Numerical Simulation and Experimental Verification of the Stiffness and Stability of Thrust Pad Aerostatic Bearings

Many researchers concentrate on improving the stiffness and stability of aerostatic bearings, however the contradiction between stiffness and stability is still existed. Therefore, orifice, multiple, and porous restrictors are designed to illustrate the influence of restrictor characteristics on the stability and stiffness of the aerostatic circular pad bearings. Because both the stiffness and stability of aerostatic bearings are determined by the internal pressure distribution, the full Navier?Stokes(N?S) equations are applied to solve internal pressure distribution in bearing film by using computational fluid dynamics(CFD) method. Simulation results present that the stiffness and stability of aerostatic circular pad bearings are influenced significantly by geometrical and material parameters, such as film thickness, orifice diameters, and viscous resistance coe cient. Verified by the experimental data, the micro vibration of orifice restrictor is almost the same as multiple restrictors with amplitude of 0.02 m/s~2, but it is much stronger than the porous restrictors with acceleration of 0.006 m/s~2. The optimal stiffness of multiple restrictors increased by 46%, compared to only 30.2 N/μm of orifice restrictor, and the porous restrictors had obvious advantage in the small film thickness less than 6 μm where the optimal stiffness increased to 38.3 N/μm. The numerical and experimental results provide guidance for improving the stiffness and stability of aerostatic bearings.

Quasi Dynamic Calculation of Local Stiffness of Angular Contact Ball Bearings

In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.

Study on High Stiffness Gas Bearing for Precision Centrifuger

A high stiffness and precision gas bearing system is developed in accordance with the requirements for a precision centrifuger. Finite element method and optimiztion of parameters are employed for optimization of gas bearing design, and this enable the bearing system to be successfully used in the inertial navigation test system.

A New Method to Calculate Water Film Stiffness and Damping for Water Lubricated Bearing with Multiple Axial Grooves

Water lubricated guide bearings for hydro turbines and pumps are conventionally designed with multiple axial grooves to provide effectively cooling and flushing away abrasives.Due to the variety of groove configuration in terms of number and size,a predication of their performance is difficult.This paper deals with an analytical procedure to investigate groove effect on load capacity,stiffness and damping for this type of bearing where it is considered as an assembly of many inclined slide bearings.The result can be applied to bearings made of hard materials combined with low bearing pressure.

Dynamic Stiffness Analysis and Experimental Verification of Axial Magnetic Bearing Based on Air Gap Flux Variation in Magnetically Suspended Molecular Pump

Current and displacement stiffness are important parameters of axial magnetic bearing(AMB)and are usually considered as constants for the control system.However,in actual dynamic work situations,time-varying force leads to time-varying currents and air gap with a specific frequency,which makes the stiffness of appear decrease and even worsens control performance for the whole system.In this paper,an AMB dynamic stiffness model considering the flux variation across the air gap due to frequency is established to obtain the accurate dynamic stiffness.The dynamic stiffness characteristics are analyzed by means of the dynamic equivalent magnetic circuit method.The analytical results show that the amplitude of current and displacement stiffness decreases with frequency increasing.Moreover,compared with the stiffness model without considering the variation of flux density across the air gap,the improved dynamic stiffness results are closer to the actual results.Through the dynamic stiffness measurement method of AMB,experiments of AMB in magnetically suspended molecular pump(MSMP)are carried out and the experimental results are consistent with theoretical analysis results.This paper proposes the dynamic stiffness model of axial magnetic bearing considering the variation of flux density across the air gap,which improves the accuracy of the AMB stiffness analysis.

Stiffness of high-speed cylindrical roller bearing subjected to radial force and bending moment

Presents a practical way of calculation for stiffness of cylindrical roller bearing based on traditional quasistatic analytical methods subject to radial force and bending moment,which take into consideration the effect of such factors as thickness of oil elastohydrodynamic film,pressure,shear force,friction force of cage,centrifugal force and slides,taken into consideration and presents the results of stiffness calculation with a typical example with an aeroengine cylindrical roller bearing were given in the paper.And,discusses the effect of major parameters’influence on stiffness.

Analysis of Improvement in the Stiffness of Externally Pressurized Gas Thrust Bearing

This paper expounds some factors on improving stiffness of externally pressurized gas thrust bearings. Especially,a pressure positive feedback thrust bearing(PPFTB) and an actively controlled thrust bearing (ACTB) are proposed.It has been found that the two new types of bearings can increase the stiffness remarkably in a certain range of fluctuating load and have won wide applications in ultra-precision machines.

Relationship of rolling bearing stiffness with diameter of roller

The theoretical formula of roller bearing stiffness is induced and compared with its empirical formula. In the experience formula the stiffness of roller bearing has nothing to do with the roller diameter. The relationship of roller bearing stiffness with roller diameter was studied using Hz contacting theory. It is concluded that conclusion in experience formula is only approximate result of data processing under special conditions, and the relation between stiffness of roller bearing and roller diameter must be taken into consideration while designing or selecting roller bearings.

The diagnostic value of liver stiffness measurement combined with S index in the degree of hepatitis B liver fibrosis

Objective:To investigate the value of liver stiffness measurement(LSM)combined with S index in predicting the degree of liver fibrosis in hepatitis B patients.Methods:A total of 187 chronic hepatitis B patients who were admitted to the Department of Infection,the First Affiliated Hospital of Hainan Medical College from January 2019 to December 2021 were selected.General data were collected,blood routine,liver function,liver fibrosis and liver stiffness measurement were tested,and S index,APRI and FIB-4 index were calculated,and liver biopsy was performed.Results:According to the pathological results of liver puncture,The patients were divided into no significant fibrosis group(n=86),significant fibrosis group(n=71)and cirrhosis group(n=30).There were significant differences in age,PLT,GGT,ALB,S index,HA,LN and LSM levels among the three groups(P<0.05).There was a good correlation between S index and the degree of hepatic fibrosis(rs=0.738,P<0.001).The AUC of S index and LSM for the diagnosis of significant fibrosis in hepatitis B were 0.873 and 0.792,respectively.And the AUC of S index and LSM for the diagnosis of liver cirrhosis were 0.966 and 0.879,respectively.The AUC for the combined diagnosis of significant fibrosis and cirrhosis were 0.908 and 0.988,respectively.The AUROC of combined detection in the diagnosis of cirrhosis was higher than that of LSM,APRI and FIB-4(P<0.05).Conclusion:LSM combined with S index has certain application value in the diagnosis of liver fibrosis/cirrhosis in hepatitis B patients.

Analysis of dynamic characteristics of self-aligning ball bearing

A dynamics model of the self-aligning ball bearing is proposed based on the Jones-Harris method （JHM）, and a computer program is developed to solve the equations by using the Newton-Raphson method. A parametric analysis of the centrifugal force and the gyroscopic moment, the contact loads, the contact angles, the radial deformation and the radial stiffness is carried out. The analytical results show that the applied loads and the rotational speed are two main factors that can influence the distributions of the contact loads and values of the contact angles. The centrifugal force and the gyroscopic moment increase with the increase in the rotational speed, resulting in the decrease of the inner raceway contact load and the increase of the outer raceway contact load. The outer raceway contact angle increases under the centrifugal force; on the contrary, the inner raceway contact angle decreases. Furthermore, the differences between the inner and the outer contact angles increase with the increase in the rotational speed. The higher rotational speed results in the decrease in radial stiffness for the self-aligning ball bearing, and the raceway curvature coefficient, to some extent, also influences the radial stiffness.

Modeling and Analysis of Novel Integrated Radial Hybrid Magnetic Bearing for Magnetic Bearing Reaction Wheel

Conventional ball bearing reaction wheel used to control the attitude of spacecraft can＇t absorb the centrifugal force caused by imbalance of the wheel rotor,and there will be a torque spike at zero speed,which seriously influences the accuracy and stability of spacecraft attitude control.Compared with traditional ball-bearing wheel,noncontact and no lubrication are the remarkable features of the magnetic bearing reaction wheel,and which can solve the high precision problems of wheel.In general,two radial magnetic bearings are needed in magnetic bearing wheel,and the design results in a relatively large axial dimension and smaller momentum-to-mass ratios.In this paper,a new type of magnetic bearing reaction wheel（MBRW） is introduced for satellite attitude control,and a novel integrated radial hybrid magnetic bearing（RHMB） with permanent magnet bias is designed to reduce the mass and minimize the size of the MBRW,etc.The equivalent magnetic circuit model for the RHMB is presented and a solution is found.The stiffness model is also presented,including current stiffness,position negative stiffness,as well as tilting current stiffness,tilting angular position negative stiffness,force and moment equilibrium equations.The design parameters of the RHMB are given according to the requirement of the MBRW with angular momentum of 30 N ？ m ？ s when the rotation speed of rotor reaches to 5 kr/min.The nonlinearity of the RHMB is shown by using the characteristic curves of force-control current-position,current stiffness,position stiffness,moment-control current-angular displacement,tilting current stiffness and tilting angular position stiffness considering all the rotor position within the clearance space and the control current.The proposed research ensures the performance of the radial magnetic bearing with permanent magnet bias,and provides theory basis for design of the magnetic bearing wheel.

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.

Effect of Manufacturing Errors on Static Characteristics of Externally Pressurized Spherical Air Bearings

Externally pressurized spherical air bearings are the key component of the three-axis air bearing table, and the manufacturing errors of the bearing affects the performance of the air bearing table. However, the manufacturing errors are unavoidable, and the pursuit to enhance the manufacturing accuracy will increase the cost greatly. In order to provide some theoretical guideline for the tolerance choice in the design of the externally pressurized spherical air bearings with inherent compensation, the effects of several manufacturing errors on the static characteristics of the air bearing are studied. Due to the complex geometry of the computational domain, an unstructured meshing technology is used for mesh generation. A finite-volume method is adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations. A modified SIMPLE algorithm which is suitable for compressible flows is applied to solve the discretized governing equations. The effects of the dimension error and the roundness error of the ball head and the ball socket on the static characteristics are investigated. The investigation result shows that the positive dimension error and the oblate spheroid-type roundness error of the ball head as well as the negative dimension error and the prolate spheroid-type roundness error of the ball socket can improve the bearing capacity and static stiffness of the air bearings by reducing the mass flow. The calculation method proposed in this paper fits well for the general principle, which can be extended to the characteristics analysis of other air bearings.

Research on the Critical Speed of a Mixed-Flow Turbocharger with Hybrid Ceramic Ball Bearing

The critical speeds for a vehicle turbocharger with hybrid ceramic ball bearing are researched. The ball bearing-rotor system produces resonance when it working in critical speed and that makes the turbocharger injury working for a long time. The calculation and analysis methods of the critical speed for the vehicle turbocharger are described. The critical speed is computed by two methods including Riccati transfer matrix and DyRoBeS finite element method for a vehicle turbocharger with hybrid ceramic ball bearing. The vibration experiment had been taken to validate the calculating result, Comparison between the results by two calculation methods and the test results show that the first critical speed differences are 6.47 % and 5.66 %, the second critical speed differences are 2.87 % and 2.94 % respectively. And then, the primary factors which influence the critical speed are analyzed, the conclusions will be helpful for the vehicle turbocharger bearing-rotor system design.

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.

Dynamic Analysis of Floating-Ring Gas Bearings

The dynamic performances of floating-ring bearing with hydrodynamic/hydrostatic gas lubrication are studied theoretically and some calculated charts of dynamic coefficients are given in the paper. The method of stability analysis is also presented and it is proved that the high speed stability of such bearings is better than other types of gas bearings.

A Study on the Dynamic Characteristics of the Damping Capillary Type Spherical Hydrostatic Bearing

The dynamic mathematical model of the damping capillary type spherical hydrostatic bearing is established firstly,then the dynamic characteristics of the hydrostatic bearing are analysized in detail.By means of theoretical reasoning,a design guide that relates to J0,the static stiffness of the hydrostatic bearing,is put forward to guarantee that the hydrostatic bearing possesses the excellent dynamic characteristics.At last,the effect of the structural parameters on J0 is studied.

Determination of ultimate bearing capacity of uplift piles using intact and non-intact load−displacement curve

Based on the field destructive test of six rock-socketed piles with shallow overburden,three prediction models are used to quantitatively analyze and predict the intact load−displacement curve.The predicted values of ultimate uplift capacity were further determined by four methods(displacement controlling method(DCM),reduction coefficient method(RCM),maximum curvature method(MCM),and critical stiffness method(CSM))and compared with the measured value.Through the analysis of the relationship between the change rate of pullout stiffness and displacement,a method used to determine the ultimate uplift capacity via non-intact load−displacement curve was proposed.The results show that the predicted value determined by DCM is more conservative,while the predicted value determined by MCM is larger than the measured value.This suggests that RCM and CSM in engineering applications can be preferentially applied.Moreover,the development law of the change rate of pullout stiffness with displacement agrees well with the attenuation form of power function.The theoretical predicted results of ultimate uplift capacity based on the change rate of pullout stiffness will not be affected by the integrity of the curve.The method is simple and applicable for the piles that are not loaded to failure state,and thus provides new insights into ultimate uplift capacity determination of test piles.

Research on static bearing characteristics of magnetic-liquid double suspension bearing

Due to low viscosity of seawater,it is difficult to form a seawater-lubricated film.It is easy to cause the overload and burning phenomenon of seawater-lubrication sliding bearing,and then the operation stability and service life can be shortened seriously.Therefore,the paper introduces an electromagnetic suspension theory into the seawater lubricated sliding bearing.Then a novel magnetic-liquid double suspension bearing can be formed,which can enhance bearing capacity and stiffness greatly.Firstly,the structural characteristics,support-adjustment mechanism of magnetic-liquid double suspension bearing is analyzed.Secondly,based on force balance equation,electromagnetic equation and flow equation,the transfer functions of single DOF bearing system of magnetic-liquid double suspension bearing under constant-flow supply model are deduced.Then bearing capacity,static stiffness and total power loss are selected as static performance indexes.The influence rule of operaton and structural parameters on the static performance of single DOF bearing system will be analyzed.The results show that bearing capacity decreases with the increase of liquid film thickness and width of edge seals,bias current and coil turns decrease.Static stiffness decreases with the increase of liquid film thickness,edge seals width,bias current and coil turns.Total power loss decreases with the increase of liquid film thickness,edge seals width,bias current and coil turns decrease.And static performance indexes can not be affected by liquid viscosity.The proposed research provides some theoretical and experimental basis for the parameter design of magnetic-liquid double suspension bearing.

Mechanical Characteristics of Radial Magnetic Bearing

This paper is based on the example of a radial magnetic bearing possessed of eight-pole, and derives the calculation formulas of static and dynamic mechanical characteristics of the bearing, in which the shape and curvature of surface, eccentricity and tilt of the journal are taken into account. Variations of the static and dynamic characteristics of the radial magnetic bearing versus static tilt parameters of journal are discussed. The outcomes show that the static tilt of the journal has influence on the mechanical characteristics of radial magnetic bearing, and change the static load capacity between two radial magnetic bearings and exert coupling effect between them. To study the dynamics of a practical rotor-magnetic bearing system, at least six stiffness coefficients in each radial magnetic bearing must be considered in ideal case, and twelve stiffness coefficients must be considered in general case of tilting journal. Such a find can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.