Analysis of rotor eddy current loss and thermal deformation of magnetic liquid double suspension bearing

Magnetic-liquid double suspension bearing(MLDSB)is a new type of suspension bearing based on electromagnetic suspension and supplemented by hydrostatic supporting.Without affecting the electromagnetic suspension force,the hydrostatic supporting effect is increased,and the real-time coupling of magnetic and liquid supporting can be realized.However,due to the high rotation speed,the rotor part produces eddy current loss,resulting in a large temperature rise and large ther-mal deformation,which makes the oil film thickness deviate from the initial design.The support and bearing characteristics are seriously affected.Therefore,this paper intends to explore the internal effects of eddy current loss of the rotor on the temperature rise and thermal deformation of MLDSB.Firstly,the 2D magnetic flow coupling mathematical model of MLDSB is established,and the eddy current loss distribution characteristics of the rotor are numerically simulated by Maxwell software.Secondly,the internal influence of mapping relationship of structural operating parameters such as input current,coil turns and rotor speed on rotor eddy current loss is revealed,and the changing trend of rotor eddy current loss under different design parameters is explored.Thirdly,the eddy cur-rent loss is loaded into the heat transfer finite element calculation model as a heat source,and the temperature rise of the rotor and its thermal deformation are simulated and analyzed,and the influ-ence of eddy current loss on rotor temperature rise and thermal deformation is revealed.Finally,the pressure-flow curve and the distribution law of the internal flow field are tested by the particle image velocimetry(PIV)system.The results show that eddy current loss increases linearly with the in-crease of coil current,coil turns and rotor speed.The effect of rotational speed on eddy current loss is much higher than that of coil current and coil turns.The maximum temperature rise,minimum temperature rise and maximum thermal deformation of the rotor increase with the increase of eddy current loss.The test results of flow-pressure and internal trace curves are basically consistent with the theoretical simulation,which effectively verifies the correctness of the theoretical simulation.The research results can provide theoretical basis for the design and safe and stable operation of magnetic fluid double suspension bearings.

Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

Estimation of the Forces on Rubbing Rotor-Bearing System

It*ss very important to identify the load on rotor bearing system. Based on load identification in time domain, a new method combined with transfer matrix method is applied in rubbing rotor bearing system to estimate the force on rubbing rotor for the first time. Avoiding calculating the modal parameters, the outside excitation force on multi point and the distribute of internal forces on rubbing rotor bearing system can be identified by this way at the same time. Finally, the simulation is made on partial lateral rubbing rotor bearing system. For the faulty of rotor/stator rub, the point where rubbing occurs and the change of impact forces can be detected by this method in order to improve the accuracy of rotor/stator rub faulty diagnosis.

COUPLED DYNAMIC CHARACTERISTICS AND CONTROL OF ROTOR-CONICAL MAGNETIC BEARING SYSTEM

The coupled dynamic characteristics of the conical electromagnetic bearing are presented and their definitions are given. On the basis of the analyses of the characteristics, the dynamic model of five degrees of freedom (five-DOF) rotor-conical electromagnetic bearing system is made, and the influence of the coupled characteristics on the system optimal controller is analyzed.

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the system.

Dynamic Responses of Rotor Drops onto Double-decker Catcher Bearing

In an active magnetic bearing （AMB） system, the catcher bearings （CBs） are indispensable to protect the rotor and stator in case the magnetic bearings fail. Most of the former researches associated with CBs are mainly focused on the dynamic responses of the rotor drops onto traditional single-decker catcher bearings （SDCBs）. But because of the lower limited speed of SDCB, it cannot withstand the ultra high speed rotation after rotor drop. In this paper, based on the analysis of the disadvantages of SDCBs, a new type of double-decker catcher bearings （DDCBs） is proposed to enhance the CB work performance in AMB system. In order to obtain thc accurate rotor movements before AMB failure, the dynamic characteristics of AMB are theoretically derived. Detailed simulation models containing rigid rotor model, contact model between rotor and inner race, DDCB force model as well as heating model after rotor drop are established. Then, using those established models the dynamic responses of rotor drops onto DDCBs and SDCBs are respectively simulated. The rotor orbits, contact forces, spin speeds of various parts and heat energies after AMB failure are mainly analyzed. The simulation results show that DDCBs can effectively improve the CBs limit rotational speed and reduce the following vibrations, impacts and heating. Finally, rotor drop experiments choosing different types of CBs are carried out on the established AMB test bench. Rotor orbits, inner race temperatures as well as the rotating speeds of both inner race and intermediate races after rotor drop are synchronously measured. The experiment results verify the advantages of DDCB and the correctness of theoretical analysis. The studies provide certain theoretical and experimental references for the application of DDCBs in AMB system.

Ultra-Robust and High-Performance Rotational Triboelectric Nanogenerator by Bearing Charge Pumping

As an emerging technology to convert environmental high-entropy energy into electrical energy,triboelectric nanogenerator(TENG)has great demands for further enhancing the service lifetime and output performance in practical applications.Here,an ultra-robust and high-performance rotational triboelectric nanogenerator(R-TENG)by bearing charge pumping is proposed.The R-TENG composes of a pumping TENG(P-TENG),an output TENG(O-TENG),a voltage-multiplying circuit(VMC),and a buffer capacitor.The P-TENG is designed with freestanding mode based on a rolling ball bearing,which can also act as the rotating mechanical energy harvester.The output low charge from the P-TENG is accumulated and pumped to the non-contact O-TENG,which can simultaneously realize ultralow mechanical wear and high output performance.The matched instantaneous power of R-TENG is increased by 32 times under 300 r/min.Furthermore,the transferring charge of R-TENG can remain 95%during 15 days(6.4×10^(6)cycles)continuous operation.This work presents a realizable method to further enhance the durability of TENG,which would facilitate the practical applications of high-performance TENG in harvesting distributed ambient micro mechanical energy.

Rotor dynamic analysis of small vehicle gasoline turbocharger in semi-floating bearings

The critical speed and unbalance response of a small vehicle gasoline turbocharger in semi-floating bearing are analyzed.The dynamical characters of semi-floating bush bearing used in small vehicle gasoline turbocharger were summarized by comparing the structure and shaft rigid mode of semi-floating bush bearings with those of floating bush bearings.The rotor model was built.The first,second and third mode of critical speeds of rotor system were computed,and the changes in the compressor or turbine bushing bearing clearances were analyzed.Compared with the experiment data,the accuracy and the rationality of computation model were verified.The unbalance response and time transient rotor response were also computed.

ANALYSIS ON MOTION STABILITY OF A HIGH-SPEED ROTOR-BEARING SYSTEM

A non-linear dynamic model of one type of high-speed rotor system with gassupporting system is set up. The laws between the capacity force and the parameters of bearing, thestatic equilibrium position and rotating speed are studied on the basis of above model. Then, thefailure rotating, speed is given in the working state, and the relation between the minimum failurerotating speed and clearance of bearing is also studied. At last, the stability and failurecondition are discussed in different working conditions.

Stability Analysis on Rotor Systems Supported by Self-acting Tilting-pad Gas Bearings with Frequency Effects

The recent research on stability of gas bearing-rotor systems still mostly adopts the same method as in oil-lubricated bearing-rotor systems.The dynamic coefficients of gas bearings in the case that the perturbation frequencies are same as the rotating speed are used to carry out the stability analysis of rotor systems.This method does not contact the frequency characteristics of dynamic stiffness and damping coefficients of gas bearings with the dynamical behaviors of rotor systems.Furthermore,the effects of perturbation frequencies on the stability of systems are not taken into account.In this paper,the dynamic stiffness and damping coefficients of tilting-pad gas bearings are calculated by the partial derivative method.On the base of solution of dynamic coefficients,two computational models are produced for stability analysis on rotor systems supported by tilting-pad gas bearings according to whether the degrees of the freedom of pads tilting motions are included in the equations of motion or not.In the condition of considering the frequency effects of dynamic coefficients of tilting-pad gas bearings,the corresponding eigenvalues of the rigid and first five vibration modes of the system with the working speeds of 8-30 kr/min are computed through iteratively solving the equations of motion of rotor-system by using two computational models,respectively.According to the obtained eigenvalues,the stability of rotor system is analyzed.The results indicate that the eigenvalues and the stability of rotor system obtained by these two computational models are well agreement each other.They all can more accurately analyze the stability of rotor systems supported by tilting-pad gas bearings.This research has important meaning for perfecting the stability analysis method of rotor systems supported by gas bearings.

Analysis on Dynamic Performance for Active Magnetic Bearing-Rotor System

In the application of active magnetic bearings (AMB), one of the key problems to be solved is the safety and stability in the sense of rotor dynamics. The project related to the present paper deals with the method for analyzing bearing rotor systems with high rotation speed and specially supported by active magnetic bearings, and studies its rotor dynamics performance, including calculation of the natural frequencies with their distribution characteristics, and the critical speeds of the system. One of the targets of this project is to formulate a theory and method valid for the analysis of the dynamic performance of the active magnetic bearing rotor system by combining the traditional theory and method of rotor dynamics with the analytical theory and design method based on modern control theory of the AMB system.

Effects of Semi-floating Ring Bearing Outer Clearance on the Subsynchronous Oscillation of Turbocharger Rotor

Semi-floating ring bearing（SFRB） is developed to control the vibration of turbocharger rotor. The outer clearance of SFRB affects the magnitude and frequency of nonlinear whirl motion, which is significant for the design of turbocharger. In order to explore the effects of outer clearance, a transient finite element analysis program for rotor and oil film bearing is built and validated by a published experimental case. The nonlinear dynamic behaviors ofrotor-SFRB system are simulated. According to the simulation results, two representative subsynchronous oscillations excited by the two hearings respectively are discovered. As the outer clearance of SFRB increases from 24 ~tm to 60 pro, the low-frequency subsynchronous oscillation experiences three steps, including a strong start, a gradual recession and a combination with the other one. At the same time, the high-frequency subsynchronous oscillation starts to appear gradually, then strengthens, and finally combines. If gravity and unbalance are neglected, the combination will start starts from high rotor speed and extents to low rotor speed, just like a ＂zipper＂. It is found from the quantitative analysis that when the outer clearance increases, the vibration amplitude experiences large value firstly, then reduction, and suddenly increasing after combination. A useful design principle of SFRB outer clearance for minimum vibration amplitude is proposed： the outer clearance value should be chosen to keep the frequency of two subsynchronous oscillations clearly separated and their amplitudes close.

Bifurcation and Chaos Analysis of Nonlinear Rotor System with Axial-grooved Gas-lubricated Journal Bearing Support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.

Research on a Rigid Rotor-Sliding Bearing System with a Squeeze Film Damper

In this paper, a dynamic model on a rigid rotor sliding bearing system with a SFD is established. The stability and bifurcation behaviors of the system are studied. On the basis of the differential equations of fluid momentum and mass continuity, the distribution pressure function is derived by taking oil film inertia force into consideration. Damping force, clearance excitation force, interference force of different frequencies and static load are also considered in the model. Finally, the governing equations of the stability and bifurcation behaviors of the system are solved by Floquet theory. Simulation of dynamic model shows that the rigid rotor sliding bearing system can maintain stability and exhibit a Hopf bifurcation phenomenon in a certain range.

Application of Computational Fluid Dynamics and Fluid Structure Interaction Techniques for Calculating the 3D Transient Flow of Journal Bearings Coupled with Rotor Systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics （CFD）-fluid structure interaction （FSI） techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ＂dynamic mesh＂ technique. A new mesh movement approacb is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the joumal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function （UDF）. The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

Dynamics of Rotor Drop on New Type Catcher Bearing

In an active magnetic bearing(AMB)system,the catcher bearings(CBs)are indispensable to protect the rotor and stator in case the magnetic bearings fail or overload.A new CB structure composed of two ball bearings is introduced.Detailed simulation models containing contact model between rotor and inner race,double-decker catcher bearing(DDCB)model as well as single-decker catcher bearing(SDCB)model are established using multibody dynamics simulation software MSC.ADAMS.Then,using those established models,the rotor orbits and the contact forces between rotor and inner race are simulated respectively after rotor drop on DDCBs and SDCBs.The simulation result shows that the rotor vibration range using DDCBs is significantly smaller than that using SDCBs;the maximum contact forces drop about 15%—27% compared with the contact forces using SDCBs.Finally,the test bench for the rotor drop experiments is built and the rotor drop experiments for different types of CBs are carried out.Labview data acquisition system is utilized to collect the displacement of rotor and the rotating frequencies of both inner race and intermediate races after rotor drop.The experimental results are comparatively analyzed,and the conclusion that DDCB can help to reduce vibration amplitude and collision force is obtained.The studies can provide certain theoretical and experimental references for the application of DDCBs in AMB system.

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.

Singularity analysis of Jeffcott rotor-magnetic bearing with time delays

A Jeffcott rotor-magnetic bearing with time delays is investigated in this paper. Firstly, it is found that the characteristic equation of the system satisfies the conditions of the singularity. Secondly, the center manifold reduction and normal form are employed to study the bifurcation from simple zero and zero-purely imaginary singularities. The results of this paper will help to understand the influence of the time delays in feedback loop on the dynamics of rotor-magnetic bearing system.

Nonlinear Vibration Induced by the Water-film Whirl and Whip in a Sliding Bearing Rotor System

Many industrial applications and experiments have shown that sliding bearings often experience fluid film whip due to nonlinear fluid film forces which can cause rotor-stator rub-impact failures. The oil-film whips have attracted many studies while the water-film whips in the water lubricated sliding bearing have been little researched with the mechanism still an open problem. The dynamic fluid film forces in a water sliding bearing are investigated numerically with rotational, whirling and squeezing motions of the journal using a nonlinear model to identify the relationships between the three motions. Rotor speed-up and slow-down experiments are then conducted with the rotor system supported by a water lubricated sliding bearing to induce the water-film whirl/whip and verify the relationship. The experimental results show that the vibrations of the journal alternated between increasing and decreasing rather than continuously increasing as the rotational speed increased to twice the first critical speed, which can be explained well by the nonlinear model. The radial growth rate of the whirl motion greatly affects the whirl frequency of the journal and is responsible for the frequency lock in the water-film whip. Further analysis shows that increasing the lubricating water flow rate changes the water-film whirl/whip characteristics, reduces the first critical speed, advances the time when significant water-film whirling motion occurs, and also increases the vibration amplitude at the bearing center which may lead to the rotor-stator rub-impact. The study gives the insight into the water-film whirl and whip in the water lubricated sliding bearing.