depth analysis of the nonlinear damping characteristics of the eddy current damper is conducted and a mastery is achieved.It breaks through the critical speed restriction and solves the problem of meeting the requirements of the high-speed state of the damper.Based on nonlinear design theory and multiple technological measures,a series of permanent magnet eddy current damping products have been developed,which have been widely used in the field of civil engineering.The main content and research results of this article are listed below:(1)A large-force-capacity,high-energy-density ball-screw type external rotating eddy current axial damper is developed.Its structural characteristics and working principles are described in detail.Its mechanical characteristics are analyzed,mainly including damping characteristics and inertial characteristics.According to the law of magnetic circuit,the eddy current damping force at low speed is estimated,and the estimation expression of the damping coefficient at low speed is obtained.The influence of its inertial mass on the vibration reduction effect of two structural systems,the single degree of freedom system and the distributed parameter system,is investigated.(2)Starting from Maxwell’s equations,based on the assumption of quasi-stable field and ignoring the end effect,a two-dimensional analytical model of the electromagnetic field of the ball-screw type external rotating eddy current axial damper is established,and the analytical expression of the relationship between damping force and velocity constitutive are derived.The theoretical formula of nonlinear eddy current damping force is obtained.Considering the influence of the three-dimensional effect,the model is revised.Based on this analytical expression,parametric analysis is carried out,and the influence of various geometric dimensions and material properties on the nonlinear characteristics of eddy currents is studied and mastered.The design theory of eddy current damper based on nonlinear analysis is established.(3)Through experimental testing and finite element simulation,the theoretical formula of nonlinear eddy current damping force is verified.The eddy current damping test was carried out in two stages.The first stage of the test is to test the rotor part of eddy current damper,for which a set of test benches are specially designed;the second stage is to test the complete machine of eddy current axial dampers of different sizes,40 T and 85 T.Two-dimensional and three-dimensional electromagnetic finite element models are established respectively,and the finite element calculation results are compared with theoretical calculation results and experimental testing results: error between the two-dimensional analytical model and the finite element model is within3%,but there is a certain deviation from the test results;the three-dimensional analytical model is closer to the test results,but the critical velocity still has a deviation of about 30%.By measuring the temperature change and considering the temperature effect into the calculation,consistent results can be obtained.(4)Using the characteristics of large-scale eddy current dampers and the asymptotic form of Bessel function,the constitutive formula of eddy current damping is simplified.The commonly used damping systems are simplified into the singledegree-of-freedom model,and its key control response quantities are proposed.Based on two equivalent methods: the probability expectation equivalent from the random vibration theory,and the maximum speed equivalent,the ranges of parameters of nonlinear eddy current damping with equivalent linear damping is given.The performance index function method is used to optimize multiple key response quantities.A practical method for the seismic optimization design of nonlinear eddy current dampers is proposed.Nonlinear eddy current damper has the self-limiting characteristic of maximum damping force.According to the calculation of 8 different seismic waves,it can generally achieve a similar or better damping effect with a damping force 4%～40% smaller than that of a linear one.(5)A realization method of bilinear Coulomb-like damping is proposed.By combining two different constitutive curves with the same maximum damping force but the critical velocity ratio between 6.4～10.4,a constitutive curve with self-limiting characteristics of damping force and higher energy-dissipation efficiency is obtained.In seismic analysis,the constitutive structure can be approximated by a bilinear curve,and the deviation is within 5%,which meets the engineering accuracy requirements.Taking a single degree of freedom structure as an example,the response spectrum of the bilinear Coulomb-like damping,linear damping and Coulomb friction damping are compared.Combined with actual engineering,the vibration reduction effects of viscous fluid damping and bilinear Coulomb-like damping are compared and the optimization is proceeded.In a 1480 m suspension bridge engineering,150 T combined eddy current dampers with bilinear Coulomb-like damping effect is designed and tested.The Coulomb-like damping can achieve almost the same vibration reduction effect as the optimal viscous fluid damping,but the maximum damping force is 13% smaller,and the overall cost is lower.