Research on the Influence of Raceway Waviness on the Vibration Characteristics of Deep Groove Ball Bearings

The dynamics model of a 2-degree-of-freedom deep groove ball bearing is established by incorporating the raceway surface waviness model comprising multiple sinusoidal functions superposition.The model is solved using the fourth-order Runge-Kutta method to obtain the vibration characteristics including displacement,velocity,acceleration,and frequency of the bearing.Validation of the model is accomplished through comparison with theoretical vibration frequencies.The influence of the amplitude of waviness of the inner and outer ring raceway surfaces of deep groove ball bearings on the vibration displacement,peak-to-peak vibration displacement and root-mean-square vibration acceleration is analyzed,and the results show that as the amplitude of the inner and outer ring raceway surfaces waviness increases,all the vibration characteristic indexes increase,indicating that the vibration amplitude of the bearings as well as the energy of the waviness-induced shock waveforms increase with the increase of the amplitude of the waviness.

Graded and Quantitative Technology and Application of Coal-Bearing Reservoir Based on Seismic Reflection Characteristics

Taiyuan formation is the main exploration strata in Ordos Basin, and coals are widely developed. Due to the interference of strong reflection of coals, we cannot completely identify the effective reservoir information of coal-bearing reservoir on seismic data. Previous researchers have studied the reservoir by stripping or weakening the strong reflection, but it is difficult to determine the effectiveness of the remaining reflection seismic data. In this paper, through the establishment of 2D forward model of coal-bearing strata, the corresponding geophysical characteristics of different reflection types of coal-bearing strata are analyzed, and then the favorable sedimentary facies zones for reservoir development are predicted. On this basis, combined with seismic properties, the coal-bearing reservoir is quantitatively characterized by seismic inversion. The above research shows that the Taiyuan formation in LS block of Ordos Basin is affected by coals and forms three or two peaks in different locations. The reservoir plane sedimentary facies zone is effectively characterized by seismic reflection structure. Based on the characteristics of sedimentary facies belt and petrophysical analysis, the reservoir is semi quantitatively characterized by attribute analysis and waveform indication, and quantitatively characterized by pre stack geostatistical inversion. Based on the forward analysis of coal measure strata, this technology characterizes the reservoir facies belt through seismic reflection characteristics, and describes coal measure reservoirs step by step. It effectively guides the exploration of LS block in Ordos Basin, and has achieved good practical application effect.

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.

An Overview of Performance Characteristics, Experiencesand Trends of Aerospace Engine Bearings Technologies

In this paper, the operating conditions, technical requirements, performance characteristics, design ideas, application experiences and development trends of aerospace engine bearings, including material technology, integration design and reliability, are reviewed. The development history of aerospace engine bearing is recalled briefly at first. Then today＇s material technologies and the high bearing performances of the bearings obtained through the new materials are introduced, which play important roils in the aeroengine bearing developments. The integration design ideas and practices are explained to indicate its significant advantages and importance to the aerospace engine bearings. And the reliability of the shaft-bearing system is pointed out and treated as the key requirement with goals for both engine and bearing. Finally, as it is believed that the correct design comes from practice, the pre-qualification rig testing conducted by FAG Aerospace GmbH ＆ Co. KG is briefly illustrated as an example. All these lead to the development trends of aerospace engine bearings from different aspects.

Characteristics of Al_2O_3, MnS, and TiN inclusions in the remelting process of bearing steel

The Al_2O_3, MnS, and TiN inclusions in bearing steel will deteriorate the steel's mechanical properties. Therefore, elucidating detailed characteristics of these inclusions in consumable electrode during the electroslag remelting process is important for achieving a subsequently clean ingot. In this study, a confocal scanning violet laser microscope was used to simulate the remelting process and observe, in real time, the behaviors of inclusions. The obtained images show that, after the temperature exceeded the steel solidus temperature, MnS and TiN inclusions in the specimen began to dissolve. Higher temperatures led to faster dissolution, and the inclusions disappeared before the steel was fully liquid. In the case of an observed Al_2O_3 inclusion, its shape changed from angular to a smooth ellipsoid in the region where the solid and liquid coexisted and it began to dissolve as the temperature continued to increase. This dissolution was driven by the difference in oxygen potential between the inclusion and the liquid steel.

Effects of Floating Ring Bearing Manufacturing Tolerance Clearances on the Dynamic Characteristics for Turbocharger

The inner and outer oil film dynamic characteristic coefficients of floating ring bearings（FRBs） change due to the manufacturing tolerance of the floating ring, journal and intermediate, which leads to high-speed turbocharger＇s vibration too large and even causes nonlinear vibration accident. However, the investigation of floating ring bearing manufacturing tolerance clearance on the rotordynamic characteristics is less at present. In order to study the influence law of inner and outer clearance on turbocharger vibration, the rotor dynamic motion equations of turbocharger supported in FRBs are derived by analyzing the size relations between floating ring, journal and intermediate for the inner and outer oil film clearances, the time transient response analysis for combination of FRBs clearance are developed. A realistic turbocharger is taken as a research object, the FE model of the turbocharger with FRBs is modeled. Under the conditions of four kinds of limit state bearing clearances for inner and outer oil film, the nonlinear transient analyses are performed based on the established FE dynamic models of the nonlinear rotor-FRBs system applied incentive combinations of gravity and unbalance force, respectively. From the waterfall, the simulation results show that the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different under the four kinds of bearing manufacturing tolerance limit clearances, and fractional frequency does not appear in the turbocharger and the amplitude is minimum under the ODMin/IDMax bearing manufacturing tolerance clearances. The turbocharger vibration is reduced by controlling the manufacturing tolerance clearance combinations of FRBs, which is helpful for the dynamic design and production-manufacturing of high-speed turbocharger.

Analysis of the Temperature Characteristics of High-speed Train Bearings Based on a Dynamics Model and Thermal Network Method

High-speed trains often use temperature sensors to monitor the motion state of bearings.However,the temperature of bearings can be affected by factors such as weather and faults.Therefore,it is necessary to analyze in detail the relationship between the bearing temperature and influencing factors.In this study,a dynamics model of the axle box bearing of high-speed trains is established.The model can obtain the contact force between the rollers and raceway and its change law when the bearing contains outer-ring,inner-ring,and rolling-element faults.Based on the model,a thermal network method is introduced to study the temperature field distribution of the axle box bearings of high-speed trains.In this model,the heat generation,conduction,and dispersion of the isothermal nodes can be solved.The results show that the temperature of the contact point between the outer-ring raceway and rolling-elements is the highest.The relationships between the node temperature and the speed,fault type,and fault size are analyzed,finding that the higher the speed,the higher the node temperature.Under different fault types,the node temperature first increases and then decreases as the fault size increases.The effectiveness of the model is demonstrated using the actual temperature data of a high-speed train.This study proposes a thermal network model that can predict the temperature of each component of the bearings on a high-speed train under various speed and fault conditions.

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.

Bearing characteristics and fatigue damage mechanism of multi-pillar system subjected to different cyclic loads

Aiming to investigate the fatigue damage mechanism and bearing characteristics of multi-pillar system under cyclic loading,a series of axial cyclic loading tests with different cyclic amplitudes were carried out on triple-pillar marble specimens.The acoustic emission(AE)and digital image correlation(DIC)were jointly applied to monitoring and recording damage evolution and failure behavior of each pillar,which reproduced the cataclysmic instability process of underground pillar groups.Experimental results indicated that the cyclic amplitude exceeding the threshold of damage initiation weakened the resistance to deformation,resulting in obvious release of dissipated energy and the reduction of bearing capacity.Conversely,after low-amplitude cyclic loading,both the pre-peak bearing capacity and the post-peak ductility of the pillar system increased due to the compaction of initial defects,indicating that the peak bearing capacity was closely related to the extent of pre-peak fatigue damage.The axial strain of each pillar was measured by DIC virtual extensometer to present the damage extent during cyclic loading phase.Meanwhile,fracture evolution of typical load drop points was also characterized by transverse strain fields(εxx),and observations showed that the damage extent of key pillar undergoing high-amplitude cyclic loads was more serious and violent,accompanied by the ejection of rock debris and loud noises.

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.

Dynamic Characteristics of High-speed Water-Lubricated Spiral Groove Thrust Bearing Based on Turbulent Cavitating Flow Lubrication Model

The water-lubricated bearings are usually the state of turbulent cavitating flow under high-speed conditions. And the distribution of cavitation bubbles and the interface effect between the two phases have not been included in previous studies on high-speed water-lubricated bearings. In order to study the influence of interface effect and cavitation bubble distribution on the dynamic characteristics of high-speed water-lubricated spiral groove thrust bearings(SGTB).A turbulent cavitating flow lubrication model based on two-phase fluid and population balance equation of bubbles was established in this paper. Stiffness and the damping coefficients of the SGTB were calculated using the perturbation pressure equations. An experimental apparatus was developed to verify the theoretical model. Simulating and experimental results show that the small-sized bubbles tend to generate in the turbulent cavitating flow when at a high rotary speed, and the bubbles mainly locate at the edges of the spiral groove. The simulating results also show that the direct stiffness coefficients are increased due to cavitation effect, and cross stiffness coefficients and damping coefficients are hardly affected by the cavitation effect. Turbulent effect on the dynamic characteristics of SGTB is much stronger than the cavitating effect.

Dynamic Characteristics of Multi-degrees of Freedom System Rotor-bearing System with Coupling Faults of Rub-impact and Crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.

Bearing capacity analysis using the method of characteristics

Using the method of characteristics,the bearing capacity for a strip footing is analyzed.The method of characteristics leads to an exact true limit load when the calculations of the three terms in the bearing capacity formula are consistent with one collapse mechanism and the soil satisfies the associated flow rule.At the same time,the method of characteristics avoids the assumption of arbitrary slip surfaces,and produces zones within which equilibrium and plastic yield are simultaneously satisfied for given boundary stresses.The exact solution without superposition approximation can still be expressed by Terzaghi＇s equation of bearing capacity,in which the bearing capacity factor N γλ is dependent on the dimensionless parameter λ and the friction angle φ.The influence of groundwater on the bearing capacity of the shallow strip footing is considered,which indicates that when the groundwater effect is taken into account,the error induced by the superposition approximation can be reduced as compared with dry soil condition.The results are presented in the form of charts which give the modified value（Nwγλc /Nγλc） of bearing capacity factor.Finally,an approximated analytical expression,which provides results in close agreement with those obtained by numerical analysis in this paper,has been suggested for practical application purposes.

Investigation of the Dynamic Characteristics of a Rotor Bearing Assembly

The dynamic characteristics of a general bearing assembly have been studied by using Finite Element Method and G-H Method. A rotcr bearirg system with distributed parameters of rigid disks and bearings was analyzed by Finite Element Method. The characteristic equaticn of the rotor bearing systern was given, and the generalized eigenvalue problem was solved by transfering that defined by one real symmetric matrix and one skew symmtric matrix into one defined by two real symmetric matrices. Whiring speeds and vibration shapes of rctor bearing systems under different spin speeds were obtained and so the natural frequencies of the rotor bearing systems could be obtaincd.

Mechanical Characteristics of a Thrust Magnetic Bearing

Static and dynamic mechanical characteristics of a thrust magnetic bearing are studied owing to the inclination of the runner disk. The application refers to a thrust magnetic bearing for a turbo expander/compressor. The static tilt of the runner disk has remarkable influence on the mechanical characteristics of thrust magnetic bearing, it can change the static load distribution between two radial magnetic bearings and will exert violent coupling effect among a thrust magnetic bearing and two radial magnetic bearings. Such a finding can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.

Study on Rheological Characteristics of a Grease Used in High Speed Bearing

On a self-made super-high shear strain rate rheometer, the rheological characteristics and apparent viscosity curves of a high-speed bearing grease were obtained under different working conditions. A new grease rheological model suited to a shear strain rate range of 0—3.5×10~6s^(-1) was presented. The results showed that the shear stress increased linearly at first and then increased nonlinearly with the increase in shear strain rate up to 1.5×10~6s^(-1), and finally the shear stress decreased slightly with the successive increase in shear strain rate. The shear stress increased with a decreasing rolling speed and an increasing contact pressure. The apparent viscosity decreased rapidly with the increase of shear strain rate at beginning and could approach the viscosity of the base oil if the shear strain rate surpassed 1.5×10~6s^(-1). The fits between the test data and the predicted values by the new model were fairly good.

Static characteristics of new type externally pressurized spherical air bearings

In order to provide some theoretical guideline for the structure design of the new type externally pressurized spherical air bearings,the static characteristics and the factors affecting the static characteristics of the air bearings were analyzed.A finite volume method was adopted to discretize the three-dimensional steady-state compressible Navier-Stokes equations,and a modified SIMPLE algorithm for compressible fluid was applied to solve the discretized governing equations.The pressure field and velocity field of the air bearings were obtained,and the factors and rules affecting the static characteristics were analyzed.The results show that the pressure of near air intakes can reach above 80% of air supply pressure,and there is a pressure steep fall around the air intakes.When the film thickness is greater than 20 μm,the bearing capacity rapidly decreases as film thickness increases.As the air supply pressure increases from 0.2 to 0.6 MPa,the maximum static stiffness increases by more than three times.The calculation method proposed well fits the general principle,which can be extended to the characteristic analysis of other air bearings.

Analysis on Static Pressure Bearing Seal Characteristics of Guide Sleeve of Electro-hydraulic Servo Cylinder

As a typical bionic walking robot, hydraulic quadruped robot has attracted much attention because of its high mobility, strong load capacity and steady motion. The electro-hydraulic servo cylinder, as its power actuator, requires low friction, good lateral load resistance and high speed motion. The electro-hydraulic servo cylinder hydrostatic bearing seal guide sleeve is taken as the research object in this paper. By using Fluent software to analyze and contrast the film characteristics of rectangular and I-shaped oil chamber of hydrostatic bearing seal guide sleeve, the relationship between piston rod moving speed, eccentricity, oil film carrying capacity, friction force and leakage volume, as well as the relationship between oil feed flow and oil film bearing capacity, friction force, inlet pressure and leakage volume were analyzed. This study provides a theoretical basis for optimizing the static pressure bearing seal parameters.

Rolling element bearing instantaneous rotational frequency estimation based on EMD soft-thresholding denoising and instantaneous fault characteristic frequency

The accurate estimation of the rolling element bearing instantaneous rotational frequency(IRF) is the key capability of the order tracking method based on time-frequency analysis. The rolling element bearing IRF can be accurately estimated according to the instantaneous fault characteristic frequency(IFCF). However, in an environment with a low signal-to-noise ratio(SNR), e.g., an incipient fault or function at a low speed, the signal contains strong background noise that seriously affects the effectiveness of the aforementioned method. An algorithm of signal preprocessing based on empirical mode decomposition(EMD) and wavelet shrinkage was proposed in this work. Compared with EMD denoising by the cross-correlation coefficient and kurtosis(CCK) criterion, the method of EMD soft-thresholding(ST) denoising can ensure the integrity of the signal, improve the SNR, and highlight fault features. The effectiveness of the algorithm for rolling element bearing IRF estimation by EMD ST denoising and the IFCF was validated by both simulated and experimental bearing vibration signals at a low SNR.

Influence of Structural Parameters of Turbocharger Floating Bearing on Its Dynamic Characteristic Coefficients

The structure parameters in an actual industrial production have a great influence on the coefficient of supercharger floating bearing dynamic characteristics,but there has been little systematic study so far.In this paper,the influence of structural parameters of the turbocharger floating bearing on its dynamic characteristic coefficientsis systematically investigated based on the theories of hydrodynamic lubrication and tribology.The influence of clearance ratio on eccentricity and the influence of internal to external radius ratios,and Sommerfeld number were analyzed.A new formula of responding characteristics of the oil film force caused by the displacement or velocity disturbance was deduced near an equilibrium in the steady state.Applying the newly developed formula,the dynamic characteristic was studied for floating bearings.Regularity for change of oil film stiffness and damping was analyzed with the structural parameters of floating bearing such as radius ratios and eccentricity.It has been found that the clearance ratio increases with eccentricity when the radius ratio is unchanged.The eccentricity decreases with the internal to external radius ratio of floating rings when the clearance ratio is constant.The absolute value of total principal stiffness and total main damping decrease with the clearance ratio and radius ratio of floating rings when the total cross damping is stable.The results and findings in this paper can contribute to nonlinear dynamics designs of turbocharger rotor-bearing systems.