Analytical modeling of active magnetic bearing geometry

The aim of this paper is to present a new graphical approach to the shape design of the active magnetic bearing (AMB) stator. The AMB is a tool to levitate the rotor without contact. The standard design method uses a computer-aided design (CAD) software in the modeling process. Therefore the designed AMB shape consists of graphical primitives like lines and arcs with fixed properties. For the advanced interdisciplinary analysis of the AMB construction the shape generation and modifications ought to be done automatically. The proposed method is based on mathematical analysis and representation of the AMB stator by curves. Second and third order Bézier curves given in polynomial and rational form are compared to the circle and arc based arcs. The fitting quality is considered for the selection of the appropriate arc representation. The obtained shapes are ready to be used in the magnetic field analysis and optimization procedures to find an optimal form of the AMB construction. The author’s experience in modeling and vector graphics was a motivation to look at the AMB construction from mathematical and programming point of view. The AMB components are modeled with parametric curves under constraints defined by the AMB static and dynamic properties. Such a described 2D or 3D model can be generated automatically in a programming way for a wide range of AMB configurations in further research. Selected configurations are presented to show features of the proposed method and realized algorithm. The selected features of the proposed solution as well as feedback from industry are discussed.     

Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance

A rotor–active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic non-linearities under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response of two modes of a rotor–AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Rung–Kutta method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported.     

A network approach to the modelling of active magnetic bearings

The modelling of active magnetic bearings based on a network approach is considered. Unlike in the standard modelling approach, where a linearization of the current-force relation for the centred shaft position is used, network models permit to include the position dependence of the bearing force in the force model. This becomes necessary when model based controllers are used to stabilize a magnetically supported shaft in tracking applications.

The approach is based on the well known application of network models to magnetic circuits. Further simplifying assumptions are discussed which allow one to obtain a network with a limited number of lumped parameters describing the magnetic behaviour of a magnetic bearing. The modelling of a combined radial and axial bearing serves as an example for the application of the proposed approach. Furthermore, the fitting of the network based model to measured characteristic force curves is discussed. In this context, a method for including saturation effects in the model is sketched.     

基于随机滤波法的滚动轴承剩余寿命预测

使用剩余寿命描述滚动轴承的潜在状态,基于随机滤波方法建立滚动轴承的剩余寿命预测模型,给出了建模步骤和方法,并讨论了模型的参数估计问题.实例分析结果验证了该建模方法和参数估计方法的有效性和准确性.     

Grain boundary sliding during ambient-temperature creep in hexagonal close-packed metals

Even at ambient temperature or less, below their 0.2% proof stresses all hexagonal close-packed metals and alloys show creep behaviour because they have dislocation arrays lying on a single slip system with no tangled dislocation inside each grain. In this case, lattice dislocations move without obstacles and pile-up in front of a grain boundary. Then these dislocations must be accommodated at the grain boundary to continue creep deformation. Atomic force microscopy revealed the occurrence of grain boundary sliding (GBS) in the ambient-temperature creep region. Lattice rotation of 5° was observed near grain boundaries by electron backscatter diffraction pattern analyses. Because of an extra low apparent activation energy of 20 kJ/mol, conventional diffusion processes are not activated. To accommodate these piled-up dislocations without diffusion processes, lattice dislocations must be absorbed by grain boundaries through a slip-induced GBS mechanism.     

Analysis of slip activity and heterogeneous deformation in tension and tension-creep of Ti–5Al–2.5Sn (wt %) using in-situ SEM experiments

The deformation behavior of a Ti–5Al–2.5Sn (wt %) near-α alloy was investigated during in-situ deformation inside a scanning electron microscope. Tensile experiments were performed at 296?K and 728?K (≈0.4?T _m), while tensile-creep experiments were performed at 728?K and 763?K. Active deformation systems were identified using electron backscattered diffraction-based slip trace analysis. Both basal and prismatic slip systems were active during the tensile experiments. Basal slip was observed for grains clustered around high Schmid factor orientations, while prismatic slip exhibited less dependence on the crystallographic orientation. The tension-creep experiments revealed less slip but more development of grain boundary ledges than in the higher strain rate tensile experiments. Some of the grain boundary ledges evolved into grain boundary cracks, and grain boundaries oriented nearly perpendicular to the tensile axis formed ledges earlier in the deformation process. Grain boundaries with high misorientations also tended to form ledges earlier than those with lower misorientations. Most of the grain boundary cracks formed in association with grains displaying hard orientations, where the c-axis was nearly perpendicular to the tensile direction. For the tension-creep experiments, pronounced basal slip was observed in the lower-stress creep regime and the activity of prismatic slip increased with increasing creep stress and temperature.     

Effect of solute atoms on grain boundary sliding in magnesium alloys

The effect of solid-solution alloying on grain boundary sliding (GBS) was investigated using pure magnesium and six kinds of Mg–X (X?=?Ag, Al, Li, Pb, Y and Zn) dilute binary solid solutions with an average grain size of 10?µm. A sharp increase in damping capacity caused by GBS was observed above a certain temperature. The temperature at which a sharp increase in damping capacity occurred depended on the alloying element. The addition of Y and Ag markedly increased the onset temperature (more than 100?K) for a sharp increase in damping capacity, whereas the addition of Zn, Al and Li slightly increased the onset temperature (less than 50?K) as compared with that for pure magnesium. Tensile tests at a temperature of 423?K revealed that the higher the onset temperature, the lower the strain rate sensitivity of the flow stress. It is suggested that the former elements (Y and Ag) are more effective in suppressing GBS in magnesium alloys than the latter ones (Zn, Al and Li). The suppression of GBS was associated with low grain boundary energy, and the extent to which the energy is reduced depended on the alloying element. It was suggested that the change in the lattice parameter (the so-called c/a ratio) affects the grain boundary energy, and thus, the occurrence of GBS.     

Wear resistance of CuZr-based amorphous-forming alloys against bearing steel in 3.5% NaCl solution

Abstract

To investigate the amorphous-crystalline microstructure on the tribocorrosion of bulk metallic glasses (BMGs), 6 mm diameter rods of Cu_46-xZr₄₇Al₇Ag_x (x = 0, 2, 4) amorphous-forming alloys with in situ crystalline and amorphous phases were fabricated by arc-melting and Cu-mould casting. Using a pin-on-disc tribometer, the tribo-pair composed by CuZr-based amorphous-forming alloys and AISI 52100 steel were studied in 3.5% NaCl solution. With the increase of Ag content from 0 to 4 at.%, the compressive fracture strength and the average hardness decrease firstly and then increase. Moreover, 4 at.% Ag addition increases the amount of amorphous phase obviously and inhibits the formation of brittle crystalline phase, resulting in the improvement of corrosion resistance and the corrosive wear resistance. The primary wear mechanism of the BMG composites is abrasive wear accompanying with corrosive wear. The tribocorrosion mass loss of Cu₄₂Zr₄₇Al₇Ag₄ composite is 1.5 mg after 816.8 m sliding distance at 0.75 m s^?1 sliding velocity under 10 N load in NaCl solution. And the volume loss evaluated from the mass loss is about 20 times lower than that of AISI 304 SS. Thus, Cu₄₂Zr₄₇Al₇Ag₄ composite may be a good candidate in the tribology application under marine environment.     

Synchronization of chaotic fractional-order systems via active sliding mode controller

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master-slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü-Lü systems, synchronizing fractional order Chen-Chen systems and synchronizing fractional-order Lü-Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.