Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeledand analyzed in a simple and novel way under three-dimensional cylindricalcoordinates. The inherent three-dimensional characteristics of the deviceare comprehensively considered, and the governing equations are solved bysimplifying the boundary conditions. The axial magnetization of the sectorshapedpermanent magnets is accurately described in an algebraic form bythe parameters, which makes the physical meaning more explicit than thepurely mathematical expression in general series forms. The parameters of theBessel function are determined simply and the magnetic field distribution ofpermanent magnets and the air-gap is solved. Furthermore, the field solutionsare completely analytical, which provides convenience and satisfactoryaccuracy for modeling a series of electromagnetic performance parameters,such as the axial electromagnetic force density, axial electromagnetic force,and electromagnetic torque. The correctness and accuracy of the analyticalmodels are fully verified by three-dimensional finite element simulations and a15 kW prototype and the results of calculations, simulations, and experimentsunder three methods are highly consistent. The influence of several designparameters on magnetic field distribution and performance is studied and discussed.The results indicate that the modeling method proposed in this papercan calculate the magnetic field distribution and performance accurately andrapidly, which affords an important reference for the design and optimizationof axial-flux permanent magnet drivers.

Three-dimensional Analytical Modeling of Axial Flux Permanent Magnets Maglev Motor

The three-dimensional(3D)analytical model of the magnetic field in an Axial Flux Permanent Magnets Maglev Motor(AFPMMM)is proposed and investigated the influence of the structural parameters on electromagnetic characteristics.Firstly,the topology and working principle of the AFPMMM is introduced,and the model is transferred into a mathematical model in 3D cartesian coordinate.Then,the volume integral method and equivalent current sheets model is applied to find the 3D magnetic field distribution function of Halbach rotor.A unified form expression can be obtained by two dimensional discrete fourier transform(2-D DFT)is applied on the 3D magnetic field distribution function.Thirdly,the conductive and nonconductive regions of AFPMMM will be formulated by the second order vector potential(SOVP)to built the 3D analytic model.The expression of the lift force,torque and power losses was derived.Besides,the relationship between electromagnetic characteristics and structural parameters of the AFPMMM were analyzed based on 3D analytic model and validated using the 3D finite element analysis(FEA).Finally,the experiments based on a small scale prototype are carried out to verify the analytical results.

Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

Analytical model for predicting time-dependent lateral deformation of geosynthetics-reinforced soil walls with modular block facing

To date,few models are available in the literature to consider the creep behavior of geosynthetics when predicting the lateral deformation(d)of geosynthetics-reinforced soil(GRS)retaining walls.In this study,a general hyperbolic creep model was first introduced to describe the long-term deformation of geosynthetics,which is a function of elapsed time and two empirical parameters a and b.The conventional creep tests with three different tensile loads(Pr)were conducted on two uniaxial geogrids to determine their creep behavior,as well as the a-Pr and b-Pr relationships.The test results show that increasing Pr accelerates the development of creep deformation for both geogrids.Meanwhile,a and b respectively show exponential and negatively linear relationships with Pr,which were confirmed by abundant experimental data available in other studies.Based on the above creep model and relationships,an accurate and reliable analytical model was then proposed for predicting the time-dependent d of GRS walls with modular block facing,which was further validated using a relevant numerical investigation from the previous literature.Performance evaluation and comparison of the proposed model with six available prediction models were performed.Then a parametric study was carried out to evaluate the effects of wall height,vertical spacing of geogrids,unit weight and internal friction angle of backfills,and factor of safety against pullout on d at the end of construction and 5 years afterwards.The findings show that the creep effect not only promotes d but also raises the elevation of the maximum d along the wall height.Finally,the limitations and application prospects of the proposed model were discussed and analyzed.

Three-dimensional structural models,evolution and petroleum geological significances of transtensional faults in the Ziyang area,central Sichuan Basin,SW China

With drilling and seismic data of Transtensional(strike-slip)Fault System in the Ziyang area of the central Sichuan Basin,SW China plane-section integrated structural interpretation,3-D fault framework model building,fault throw analyzing,and balanced profile restoration,it is pointed out that the transtensional fault system in the Ziyang 3-D seismic survey consists of the northeast-trending F_(I)19 and F_(I)20 fault zones dominated by extensional deformation,as well as 3 sets of northwest-trending en echelon normal faults experienced dextral shear deformation.Among them,the F_(I)19 and F_(I)20 fault zones cut through the Neoproterozoic to Lower Triassic Jialingjiang Formation,presenting a 3-D structure of an“S”-shaped ribbon.And before Permian and during the Early Triassic,the F_(I)19 and F_(I)20 fault zones underwent at least two periods of structural superimposition.Besides,the 3 sets of northwest-trending en echelon normal faults are composed of small normal faults arranged in pairs,with opposite dip directions and partially left-stepped arrangement.And before Permian,they had formed almost,restricting the eastward growth and propagation of the F_(I)19 fault zone.The F_(I)19 and F_(I)20 fault zones communicate multiple sets of source rocks and reservoirs from deep to shallow,and the timing of fault activity matches well with oil and gas generation peaks.If there were favorable Cambrian-Triassic sedimentary facies and reservoirs developing on the local anticlinal belts of both sides of the F_(I)19 and F_(I)20 fault zones,the major reservoirs in this area are expected to achieve breakthroughs in oil and gas exploration.

Shear behavior of single-joint bolted sandstone subjected to dryewet cycles:Experimental and analytical approaches

A series of direct shear tests under constant normal loading conditions were carried out on specimens of bolted sandstone single-joint treated with different numbers of dryewet cycles.The experimental results show that the peak shear strength and shear stiffness of bolted sandstone joints were significantly reduced after 12 dryewet cycles.The decrease in the shear strength of rough joints is more significant than that of flat joints.Due to the decrease in the strength of the surrounding rock,the deformation characteristics of the bolts are significantly affected by the number of dryewet cycles performed.With an increase in the number of dryewet cycles,the plastic hinge length of the bolt gradually increases,resulting in an increase in the corresponding shear displacement when the bolt breaks.Compared with the tensileeshear failure mode of the bolts in flat joints,the tensileebending failure mode arises for bolts in rough joints.A shear curve model describing the whole process of bolted rock joints is established based on the deterioration of rock mechanical parameters caused by dry‒wet cycles.The model proposed considers the change in the friction angle of the joint surface with the shear displacement,which is applied to the derivation of the model by introducing the dynamic evolutionary friction angle parameter.The reasonably good agreement between a predicted curve and the corresponding experimental curve indicates that this method can effectively predict the shear strength of a bolted rock joint involving rough joint under dryewet cycling conditions.

Consolidation of high replacement ratio stone column-reinforced ground:Analytical solutions incorporating clogging effect

The utilization of stone columns has emerged as a popular ground improvement strategy,whereas the drainage performance can be adversely hampered by clogging effect.Despite the ample progress of calculation methods for the consolidation of stone column-improved ground,theoretical investigations into the clogging effect have not been thoroughly explored.Furthermore,it is imperative to involve the column consolidation deformation to mitigate computational error on the consolidation of composite ground with high replacement ratios.In this context,an analytical model accounting for the initial clogging and coupled time and depth-dependent clogging of stone columns is established.Then,the resulting governing equations and analytical solutions are obtained under a new flow continuity relationship to incorporate column consolidation deformation.The accuracy and reliability of the proposed model are illustrated by degradation analysis and case studies with good agreements.Subsequently,the computed results of the current study are juxtaposed against the existing models,and an in-depth assessment of the impacts of several crucial parameters on the consolidation behavior is conducted.The results reveal that ignoring column consolidation deformation leads to an overestimate of the consolidation rate,with maximum error reaching up to 16%as the replacement ratio increases.Furthermore,the initial clogging also has a significant influence on the consolidation performance.Additionally,the increment of depth and time-clogging factors a and b will induce a noticeable retardation of the consolidation process,particularly in the later stage.

An improved analytical solution for solving the shield tunnel uplift problem

The problem of shield tunnel uplift is a common issue in tunnel construction.Due to the decrease in shear stiffness at the joints between the rings,uplift is typically observed as bending and dislocation deformation at these joints.Existing modeling methods typically rely on the Euler-Bernoulli beam theory,only considering the bending effect while disregarding shear deformation.Furthermore,the constraints on the shield tail are often neglected in existing models.In this study,an improved theoretical model of tunnel floating is proposed.The constraint effect of the shield machine shell on the tunnel structure is considered using the structural forms of two finite long beams and one semi-infinite long beam.Furthermore,the Timoshenko beam theory is adopted,providing a more accurate description of tunnel deformation,including both the bending effect and shear deformation,than existing models.Meanwhile,the buoyancy force and stratum resistance are calculated in a nonlinear manner.A reliable method for calculating the shear stiffness correction factor is proposed to better determination of the calculation parameters.The proposed theoretical model is validated through five cases using sitemonitored data.Its applicability and effectiveness are demonstrated.Furthermore,the influences of soil type,buried depth,and buoyancy force on the three key indicators of tunnel floating(i.e.the maximum uplift magnitude,the ring position with the fastest uplift race,and the ring position with the maximum uplift magnitude)are analyzed.The results indicate that the proposed model can provide a better understanding of the floating characteristics of the tunnel structure during construction.

Effects of three-dimensional quality assessment nursing intervention on efficacy and disease management of patients undergoing esophageal cancer surgery

BACKGROUND Esophageal cancer is one of the most common malignant tumors.The three-dimensional quality structure model is a quality assessment theory that includes three dimensions:Structure,process,and results.AIM To investigate the effects of nursing interventions with three-dimensional quality assessment on the efficacy and disease management ability of patients undergoing esophageal cancer surgery.METHODS In this prospective study,the control group received routine nursing,and the intervention group additionally received a three-dimensional quality assessment intervention based on the above routine care.Self-efficacy and patient disease management abilities were evaluated using the General Self-Efficacy Scale(GSES)and Exercise of Self-Care Agency scale,respectively.IBM SPSS Statistics for Windows,version 17.0,was used for the data processing.RESULTS This study recruited 112 patients who were assigned to the control and experi-mental groups(n=56 per group).Before the intervention,there was no significant difference in GSES scores between the two groups(P>0.05).After the inter-vention,the GSES scores of both groups increased,with the experimental group showing higher values(P<0.05).At the time of discharge and three months after discharge,the scores for positive attitudes,self-stress reduction,and total score of health promotion in the experimental group were higher than those in the control group(P<0.05).CONCLUSION The implementation of a three-dimensional quality structure model for postoperative patients with esophageal cancer can effectively improve their self-management ability and self-efficacy of postoperative patients.

Research on Three-Dimensional Simulation of the Internal Arc Gear Skiving

Aiming at the problems that the simulation accuracy which is reduced due to the simplification of the model,a three-dimensional simulation method based on solid modeling is being proposed.By analyzing the motion relationship and positional relationship between the caries knife and the workpiece,the coordinate system of the caries machining was established.With the MATLAB software,the cutting edge model and the blade sweeping surface model of the boring cutter are sequentially established.Boolean operation is performed on the blade swept surface formed by the tooth cutter teeth with time t and the workpiece tooth geometry as well as the undeformed three-dimensional chip geometry model and the instantaneous cogging geometry model are obtained at different times.Through the compare between gear end face simulation tooth profile and the theoretical inner arc tooth profile,we verified the accuracy and rationality of the proposed method.

Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Study of the geomagnetic field's regional gradients in Chinese continent using three-dimensional surface Spline model

We combined domestic ground-based and satellite magnetic measurements to create a regional three-dimensional surface Spline(3DSS)gradient model of the main geomagnetic field over the Chinese continent.To improve the precision of the model,we considered the data gap between the ground and satellite data.We compared and analyzed the results of the Taylor polynomial,surface Spline,and CHAOS-6(the CHAMP,?rsted and SAC-C model of Earth’s magnetic field)gradient models.Results showed that the gradients in the south-north and east-west directions of the four models were consistent.The 3DSS model was able to express not only gradients at different altitudes,but also average gradients inside the research area.The two Spline models were able to capture more information on gradient anomalies than were the fitted models.Strong local anomalies were observed in northern Xinjiang,Beijing,and the junction area between Jiangsu and Zhejiang,and the total intensity F decreased whereas the altitude increased.The gradient decreased by 21.69%in the south-north direction and increased by 11.78%in the east-west direction.In addition,the altitude gradient turned from negative to positive while the altitude increased.The Spline model and the two fitted models differed mainly in the field sources they expressed and the modeling theory.

Analytical model of 2D leakoff in waterflood-induced fractures

Waterflood-induced fractures,also known as self-induced fractures,spontaneously form at injection wells during waterflooding.These fractures propagate long distances through rock,allowing injected fluids to travel far away from a well,both within and outside the flooding layer.Essentially,the me-chanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures,which are intentionally created for reservoir stimulation.Fracturing models developed for hydraulic fractures can also be applied to waterflood-induced fractures.However,waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in time.As a result,fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional(2D),a characteristic that is often ignored in a majority of modern fracturing simulators,making their appli-cation to waterflood fractures unreliable.In this work,we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing simulators.We incorporate the developed solution into the classical Perkins-Kern-Nordgren(PKN)model of fracture growth,which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture ge-ometry at large time.The conducted parametric study shows while a toughness-dominated regime af-fects fracture evolution,most of fracture lifetime occurs in a viscosity-and-leakoff-dominated regime.We also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination(~~M and~~K).Finally,we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of zones.The study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry predictions.The present work,thus,plays an important role in improving waterflood fracture modelling,as it highlights the significance of 2D leakoff in waterflood-induced fractures and provides a reliable analytical model for fluid leakoff that can be incorporated into modern fracture simulators.

Can preoperative planning using IRIS™three-dimensional anatomical virtual models predict operative findings during robot-assisted partial nephrectomy?

Objective To evaluate the predictive validity of IRIS™(Intuitive Surgical®,Sunnyvale,CA,USA)as a planning tool for robot-assisted partial nephrectomy(RAPN)by assessing the degree of overlap with intraoperative execution.Methods Thirty-one patients scheduled for RAPN by four experienced urologists were enrolled in a prospective study.Prior to surgery,urologists reviewed the IRIS™three-dimensional model on an iphone Operating System(iOS)app and completed a questionnaire outlining their surgical plan including surgical approach,and ischemia technique as well as confidence in executing this plan.Postoperatively,questionnaires assessing the procedural approach,clinical utility,efficiency,and effectiveness of IRIS™were completed.The degree of overlap between the preoperative and intraoperative questionnaires and between the planned approach and actual execution of the procedure was analyzed.Questionnaires were answered on a 5-point Likert scale and scores of 4 or greater were considered positive.Results Mean age was 65.1 years with a mean tumor size of 27.7 mm(interquartile range 17.5-44.0 mm).Hilar tumors consisted of 32.3%;48.4%of patients had R.E.N.A.L.nephrometry scores of 7-9.On preoperative questionnaires,the surgeons reported that in 67.7%cases they were confident that they can perform the procedure successfully,and on intraoperative questionnaires,the surgeons reported that in 96.8%cases IRIS™helped achieve good spatial sensation of the anatomy.There was a high degree of overlap between preoperative and intraoperative questionnaires for the surgical approach,interpreting anatomical details and clinical utility.When comparing plans for selective or off-clamp,the preoperative plan was executed in 90.0%of cases intraoperatively.Conclusion A high degree of overlap between the preoperative surgical approach and intraoperative RAPN execution was found using IRIS™.This is the first study to evaluate the predictive accuracy of IRIS™during RAPN by comparing preoperative plan and intraoperative execution.

Experimental investigation and analytically modeling of hysteretic behavior of rigid bus-flexible connectors of 220 kV electrical substations

This paper describes the quasi-static testing and analytical modelling of the hysteretic behavior of aluminum alloy rigid bus-flexible connectors of 220 kV electrical substations.The main objective of the study is to experimentally investigate the hysteretic behavior of six different types of rigid bus-flexible connectors 220 kV electrical substations when subjected to cyclic loading.Another objective is to theoretically study the flexibility and effectiveness of a previously proposed analytical model in fitting the experimental hysteresis loops of the tested rigid bus-flexible connectors.The experimental investigation indicates that the tested rigid bus-flexible connectors exhibit highly asymmetric hysteresis behavior along with tension stiffening effect.The theoretical study demonstrates that the generalized Bouc-Wen model has high flexibility and is effective in fitting the experimental hysteresis resisting force-displacement curves of the six tested rigid bus-flexible connectors.

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

We search for analytical wave solutions of an electronically and biologically important model named as the Fitzhugh–Nagumo model with truncated M-fractional derivative, in which the expafunction and extended sinh-Gordon equation expansion(ESh GEE) schemes are utilized. The solutions obtained include dark, bright, dark-bright, periodic and other kinds of solitons. These analytical wave solutions are gained and verified with the use of Mathematica software. These solutions do not exist in literature. Some of the solutions are demonstrated by 2D, 3D and contour graphs. This model is mostly used in circuit theory, transmission of nerve impulses, and population genetics. Finally, both the schemes are more applicable, reliable and significant to deal with the fractional nonlinear partial differential equations.

Hydrodynamic Performance of a Newly-Designed Pelagic and Demersal Trawls Using Physical Modeling and Analytical Methods for Cameroonian Industrial Fisheries

This study proposed the newly-designed Pelagic and demersal trawls for the fishing vessels operating in Cameroonian waters in pelagic and demersal fishing grounds. The engineering performances of both trawls were investigated using physical modelling method and analytical method based on the predicted equations. In a flume tank, a series of physical model tests based on Tauti’s law were performed to investigate the hydrodynamic and geometrical performances of both trawls and to assess the applicability of the analytical methods based on predicted equations. The results showed that in model scale, the working towing speed and door spread for the pelagic trawl were 3.5 knots and 1.85 m, respectively, and for the bottom trawl net they were 4.0 knots and 1.8 m. At that speed and door spread, the drag force, net opening height, and wing-end spread of the pelagic model trawl were 36.73 N, 0.89 m, and 0.86 m, respectively, and the swept area was 0.76 m2. Bottom trawl speed and door spread were 30.43 N, 0.38 m, and 0.45 m, respectively, and the swept area was 0.25 m2. The maximum difference between the experimental and analytical results of hydrodynamic performances was less than 56.22% and 41.45%, respectively, for pelagic and bottom trawls, the results of the geometrical performances obtained using predicted equations were close to the experimental results in the flume tank with a maximum relative error less than 12.85%. The newly developed pelagic and bottom trawls had advanced engineering performance for high catch efficiency and selectivity and could be used in commercial fishing operations in Cameroonian waters.

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing

Analytically solving a three-dimensional （3-D） bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change.