Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅰ:Theoretical Formulation

Ball bearings play an important role in various rotating machineries,but the complicated kinematic and tribological features of ball bearings make many aspects of their operating behaviors still inconclusive.Most theoretical analyses of ball bearings up to date are based on either the hypothesis of race control or other empirical models to determine the ball motion of ball bearings,but none of these strategies can reveal and consequently employ the intrinsic coupling mechanism between the spin and the tangential traction of contacting bodies rolling upon one another.To remedy the deficiency of current analytical models for ball bearing analysis,the rolling contact theory is employed to establish an explicit link between motions and interactions within ball bearings.A differential slip model is established to precisely define the slip component due to the significant curvature of the common contact patches between the ball and inner/outer raceways.The creepage and the spin ratio are formulated to accurately define the relative rigid motion between the ball and the inner/outer raceway.Then a quasi-static analytical model is established that can accurately determine the motions of the balls and races of the ball bearing.It can also give a vivid description of the slip and traction distributions within the contact area.The analytical model can be effectively used to analyze the operational conditions and tribological features of solid-lubricated ball bearings.It can also be used optimize the construction of ball bearings for specific applications.

Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅱ:Results and Discussion

Ball bearings are widely employed mechanical components characterized by high precision and quality,and usually play important roles in various rotary machines and mechanisms.Many advanced applications require a deep understanding of their various kinematic and tribological characteristics that are essential to predict the fatigue endurance,relieve the vibration and minimize the power dissipation of ball bearings in particular applications.An angular contact ball bearing under a specified operating condition is simulated with the quasi-static/creepage analytical model proposed in the preceding article.The results demonstrate that the ball bearing is a statically determinate system.That the balls spin on both inner and outer races means the ball is controlled by neither the inner nor the outer raceway.The friction between the ball and raceway renders the inner and outer contact angles unequal.The larger the coefficient of friction is,the larger the angle deviation.The tangential traction perpendicular to the rolling direction due to the spin induces a gyro-like rotation of the ball with respect to the raceway even if no inertial effects are considered.The tangential elastic compliance of contacting surfaces gives rise to locked areas within the contact patch and transforms the sliding lines from circles into spirals.The differential slip due to the close conformity of the ball and raceway makes the sliding and traction distributions asymmetric,which will influence the location of the spinning center of the ball with respect to the raceway.The quasi-static/creepage model can be used to reveal the operating behaviors of ball bearings running under steady conditions and to optimize the design of ball bearings for specific applications.

THERMOHYDRODYNAMIC LUBRICATION ANALYSIS ON EQUILIBRIUM POSITION AND DYNAMIC COEFFICIENT OF JOURNAL BEARING

The finite element method （FEM） is introduced to calculate the oil film pressure and temperature distribution of a journal bearing. The perturbation is performed directly on the finite element equation. Consequently, the Jacobian matrices of the oil film forces are concisely obtained. The equilibrium position of the bearing with a given static load is found by the Newton-Raphson method. As byproducts, dynamic coefficients are obtained simultaneously without any extra computing time. From the numerical results, it is concluded that the effects of film temperature on stiffness coefficients are bigger than those on damping coefficients. With the increase of rotational speed, the load capacity and the stiffness coefficients of the journal bearing are increased when the eccentricity is small, while decreased when the eccentricity is big.

Seismic-induced surficial failure of cohesive slopes using three-dimensional limit analysis:A case study of the Wangjiayan landslide in Beichuan, China

A seismic-induced landslide is a common geological catastrophe that occurs in nature.The Wangjiayan landslide,which was triggered by the Wenchuan earthquake,is a typical case in point.The Wanjiayan landslide caused many casualties and resulted in enormous property loss.This study constructs a simple surficial failure model based on the upper bound approach of three-dimensional(3D)limit analysis to evaluate the slope stability of the Wangjiayan case,while a traditional two-dimensional(2D)analysis is also conducted as a reference for comparison with the results of the 3D analysis.A quasi-static calculation is used to study the effect of the earthquake in terms of horizontal ground acceleration,while a parametric study is conducted to evaluate the critical cohesion of slopes.Rather than employing a 3D analysis,using the 2D analysis yields an underestimation regarding the safety factor.In the Wangjiayan landslide,the difference in the factors of safety between the 3D and 2D analyses can reach 20%.The sliding surface morphology as determined by the 3D method is similar to actual morphology,and the parameters of both are also compared to analyze the reliability of the proposed 3D method.

Developing a novel big dataset and a deep neural network to predict the bearing capacity of a ring footing

The accurate prediction of the bearing capacity of ring footings,which is crucial for civil engineering projects,has historically posed significant challenges.Previous research in this area has been constrained by considering only a limited number of parameters or utilizing relatively small datasets.To overcome these limitations,a comprehensive finite element limit analysis(FELA)was conducted to predict the bearing capacity of ring footings.The study considered a range of effective parameters,including clay undrained shear strength,heterogeneity factor of clay,soil friction angle of the sand layer,radius ratio of the ring footing,sand layer thickness,and the interface between the ring footing and the soil.An extensive dataset comprising 80,000 samples was assembled,exceeding the limitations of previous research.The availability of this dataset enabled more robust and statistically significant analyses and predictions of ring footing bearing capacity.In light of the time-intensive nature of gathering a substantial dataset,a customized deep neural network(DNN)was developed specifically to predict the bearing capacity of the dataset rapidly.Both computational and comparative results indicate that the proposed DNN(i.e.DNN-4)can accurately predict the bearing capacity of a soil with an R2 value greater than 0.99 and a mean squared error(MSE)below 0.009 in a fraction of 1 s,reflecting the effectiveness and efficiency of the proposed method.

Fractional Envelope Analysis for Rolling Element Bearing Weak Fault Feature Extraction

The bearing weak fault feature extraction is crucial to mechanical fault diagnosis and machine condition monitoring. Envelope analysis based on Hilbert transform has been widely used in bearing fault feature extraction. A generalization of the Hilbert transform, the fractional Hilbert transform is defined in the frequency domain, it is based upon the modification of spatial filter with a fractional parameter, and it can be used to construct a new kind of fractional analytic signal. By performing spectrum analysis on the fractional envelope signal, the fractional envelope spectrum can be obtained. When weak faults occur in a bearing, some of the characteristic frequencies will clearly appear in the fractional envelope spectrum. These characteristic frequencies can be used for bearing weak fault feature extraction. The effectiveness of the proposed method is verified through simulation signal and experiment data. © 2017 Chinese Association of Automation.

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.

Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

Design and Analysis of a Magnetic Bearings with Three Degrees of Freedom

The current research of supporting and transmission system in flywheel energy storage system(FESS) focuses on the low consumption design. However, friction loss is a non-negligible factor in the high-speed but lightweight FESS energy and momentum storage with mechanical-type supporting system. In order to realize the support system without mechanical loss and to maximize the e ciency of the flywheel battery, a permanent magnet biased magnetic bearings(PMBMB) is applied to the FESS with the advantages of low loss, high critical speed, flexible controllability and compact structure. In this frame, the relevant research of three degrees of freedom(3-DOF) PMBMB for a new type FESS is carried out around the working principle, structural composition, coupling characteristics analysis, mathematical model, and structural design. In order to verify the performance of the 3-DOF PMBMB, the radial force mathematical model and the coupling determination equations of radial two DOF are calculated according to an equivalent magnetic circuit, and radial–axial coupling is analyzed through finite element analysis. Moreover, a control system is presented to solve the control problems in practical applications. The rotor returns to the balanced position in 0.05 s and maintains stable suspension. The displacement fluctuation is approximately 40 μm in the y direction and 30 μm in the x direction. Test results indicate that the dynamic rotor of the proposed flywheel energy storage system with PMBMB has excellent characteristics, such as good start-of-suspension performance and stable suspension characteristics. The proposed research provides the instruction to design and control a low loss support system for FESS.

A finite element analysis of a large thrust elastic metal-plastics bearing bush for a hydraulic turbine

Presents the study on the pressure and friction fields of the lubricant film on the surface of a large thrust elastic metal plastic bearing bush in a hydraulic turbine using the method of finite element analysis and the stress and displacement fields in the vertical direction of the bush surface obtained to provide a theoretical basis for the design of contour lines and investigation into the causes for destruction of bushes, and concludes with test results that 1) the stress on the surface of the bush is not uniform; 2) a tension stress tends to occur near the oil ingress and egress edges but it is minor; 3) the biggest displacement in the vertical direction appears where x=84 and Y=1 153 and has a value of 0.022 mm; 4) the deformation of the bearing bush is harmful to the maintenance of lubricant film.

Seismic bearing capacity of strip footing on partially saturated soil using modal response analysis

The present study proposes a novel and simplified methodology to assess the seismic bearing capacity(SBC) of a shallow strip footing by incorporating strength non-linearity arising due to partial saturation of a soil matrix. Furthermore, developed methodology incorporates the modal response analysis of soil layers to assess SBC. A constant matric suction distribution profile has been considered throughout the depth of the soil. The Van Genuchten equation and corresponding fitting parameters have been considered to quantify matric suction in the analysis. SBC has been obtained for three different geomaterials;viz. sand, fly ash and clay, based on their predominant grain size and diverse soil water characteristics curve(SWCC) attributes. Variation of SBC with different modes of vibration and damping ratio are reported for ranges of matric suction pertinent to the geomaterials considered in the study. The relative significance of matric suction on SBC has been reported for suction values within the transition zone of each geomaterial. It is observed that the SBC of sand is drastically reduced, with matric suction reaching beyond the residual suction value. The SBC of fly ash remains constant beyond the residual suction value, whereas the SBC of clay shows an increasing trend toward the practical range of matric suction values.

Numerical analysis on bearing capacity of middle pylon caisson foundation of Taizhou Bridge

Because of the computation difficulty of the beating capacity of large underwater caisson foundation on thick overburden layer ground, the geotechnieal software FLAC3D was utilized in the 3D numerical analysis on the bearing capacity of middle pylon foundation. From the computational results, it is concluded that the caisson foundation has a good bearing capacity on thick overburden layer ground and the beating capacity can be improved assuming that the soil near the area of basal comer is reinforced.

Resonance analysis of single DOF parameter-varying system of magnetic-liquid double suspension bearing

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.

Simulation Analysis Module of High-speed Rail Bearings Based on Secondary Development in ADAMS

This paper develops a strong secondary development based on ADAMS feature which creates high-speed rail bearings for simulation analysis module. This thesis is in the case of non-circular pattern instructions of how to achieve rapid roller modeling, with analysis of functions and parameters required for the design of the simulation module of the high-speed rail bearing, as well as the design of dialog boxes, the environment and file structure. The specific modules is based on the secondary development language provided by ADAMS ! View. Through the menus, dialog boxes which input parameters, it can achieve high iron bearing automatic modeling, dynamic analysis and post-processing to simplify the analysis of high-speed rail bearing operations, as well as improving the high-speed rail bearing development efficiency.

Stability Analysis of Space Compcoite Structore and Its Ultimate Bearing Capacity

In this paper, using incremental equilibrium equation, the authors have studiedthe effeet of ultimate bearing capacity of every component on structuralstability, and discussed the stability analysis method for space compositestructures. With the help of the test results for the concrete filled ateel tubeskeleton of the long-spen RC arch bridse, it is proved that the proposed methodis accurate and reliable.

Chemical Analysis Method for Carbon Bearing Refractory Products——Determination of the Total Carbon by Combustion Gravimetric Method

GB/T 13245-91 1 Theme and Scope This standard specifies the method abstract, reagents, apparatus, specimen, analyzing procedure, result calculation and permissible tolerance used for determination of the total carbon with combustion gravimetric method.

Finite Element Analysis of 6300 Deep Groove Ball Bearing

Rolling bearing is widely used in mechanical support, its general components are the inner ring, outer ring, the ball, retainer etc.. Now many companies in developed countries and university in the rolling bearing as the research object, and has made great progress in design theory, the experiment method and production technology etc. We will use the finite element ANSYS to establish the model of deep groove ball bearing. Through the contact analysis, we can get the contact stress between the rings and balls, strain, contact state, penetration, sliding distance and the friction stress distribution. These values are compared to the theoretical values with Hertz theory, and they have better consistency, provide the good theoretical basis for the optimization design of rolling bearings.

Theoretical Analysis of Bearing Capacity of Shallowly Embeded Rectangular Footing of Marine Structures

In this paper, the finite element analysis software ABAQUS is used to analyze the ultimate bearing capacity of three-dimensional rectangular footing of marine structures. The deformation law and the failure mode of homogeneous seabed soil beneath the rectangular footing are analyzed in detail. According to the equivalent plastic strain of soil under rectangular footing, an allowable velocity field of homogeneous seabed soil is reasonably constructed. Based on the plastic limit analysis theory of soil mass and by using the Mohr-Coulomb yield criterion, an upper bound solution of the ultimate bearing capacity of three-dimensional rectangular footing on general homogeneous seabed soil is derived, and a correction factor of ultimate bearing capacity of three-dimensional rectangular footing is given. To verify the rationality and applicability of this theoretical solution, some numerical solutions are achieved using the general-purpose FEM analysis package ABAQUS, and comparisons are made among the derived upper bound solution, the solution of Vesic, and the solution of Salgado et al. The results indicate that the upper bound solution of the three-dimensional shallowly embedded rectangular footing proposed in this paper is accurate in calculating the bearing capacity of homogeneous seabed soil. For undrained saturated clay foundation and sandy foundation with smaller internal friction angle, this upper bound solution can evaluate the ultimate bearing capacity of rectangular footing; with the gradual increase of the internal friction angle of the soil, the ultimate bearing capacity of the proposed upper bound solution is slightly higher than that of the rectangular footing.

MODEL MEASUREMENT AND ANALYSIS OF ROTOR BEARING SYSTEM OF OE-SPINNING

This paper describes a CAD compatible software which can conduct model measurementand analysis on a dedicated computer system.This system which can provide modal testing andanalysis capability is also demonstrated briefly.It addresses four main tasks:(1)modal testingand data acquisition,(2)data analysis and correlation,(3)output of modal analysis results,(4)predictions of modal parameters using Structural Dynamic Modification (SDM)software.

Analysis on Bearing Capacity of Tunnel-Type Anchorage of a Long-Span Suspension Bridge

Due to complicated rock structure and environment, a prototype test for a tunnel-type anchorage is infeasible. Based on the rock mass parameters from tests, a three-dimensional （3D） elastoplastic analysis was performed to simulate the influence of the construction procedure of Siduhe bridge with tunnel-type anchorage （TTA） in Hubei Province, China. The surrounding rock and concrete anchorage body were simulated by 8 nodes 3D brick elements. The geostatic state of the complex geometric structure was established with initial data. The in-situ concrete casting of the anchorage body and excavation of the rock mass were simulated by tetrahedral shell elements. The results show that the surrounding rock is in an elastic state under the designed cable force. The numerical overloading analysis indicates that the capacity of the surrounding anchorage is 7 times that of the designed cable force. The failure pattern shows that two anchorage bodies would be pulled out in the end. The maximum shear stress appears 10 m before the back anchorage face. The maximum range influenced by the TTA under ultimate loads is about 16 m.