Difference in Unbalanced Magnetic Force of Fractional-Slot PM Machines between Internal and External Rotor Topologie

This paper presents a comparative investigation into unbalanced magnetic force(UMF)of asymmetric permanent magnet machines without rotor eccentricities,particularly focusing on the difference between internal-and external-rotor topologies.The asymmetric field distribution results in radial and tangential asymmetric force waves.Although the radial and tangential stresses are in different direction,the UMF components they produce are nearly aligned.The UMF from asymmetric radial force wave can be additive or subtractive to that from asymmetric tangential force wave.Investigation shows that for the same pole slot number combination,if the UMFs due to radial and tangential force waves are additive in internal rotor machine,they are subtractive in the external rotor counterpart,and vice versa.Investigation reveals a general rule determining whether additive or cancelling:for a UMF produced by any two field harmonics,they are additive if the higher order is produced by the outer part outside the airgap,but cancelling if the higher order is produced by the inner part.Therefore,for a machine with pole number 2p=3k+1,they are additive if it is an external-rotor machine,but otherwise subtractive.On the other hand,for a machine with pole number 2p=3k-1,they are subtractive if it is an external-rotor machine,but otherwise additive.For the UMF due to armature reaction only,they are subtractive for external-rotor machines,but otherwise additive.The investigation is carried out by an analytical model and validated by finite element analysis.

Flow excitation mechanisms of unbalanced impeller forces after pump power-trip of ultra-high head pump-turbines

To elucidate the dynamic mechanisms of unbalanced impellers in ultra-high head pump-turbines(PTs),this study employed a one-and three-dimensional coupled method to simulate the pump power-trip(PPT)process of an ultra-high head PT.The investigation revealed two novel pulsation frequency components,denoted as fDVand fINFT,associated with impeller forces.The pulsation intensities of these components were markedly higher than those of rotor-stator interaction frequency components in ultra-high head PTs.Notably,the fDVcomponents exhibited pulsations at 1–2 times the rated rotation frequency of the impeller,spanning the entire transition period.Meanwhile,the fINFTcomponents constituted a complex frequency band with various frequency values,primarily occurring near conditions(Q=0,n=0,M=0,and d M/dt=0).These two pulsation frequency components were predominantly linked to the unsteady evolution of dean vortices inside the volute and complex transitions of the flow pattern within the impeller,respectively.It is crucial to note that these unbalanced flow-induced impeller axial forces can elevate the risk of accidents where the rotor is subjected to significant upwind axial forces.These findings offer valuable insights into mitigating the risk of rotor lifting due to axial forces during PT events in ultra-high head PTs.

Study of Slope Reinforcement Force Based on FLAC

A slope will slide if the unbalanced force does not tend to zero when the stability of the slope is analyzed with the help of FLAC. Thus the ultimate reason of slope sliding is the unbalanced force determined by FLAC. The slope will remain stable if the unbalanced force is counterbalanced by a reinforcement force which is produced by a suitable reinforcement method. In this paper, the stability of the slope was analyzed by using FLAC, and the unbalanced force of the slope was obtained through the FISH function in FLAC. According to the equilibrium conditions, the relationship between the reinforcement force and unbalanced force was derived and accordingly the reinforcement force was determined. The reinforcement design was adopted by using pre-stressed anchor bars on the basis of the reinforcement force. An example is used to show that the effect of slope reinforcement based on the reinforcement force is safe and economical. The method doesn＇t need to suppose a sliding surface to obtain the reinforcement force, and it is also clear in physical meaning. So this method realized the organic unification of the stability analysis and the slope reinforcement.

Stability and reinforcement analyses of high arch dams by considering deformation effects

The strict definition and logical description of the concept of structure stability and failure are presented. The criterion of structure stability is developed based on plastic complementary energy and its variation. It is presented that the principle of minimum plastic complementary energy is the combination of structure equilibrium, coordination condition of deformation and constitutive relationship. Based on the above arguments, the deformation reinforcement theory is developed. The structure global stability can be described by the relationship between the global degree of safety of structure and the plastic complementary energy. Correspondingly, the new idea is used in the evaluations of global stability, anchorage force of dam-toe, fracture of dam-heel and treatment of faults of high arch dams in China. The results show that the deformation reinforcement theory provides a uniform and practical theoretical framework and a valuable solution for the analysis of global stability, dam-heel cracking, dam-toe anchorage and reinforcement of faults of high arch dams and their foundations.

Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

The rigid body limit equilibrium method(RBLEM) and finite element method(FEM) are two widely used approaches for rock slope's stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety(FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory(DRT) is developed. With this theory, plastic complementary energy(PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope's stability evaluation and reinforcement engineering practice in southwest of China.

Electromagnetic Performance Prediction for the Symmetrical Dual Three-phase Surface-mounted PMSM under Open-phase Faults Based on Accurate Subdomain Model

The paper presents an accurate analytical subdomain model for predicting the electromagnetic performance in the symmetrical dual three-phase surface-mounted permanent magnet synchronous machine(PMSM)under open-phase faulty conditions.The model derivations are extended from previous accurate subdomain models accounting for slotting effects.Compared with most conventional subdomain models for traditional three-phase machines with nonoverlapping winding arrangement,the subdomain model proposed in this paper applied for the 24-slot/4-pole dual three-phase machine with symmetrical overlapping winding arrangement.In order to investigate the postfault electromagnetic performance,the reconfigured phase currents and then current density distribution in stator slots under different open-circuit conditions are discussed.According to the developed model and postfault current density distribution,the steady-state electromagnetic performance,such as the electromagnetic torque and unbalanced magnetic force,under open-circuit faulty conditions are obtained.For validation purposes,finite element analysis(FEA)is employed to validate the analytical results.The result indicate that the postfault electromagnet performance can be accurately predicted by the proposed subdomain model,which is in good agreement with FEA results.

Vibration and Noise Optimization of New Asymmetric Modular PMaSynRM

An optimized structure to weaken the vibration and noise of a new asymmetric permanent magnet-assisted synchronous reluctance motor(PMaSynRM)is proposed.The new asymmetric PMaSynRM has the advantages of a low torque ripple and high fault tolerance.However,the asymmetric structure generates an unbalanced magnetic force(UMF),which results in vibration and noise problems.In this study,the vibration and noise of the motor are analyzed and optimized.First,the radial pressure is analyzed,and an optimized structure is proposed.The electromagnetic performance of the motor before and after optimization is analyzed using the finite element method.Second,a three-dimensional model is established,and modal analysis is conducted considering the orthotropy of the stator and effective windings.Finally,the vibration and noise are simulated and analyzed,and the validity of the analysis results is verified experimentally.The analysis results indicate that the optimized motor realizes a reduction in the motor vibration and noise.

Fracture analysis of rock mass based on 3-D nonlinear Finite Element Method

Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.

Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

In this paper,the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated.The rotor is modeled as a rigid body that is supported by two magnetic bearings with eightpolar structures.The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations(ODEs)are derived,and for solving these equations,the homotopy perturbation method(HPM)is used.By applying HPM,the possibility of presenting a harmonic semi-analytical solution,is provided.In fact,with equality the coefficient of auxiliary parameter(p),the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects.By considering some initial condition for displacement and velocity in the horizontal and vertical directions,free vibration analysis is done and next,the forced vibration analysis under the effect of harmonic forces also is investigated.Likewise,various parameters on the vibration behavior of rotor are studied.Changes in amplitude and response phase per excitation frequency are investigated.Results show that by increasing excitation frequency,the motion amplitude is also increases and by passing the critical speed,it decreases.Also it shows that the magnetic bearing system performance is in stable maintenance of rotor.The parameters affecting on vibration behavior,has been studied and by comparison the results with the other references,which have a good precision up to 2nd order of embedding parameter,it implies the accuracy of this method in current research.