Force Of Bearing Research Articles

Evaluation of Seismic Response Considering the Ageing Effect of Rubber and Lead-Rubber Bearings Applied to PSC Box Bridge

The number of aged bridges is increasing so that bridges over 30 years old account for about 11% of all bridges. Consequently, the development of a seismic performance evaluation method that considers the effects of ageing is essential for a seismic retrofitting process for improvement of the seismic safety of existing old bridges. Assessment of the damage situation of bridges after the recent earthquakes in Korea has been limited to the bearings, anchor, and concrete mortar on piers. The purpose of this study is to evaluate the seismic responses of PSC box girder bridges by considering the ageing effect of rubber bearings (RBs) and lead-rubber bearings (LRBs). The modification factor proposed by AASHTO is used to take into account the ageing effect in the bearings. PSC box girder bridges with RBs and LRBs were 3D modeled and analyzed with the OpenSEES program. In order to evaluate the ageing effect of RBs and LRBs, 40 near fault and 40 far field records were used as the input earthquakes. When considering the effect of ageing, the displacement responses and shear forces of bridge bearings (RBs and LRBs) were found to increase mostly under the analytical conditions. It was shown that the effect of ageing is greater in the case of RBs than in the case of LRBs.

Dynamic modeling and comparative analysis of a 3-PRR parallel robot with multiple lubricated joints

This paper presents a methodology to study the dynamic response of a parallel robot with multiple lubricated joints. Based on Gumbel’s boundary conditions, the hydrodynamic force of the journal bearing is calculated with the Pinkus–Sternlicht model. Considering the dynamic loads on the multiple lubricated joints, the Pinkus–Sternlicht model is modified to ensure numerical stability of the solution of the system’s equations. A comparative analysis of four joint force models is presented to show the advantages of the modified model for a 3-PRR (P and R represent prismatic and revolute pairs respectively and the underline of the P represents the actuated joint) parallel robot. The improvement in the numerical stability of the modified Pinkus–Sternlicht model is proven. Subsequently, the dynamic behavior of the 3-PRR parallel robot with multiple lubricated joints is analyzed comprehensively, compared with the 3-PRR parallel robot with multiple dry clearance joints. Simulation results demonstrate the validity of the dynamic methodology containing the modified Pinkus–Sternlicht model for the 3-PRR parallel robot with multiple lubricated joints. This dynamic methodology can illustrate the better periodicity of such parallel robots considering lubricated joints.

Suspension Force Error Source Analysis and Multidimensional Dynamic Model for a Centripetal Force Type-Magnetic Bearing

The traditional modeling methods on suspension force of magnetic bearings are mainly based on static fields analysis, and lack of consideration for the effect of real-time temperature and rotation speed. However, the action area of Maxwell force and the air gap size in the calculation formula of the suspension force dynamically change with temperature rise and rotation speed. Therefore, the accuracy of model results on suspension force is compromised. In this article, taking the centripetal force type-magnetic bearing as an example, the error sources that affect the accuracy of the suspension force are analyzed meticulously. Then, based on the suspension force error sources results, a dynamic model involving multiple dimensional variables is proposed, which includes control current, displacement, temperature, and rotational speed. Superior to the traditional static models, the temperature and rotation speed are integrated into the proposed multidimensional model besides the traditional current and displacement. To prove the validity of suspension force error sources analysis and the accuracy of the proposed model, the dynamic stiffness experiments are carried out. The experiment results show that the multidimensional model is more practical and has higher precision than the traditional static model.

Study on Lubrication and Friction Performance of Grease Lubricated Sliding Bearings

In order to study the friction performance of grease lubricated sliding bearings of construction machinery under long-term radial heavy load, a bearing testing machine was developed to measure the changes of friction force, friction coefficient and temperature rise of such bearings. The testing machine can not only simulate the operation process of bearings under low speed and heavy load conditions, but also evaluate the operation state of grease during grease lubrication. Through durability tests on bearings designed and produced by three different manufacturers, the friction coefficient between bearings and pin shafts can be accurately obtained, the current lubrication and wear conditions of bearings can be detected, the advantages and disadvantages of bearing performance can be judged, and at the same time, reference can be provided for designers to estimate bearing life and optimize design.

НЕЛИНЕЙНЫЕ НОРМАЛЬНЫЕ ФОРМЫ КОЛЕБАНИЙ КОНЕЧНОЭЛЕМЕНТНОЙ МОДЕЛИ РОТОРА НА ШАРИКОПОДШИПНИКАХ

The relevance of the work is due to the increase in power and the minimization of the weight of modern aircraft, which is associated with an increase in dynamic loads on the units and the development of the nonlinearity of dynamic processes in them. The problem of designing devices and units operating at high dynamic loads can be solved by developing and applying in designing nonlinear models and methods for analyzing nonlinear oscillatory processes. The use of nonlinear models and methods in design and calibration calculations makes it possible to predict dynamic processes in those aircraft operating modes that cannot be achieved using linear models. The research aims to develop models and methods for analyzing nonlinear oscillatory processes for designing equipment and aircraft assemblies. The rotors, in which two paddle wheels mounted on the cantilever ends of the shaft, are most often used in engines, turbo-pump rocket units, and turbo coolers of aircraft. The shaft deflections have the same order as the elastic deformations of the bearings. Approximation of the axis of the deformed shaft of such rotor design is difficult to implement by sinusoidal functions, therefore the finite element method is used. The finite elements approximate the areas of the shaft of the constant cross section. Disks and supports are placed in the nodes. The inertia forces and moments of inertia forces of the disks are considered linear boundary conditions at the nodes of finite elements. The elastic forces of bearings are considered non-linear boundary conditions at the nodes. The interpolation polynomials of these finite elements are functions of the bent axis of the beam with unit displacements of the nodal sections. The oscillation equations of the shaft are obtained by the Galerkin method with a simultaneous approximation of differential equations and boundary conditions. For the analysis of free vibrations, we use the method of nonlinear normal modes (NNM), which allow us to reduce the analysis of a system with a finite number of degrees of freedom to an analysis of an oscillator with one degree of freedom. Following this method all phase coordinates are represented as functions of one pair of phase coordinates, they are a generalized displacement which can be chosen arbitrarily and a corresponding generalized velocity. Elements of these functions are represented by Taylor series. The rotors on angular contact ball bearings with axial preload are investigated in the work. The preload is used to eliminate the opening of the gaps between the balls and the racers during vibrations, which can lead to shocks and increased vibrations. For the convenience of using the NNM method, the elastic forces are represented as power series in generalized coordinates. The equation of oscillations for each NNM is solved by the method of harmonic balance. The shapes and backbone curves of free non-linear oscillations of the rotor are constructed.

Permanent magnet thrust bearings for flywheel energy storage systems: Analytical, numerical, and experimental comparisons

A new type of flywheel energy storage system uses a magnetic suspension where the axial load is provided solely by permanent magnets, whereas active magnetic bearings are only used for radial stabilization. This means that the permanent magnet bearing must provide all the axial damping. Furthermore, it must have as low a negative radial stiffness as possible to reduce the workload on the radial active magnetic bearings. Many different mathematical models for determining force, stiffness, and damping of permanent magnet bearings are available in the literature. This work will further develop the most applicable analytical and numerical methods in order to make them directly implementable for designing permanent magnet thrust bearings for flywheel energy storage systems. The outcome is a fast and efficient method for determining force, stiffness, and damping when the bearing setup contains magnetic materials with relative permeability higher than one as well as when it does not. The developed method is validated against numerical and experimental results with good agreement.

Integral definition method to solve magnetic force of axial permanent magnetic bearing

In the design process of the permanent magnetic bearing, the calculation of the magnetic force between the magnetic rings is an important element. Transforming complicated physical problems into mathematical problems by establishing the mathematical model of the magnetic ring is a common method when calculating the magnetic force. In this paper, the equivalent magnetic charge model of a permanent magnet bearing is established by the former’s magnetic charge viewpoint, and the quadratic integral based on this model is solved by the integral definition method. This paper compares the results of integral definition method with those obtained by Monte Carlo method and ANSYS in order to verify the correctness.

Research on the force of radial bearing of a nuclear main pump rotor system by database method

This paper discusses the method of solving the radial sliding bearing force of a nuclear main pump rotor system using the pre-built database. For a sliding bearing with a certain size, the Reynolds equation can be decomposed and be equivalent of the problem of solving the liquid film pressure in both pure rotation and pure extrusion states. A database for solving the bearing force is established by pre-calculating the liquid film pressure of the radial sliding bearing under these two states with different eccentricities. By comparing with three analytical models, the bearing forces obtained by this method are closer to the results obtained by the finite difference method. And compared with the finite difference method, the method is much faster.

Order reduction and bifurcation analysis of a flexible rotor system supported by a full circular journal bearing

Journal bearing has been widely used in the wide range of rotating machineries to support large loads and to add significant damping to the system. Conventionally, its fluid film force is represented by the linear model of spring and damper around its equilibrium position in the vibration analysis of the rotor system. However, the fluid film force of the journal bearing is essentially nonlinear, and it is necessary to consider its nonlinearity to expect the characteristics of the limit cycle at around the instability point. This paper investigated the order reduction and bifurcation analysis of a flexible rotor system supported by a full circular journal bearing. The fluid film force is derived under the conditions of both infinitesimal length approximation and half-Zommerfeld boundary condition, and its polynomial function approximation expression is used. Order reduction in the FEM rotor model retaining the nonlinearity of the journal bearing was performed by utilizing the substructure synthesis method. Then, its bifurcation phenomena at around the instability point are investigated by applying the center manifold theory and using the normal form theory. The influences of various parameters, such as kinematic viscosity, bearing length, and the disk position, on the bifurcation phenomena at around the instability point were investigated and explained. Furthermore, the validity of the derived analytical observation was confirmed by numerical simulation and experiment. By invoking these analytical techniques and obtained results, the bifurcation characteristics can be expected theoretically at the design stage of the journal bearing and rotor system.

Reduction of Sticking in a Linear-Guideway Type Recirculating Ball Bearing

This paper deals with the reduction of sticking in a linear-guideway type recirculating ball bearing (linear bearing), which is the significant increase in the required driving force for a linear bearing in a back-and-forth short stroke operation. First, the driving force of a linear bearing with five carriage-body types (A–E, having different dimensions and shapes) under rolling moment load was measured. Simultaneously, the ball's position in the load zone was observed. The experimental results showed that regardless of the carriage-body types, the increasing rate of the driving force and the interspace (space between balls around the center of the load zone on the raised side) decreases and sticking tends to hardly occur as the maximum linear velocity and the stroke length increase. Also, the occurrence of sticking was affected by the carriage-body types. Finally, to examine the relationship of carriage-body types, carriage-body deformation, and the occurrence of sticking, the carriage-body deformation (caused by preloading and tightening torque of bolts) was calculated by finite element method (FEM). The FEM results showed that carriage-body type, which is more deformable, had a tendency to reduce sticking.

Numerical Determination of Contact Forces in Radial Roller Bearings with Flexible Rings

Four different approaches have been proposed to account for flexibility of the bearing rings and the neighboring parts of the shaft and the housing in computing the radial contact forces acting onto the rolling elements. A numerical example is presented to demonstrate efficacy and performance of the developed models. Their applicability is estimated for various conditions.

Simulation of oil whirl for geared rotor journal bearing system

This study developed a dynamic model of gear-pair system, involving nonlinear oil film force of hydrodynamic bearings and the gear mesh force with backlash. Based on this model, numerical simulations are made about instability led by the oil whirl in geared rotor journal bearing system. By comparing responses between single rotor journal bearing system and geared rotor system, evolution of oil whirl from individual rotor to adjacent geared rotors is examined. The results show that dynamic mesh force can transfer the excitations from the adjacent rotors, making different influences on the stability for individual rotors. The stabilities of the geared rotors are not independent with each other, but coupled by the mesh force. This coupling can be accompanied with tooth separation.

A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves

• A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves is proposed. • The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. • The method facilitates the accurate calculation of the fluid film force of a journal bearing and saves computational costs. • The effects of the bearing parameters on the nonlinear fluid film forces are analyzed. A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves under the cavitation boundary condition is proposed. The pressure distribution of the Reynolds equation of a finitely long journal bearing with axial grooves is expressed as a particular solution and a homogeneous solution. The particular solution and the homogeneous solution are separated, respectively, into an additive form and a multiplicative form by the method of separation of variables. The circumferential separable function of the homogeneous solution can be expanded on the basis of the infinite series of trigonometric functions. The pressure distribution of the particular solution is obtained by the Sommerfeld transformation. The termination positions of the fluid film are determined by the continuity condition. The analytical expressions for the nonlinear fluid film forces of a finitely long journal bearing with two axial grooves are obtained. The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. The effects of the bearing parameters on the nonlinear fluid film forces are analyzed.

Suppression of Self-Excited Vibration by Compensating the Unstable Force of Oil Film Bearing Utilizing Electro-Magnetic Actuator

Suppression of Self-Excited Vibration by Compensating the Unstable Force of Oil Film Bearing Utilizing Electro-Magnetic Actuator

Analysis of Changes in Bearing and Contact Forces for Different Versions of the Gear Drive of a Planetary Mill

Questions connected with the determination of the dynamic loads arising in the mobile components of a planetary mill with a gear drive are considered. The influence of the structural and technological parameters on the magnitude of the loads is analyzed. A horizontal planetary mill with external (respectively, internal) spinning of the grinding drums was selected to conduct the study. Inertial forces that exert a significant influence on the motion were determined in the course of a power calculation of the planetary mill drive. Kinetostatics equations based on the d’Alembert principle were compiled. The angular velocity of the pinion carrier, the relationship between the geometrical parameters and the degree of loading of the drums were varied in the calculations. It was found that the support reaction and the circumferential force both vary according to the law of cosines over a narrow range. A method of calculating the dynamic loads on the support nodes of a planetary mill that takes into account the effect of the maximum number of parameters is developed.

Experimental analysis on force and correction factor of an active magnetic thrust bearing

Active magnetic thrust bearing (AMTB) is a device which is used to support an object by controlling the magnetic field. In practice, there is lot of difference between theoretical force and actual force developed between the stator and rotor of an AMTB. This difference is mainly due to fringing, leakage, variation in material properties, misalignments, vibrations, and temperature effects, etc. The difference is also varying with the air gap between stator and rotor and the current supplied. In this work, an experimental approach has been proposed to study the loss factor and efficiency of an Active Magnetic Thrust Bearing. A prototype of AMTB has been made and experimented at different air gaps. Based on the study of single acting actuator, the control performance of a double actuator has been studied. From the study of single acting actuator efficiency and double acting actuator control performance, an optimum air gap has been suggested.

Dynamic characteristics of triaxial active control magnetic bearing with asymmetric structure

Abstract Supporting forces of magnetic bearings are lower than those of mechanical bearings. In order to solve these problems, this paper proposes a new three-axis active control magnetic bearing (3-axis AMB) with an asymmetric structure where its rotor is attracted only in one axial direction due to a negative pressure of fluid. Our proposed 3-axis AMB can generate a large suspension force in one axial direction due to the asymmetric structure. The performances of our proposed 3-axis AMB are computed through 3-D finite element analysis.

Nonlinear dynamic analysis and experimental verification of a magnetically supported flexible rotor system with auxiliary bearings

In this paper, nonlinear dynamic analysis and experimental verification of a flexible rotor supported on the active magnetic bearings (AMB) are studied. The model of the system is formulated by eight degrees of freedom. This model takes in to account the gyroscopic moments of the disk, geometric coupling of the magnetic actuators and contact forces of the auxiliary bearings. The equations of motion are solved using the Rung–Kutta method. The effects of auxiliary bearings stiffness and rotational speed on the dynamic behavior of the system are investigated by the bifurcation diagrams, dynamic trajectories, power spectra analysis, Poincare´ maps and maximum Lyapunov exponent. In the experimental test rig, two special flexible supports are constructed that can adjust the required stiffness of the auxiliary bearings. The results indicate that the auxiliary bearings stiffness and rotational speed have significant effects on the dynamic responses and can be used as effective control parameters for the system. Good correlation between the experimental and theoretical results is found. Very rich forms of periodic, quasi-periodic, period −4 and chaotic vibrations are observed. The present study can be useful in designing and selection of suitable operating parameters. As a result, the system can avoid the undesirable behavior

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

Dynamic and Thermal Analysis of Rotor Drop on Sleeve Type Catcher Bearings in Magnetic Bearing Systems

The catcher bearing (CB) is a crucial part of the magnetic bearing system. It can support the rotor when the magnetic bearing is shut down or malfunctioning and limit the rotor's position when large vibration occurs. The sleeve bearing has the advantages of a relatively large contact surface area, simple structure, and an easily replaced surface. There are already many applications of the sleeve type CBs in the industrial machinery supported by the magnetic bearings. Few papers though provide thorough investigations into the dynamic and thermal responses of the sleeve bearing in the role of a CB. This paper develops a coupled two-dimensional (2D) elastic deformation—heat transfer finite element model of the sleeve bearing acting as a CB. A coulomb friction model is used to model the friction force between the rotor and the sleeve bearing. The contact force and 2D temperature distribution of the sleeve bearing are obtained by numerical integration. To validate the finite element method (FEM) code developed by the author, first, the mechanical and thermal static analysis results of the sleeve bearing model are compared with the results calculated by the commercial software solidworks simulation. Second, the transient analysis numerical results are compared with the rotor drop test results in reference. Additionally, this paper explores the influences of different surface lubrication conditions, different materials on rotor-sleeve bearing's dynamic and thermal behavior. This paper lays the foundation of the fatigue life calculation of the sleeve bearing and provides the guideline for the sleeve type CB design.