Magnetic-liquid double suspension bearing(MLDSB)is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting.Its bearing capacity and stiffness can be greatly improved,and then it is su...Magnetic-liquid double suspension bearing(MLDSB)is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting.Its bearing capacity and stiffness can be greatly improved,and then it is suitable for the occasions of medium speed,heavy load.When the bearing system is excited by periodic force,the flow q and current i regulated by the double-closed-loop control mechanism change periodically.Then the risk of parametric resonance in MLDSB is greatly aggravated by the change of the parameter system,which seriously affects its operation stabil-ity and reliability.Therefore,this paper intends to study the resonance characteristics of the parame-ter system of MLDSB.Firstly,Marshall-Duffing equation of the parametric system is established by taking the flow q and the current i as variables respectively.Then,by using the asymptotic method,the occurrence condition and variation rule of the principal,1/2 Harmonic and 1/3 Harmonic para-metric resonance are solved.The results show that only the 1/2 Harmonic resonance of the flow q parameter varying system occurs accompanied by the resonance condition of high frequency.The principal,1/2 Harmonic and 1/3 Harmonic parametric resonance of the current i occur accompanied by the resonance condition of high frequency.And the 1/2 Harmonic resonance of the current i oc-curs accompanied by the non-single value bifurcation and dynamic bifurcation.The paper can pro-vide theoretical reference for the parameter design and stable operation of MLDSB.展开更多
Because of hydraulic-electromagnetic double supporting forms,the supporting capacity and stiffness of magnetic-liquid double suspension bearing(MLDSB)can be improved sharply and then it is more suitable for medium spe...Because of hydraulic-electromagnetic double supporting forms,the supporting capacity and stiffness of magnetic-liquid double suspension bearing(MLDSB)can be improved sharply and then it is more suitable for medium speed,heavy load and frequent-starting occasions.Due to the multiple uncertainty,such as the coupling,the unmodeled dynamics,the parameter perturbation and the external disturbance perturbation,the robust stability and stiffness of control system of MLDSB are hard to meet the design requirements.Firstly,the structural features and the regulation mechanisms of MLDSB are presented and the radial 4-DOF kinetic equations are established.Secondly,the influence factors of the control system's coupling on unbalanced vibration caused by the deviation of the rotor center of mass are revealed,and then the weighting function of suppressing the unbalanced vibration can be obtained.Finally,H∞ controller of MLDSB is designed with H∞ mixed-sensitivity method,and the control performances of H∞ controller is compared with the state feedback controller.The simulation results show that single degree of freedom(DOF)supporting system of MLDSB with H∞ controller has good robust stability,stiffness and the ability to suppress unbalanced external disturbances.This study can provide the theoretical reference for stabilized suspension and control of MLDSB.展开更多
The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the met...The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the method of linear and nonlinear treatment,the mathematical expression and parameters sensitivity of relative error of stiffness and damping are presented.Finally,the main factors of magnetic-liquid double suspension bearing(MLDSB)are analyzed,and the influence on bearing performance indicators of single DOF nonlinear autonomous bearing system of main factors is revealed.The results show that linear stiffness/damping is the first part of equivalent stiffness/damping,and the second and third parts are high order minor term of Tayor series transform.The film thickness,the magnetic-liquid proportionality coefficient,the mass of rotor are the major influence factor of the bearing performance.The research can provide the theoretical reference for the design and nonlinear analysis of MLDSB.展开更多
Magnetic-liquid suspension guide-way system( MLSGS) is coupled supported by permanent magnetic suspension and hydrostatic bearing. The structure and bearing mechanism of MLSGS of heavy computer numerical control( CNC)...Magnetic-liquid suspension guide-way system( MLSGS) is coupled supported by permanent magnetic suspension and hydrostatic bearing. The structure and bearing mechanism of MLSGS of heavy computer numerical control( CNC) machine tools are introduced and the mathematical expression of bearing force of bearing unit is derived and it can be broken apart into six parts which sustains directly the coordinate components of broad external load,where the air gap of permanent magnet and hydrostatic oil film can be simplified as elastic supports,the compatibility equations of deformations for oil films and air gap are presented,and then the bearing capacity calculation of the bearing unit is transformed into a determinate problem. Considering the guide-way as a rigid body,the mathematics expression between the bearing unit's bearing force and the oil film variation is linearized,and the oil pocket's bearing capacity which bears different components of the external load is calculated separately. The six components of the bearing unit are added up,and the final general mathematics expression is derived. The proposed research offers a general simple method for calculating the bearing capacity of MLSGS with complicate constraint,which can be mastered simply by engineering designer and can improve design efficiency and accuracy.展开更多
基金Supported by the National Natural Science Foundation of China(No.52075468)General Project of Natural Science Foundation of Hebei Prov-ince(No.E2020203052)+2 种基金Youth Fund Project of Scientific Research Project of Hebei University(No.QN202013)Basic Innovation Scientif-ic Research Cultivation Project of Yanshan University(No.2021LGZD003)the Shaanxi Key Laboratory of Hydraulic Technology Fund(No.YYJS2022KF14).
文摘Magnetic-liquid double suspension bearing(MLDSB)is mainly supported by electromagnetic suspension and supplemented by hydrostatic supporting.Its bearing capacity and stiffness can be greatly improved,and then it is suitable for the occasions of medium speed,heavy load.When the bearing system is excited by periodic force,the flow q and current i regulated by the double-closed-loop control mechanism change periodically.Then the risk of parametric resonance in MLDSB is greatly aggravated by the change of the parameter system,which seriously affects its operation stabil-ity and reliability.Therefore,this paper intends to study the resonance characteristics of the parame-ter system of MLDSB.Firstly,Marshall-Duffing equation of the parametric system is established by taking the flow q and the current i as variables respectively.Then,by using the asymptotic method,the occurrence condition and variation rule of the principal,1/2 Harmonic and 1/3 Harmonic para-metric resonance are solved.The results show that only the 1/2 Harmonic resonance of the flow q parameter varying system occurs accompanied by the resonance condition of high frequency.The principal,1/2 Harmonic and 1/3 Harmonic parametric resonance of the current i occur accompanied by the resonance condition of high frequency.And the 1/2 Harmonic resonance of the current i oc-curs accompanied by the non-single value bifurcation and dynamic bifurcation.The paper can pro-vide theoretical reference for the parameter design and stable operation of MLDSB.
基金Supported by the National Nature Science Foundation of China(No.51705445,52075468)General Project of Natural Science Foundation of Hebei Province(E2020203052)+1 种基金Youth Fund Project of Scientific Research Project of Hebei University(QN202013)Open Project Funding of Jiangsu Provincial Key Laboratory of Advanced Manufacture and Process for Marine Mechanical Equipment and Open Project Funding of Fluid Power Transmission Control Laboratory of Yanshan University.
文摘Because of hydraulic-electromagnetic double supporting forms,the supporting capacity and stiffness of magnetic-liquid double suspension bearing(MLDSB)can be improved sharply and then it is more suitable for medium speed,heavy load and frequent-starting occasions.Due to the multiple uncertainty,such as the coupling,the unmodeled dynamics,the parameter perturbation and the external disturbance perturbation,the robust stability and stiffness of control system of MLDSB are hard to meet the design requirements.Firstly,the structural features and the regulation mechanisms of MLDSB are presented and the radial 4-DOF kinetic equations are established.Secondly,the influence factors of the control system's coupling on unbalanced vibration caused by the deviation of the rotor center of mass are revealed,and then the weighting function of suppressing the unbalanced vibration can be obtained.Finally,H∞ controller of MLDSB is designed with H∞ mixed-sensitivity method,and the control performances of H∞ controller is compared with the state feedback controller.The simulation results show that single degree of freedom(DOF)supporting system of MLDSB with H∞ controller has good robust stability,stiffness and the ability to suppress unbalanced external disturbances.This study can provide the theoretical reference for stabilized suspension and control of MLDSB.
基金the National Natural Science Foundation of China(No.51705445)General Project of Natural Science Foundation of Hebei Province(No.E2016203324)Youth Fund Project of Scientific Research Project of Hebei University(No.QN202013).
文摘The mathematical model of single degree of freedom(DOF)nonlinear autonomous bearing system under constant flow supporting model is deduced.The single DOF nonlinear autonomous bearing system is transformed with the method of linear and nonlinear treatment,the mathematical expression and parameters sensitivity of relative error of stiffness and damping are presented.Finally,the main factors of magnetic-liquid double suspension bearing(MLDSB)are analyzed,and the influence on bearing performance indicators of single DOF nonlinear autonomous bearing system of main factors is revealed.The results show that linear stiffness/damping is the first part of equivalent stiffness/damping,and the second and third parts are high order minor term of Tayor series transform.The film thickness,the magnetic-liquid proportionality coefficient,the mass of rotor are the major influence factor of the bearing performance.The research can provide the theoretical reference for the design and nonlinear analysis of MLDSB.
基金Support by National Natural Science Foundation of China(51705445)Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems(GZKF-201714)Natural Science Foundation of Hebei Province of China(E2016203324)~~
基金Supported by the National Natural Science Foundation of China(No.51705445)the Natural Science Foundation of Hebei Province(No.E2016203324)the Provincial and Ministerial Level Scientific Research Institutions Open Fund of Civil Aviation University of China
文摘Magnetic-liquid suspension guide-way system( MLSGS) is coupled supported by permanent magnetic suspension and hydrostatic bearing. The structure and bearing mechanism of MLSGS of heavy computer numerical control( CNC) machine tools are introduced and the mathematical expression of bearing force of bearing unit is derived and it can be broken apart into six parts which sustains directly the coordinate components of broad external load,where the air gap of permanent magnet and hydrostatic oil film can be simplified as elastic supports,the compatibility equations of deformations for oil films and air gap are presented,and then the bearing capacity calculation of the bearing unit is transformed into a determinate problem. Considering the guide-way as a rigid body,the mathematics expression between the bearing unit's bearing force and the oil film variation is linearized,and the oil pocket's bearing capacity which bears different components of the external load is calculated separately. The six components of the bearing unit are added up,and the final general mathematics expression is derived. The proposed research offers a general simple method for calculating the bearing capacity of MLSGS with complicate constraint,which can be mastered simply by engineering designer and can improve design efficiency and accuracy.
