Magnitude Of Eccentricity Research Articles

Study on Stator-Rotor Misalignment in Modular Permanent Magnet Synchronous Machines with Different Slot/Pole Combinations

Addressing stator-rotor misalignment, usually called eccentricity, is critical in permanent magnet (PM) machines since significantly high radial forces can be developed on the bearings, which can trigger a major fault and compromise the structural integrity of the machine. In this regard, this paper aims to provide insight into the unaddressed identification and analysis of the impact of eccentric tolerances on relevant performance indices of permanent magnet synchronous machines (PMSMs) with modular stator core. Static and dynamic eccentricity are assessed for different slot/pole combinations through the finite element method (FEM), and the results are compared with those of PMSMs with a conventional stator core. The unbalanced magnetic forces (UMF), cogging torque, back-emf, and mean torque variations are described and related to the eccentricity magnitude and classification. The main findings indicate that severe radial forces and significant additional cogging torque harmonics are generated because of eccentricity. Additionally, it is found that the main differences between modular PMSMs and conventional PMSMs rely on the value of slots per pole per phase.

Buckling strength and post-ultimate behaviour of lipped channel section short columns under eccentric compression

The paper presents the results of a large experimental testing campaign and of a numerical parametric study on the influence of the load eccentricity on the buckling behaviour and the ultimate strength of thin-walled cold-formed steel columns with lipped channel cross-section subjected to eccentric compression around the major axis. The numerical study was carried out using the finite element method (code Ansys) and the finite strip method (code CUFSM). The selected numerical results were compared with the experimental test results. Some conclusions concerning sensitivity of buckling strength and redundancy of load-carrying capacity in the post-buckling (either elastic–plastic or plastic) range to the magnitude of eccentricity, depending on the eccentricity position according to major axis and column dimensions are derived.

Effects of a tilted flat-ended punch on the receding contact between a graded and a homogeneous layer

This paper considers the receding contact problem between an exponentially graded layer and a homogeneous layer under the indentation of a tilted rigid flat-ended punch. In the presence of an offset load deviated from the symmetry axis of the rigid punch, the contact pressures both under the rigid punch and along the receding contact interface between the layers lose symmetry. Depending on the magnitude of eccentricity, either complete or incomplete contact may take place under the rigid flat-ended punch, whereas a receding type of contact always occurs along the interface separating the graded and the homogeneous layers. Fourier integral transforms help to convert the governing equations and mixed boundary conditions of the double-contact problem into dual Fredholm integral equations of the second kind with Cauchy-type singular kernels. Gauss–Chebyshev and Gauss–Jacobi numerical quadratures are subsequently employed to discretize and collocate the dual singular integral equations, together with the four force and moment equilibrium equations, for the complete and incomplete contact, as well as the transitional status corresponding to the critical load eccentricity. Extensive parametric studies indicate that the critical load eccentricity depends on the property gradation of the graded layer and the layer-thickness ratio, but not on the magnitude of the indentation load. The extent of contact both under the rigid flat-ended punch and along the receding contact interface is also independent of the magnitude of the indentation load. The results suggest reasonable departures from the contact properties of a homogeneous half-plane under a tilted rigid flat-ended punch, indicating the valuable information on optimizing the double-contact properties in terms of the property gradation and layer-thickness ratio under a given eccentricity.

Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator

Within this work, the radial Proportional Derivative (PD-) controller along with the eight-poles electro-magnetic actuator are introduced as a novel control strategy to suppress the lateral oscillations of a non-linear Jeffcott-rotor system. The proposed control strategy has been designed such that each pole of the magnetic actuator generates an attractive magnetic force proportional to the radial displacement and radial velocity of the rotating shaft in the direction of that pole. According to the proposed control mechanism, the mathematical model that governs the non-linear interactions between the Jeffcott system and the magnetic actuator has been established. Then, an analytical solution for the obtained non-linear dynamic model has been derived using perturbation analysis. Based on the extracted analytical solution, the motion bifurcation of the Jeffcott system has been investigated before and after control via plotting the different response curves. The obtained results illustrate that the uncontrolled Jeffcott-rotor behaves like a hard-spring duffing oscillator and responds with bi-stable periodic oscillation when the rotor angular speed is higher than the system’s natural frequency. It is alsomfound that the system, before control, can exhibit stable symmetric motion with high vibration amplitudes in both the horizontal and vertical directions, regardless of the eccentricity magnitude. In addition, the acquired results demonstrate that the introduced control technique can eliminate catastrophic bifurcation behaviors and undesired vibration of the system when the control parameters are designed properly. However, it is reported that the improper design of the controller gains may destabilize the Jeffcott system and force it to perform either chaotic or quasi-periodic motions depending on the magnitudes of both the shaft eccentricity and the control parameters. Finally, to validate the accuracy of the obtained results, numerical simulations for all response curves have been introduced which have been in excellent agreement with the analytical investigations.

Effect of tool eccentricity on the periodic material flow in friction stir welding process

The periodic material flow behavior has been widely considered as one of the most crucial characteristics during friction stir welding (FSW) process, but its formation and evolution mechanisms are still not fully understood. Recently, increasing evidences indicate that the original cause of the periodic feature is supposed to be tool eccentricity, rather than geometrical effect of the tool, which is the traditional viewpoint. In this study, numerical simulation based on computational fluid dynamics (CFD) is employed to investigate the effect of tool eccentricity during FSW. A 3D model is first improved for comparison of the thermal-physics responses around the tool in FSW with and without tool eccentricity. Then, a 2D model with refined mesh and volume of fluid (VOF) technique is proposed for detailed material flow during tool rotating, and several tool eccentricity magnitudes are considered. Particularly, the interrelationships between tool eccentricity magnitude, pin orientation, material flow velocity and marker material distribution around the tool are analyzed to elucidate the formation mechanism of the periodic feature as a result of tool eccentricity in detail. It is demonstrated that the tool eccentricity in FSW causes the transformation of material flow velocity around the tool, especially the evident variation of material flow direction, which starts formation of the periodic feature. Moreover, the numerical result is found to be in good agreement with the experimental observation, which verifies the precision of the present method and further confirms the significance of tool eccentricity on the formation of the periodic material flow behavior in FSW.

Analysis of the work of steps using the eccentricity limiter for drilling wells with a diameter of 393,7 mm

Based on the results of the analysis of theoretical and practical studies of drilling large diameter boreholes, a method is proposed for designing the bottom hole assembly with two rock cutting tools, taking into account geological and technical factors that influence the formation of the well trajectory. Prospects for controlling the direction of the wellbore are substantiated using the limiter of the eccentricity value. The calculation of double-hole assemblies of the bottom of the drill string with different diameters of eccentricity limiters, allowing to achieve eccentricities of 10 mm, 20 mm, 30 mm and 40 mm has been performed. The analysis of the operation of the mentioned bottom hole assemblies when drilling a well to a depth of 900 m is carried out. The analysis is carried out in the field of construction of deep boreholes of large diameter and the efficiency of drilling a pilot hole of a smaller diameter with simultaneous formation of the final diameter using a reamer is substantiated. A brief analysis of modern foreign and domestic studies and publications related to the expansion of the pilot wellbore is presented, as well as the influence of the expansion eccentricity on the elastic-deformation state of the BHA and, as a result, on the deviation of the well is considered. A conclusion is made about the possibility of using the phenomenon of eccentric expansion to control the trajectory of the wellbore. The graphical dependences of the change in the intensity of the borehole deviation during deepening using the eccentricity of the limiter for a specific BHA, including a bit with a diameter of 295.3 mm and a reamer with a size of 393.7 mm, are shown. It is shown that with this type of arrangement at different values ​​of eccentricities, it is possible to achieve the intensity of borehole curvature in the range from 0 deg/10 m to 0.44 deg/100 m, 0075, indicating a change in the direction and magnitude of eccentricity during drilling. The graphical dependences of the change in the zenith angle of the well when deepening it for the assembly of the bottom of the drill string with different diameters of the eccentricity limiter are given. The graphical dependencies indicate that when using stops of different sizes, which make it possible to control the eccentric displacement of the reamer at the final drilling depth of a section of 500 m, it is possible to reduce the increase in the zenith angle of the well from 17.5 degrees to 10 degrees. It is concluded that by using the limiters of the eccentric displacement of the expander relative to the pilot borehole, it is possible to control the deviation of the well during the construction of conditionally vertical and inclined sections.

Critical Hydraulic Eccentricity Estimation in Vertical Turbine Pump Impeller to Control Vibration

In many applications, pumps are tested against standard specifications to define the maximum allowable vibration amplitude limits of a pump. It is essential to identify the causes of vibration and methods to attenuate the same to ensure the safe and satisfactory operation of a pump. Causes of vibration can be classified mainly into mechanical and hydraulic nature. Respective unbalance masses are the two major factors which cause dynamic effects and excitation forces leading to undesirable vibrations. In this paper, the procedure of vibration magnitude measurement of a vertical turbine pump at site and the process of dynamic balancing to measure mechanical unbalance of an impeller are explained. After that, the impact of hydraulic eccentricity on the vibration displacement of a vertical turbine pump has been explained using numerical simulation procedure based on “One-way Fluid Structure Interaction (FSI).” The experimental results from a pump at site are used to compare the numerical results. After the solver validation, the one-way FSI approach is used to find the critical hydraulic eccentricity magnitude of a vertical turbine pump impeller to limit the vibration magnitudes on motor component to less than 100 μm. From the numerical simulations, it is deduced that the critical hydraulic eccentricity should be limited to 400 μm in X and Y direction. The process can be used as a guideline procedure for limiting the hydraulic unbalance in vertical turbine pumps by limiting the hydraulic eccentricity.

On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem

A planar restricted elliptic three-body problem is considered. The motions close to the triangular libration points are studied. The problem parameters (the eccentricity of the orbit of the main attracting bodies and the ratio of their masses) are assumed to lie inside the linear stability region of the libration points. The magnitude of eccentricity is considered small. A linear canonical, periodic in true anomaly transformation is obtained analytically up to the second degree of eccentricity inclusive that reduces the Hamiltonian function of the linearized equations of perturbed motion to real normal form in the vicinity of the libration points. This form corresponds to two harmonic oscillators not connected to one another, with frequencies depending on the problem parameters. In constructing the normalizing canonical transformation, the Depri-Hori method of the perturbation theory of Hamiltonian systems is used. Its implementation in the problem under study relies heavily on computer systems of analytical calculations.

Numerical Investigations of the Savonius Turbine with Deformable Blades

Savonius wind turbines are characterized by various advantages such as simple design, independence of wind direction, and low noise emission, but they suffer from low efficiency. Numerous investigations were carried out to face this problem. In the present paper, a new idea of the Savonius turbine with a variable geometry of blades is proposed. Its blades, made of elastic material, were continuously deformed during the rotor revolution to increase a positive torque of the advancing blade and to decrease a negative torque of the returning blade. In order to assess the turbine aerodynamic performance, a two-dimensional numerical model was developed. The fluid-structure interaction (FSI) method was applied where blade deformations were defined by computational solid mechanics (CSM) simulations, whereas computational fluid dynamics (CFD) simulations allowed for transient flow prediction. The influence of the deformation magnitude and the position of maximally deformed blades with respect to the incoming wind direction were studied. The aerodynamic performance increased with an increase in the deformation magnitude. The power coefficient exceeded Cp = 0.30 for the eccentricity magnitude of 10% and reached 0.39 for the highest magnitude under study. It corresponded to 90% improvement in comparison to Cp = 0.21 in the case of the fixed-shape Savonius turbine.

Analyzing the Effects of Soil-Structure Interactions on the Static Response of Onshore Wind Turbine Foundations Using Finite Element Method

The use of wind turbines to generate electricity has increased in recent years. One of the most important parts of a wind turbine is the foundation, which should be designed accurately because it is influenced by difference forces. Soil cannot carry tension stress; thus, when a wind turbine foundation is applied eccentricity forces, a gap appears between the soil and foundation. The gap will have no positive effect on the ultimate bearing capacity of the foundation. This must be considered when designing the dimensions of an onshore wind turbine on a spread foundation using finite element software in order to avoid error during analysis. In the current study, a spread foundation of an onshore wind turbine was simulated using ABAQUS and PLAXIS-3D software. Based on the results, the effects of Soil-Structure Interaction (SSI), eccentricity of forces, soil strength parameters and the foundation buried depth on static response of the foundation are discussed. The results indicate that the influence of soil-structure interaction is depend on magnitude of eccentricity of forces and depth of foundation, so that soil-structure interaction has little impact on settlement of foundation when eccentricity of forces is less than 1/6 of the diameter of the foundation and this has important effect when the eccentricity forces at an amount exceeding 1/6 of the diameter of the foundation. In addition, this effect decreases with increasing the foundation buried depth and independent of the soil strength parameters (φ´ and C).

Influence of an eccentricity imperfection on the stability and vibration behavior of fluid-conveying functionally graded pipes

An eccentricity imperfection may be occurred in the pipes due to the inappropriate manufacturing process. Hence, the dynamic behavior of such geometrically imperfect pipes is extremely required to be explored and compared with the perfect ones. This work investigates the stability and free vibration of fluid-conveying homogenous and functionally graded (FG) pipes with consideration of eccentricity as a geometric imperfection. Three different fluid-conveying pipes are investigated; (i) the homogenous pipe with an eccentricity imperfection, (ii) the FG pipe without imperfection or concentric FG pipe and, (iii) the fluid-conveying FG pipe with an eccentricity imperfection. The governing equations of the fluid–structure interaction system are derived by including the effect of shear deformation using the Timoshenko beam theory. The finite element method is applied to discretize the governing equations and solve the eigenvalue problem of a clamped-clamped pipe. Consequently, the complex modal analysis is used to obtain the natural frequencies and critical velocities of homogenous and FG pipelines with and without eccentricity imperfection. Finally, the effects of different magnitudes of eccentricity and power-law exponent on the critical fluid velocity are investigated. This investigation is expected to provide more insight for the applications of geometrically imperfect pipes in the pipeline systems.

The role of punch eccentricity in small punch testing

The small punch testing technique under quasi-static loading was examined in the view of punch eccentricity role. It might arise especially when the ball is used as the penetrating tool, instead of hemispherical-ended punch. The austenitic stainless steel AISI 316L was chosen to execute several various “large scale” tests in order to calibrate the multi-linear stress–strain relationship along with the ductile fracture criterion KHPS. All the calibration procedure was performed without using the small punch testing. Then, the model was applied to small punch tests to observe the prediction ability when compared to real small punch experiments. Consequently, a numerical study was conducted to see the role of eccentricity in the case of 2 and 2.5 mm ball diameters used as the penetrating tool. The magnitude of eccentricity up to 0.3 mm was numerically tested. The results showed negligible role of eccentricity for 2 mm ball diameter and minor role for 2.5 mm diameter and studied material.

Numerical evaluation of multilobe bearings using the spectral method

Hydropower rotors and pumps have the specificity to be oriented vertically, meaning that the bearing forces have to be evaluated at each time-step depending on the position of the rotor for dynamical analyses. If the bearing forces cannot be evaluated analytically, a suitable numerical method should be used to calculate the pressure distribution over the bearing domain. This process can be computationally expensive as it should be performed for each discrete time-step. As a result, a comparison between the spectral method, the finite difference method, and the finite element method is performed to investigate which method is more adapted to dynamical analysis of the bearing. It is observed that the spectral method has the advantage of having a reasonable simulation time for any eccentricity magnitude with a moderate number of interpolation points. However, this method should be restricted to simple bearing models such as plain bearings or multilobe bearings due to the advantage of finding a global numerical solution directly on the entire bearing/pad domain.

Unbalanced Magnetic Force Analysis in Eccentric Surface Permanent-Magnet Motors Using an Improved Conformal Mapping Method

This paper introduces an improved conformal mapping (ICM) method for the calculation and analysis of unbalanced magnetic force (UMF) in eccentric surface-mounted permanent-magnet (SMPM) motors considering the static, dynamic, and mixed rotor eccentricities. Having the on-load air gap field components obtained through ICM, and by using the Maxwell Stress Tensor method, the ICM method accurately predicts the on-load components of magnetic local traction and UMF due to PMs, the armature reaction, and the mutual interaction between both fields under the rotor eccentricity. The other purpose of this paper is to illustrate the difference between the influences of static, dynamic, and mixed rotor eccentricities on the UMF using the ICM method. The influence of initial eccentricity angle and the magnitude of eccentricity on the UMF are also investigated under the static, dynamic, and mixed rotor eccentricities. The predicted results obtained through ICM are verified by comparing with the corresponding results obtained through finite element method and the frozen permeability method. The ICM method is also validated by the experiment.

Nonlinear dynamic behaviour of a rotor–foundation system coupled through passive magnetic bearings with magnetic anisotropy – Theory and experiment

In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy) of the magnetic field and the weak nonlinearity of the magnetic forces. Through mathematical modelling the nonlinear equations of motion are established for describing the shaft and bearing housing lateral dynamics coupled via the nonlinear and non-uniform magnetic forces. The equations of motion are solved in the frequency domain by the methods of Finite Difference and pseudo-arclength continuation. The theoretical findings are validated against experiments carried out using a dedicated test-rig and a special device for characterisation of the magnetic anisotropy.The characterisation of the magnetic anisotropy shows that it can be quantified as magnetic eccentricities having an amplitude and a phase, which result in linear and parametric excitation. The magnetic eccentricities are also determined using the steady-state response of the rotor–bearing system due to forcing from the magnetic anisotropies and several levels of mass imbalance. Discrepancies in the results from the two methods in terms of magnetic eccentricity magnitude are due to additional geometric eccentricities in the shaft. The steady-state system response shows clear nonlinear phenomena, e.g. bent resonance peaks, jump phenomena and nonlinear cross-coupling between the two orthogonal directions, especially during counter-phase motion between shaft and bearings. The clear nonlinear behaviour is facilitated by the lack of damping resulting in relatively large vibrations. The overall nonlinear dynamic behaviour is well captured by the theoretical model, thereby validating the modelling approach.

Global Analysis of Gravity Gradient Satellite's Pitch Motion in an Elliptic Orbit

Pitch motion of a gravity gradient satellite in an elliptical orbit is studied. The cell mapping method is employed to find periodic solutions and analyze the global behavior of the system. Stability characteristics of the solutions are established using a point mapping approximation algorithm. The proposed approach does not depend on existence of a small parameter and, therefore, no limitations are imposed on the magnitudes of eccentricity or amplitude of motion. This is in contrast to the perturbation based approaches that require assumptions of small orbital eccentricity and small motion. As a result, stable periodic solutions of twice and three times the orbital period are found for some different eccentricities and inertia parameters. Global behavior and evolution of periodic solutions are also demonstrated using invariant surfaces and bifurcation diagrams.

Crystal structures and enhancement of photoluminescence intensities by effective doping for lithium tantalate phosphors

Crystal structures of (Li0.925Eu3+0.025)TaO3, (Li0.968Eu3+0.032)(Ta0.81Ti0.19)O2.937, (Li0.967Sm3+0.033)(Ta0.89Ti0.11)O2.978, and (Li0.950Sm3+0.033Mg0.017)(Ta0.89Ti0.11)O2.987were investigated by X-ray powder diffraction. The initial structural parameters, taken from those of the isomorphous compound (Li0.977Eu3+0.023)(Ta0.89Ti0.11)O2.968(space groupR3candZ= 6), were refined by the Rietveld method. A pattern-fitting method based on the maximum-entropy method was subsequently used to determine the three-dimensional electron-density distributions (EDDs) that are free from the structural bias. We confirmed that the EDDs are in accord with the resulting structural models, each of which was composed of the [(Ta, Ti)O6] octahedron and [(Li, Eu, Sm, Mg)O12] polyhedron. We compared these polyhedra and found that the prominent difference among these compounds was the centroid-to-(Li, Eu, Sm, Mg) distance (eccentricity) of [(Li, Eu, Sm, Mg)O12]. The high correlation was demonstrated between the magnitude of eccentricity and photoluminescence intensity under near ultraviolet excitation.

Performance of CFRP Wrapped Square Reinforced Concrete Columns Subjected to Eccentric Loading

Abstract Strengthening concrete columns with fibre-reinforced polymers (FRP) has been studied extensively, but the majority of published studies have focused on circular columns. Most concrete columns in the field have square or rectangular cross sections and resist eccentric loading as well. The objective of this study is to investigate the performance of square reinforced concrete (RC) columns wrapped with carbon FRP subjected to eccentric loading. The influence of two parameters was studied including the number of FRP layers and the magnitude of eccentricity. Compression testing was conducted on twelve short square RC columns wrapped with CFRP composites. The columns had a dimension of 200 mm x 200 mm x 800 mm and a round corner with a radius of 34 mm. The results of the study demonstrated that wrapping the square RC columns under eccentric loading with CFRP enhanced their performance by providing higher load carrying capacity and ductility compared to unwrapped RC columns.

Axial and Flexural Performance of Square RC Columns Wrapped with CFRP under Eccentric Loading

AbstractThe majority of studies on fiber-reinforced-polymer (FRP) strengthened concrete columns deal with columns of a circular cross section. However, most concrete columns in the field have square or rectangular cross sections and resist eccentric loads. This paper presents the results of an experimental study on the performance of carbon-fiber-reinforced-polymer (CFRP) wrapped square reinforced concrete (RC) columns under eccentric loading. The influence of the number of CFRP layers, the magnitude of eccentricity, and the presence of vertical CFRP straps were investigated by testing 16 specimens. The specimens had the dimensions 200×200×800 mm and round corners with a radius of 34 mm. Twelve specimens were tested as columns and four specimens as beams. The results of this study showed that CFRP wrapping enhanced the load-carrying capacity and ductility of the columns under eccentric loading. Furthermore, the application of the vertical CFRP straps significantly improved the performance of the columns ...

Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis

The analysis of moiré patterns generated by a pair of circular gratings requires complex computation, especially for high resolution in-plane displacement measurements. In this paper, the Fourier transformation method developed by previous researchers for analyzing the moiré patterns was applied to digitally generated and real moiré patterns. The real moiré patterns were formed by low-frequency gratings, typically used in crack growth monitoring. Due to the failure of the Fourier transformation method when applied to moiré patterns generated by low-frequency gratings, the performance of the recently proposed graphical analysis method that determines the displacement values accurately from the moiré patterns was compared with the Fourier transformation approach. In this method, the moiré patterns were spatially transformed from Cartesian-to-polar coordinate system. The morphological grayscale dilation operation was used to eliminate the residual grating in the transformed pattern and preserve only the moiré fringes. The centerline of each moiré fringe was fitted with a sine function, and the eccentricity magnitude and directions between the two gratings were determined directly from the amplitude and the phase shift of the fitted function. The comparison shows that the proposed graphical analysis method is able to give high in-plane displacement accuracy with a mean error of −0.002mm and 0.451° in the eccentricity magnitude and direction, respectively, without the need for complex computation using Fourier transformation.