考虑涡流效应的磁悬浮转子非线性振动分析
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摘要
通过建立电磁力的时域模型,利用数值仿真方法,研究存在涡流效应的磁悬浮转子的非线性振动特性。结果表明:在主共振响应方面,整体涡流效应越强,转子频响曲线左偏程度越大,甚至出现"跳跃",转子在共振区的振幅也越大;涡流效应使转子振幅的频谱中产生超谐波和次谐波频率成分,增大谐波的响应幅值。
The time domain model is built for electromagnetic force,and the nonlinear vibration characteristics of magnetically suspended rotor considering effect of eddy currents are studied by using numerical simulation method. The results show that in the aspect of primary resonant response,the more powerful effect of eddy currents is,the greater the left deviation degree of rotor frequency response curve,even appearing"jump",the larger the amplitude of rotor in resonance region is. The frequency component of ultraharmonics and subharmonics are generated from frequency spectrum of vibration amplitude of rotor by effect of eddy currents,and the response amplitude of harmonics is increased.
The time domain model is built for electromagnetic force,and the nonlinear vibration characteristics of magnetically suspended rotor considering effect of eddy currents are studied by using numerical simulation method. The results show that in the aspect of primary resonant response,the more powerful effect of eddy currents is,the greater the left deviation degree of rotor frequency response curve,even appearing"jump",the larger the amplitude of rotor in resonance region is. The frequency component of ultraharmonics and subharmonics are generated from frequency spectrum of vibration amplitude of rotor by effect of eddy currents,and the response amplitude of harmonics is increased.
引文
[1]SCHWEITZER G,LANGE R.Characteristics of a magnetic rotor bearing for active vibration control[C]∥Conference on Vibrations in Rotating Machinery,Cambridge,1976.
[2]MYSTKOWSKI A,PAWLUSZEWICZ E B I.Feedback linearization of extended relative degree model of nonlinear active magnetic bearing system[C]∥21st International Conference on Methods and Models in Automation and Robotics,Miedzyzdroje,Poland,2016:460-465.
[3]SAEED N A A,KAMEL M.Nonlinear PD-controller to suppress the nonlinear oscillations of horizontally supported Jeffcott-rotor system[J].International Journal of Non-Linear Mechanics,2016,87:109-124.
[4]LI Y Y,GANG L,YU S,et al.Effects of magnetic flux leakage of axial electromagnetic bearing on bearing system[J].International Journal of Applied Electromagnetics&Mechanics,2015,48(4):357-366.
[5]KEOGH P S.Contact dynamic phenomena in rotating machines:active/passive considerations[J].Mechanical Systems and Signal Processing,2012,29:19-33.
[6]INAYAT H J I.Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings[J].Chaos Solitons and Fractals,2009(41):2664-2671.
[7]SAEED N A,EISSA M,EL-GANINI W A.Nonlinear oscillations of rotor active magnetic bearings system[J].Nonlinear Dynamics,2013,74(1/2):1-20.
[8]RYOSUKE A,TOSHIHIKO S,HIROKI G.Internal resonance of a flexible rotor supported by a magnetic bearing[J].International Journal of Applied Electromagnetics and Mechanics,2012(39):941-948.
[9]EISSA M,KAMEL M,BAUOMY H S.Dynamics of an AMB-rotor with time varying stiffness and mixed excitations[J].Meccanica,2012,47(3):585-601.
[10]KAMEL M,BAUOMY H S.Nonlinear behavior of a rotorAMB system under multi-parametric excitations[J].Meccanica,2010(45):7-22.
[11]ZHANG W,ZU J W.Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness[J].Chaos Solitons and Fractals,2008(38):1152-1167.
[12]INAYAT H J I.Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings[J].Communications in Nonlinear Science Numerica Simulation,2010(15):764-777.
[13]GHAZAVI M R,SUN Q.Bifurcation onset delay in magnetic bearing systems by time varying stiffness[J].Mechanical Systems and Signal Processing,2017(90):97-109.
[14]ZMOOD R B,ANAND D K,KIRK J A.The influence of eddy currents on magnetic actuator performance[J].Proceedings of the IEEE,1987,75(2):259-260.
[15]TSUYOSHI I,YUKIO I.Nonlinear forced oscillation in a magnetically levitated system:the effect of the time delay of the electromagnetic force[J].Nonlinear Dynamics,2008(52):111.
[2]MYSTKOWSKI A,PAWLUSZEWICZ E B I.Feedback linearization of extended relative degree model of nonlinear active magnetic bearing system[C]∥21st International Conference on Methods and Models in Automation and Robotics,Miedzyzdroje,Poland,2016:460-465.
[3]SAEED N A A,KAMEL M.Nonlinear PD-controller to suppress the nonlinear oscillations of horizontally supported Jeffcott-rotor system[J].International Journal of Non-Linear Mechanics,2016,87:109-124.
[4]LI Y Y,GANG L,YU S,et al.Effects of magnetic flux leakage of axial electromagnetic bearing on bearing system[J].International Journal of Applied Electromagnetics&Mechanics,2015,48(4):357-366.
[5]KEOGH P S.Contact dynamic phenomena in rotating machines:active/passive considerations[J].Mechanical Systems and Signal Processing,2012,29:19-33.
[6]INAYAT H J I.Geometric coupling effects on the bifurcations of a flexible rotor response in active magnetic bearings[J].Chaos Solitons and Fractals,2009(41):2664-2671.
[7]SAEED N A,EISSA M,EL-GANINI W A.Nonlinear oscillations of rotor active magnetic bearings system[J].Nonlinear Dynamics,2013,74(1/2):1-20.
[8]RYOSUKE A,TOSHIHIKO S,HIROKI G.Internal resonance of a flexible rotor supported by a magnetic bearing[J].International Journal of Applied Electromagnetics and Mechanics,2012(39):941-948.
[9]EISSA M,KAMEL M,BAUOMY H S.Dynamics of an AMB-rotor with time varying stiffness and mixed excitations[J].Meccanica,2012,47(3):585-601.
[10]KAMEL M,BAUOMY H S.Nonlinear behavior of a rotorAMB system under multi-parametric excitations[J].Meccanica,2010(45):7-22.
[11]ZHANG W,ZU J W.Transient and steady nonlinear responses for a rotor-active magnetic bearings system with time-varying stiffness[J].Chaos Solitons and Fractals,2008(38):1152-1167.
[12]INAYAT H J I.Nonlinear dynamics of a statically misaligned flexible rotor in active magnetic bearings[J].Communications in Nonlinear Science Numerica Simulation,2010(15):764-777.
[13]GHAZAVI M R,SUN Q.Bifurcation onset delay in magnetic bearing systems by time varying stiffness[J].Mechanical Systems and Signal Processing,2017(90):97-109.
[14]ZMOOD R B,ANAND D K,KIRK J A.The influence of eddy currents on magnetic actuator performance[J].Proceedings of the IEEE,1987,75(2):259-260.
[15]TSUYOSHI I,YUKIO I.Nonlinear forced oscillation in a magnetically levitated system:the effect of the time delay of the electromagnetic force[J].Nonlinear Dynamics,2008(52):111.