This tutorial teaches the basic methods to define problems, perform calculations and to get related results. Pictures shown here are from calculations with version 3.0, but of course the tutorial can be used without any change in version 3.1, 3.2 and 3.3 too. Tutorials 3.1, 3.2 and 3.3 below are related to the new sorts of magnets and methods, which have been introduced in those versions.
This tutorial shows the basic handling of the software as well as its basic characteristics. The problem which shall be teated here consists of a cylinder made of six homogenous segments of anisotropic ferrite, having a remanence induction of 0.40T each. The example below and similar problems ca be treated by use of the demo version of PS-PERMAG and for sure by the full versions 3.0 or 3.1. The additional features of both versions which are not shown here can also be learned easily by use of their extensive help system. The treatment of the new two pole sensormagnets of version 3.1 with enhanced geometric details can be studied in Tutorial 3.1
After starting PS-PERMAG a 3D model of an illustrative permanent magnet shows up on the screen. To define the above described magnet please click on the M symbol at the top symbol bar. M stands for circumferentially magnetized multipolar cylinders with homogenous magnetization in each pole. This opens an input dialog for the data input, see picture below. Here the basic data of the magnet have to be put in. Background for defining a cylindrical magnet is always a cylindrical coordinate system. This means e.g. that at half the axial length of the magnet there is always z=0. At zero angle phi=0 there always starts an outward oriented pole.
This tutorial shows the geometry input of the new sorts of two pole sensormagnets with depression and ledges, which have been added in PS-PERMAG version 3.1. The basic use of PS-PERMAG can be studied in Tutorial 3.0.
The following treats a two pole, axially magnetized sensormagnet. The geometry input of the other two new sorts of magnets, i.e. two pole diametrical and two pole axial-lateral, has to be done by the same way. First there has to be defined a basic cylinder. Depressions and ledges will be subtracted from this basic cylinder by up to four additional help volumes.
In this tutorial we explain three new features of verion 3.2. These are the rotatable result coordinates, the cuboit-kit system as well as the feature of axial magnetic bearings.
In this tutorial new characteristics of version 3.3 will be elucidated. On one hand this is a continuously changable shape of magnetic polarization within one single sort of magnet. This has been introduced for circumferentially magnetized bow shaped as well as axially magnetized bow shaped cylinder magnets. For multipolar cuboids beside the known alternating rigid magnetization an axially bow shaped magnetization has been added. The latter can also here change its shape in a continuous way. Beside these features, for all magnets the output of two dimensional vector sums in all three spatial planes have been added in version 3.3.
Bow shaped magnetized magnets on circumference (L-symbol in symbolbar) have by default a sinus shape of polarization with slowly decreasing strength to the inside of the specimen. By this resulting fields do not show any harmonic distortion. On the other hand, for specific applications a more trapezoidal magnetization might be demanded. All kinds of polarization shapes between perfectly sinusoidal and nearly perfectly radial, with an only minor residual transition zone, can now be be realized for this kind of magnet. This can be done by the new so called deformation parameter. The deformation parameter can be varied between 0 and 1. By that nearly all shapes of magnetization with continuously varying direction within one pole can be modelled. Following picture provides the input dialog of a bow shaped magnetized magnet with the new introduced deformation parameter:
When a deformation parameter > 0 has been given in, a diagram opens which shows the distribution of radial and tangential components of magnetization at the pole surface, also including the polarization's vector sum. By that the grade of deviation from a perfectly sinusoidal polarization is being visualized, together with an impression about the size of transitions zones between poles. For a laterally bow shaped magnetization this is provided always for a whole pole pair. For the four pole magnet above one pole pair covers 180°. In the following picture the deformation parameter has a value of 0.3.
Deviations from a perfectly sinusoidal polarization by use of a deformation parameter have been implemented into version 3.3 also for axially lateral cylinder magnets, i.e. magnets with a bow shaped magnetization at one head face. The Following picure reveals the related input dialog for a six-pole magnet, here also with a deformation paramter of 0.3.
Next there is provdided the distribution of polarization components at the magnets pole face as well as the related vector sum. One pole pair here comprises 120°.
The impact on the axial field distribution near the magnets surface can be seen in the following screenshot by some Fourier series aproximations of the signal for a few orders of higher harmonics. The deviation from a perfectly sinusoidal magnetization leads to a harmonic distortion of around 9%, as can be seen on the right side by the respective figure below the listing of Fourier coefficients.
A bow shaped magnetization has been implemented into version 3.3 as a new option for the multipolar cuboid (C-option in symbol bars). The default magnetization for this kind of specimen is still a rigid, alternating magnetization with an uniform direction within the single poles. By marking the respective dialog input as being shown in the following picture, magnetization can be switched to a bow shaped one. If in the input dialog the deformation parameter below is still set to zero, then the polarization will be perfectly sinusoidal, while with other values it is deformed. In case the deformation parameter is 1 a nearly perfect axial magnetization with only minor transition zones to the other poles will me modelled. When a bow shaped magnetization has been chosen there is always a slow decrease of vector sum of magnetization into the inside of the magnet, as it is mostly the case for a real magnetization process. If the bow shaped magnetization were not marked the deformation parameter would not have an impact on the default rigid magnetization.
The screenshot below additionally highlights buttons for listings and and diagrams for two- dimensional vector sums, which have been implemented for all kinds of magnets in version 3.3. Those will be treated in the next subchapter.
The next provides the distribution of polarization components when there is the maximum deformation of 1. In the respective diagram for cuboids the polarization shape is always shown along one pole only. In case that the deformation parameter is at its maximum value, the transition zone has only a marginal size as it would take place e.g. after a skillful pulse magnetization process. In case of a perfectly rigid magnatization with perfect uniformity within each single pole, then the option of a bow shaped magnetization should stay unmarked.
The graph below this provides the axial field component near the magnet's surface along the above depicted path after an export of results to a spreadsheet program. Here a bow shaped magnetization was modelled for deformation paramaters of 0.0, 0.25, 0.4 and 1.0. Additionally the result for the rigid polarization has been included.
The output of two dimensional vector sums is valuable especially for the design of magnetic sensor systems, as here often results in one plane are of interest. For all kinds of field paths these planes can be Cartesian planes (e.g. xy) or cylindric planes (e.g. radial.tangential) acoording to the chosen result coordinate system. The following picture provides for the above defined cuboid system the Bxz- vector sum as a function of the path position, here for a bow shaped magnetization with deformation parameter 0.4. Values always can be displayed as listings as well as graphs. These new features have been implemented to all kinds of magnets that are treated by the PS-PERMAG of the software.
