Magnetocaloric materials are researched as promising alternatives to conventional gas compression technologies for heat conversion. Within the known magnetocaloric
materials, the MM'X system is promising as it features a strong first order magnetostructural transition (MST) enabled by partial substitution of M, M' and X sites, where M and M' are
transition metals and X is a p-block element in orthorhombic/hexagonal structures[1]. Commonly used intermetallics (MnNiGe, MnCoGe [2,3]) employ Ge and Co, which are critical for
their applications in electronics, and cathode materials for batteries, respectively. In the present study, Fe and Al substitutions inside a MnNiSi-based intermetallic induce a MST without
critical or expensive elements. All alloys have been synthesized by arc melting, and heat treated followed by quenching. By convenient substitution, the studied Mn1-xNi1-xFe2xSi0.95Al0.05
alloys exhibit Curie temperatures around room-temperature, which were captured by Vibrating Sample Magnetometry (VSM) as well as In-field differential scanning calorimetry (DSC)
[4]. The VSM magnetization over temperature data in the Mn0.69Ni0.69Fe0.62Si0.95Al0.05 sample with applied field μ0H = 1 T shown in Fig. 1 displays an abrupt variation of magnetization
with temperature, where the derivatives of magnetization exhibit a minimum between 279 and 290 K during cooling and heating, respectively. From the VSM measurements, what can be
thought of as a single-phase transition due to a single derivative minimum can be elucidated with the use of a 1K/min heating/cooling rate in the DSC. In fact, this MST is a convolution of
different transitions all close to one another, as shown during the cooling protocol in Fig. 2 from in-field DSC data with 1 T applied field. The main article will investigate the cause of such
distribution of transitions and its effect on the isothermal entropy change during heating and cooling transformations, as evaluated by a concurrent VSM and DSC study. 

**References:** 

[1] W. Bazela, A. Szytula, J. Todorovic, A. Zieba, Crystal and magnetic structure of the NiMnGe1−nSin System, Phys. Status Solidi. 64 (1981) 367–378.
https://doi.org/10.1002/pssa.2210640140. 
[2] A. Taubel, T. Gottschall, M. Fries, T. Faske, K.P. Skokov, O. Gutfleisch, Influence of magnetic field, chemical pressure and hydrostatic pressure on the structural and magnetocaloric
properties of the Mn-Ni-Ge system, J. Phys. D. Appl. Phys. 50 (2017). https://doi.org/10.1088/1361-6463/aa8e89. 
[3] S.K. Pal, C. Frommen, S. Kumar, B.C. Hauback, H. Fjellvåg, G. Helgesen, Enhancing giant magnetocaloric effect near room temperature by inducing magnetostructural coupling in
Cu-doped MnCoGe, Mater. Des. 195 (2020) 109036. https://doi.org/10.1016/j.matdes.2020.109036. 
[4] K.K. Nielsen, H.N. Bez, L. Von Moos, R. Bjørk, D. Eriksen, C.R.H. Bahl, Direct measurements of the magnetic entropy change, Rev. Sci. Instrum. 86 (2015).
https://doi.org/10.1063/1.4932308. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/32e13598a89f4ff80df494dab41026c2.png)

Study of the magnetostructural transition in critical element free Mn1

With the increasing focus on energy efficiency for the green transition, there is a desire to identify and reduce all losses possible. For rotary machines losses occur as friction at the bearings, and therefore frictionless magnetic bearings can be an important upgrade to high-speed machinery. However, as proven by Samuel Earnshaw in 1842 magnetic bearings are inherently unstable. Typically, magnetic bearings are stable in the lift (often vertical) direction. This results in instability in the radial direction and therefore some kind of stabilizing force is required in this direction [1]. For a magnetic bearing, the radial stiffness determines the active force needed to keep the bearing stable. Thus there is a compromise in designing a magnetic bearing which can both lift as high a load as possible and at the same time have a low and constant radial instability [2-5]. Here we describe a new magnetic bearing aiming to fulfill these requirements [6]. The bearing consists of two nested conical axi-symmetric permanent magnet rings with quadratic cross-sections, as shown in Fig. 1. This configuration is a superposition between a radially magnetized bearing and an axially magnetized bearing. The rotor and stator are centered on the same axis, and when load is applied on the rotor bearing this will move along the z-axis. The stator has a magnetization direction that is along the inwards normal to its surface, while the rotor has a magnetization direction outwards normal to its surface. Thus, there is repulsion between the rings. The idea behind this design is that the magnetic forces will both have a component providing a lifting force along the z-axis, but also a component along the radial direction, which might allow the stiffness along this direction to be controlled. Such a design of tilted conical rings of permanents magnets can easily be made of cubes of permanent magnets placed in a ring. We consider a design where there is a minimum distance between rotor and stator of 0.2 mm and where the conical rings that make up both the rotor and the stator have quadratic cross-section side lengths of 3 mm. The radius of the center of the tilted ring in the stator is fixed at 24 mm, while it is varied for the rotor. We consider different tilt angles of the stator/rotor rings in the bearing and we also consider ring geometries with twice the cross-section and different magnetization directions. The “single” bearing consists of two tilted concentric rings with opposite magnetization as described above, the “double” bearing has two magnets in each tilted ring, and finally the “alternating” bearing has the magnetization of one part of the ring reversed in both the stator and rotor. All configurations are illustrated in Fig. 1. We assume that the permanent magnets in the bearing have a remanence of 1.4 T and a relative permeability of 1. We determine the force and stiffness of the bearing using a magnetostatic finite element (FEM) axi-symmetric model in Comsol Multiphysics. As the simulations are 2D axi-symmetric a very high mesh resolution can be used, eliminating the known convergence issues with bearing models in 3D [7]. We have conducted a variation study to determine the optimal geometry of the bearing as function of the tilt angle and the bearing type. Tilt angles from 0 to 90 degrees in steps of 15 degrees were modelled. Combined with the three bearing types studied, this gives a total of 21 bearings modelled. For each of these we use an adaptive routine to determine the optimal rotor radius to a precision of 0.1 mm. We show that the optimal value of the rotor radius is almost identical for the different bearing geometries considered, with decreasing rotor radius for increasing tilt angle. Following this we determine which bearing would be easiest to control, i.e. has a constant stiffness value, but which also provides a high lifting force. We investigate this by calculating the relative standard deviation for both the axial force and stiffness. This is shown in Fig. 2 for all studied bearings which are stable in the axial direction. Choosing the best bearing depends on the desired characteristics of the bearing. If one desires a bearing that is easy to control, i.e. has a mostly constant stiffness, for a 3 mm axial displacement the double geometry with a tilt angle between 60-75 degrees is clearly the best. When a smaller axial displacement of 1 mm is considered, all bearings with a tilt angle of 60 degrees display almost constant stiffness. This is a remarkable property, as such a bearing is very easy to control with an active bearing. In this bearing the exact load on the rotor is not of importance, as long as it is between the minimum and maximum lift, and at the same time the stiffness is constant regardless of the load. We thus show that by varying the tilt angle and the bearing geometry it is possible to tailor a bearing to the desired characteristics and achieve an easily controllable bearing with a high lifting force.

**References:**

[1] J. P. Yonnet, IEEE Transactions on Magnetics, Vol. 17, p.1169-1173 (1981) [2] J. G. Detoni, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 228, p.1829-1844 (2014) [3] J. Sun, D. Chen and Y. Ren. , IEEE Transactions on Instrumentation and Measurement, Vol. 62, p.2960-2965 (2013) [4] L. Zhang, H. Wu, P. Li, Y. Hu and C. Song, Mathematical Problems in Engineering, Vol. 2019, p.4265698 (2019) [5] K. K. Nielsen, C. R. H. Bahl, N. A. Dagnaes, I. F. Santos and R. Bjørk, IEEE Transactions on Magnetics, 10.1109/TMAG.2020.3042957 (2020) [6] R. Bjørk and C. R. H. Bahl, “A conical passive magnetic bearing with constant stiffness”, submitted for publication (2021) [7] N. A. Dagnæs-Hansen and I. F. Santos., Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 233, p.5280-5293 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/da90a1119a35e4bf7055dcd0b30f5edb.jpg)
Fig.1: The bearing geometry considered. The stator, shown in green, and the rotor, shown in grey, each consists of two tilted rings of permanent magnets with a quadratic cross-section. Their direction of magnetization is also indicated. On the right is shown a cross-section of the bearing, with the three types of magnet configurations considered. The bearing illustrated here has a tilt angle of 30 degrees.

![](https://assets.underline.io/uploads/markdown_image/1/image/015e67cee587135f544e04ac077b1ccd.jpg)
Fig.2: The relative standard deviation of the stiffness in the z-direction in percent as function of the relative standard deviation of the force in the z-direction in percent.

 A constant stiffness magnetic bearing

NOB: Magnetocaloric Materials I

technical paper

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