Lie Yu

Dynamic Stiffnesses of Active Magnetic Thrust Bearing Including Eddy-Current Effects

The eddy currents induced in a thrust bearing result not only in a power loss of the system but also in phase lag and a decrease in magnitude of the magnetic force. Therefore, an accurate model including eddy-current effects would be highly beneficial at the design stage. We present a linear model including eddy-current effects for a typical active magnetic thrust bearing (AMTB). We define and calculate the dynamic current stiffness and displacement stiffness using both an analytical method and transient finite element (FE) analysis. We present a simple magnetic circuit model including eddy currents from which the two stiffnesses can be derived analytically. Furthermore, by using a transient analysis of the FE model, flux saturation, leakage, and fringing effects can all be taken into account. We show that the two stiffnesses have the same frequency response characteristics, both in the analytical model and from the results of the linear FE analysis, when the leakage and fringing effects are ignored. Even in the more practical case when the flux saturation, leakage and fringing effects are considered, the two stiffnesses can be considered to have the same frequency response characteristics within the 3 dB bandwidth without introducing much error. The open-loop frequency response of the two stiffnesses derived from the analytical model and the FE model agrees well with the experimental results.

Research on the Static and Dynamic Characteristics of Misaligned Journal Bearing Considering the Turbulent and Thermohydrodynamic Effects

Journal misalignment usually exists in journal bearings that affect nearly all the bearings static and dynamic characteristics including minimum oil film thickness, maximum oil film pressure, maximum oil film temperature, oil film stiffness, and damping. The main point in this study is to provide a comprehensive analysis on the oil film pressure, oil film temperature, oil film thickness, load-carrying capacity, oil film stiffness, and damping of journal bearing with different misalignment ratios and appropriately considering the turbulent and thermo effects based on solving the generalized Reynolds equation and energy equation. The results indicate that the oil thermo effects have a significant effect on the lubrication of misaligned journal bearings under large eccentricity ratio. The turbulent will obviously affect the lubrication of misaligned journal bearings when the eccentricity or misalignment ratio is large. In the present design of the journal bearing, the load and speed become higher and higher, and the eccentricity and misalignment ratio are usually large in the operating conditions. Therefore, it is necessary to take the effects of journal misalignment, turbulent, and thermal effect into account in the design and analysis of journal bearings.

Annealing effects on magnetic properties and strength of organic-silicon epoxy resin-coated soft magnetic composites

Soft magnetic composites (SMCs) can be described as soft magnetic powders covered by electrically insulating layers. In this work, iron powders with high purity and organic-silicon epoxy resin were chosen for good magnetic properties, thermal stability, and mechanical properties, respectively. The effect of amount of resin, different annealing temperatures on the microstructure, and performance of SMCs was investigated. Results show that organic-silicon epoxy resin has excellent properties as dielectric coating materials for coating iron powders and maximum heat-resistant temperature is about 400 ℃. According to magnetic properties and flexural strength analysis, the optimum annealing temperature of organic-silicon epoxy resin-coated composite is 200 ℃. Furthermore, the finite element analysis indicates that the strength of the whole composites is related to the adhesion of resin and iron and the strength of resin itself.

Pressure distribution for multi-lobe bearings using Fourier analysis

During the past decades, researchers have focused a great deal of attention on the lobe bearings because of their superior stability. In this paper, a comprehensive methodology for determining the performances of bearings is developed based on the Fourier analysis. The advantage of this method is no longer to treat each lobe as an individual partial bearing like before, but to take into account the inherent relevance and coupling effects among lobes, etc. This article firstly puts forward universal frameworks of mathematical procedure, within which two multi-lobe journal bearings, namely, three- and four-lobe bearing are investigated. For the bearings with similar topology structure, the results show that the Fourier expansions of oil-film thickness are composed of the same family of harmonic basis functions. And those functions are merely related to the number of bearing lobes N. The results also show that both the oil-film profile and pressure field of the whole bearing completely inherit the periodicity from the periodic bearing structure and own the same period 2π/N commonly. Again, the simulated results construct the corresponding relationship between the expanded terms of oil-film thickness and pressure field. Further, quantitatively analyzing the variations of the pressure component indicates that as the order increases, the maximum of the pressure component decreases gradually. That provides a more convenient approach to obtain a satisfied prediction of the performance of the bearings just by using finite Fourier harmonic terms.

Rotordynamics analysis of a quill-shaft coupling-rotor-bearing system

A quill-shaft coupling-rotor-bearing system is modeled and reported in this paper. The system consists of two rotors connected by a quill-shaft coupling in which each rotor is supported by two bearings. The stiffness matrix of the quill-shaft coupling is deduced and the equation of motion of the system is obtained by using the finite element method. Finally, the rotordynamics analysis of the system is conducted. The numerical results show that more frequency veering points occur for the quill-shaft coupling-rotor-bearing system compared with those of single rotor. In addition, the stiffness of the flexural element has significant effects on the first bending natural frequency of the quill shaft when the length of the quill shaft becomes shorter.

Influence of the component size ratio on densification and magnetic property of soft magnetic composites

To analyze the influence of the component size ratio (matrix/inclusion) on the densification and magnetic property, the equivalent model of SMCs at particle scale was used for static case. The relation of porosity, density against the component sizeratio δ isdeduced. Tocalculatetheeffective permeabilityofthe model, theequivalent magnetic circuitmethod andmagnetic energy method are proposed and compared. The results show that the densification and effective permeability are dependent on the component size ratio. The effect of porosity is even more pronounced for the effective permeability. In addition, the results of this model are consistent with the experimental results.

Effect of Mesh Size of Finite Element Analysis in Modal Analysis for Periodic Symmetric Struts Support

Meshing for finite element analysis accuracy plays a very important part in numerical simulation of Periodic Symmetric Struts Support (PSSS). Different accuracy can be obtained by different element sizes or types. Three element types and eight element sizes are used for comparing the accuracy of modal analysis in this paper. Comparing with the mutual relations of different accuracy, the scientific basis is provided for selecting the correct mesh size and improves the efficiency of numerical calculation in modal analysis.

The effect of compaction parameters and dielectric composition on properties of soft magnetic composites

This paper investigated the effect of compaction parameters and dielectric composition on mechanical, magnetic and electrical properties of iron-organosilicon epoxy resin soft magnetic composites. In this work, iron powders with high purity were covered by an organic material (organosilicon epoxy resin) and then by coupling agent (KH-550). The coated powders were then cold compacted at 600, 800 and 1000 MPa and cured under vacuum respectively. The results show that the saturation magnetic flux density and electrical resistivity are dependent on compaction pressure and resin content. Increase in the organic phase content leads to decrease of the saturation magnetic flux density, while increase of the electrical resistivity. Furthermore, the samples with 0.9 wt% resins + 0.1 wt% coupling agent at compaction pressure of 800 MPa shows better properties than the others.

Modeling of Switching Ripple Currents (SRCs) for magnetic bearings including eddy current effects

In magnetic thrust bearings (MTBs), eddy currents induced in the solid stator and thrust disk not only result in performance degrading of the bearing, but also influence the SRC of the coil when driven by a switching power amplifier. In this paper, a fractional differential equation (FDE) model of the SRC considering the effects of eddy current is proposed and a numerical solution can be obtained from it by a predictor-corrector algorithm. Results from finite element method (FEM) and experiments show its validity. The presented model can be applied to the studies of self-sensing of non-laminated magnetic bearings.

Axial stiffness of a rotating trunnion joint

A trunnion joint is modeled as a circular plate with two types of outer boundary conditions. One is clamped supported and the other is simply supported. Symmetrical bending deflection is produced when an external force acts on the inner side of the circular plate. The governing equations of the circular plate with these two kinds of boundary conditions are solved by using finite difference method, and the axial stiffness of the circular plate is obtained according to the relationship between the external force and the bending deflection of the circular plate. In order to verify the accuracy of the finite difference method, a finite element method was also given. The effects of rotational speed and the ratio of inner radius to outer radius of the circular plate on the axial stiffness are studied. It is shown that the rotational speed can significantly affect the axial stiffness of the trunnion joint for these two cases, especially for a lower ratio of inner radius to outer radius of the circular plate. The axial stiffness increases monotonically with the increase in rotational speed. More specifically, for a lower ratio of inner radius to outer radius of the circular plate, the axial stiffness with the simply supported boundary condition at high rotational speed is more than twice as much as the case without considering the rotational speed. Correspondingly, it is more than one and a half times for the clamped supported boundary condition.