Remarks on Selecting Length of Cylindrical Sample to Determine Magnetic Properties of its Material

Авторы: Sandulyak A.V., Tkachenko R.Yu., Sandulyak D.A., Sandulyak A.A., Polismakova M.N., Ershova V.A. Опубликовано: 03.07.2021
Опубликовано в выпуске: #2(135)/2021  
DOI: 10.18698/0236-3933-2021-2-147-159

Раздел: Приборостроение, метрология и информационно-измерительные приборы и системы | Рубрика: Методы и приборы контроля и диагностики материалов, веществ и природной среды  
Ключевые слова: relative length, sample, induction field dependence, permeability field dependence, transient value

When experimentally studying magnetic properties of the ferromagnetic materials, preferences are often given to a more convenient method involving the use of sufficiently long cylindrical samples with the L length and the D diameter placed in the solenoid field as an alternative to the method based on using classical samples of the toroidal shape (to exclude manifestations of the demagnetizing factor). Currently, required justification is practically missing for specific values of the relative L/D length, which would indicate such [L/D] values (for L/D ≥ [L/D]), at which magnetic properties of a sample (already long enough) correspond to magnetic properties of its material. While the existing recommendations such as [L/D] = 50 are postulated, let us note that relevant experimental studies of magnetic properties of the cylindrical samples with the L/D parameter targeted variation were not made. An attempt was made to fill this gap. For cylindrical steel samples with the different L/D values (from 1 to 50), families of the B magnetic induction and of the μ permeability field dependencies were obtained experimentally using the ballistic method. The sought [L/D] values were determined from the B and μ dependencies on the L/D by the junction abscissa of the ascending and self-similar branches. It was established that in the accepted field strength in the range of H = 0.94--54.2 kА/m magnetizing field, the [L/D] parameter is a variable substantially depending on H (and/or μ). It varies from [L/D] = 10--15 at H = 54.2 kA/m (μ = 30) to [L/D] = 50--60 at H = 4.7 kA/m (μ = 270). And at H < 4.7 kA/m, [L/D] > 50--60, i.e., more than is commonly believed. Thus, it was stated that the data on magnetic properties obtained when using even long samples (L/D = 50) and declared as data on the magnetic properties of the corresponding material, are only close to those with H < 4.7 kA/m. Phenomenological expressions were obtained for the [L/D] determination: exponential with the H argument and logarithmic with the μ argument

The study was carried out with financial support of the RFBR and the London Royal Society (project no. 20-52-10006); Ministry of Education and Science of the Russian Federation within the framework of the State Assignment in the field of science (project no. 0706-2020-0024); grant of the President of the Russian Federation for state support of young scientists (project MK-807.2020.8)


[1] Perigo E.A., Weidenfeller B., Kollar P., et al. Past, present, and future of soft magnetic composites. Appl. Phys. Rev., 2018, vol. 5, no. 3, art. 031301. DOI: https://doi.org/10.1063/1.5027045

[2] Kifer I.I. Ispytaniya ferromagnitnykh materialov [Tests on ferromagnetic materials]. Moscow, Energiya Publ., 1969.

[3] Chen D-X., Brug J.A., Goldfarb R.B. Demagnetizing factors for cylinders. IEEE Tran. Magn., 1991, vol. 27, no. 4, pp. 3601--3619. DOI: https://doi.org/10.1109/20.102932

[4] Chen D.-X., Pardo E., Zhu Y.-H., et al. Demagnetizing correction in fluxmetric measurements of magnetization curves and hysteresis loops of ferromagnetic cylinders. J. Magn. Magn. Mat., 2018, vol. 449, pp. 447--454. DOI: https://doi.org/10.1016/j.jmmm.2017.10.069

[5] Im S.H., Park G.S. A research on the demagnetizing factors for magnetic hollow cylinders. 21st Proc. ICEMS, 2018, pp. 2629--2632.

[6] Caciagli A., Baars R.J., Philipse A.P., et al. Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization. J. Magn. Magn. Mat., 2018, vol. 456, pp. 423--432. DOI: https://doi.org/10.1016/j.jmmm.2018.02.003

[7] Wang M., Feng J., Shi Y., et al. Demagnetization weakening and magnetic field concentration with ferrite core characterization for efficient wireless power transfer. IEEE Trans. Ind. Electron., 2019, vol. 66, no. 3, pp. 1842--1851. DOI: https://doi.org/10.1109/TIE.2018.2840485

[8] Marinica O.M. Study of static magnetic properties of transformer oil based magnetic fluids for various technical applications using demagnetizing field correction. J. Nanomater., 2017, vol. 2017, art. 54076799. DOI: https://doi.org/10.1155/2017/5407679

[9] Sandulyak A.V., Sandulyak D.A., Ershova V.A., et al. Magnetic characteristics of "short" porous magnetic: by the example of filling of spheres. Fundamental’nye i prikladnye problemy tekhniki i tekhnologii [Fundamental and Applied Problems of Engineering and Technology], 2019, no. 3, pp. 121--133 (in Russ.).

[10] Sandulyak A.V. Magnitno-fil’tratsionnaya ochistka zhidkostey i gazov [Magnetic and filtration purification of liquids and gases]. Moscow, Khimiya Publ., 1988.

[11] Chechernikov V.I. Magnitnye izmereniya [Magnetic measurements]. Moscow, MSU Publ., 1969.

[12] Kazin P.E., Kul’bakin I.V. Metody issledovaniya magnitnykh svoystv materialov [Study methods for magnetic properties of materials]. Moscow, MSU Publ., 2011.

[13] Il’in N.A., Klimov A.A., Tiercelin N., et al. Dynamics of magnetization in multilayer TbCo / FeCo structures under the influence of femtosecond optical excitation. Rossiyskiy tekhnologicheskiy zhurnal [Russian Technological Journal], 2019, vol. 7, no. 3, pp. 50--58 (in Russ.). DOI: https://doi.org/10.32362/2500-316X-2019-7-3-50-58

[14] Sandulyak A.A., Sandulyak A.V., Ershova V.A., et al. Definition of a magnetic susceptibility of conglomerates with magnetite particles. Particularities of defining single particle susceptibility. J. Magn. Magn. Mat., 2017, vol. 441, pp. 724--734. DOI: https://doi.org/10.1016/j.jmmm.2017.06.027

[15] Sandulyak D.A., Sandulyak A.A., Kiselev D.O., et al. Determining the magnetic susceptibility of ferroparticles from the susceptibility of their dispersive samples. Meas. Tech., 2017, vol. 60, no. 9, pp. 928--933. DOI: https://doi.org/10.1007/s11018-017-1295-z

[16] Sandulyak A.V., Sandulyak A.A., Ershova V.A. Magnetization curve of a granulated medium in terms of the channel-by-channel magnetization model (new approach). Dokl. Phys., 2007, vol. 52, no. 4, pp. 179--181. DOI: https://doi.org/10.1134/S1028335807040027

[17] Sandulyak A.A., Ershova V.A., Ershov D.V., et al. On the properties of "short" granular magnets with disordered chains of grains: a field between grains. Phys. Solid State, 2010, vol. 52, no. 10, pp. 2108--2115. DOI: https://doi.org/10.1134/S106378341010015X

[18] Sandulyak A.V., Sandulyak A.A., Polismakova M.N., et al. Magnetometer with sheric pole pieces: identification zone with a stable force factor. Rossiyskiy tekhnologicheskiy zhurnal [Russian Technological Journal], 2017, vol. 5, no. 6, pp. 43--54. DOI: https://doi.org/10.32362/2500-316X-2017-5-6-43-54

[19] Yaglidere I., Gunes E.O. A novel method for calculating the ring-core fluxgate demagnetization factor. IEEE Trans. Magn., 2018, vol. 54, no. 2, art. 4000411. DOI: https://doi.org/10.1109/TMAG.2017.2765624

[20] Prozorov R., Kogan V.G. Effective demagnetizing factors of diamagnetic samples of various shapes. Phys. Rev. Appl., 2018, vol. 10, no. 1, p. 014030. DOI: https://doi.org/10.1103/PhysRevApplied.10.014030