Sinusoidal Magnetic Flux Research Articles

Methodology for determining the degree of magnetic induction of transformers with a sinusoidal magnetic flux

The research presented in the article is aimed at reducing losses in the magnetic circuits of electrical machines. These losses amount to up to 5 % of the generated electricity, do not depend on the load and can increase over the life of the equipment. To effectively design and construct transformers with low no-load losses, total losses in steel are minimized by optimizing the crystal grain size and thickness of core sheets, improving the steel texture and magnetic circuit design, etc. However, the hysteresis, classical eddy current and anomalous eddy current components of losses in steel react in different directions to these measures, which does not effectively minimize total losses. To determine the three components of losses, a modernized method of three frequencies is proposed, which takes into account the dependence of the hysteresis loss coefficient on frequency. A formula for correcting this coefficient is derived. It is shown that the indicator of the degree of magnetic induction given in most modern scientific sources in the expression for eddy current anomalous losses has become irrelevant. A method for calculating this indicator for the core of a specific transformer is presented, which uses the loss components and total losses in steel found by the method of three frequencies and the total losses in steel at a reduced primary voltage. For the transformer under study, the degree of magnetic induction in anomalous losses was 1.88. The results obtained can be used in the design of dry and oil transformers of different powers operating with a sinusoidal magnetic flux.

Symmetric Resonance Mechanism for Elimination of Parasitic Torque of a Permanent Magnet Generator under Stable Load

Vibration and torque ripple of the permanent magnet generator axis cause excessive wearing up of the generator, noise, efficiency reduction. The article theoretically considers the possibility of eliminating the oscillation of the rotation torque of the permanent magnets generator at constant load due to mutual compensation of the interaction of coils with the field of permanent magnets in the case of certain symmetry of this field. This effect is called pi resonance. For a given class of model functions of the magnetic field density of permanent magnets, it is shown that full compensation occurs with a certain number of coils (Ns) and magnets (Nr), while for other combinations of {Ns, Nr} the interaction is in the nature of oscillations. Pi resonance tables are given for a number of model field density functions represented by Fourier series up to the fifth power. Pi resonance is primarily realized in the case of a small difference in the values of Nr and Ns, which corresponds to the location near the main diagonal of the pi resonance table, as well as at the values of Nr, Ns corresponding to prime numbers. The number of configurations {Nr, Ns} providing pi resonance (compensation of parasitic torques) is the largest for the sinusoidal magnetic flux density and decreases if the magnetic flux density function is approximated by a high-degree Fourier series. It is shown that in the absence of coil cores, pi resonance is possible at Nr = Ns. An additional possibility of pi resonance is shown when placing coils on opposite sides of the rotor. A simplified method of investigating the system (without integrating the equation for the induction current) is substantiated. The results can be used in the design of permanent magnets generators and motors.

Linearization Approach for Symmetric Hysteresis Loop Modeling and Core Loss Prediction

First, the paper proposes the method for interpolation of any experimentally obtained symmetric hysteresis loop curve (SHLC) with accuracy and computation efficiency at discrete Fourier transformation (DFT) level. Second, the method has been further developed so that, based on the family of the properly chosen and measured SHLCs, it reliably and accurately predicts an arbitrary inner SHLC. Sinusoidal magnetic flux, along with applied zero crossing sampling system, allows for the introduction of the pure linearization approach. The novelty of this approach is a direct transformation of a cosine polynomial (CP) interpolating of one SHLC over the set of equidistant nodes in the electric angle (EA) domain to the algebraic polynomial (AP) interpolating the same SHLC over the set of nonequidistant Chebyshev nodes in the magnetic flux (MF) domain, with the accuracy remaining unchanged. Based on the results of the interpolation error analyses, the SHLC measurement has been proposed for nonequidistant values of magnetic flux at the loop tip, matching the Chebyshev nodes of the second kind. This is the second novelty which enables a successful prediction of an arbitrary inner SHLC.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18716

Eddy current damper for passive reaction force compensation of a linear motor motion stage

This article presents an eddy current damper of a passive reaction force compensation mechanism for a linear motor motion stage. The reaction force compensation mechanism with a movable magnet track and eddy current damper resolves problems with the existing spring-based reaction force compensation mechanism such as resonance, design freedom, and difficulty of assembly and manufacturing. A simplified mathematical model of the eddy current damper is derived considering the sinusoidal magnetic flux density distribution and effective width of the eddy current damper, which shows important design factors of the eddy current damper–based reaction force compensation mechanism. Then, force of the eddy current damper according to the constant speed motion of the magnet track is investigated using multi-physical finite element analysis and is verified by experiments. Finally, the passive reaction force compensation with movable magnet track and eddy current damper is identified by experiments, and the finite element analysis of the eddy current damper is verified with free and forced vibration responses.

Eddy current damper type reaction force compensation mechanism for linear motor motion stage

The base vibration of a linear motor motion stage has been reduced with a passive reaction force compensation (RFC) mechanism based on a movable magnet track and springs. This paper presents the design procedure of an eddy-current damper (ECD) type RFC mechanism for a linear motor motion stage. The RFC mechanism with a movable magnet track and an ECD can overcome the disadvantages of the spring based RFC mechanism such as resonance and difficulty of assembly due to springs. A lumped parameter model for the ECD type RFC mechanism is derived considering sinusoidal magnetic flux density and the effective width of the ECD according to magnet track motion. Then, an iterative design procedure for ECD type RFC mechanisms is proposed to meet system requirements such as the transmission ratio of the reaction force and the maximum magnet track motion. Finally, a design example illustrates the effectiveness of the proposed design procedure for an ECD type RFC mechanism.

The theorem about the transformer excitation current waveform mapping into the dynamic hysteresis loop branch for the sinusoidal magnetic flux case

This paper analyses aspects of the approximation theory application on the certain subsets of the measured samples of the transformer excitation current and the sinusoidal magnetic flux. The presented analysis is performed for single-phase transformer case, Epstein frame case and toroidal core case. In the paper the theorem of direct mapping the transformer excitation current in the stationary regime is proposed. The excitation current is mapped to the dynamic hysteresis loop branch (in further text DHLB) by an appropriate cosine transformation. This theorem provides the necessary and satisfactory conditions for above described mapping. The theorem highlights that the transformer excitation current under the sinusoidal magnetic flux has qualitatively equivalent information about magnetic core properties as the DHLB. Furthermore, the theorem establishes direct relationship between the number of the transformer excitation current harmonics and their coefficients with the degree of the DHLB interpolation polynomial and its coefficients. The DHLB interpolation polynomial is calculated over the measured subsets of samples representing Chebyshev nodes of the first and the second kind. These nonequidistant Chebyshev nodes provides uniform convergence of the interpolation polynomial to the experimentally obtained DHLB with an excellent approximation accuracy and are applicable on the approximation of the static hysteresis loops and the DC magnetization curves as well.

Semi-physical parameter identification for an iron-loss formula allowing loss-separation

This paper presents a semi-physical parameter identification for a recently proposed enhanced iron-loss formula, the IEM-Formula. Measurements are performed on a standardized Epstein frame by the conventional field-metric method under sinusoidal magnetic flux densities up to high magnitudes and frequencies. Quasi-static losses are identified on the one hand by point-by-point dc-measurements using a flux-meter and on the other hand by extrapolating higher frequency measurements to dc magnetization using the statistical loss-separation theory (Jacobs et al., “Magnetic material optimization for hybrid vehicle PMSM drives,” in Inductica Conference, CD-Rom, Chicago/USA, 2009). Utilizing this material information, possibilities to identify the parameter of the IEM-Formula are analyzed. Along with this, the importance of excess losses in present-day non-grain oriented Fe-Si laminations is investigated. In conclusion, the calculated losses are compared to the measured losses.

Modeling of Novel Permanent Magnet Pole Shape SPM Motor for Reducing Torque Pulsation

This paper deals with the modeling of a novel permanent magnet (PM) pole shape for a surface-mounted permanent magnet (SPM) motor so as to generate sinusoidal back EMF and linear electromagnetic torque. Conventional SPM motors have a square-shaped PM pole structure; therefore, square back EMF is generated along with the torque pulsations. This novel SPM motor has sinusoidal PM pole shape in the axial direction; therefore, sinusoidal back EMF is generated due to the sinusoidal magnetic flux distribution. Sinusoidal back EMF eliminates most of the cogging torque; thus, a linear electromagnetic torque is generated. Square and sinusoidal current excitation is provided as to analyze the electromagnetic torque characteristics of SPM motor models. As compared to square current excitation, sinusoidal current excitation shows better linearity as well as average electromagnetic torque for the novel SPM motor model. 3-D finite element analysis (FEA) is utilized to analyze and compare the back EMF, cogging torque, and electromagnetic torque of conventional and proposed novel PM pole shaped SPM motor models for both square and sinusoidal current excitation.

A newly developed ripple-free precision toroidal type motor

Demands for ripple-free spindle rotation have recently increased in a variety of industrial sectors, i.e., electron beam mastering systems, semiconductor production instruments, etc. However, typical electric motors usually have torque ripple caused by the cogging force and uneven magnetic flux density, which deteriorates the spindle performance. This paper presents a newly developed torque ripple-free precision toroidal type motor. The magnet yoke of the developed motor is designed so as to provide an ideal sinusoidal magnetic flux distribution which can generate smooth torque. Evaluation results confirmed that the developed motor achieves superior performance.

Iron Loss Analysis Considering Excitation Conditions Under Alternating Magnetic Fields

In this paper, the nature of iron loss in electrical steel during alternating field excitation is investigated more precisely. The exact definition of AC iron loss is cleared by accurately measuring the iron loss for conditions of both the sinusoidal magnetic field and sinusoidal magnetic flux density. The results of this approach to iron loss calculations in electrical steel are compared to experimentally-measured losses. In addition, an inverse hysteresis model considering eddy current loss was developed to analyze the iron loss when the input is the voltage source. With this model, the inrush current in the inductor or transformer as well as the iron loss can be calculated.

On the Use of Pulse Width Modulation Method for the Elimination of Flux Density Harmonics in the Air-Gap of Surface PM Motors

This paper presents a novel design for the elimination of radial air-gap flux density harmonics of surface mounted permanent magnet (PM) motors by using the pulse width modulation (PWM) method. Instead of conventional full arc-shape magnets, the block magnets are configured to have a shape similar to PWM signals used in power electronics in order to achieve a quasi sinusoidal radial magnetic flux density in the air-gap. Then the obtained electromotive force does not contain the low order harmonics and is almost sinusoidal. The computation of the block magnet sizes is performed by solving a constrained optimization problem. All important variable parameters and constraints are carefully considered in the design process. The solutions are achieved with an optimal design method based on finite element analysis and Matlab optimization toolbox. The effect of different PWM segmented configurations on the flux density waveforms illustrates a high improvement in the quality of the back-EMF as well as the torque.

Control of flux in magnetic circuits for Barkhausen noise measurements

The consistency of magnetic Barkhausen noise (MBN) measurements under applied sinusoidal magnetic field control and sinusoidal magnetic circuit flux control was investigated under variable circuit permeability conditions. A U-core electromagnet was used to provide the alternating magnetic excitation. The magnetic circuit permeability was changed by varying excitation magnet lift-off and by using samples with known magnetic anisotropy. By controlling the circuit magnetic flux, measured as the flux in one of the U-core poles near the sample, MBN measurements were found to be consistent and independent of the excitation magnet lift-off in both a Si–Fe steel sample and an interstitial free (IF) steel sample at peak sample flux densities greater than 1.16 T and 0.29 T respectively. Consistency within a 95% confidence level was demonstrated for lift-off values of 0.6 mm or less, with decreasing sensitivity to lift-off observed at higher fluxes. MBN anisotropy measurements were also performed using both field control and flux control. Under field control conditions a component of the anisotropy signal was found to be dependent on the magnetic circuit permeability. This permeability dependence was absent when using flux control. The results demonstrated that flux control should be used when performing MBN measurements on samples where lift-off may be an issue, as values obtained will have less dependence on the excitation magnet characteristics than when field control is used.

Design of the Rotary Magnetic Position Sensor With the Sinusoidally Magnetized Permanent Magnet

This paper proposes a rotary magnetic position sensor (RMPS) which has a sinusoidally magnetized permanent magnet (PM) with a small number of poles. To make the sinusoidal magnetic flux density distribution from the PM, a magnetizing fixture is designed by adjusting its pole shape. The magnetization process is analyzed using the Preisach model and two-dimensional finite-element method (FEM). The simulation result of the magnetization is compared with the experimental one. Also, the ability of position detection from two sinusoidal signals is shown

Rotor Pole Design in Spoke-Type Brushless DC Motor by Response Surface Method

This paper proposes a novel rotor pole shape which consists of a uniform surface and an eccentric surface to make a sinusoidal magnetic flux density in air gap in order to reduce cogging torque, torque ripple, and harmonics of back-electromotive force waveform in spoke-type brushless DC motor. In the process of design and analysis, response surface methodology and the 2-D finite-element method are employed to obtain the rotor geometry and verify the results of the novel rotor pole shape

Precise AC magnetic measurement under sinusoidal magnetic flux by using digital feedback of harmonic compensation

This paper presents an important improvement for precise AC magnetic measurement under sinusoidal magnetic flux by using the digital feedback of harmonic compensation. Core loss-testing can be simply carried out with the sinusoidal magnetic flux even at a magnetic induction up to 1.87 T. The principle, circuit diagram, experimental results and its analysis are reported. Also it is found that the hysteresis loss per cycle P is smaller after correcting the magnetic flux waveform than before.

Simple modeling of the AC hysteretic property of a grain-oriented silicon steel sheet

A homogenized model based on the Pry and Bean model is generalized to represent the ac hysteretic characteristics of an actual grain-oriented silicon steel sheet. A parameter for the frequency dependence of eddy-current loss is introduced. The generalized model improves the evaluation accuracy of eddy-current loss and the representation of ac B--H loops under the condition of a sinusoidal magnetic flux. The generalized model also accurately represents ac B--H loops having minor loops.

Exciting signal generator for SSTs

The exactly defined magnetic flux waveform (usually sinusoidal one) is the important magnetization condition for the single sheet tester (SST) measurements. The sinusoidal magnetic flux waveform is kept by the DSP controlled exciting signal generator that generates magnetizing voltage with the arbitrary waveform and given frequency. The digital signal processor (DSP) and robust software give possibility for the efficient and adaptive signal processing taking into account strong non-linearity of measured materials, feedback loop stability and required real-time control.

Linearity of high-T c dc superconducting quantum interference device operated in a flux-locked loop

Measurements have been made of the linearity of a high transition temperature dc superconducting quantum interference device (SQUID) operated at 77 K with 130 kHz flux modulation in a flux-locked loop. The degree of nonlinearity was determined from harmonic generation. A sinusoidal magnetic flux with harmonic content less than −130 dB was applied to the SQUID, which was cooled in a magnetic field below 10−7 T, and the harmonics at the output of the flux-locked loop were measured with a spectrum analyzer. For input signals at frequencies up to 248 Hz and amplitudes up to 20Φ0 rms (Φ0 is the flux quantum), the second, third, and fourth harmonics were each at least 115 dB below the fundamental. At higher frequencies the harmonic content began to increase because of the reduction in the open-loop gain of the flux-locked loop. The magnitude of the harmonics was not measurably changed when the SQUID was cooled in a field of 100 μT. The amplitudes of the even harmonics depended critically on the amplitude of the 130 kHz flux modulation, and became zero when its peak-to-peak value was precisely Φ0/2.

Characterisation of nonoriented electric alloys under nonconventional conditions

The variations of magnetic and loss characteristics of nonoriented cobalt-iron and silicon-iron sheets have been investigated using an Epstein frame. Cobalt-iron alloys have been tested under sinusoidal magnetic flux density with respect to frequency and temperature. Both kinds of alloys have also been investigated with respect to frequency, time constant wavefront and temperature under trapezoidal flux density. The qualitative behaviour is identical under both flux density conditions for all these alloys. These investigations have made it possible to model the variations of iron losses with experimental parameters, except the temperature. These quantitative evolutions differ with alloy and flux-density conditions and do not confirm several propositions of different authors.

Caractérisation des tôles Fer-Silicium en régime dynamique pulsant

Using a characterization method based on the Epstein's frame principle, we study the evolution of the magnetic and losses characteristics of NO Fe-Si sheets with respect to the fundamental frequency, the temperature and the wave front under time-variable sinusoidal or constant wave front trapezoidal magnetic flux density. At last, we modelise the evolution of the iron losses with respect to these parameters, except the temperature