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.

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.

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.

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.

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.