Single-step Manufacturing of Flux-Directed Permanent Magnet Assemblies

Abstract

A flux directed magnet and a method of manufacturing a flux-directed magnet in a reduced number of process steps is described and claimed. The present invention is, in an embodiment, a single-step manufacturing of flux directed magnet assemblies such as, but not limited to, Halbach arrays of arbitrary multipole order. Even tube-shaped flux directed magnet assemblies such as Halbach arrays with large aspect ratio, i.e. length to diameter, can be produced in single steps using the method of the invention. Alternatively, the present invention may be one step of a plurality of steps in a process for manufacturing of flux directed magnet assemblies.

Claims

1. A method for producing a flux-directed magnet assembly, comprising the steps of: a. Providing an assembly having a first region, second region and a third region in cross section, wherein said second region is disposed between said first and said third regions, and wherein said second region comprises permanent magnet material; and b. Wherein, in said cross section of said flux directed magnet assembly, said first region, said second region, and said third region form concentric circles, said second region being defined as having a radius; and c. Wherein, for inside-directed flux, said first region contains an enhanced magnetic flux and said third region is quasi flux-free, and wherein for outside-directed flux said first region is quasi flux-free said third region contains an enhanced magnetic flux; d. Wherein the magnetization of any point in said second region is defined as being continuously variable, substantially independent for the point along the radius due to the operation of the magnetization field as being above the saturation magnetization of the permanent magnetic material, and is given by the equations:
M_r(?)=B_rem*cos(n?)
M_?(?)=B_rem*sin(n?) where ? is the azimuthal direction, Brem is the remanent flux density of the magnetic material and n is the multipole order; and e. wherein the absolute value of the magnetization is substantially constant throughout said second region. f. using amplitudes B.sub.rem of different size in front of the cosine and sine functions above enables flux-directed assemblies with elliptical cross section.

2. The method for producing a flux directed magnet assembly of claim 1, wherein said magnetic flux directed magnet assembly is defined as a Halbach array.

3. The method of claim 1, wherein the equations for the magnetic flux density in said first region and said second region for inside-directed flux, multipole order greater than 1 in cylindrical coordinates are: for said first region, (n>1):
B_r?|=(B_rem*n)/(n?1)*(1?(R_i/R_o)?(n?1))*(r/R_i)(n?1)*cos(n?)
B_??|=?(B_rem*n)/(n?1)*(1?(R_i/R_o)?(n?1))*(r/R_i)(n?1)*sin(n?) For said second region, (n>1):
B_r??=(B_rem*n)/(n?1)*(1?(r/R_o)?(n?1))*cos(n?)
B_???=?B_rem/(n?1)*(1?n(r/R_o)?(n?1))*sin(n?)

4. The method of claim 1, wherein the equations for the magnetic flux density in said second region and said third region for outside-directed flux, multipole order greater than 1 in cylindrical coordinates are: For said third region, (n<?1):
B_r?|?=(B_rem*n)/(n?1)*(1?(R_i/R_o)?(1?n))*(R_o/r)?(1?n)*cos(n?)
B_??|?=?(B_rem*n)/(n?1)*(1?(R_i/R_o)?(1?n))*(R_o/r)?(1?n)*sin(m?) For said second region, (n<?1):
B_r??=(B_rem*n)/(n?1)*(1?(R_i/r)(1?n))*cos (n?)
B_??=?B_rem/(n?1)*(1?n(R_i/r)?(1?n))*sin(n?)

5. The method of any of claims 1-4, wherein said magnetic flux is produced by at least one double-helix magnet configurations.

6. The method of claims 1-4, wherein said magnetic flux is produced by at least one direct double-helix magnet configurations.

7. The method of any of claims 1-6, wherein the magnetic material is further defined as being manufactured from a powdered metal, produced by the steps of: a. Preparing the powdered metal by providing the appropriate amounts of neodymium, iron, and boron; b. Heating the powdered to a melting point under vacuum. c. Cooling said powdered metal; d. Crushing and then grinding said powdered metal into a fine powder. e. Placing said powdered metal into a die that has the approximate shape of the finished magnet; f. Applying a magnetic field to the powdered material to line up the powder particles; g. While the magnetic force is being applied, pressing the powder from the top and bottom with hydraulic or mechanical rams to compress it to within about 0.125 inches (0.32 cm) of its final intended dimensions; h. Sintering the compressed powdered metal, which fuses the powder into a solid piece; i. Annealing the compressed powdered metal the sintered material in a second controlled heating and cooling process to remove residual stresses within the material and strengthen it; j. Machining the annealed material to produce a smooth surface; and k. Applying a protective coating to the annealed material.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accompanying drawings, which are incorporated into and form a part of the specification, illustrate one or more embodiments of the present invention and, together with the description, serve to explain the principles of the invention. The drawings are only for the purpose of illustrating the preferred embodiments of the invention and are not to be construed as limiting the invention. In the drawings:

[0012] FIG. 1 depicts three concentric regions with unique flux density distributions for a doughnut shaped Halbach array.

[0013] FIG. 2 depicts a flux density distribution of Halbach array for Region I and Region III with quadrupole configuration. The color coding shows the total flux density in Tesla, the arrows show the field direction. The dashed lines indicate the radial boundaries of the permanent magnet material.

[0014] FIG. 3 depicts a radial dependence of a radial field component (left), azimuthal field component (middle) and total field (right) for an azimuth of Phi=22.5 degree. An angle of 22.5 degree is chosen, where both field components, B.sub.r and B.sub.phi are relatively large.

[0015] FIG. 4 depicts a flux density distribution of a Halbach array for Region-I, -II and -III with quadrupole configuration. The color coding shows the total flux density in Tesla, the arrows show the field direction. The dashed lines indicate the radial boundaries of the permanent magnet material.

[0016] FIG. 5 depicts a radial dependence of a radial field component (left), azimuthal field component (middle) and total field (right) for an azimuth of Phi=22.5 degree. An angle of 22.5 degree is chosen, where both field components, B.sub.r and B.sub.phi are relatively large.

[0017] FIG. 6 depicts a 2-D coil configuration for the magnetizer comprising of two inner and two outer DH/DDH coils placed concentrically to magnet ring with center radius R.sub.h. Coils at R1 &R4 are coupled to generate angular field at R.sub.h. Coils at R.sub.2&R.sub.3 are coupled to generate radial field at R.sub.h.

[0018] FIG. 7 depicts steps of: step 1forming die/tooling/rotor-housing; step 2filing, compressing and annealing process; step 3flux-directed magnetizing; step 4finished rotor.

[0019] FIG. 8 depicts a example of a four coil, flux-directed magnetizing coil system (Step 3 of FIG. 7).

[0020] FIG. 9 depicts a 2-D analysis of the magnetized rotor having a flux directed field configuration.

DETAILED DESCRIPTION OF THE INVENTION

[0021] The claimed single-step manufacturing process of Halbach arrays, requires a detailed understanding of the magnetization distribution of the permanent magnet material. For circular Halbach arrays three concentric regions can be identified, as shown in FIG. 1. The grey ring array 002 represents the permanent magnet material, the inner 001 and outer 002 regions contain either the enhanced magnetic flux or are quasi flux-free, depending on the type of Halbach array. For inside-directed flux, 001 contains the enhanced magnetic flux, and 003 is flux free. For the opposite case of outside-directed flux, 001 is flux free, and the enhanced flux is directed into 003 Region-III.

[0022] The magnetization of the magnetic material at any point inside of Region-II is described by the following equations.sup.1, .sup.1 Analysis of the magnetic field, force, and torque for two-dimensional Halbach cylinders, R. Bjork et al., published in Journal of Magnetism and Magnetic Materials, Vol. 322(1), 133-141, 2014

M.sub.r(?)=B.sub.rem*cos(n?)

M.sub.?(?)=B.sub.rem*sin(n?)Equation 1:

where ? is the azimuthal direction, B.sub.rem is the remanent flux density of the magnetic material and n is the multipole order. For a positive value of n the resulting flux is directed towards the inside and for negative values of n the flux is outward-directed. As can be seen from these equations the absolute value of the magnetization is constant throughout Region-II, the radial and azimuthal components vary in a sinusoidal fashion.

[0023] If the amplitudes, B.sub.rem, in front of the cosine and sinus functions of Equation 1 are different the equations describe a Halbach array with elliptical instead of circular cross section; in all other aspects the features of the resulting magnet array remains unchanged. Such magnet assemblies have applications in charged particle beam optics.

[0024] The resulting distribution of the local flux density in 001 Region-I and 002 Region-II with a multipole order greater than 1, for inside-directed flux, and in cylindrical coordinates are described by the equations in Table 1.sup.1. The equations for the flux density in Region-II and Region-III for outside-directed flux, multipole order greater than 1 in cylindrical coordinates are presented in Table 2. The special case for a dipole Halbach array with inside-directed flux are presented in Table 3. In the three sets of equations R.sub.i and R.sub.o are the inner and outer radii of the permanent magnet material, n is the multipole order, and B.sub.rem is the remanent field strength of the permanent magnet material.

TABLE-US-00001 TABLE 1 Equations for Halbach array for inside-directed flux. Region-I (n > 1): [00001]$B_r^I=\frac{B_{\mathrm{rem}}*n}{n-1}*\left(1-{\left(\frac{R_t}{R_o}\right)}^{n-1}\right)*{\left(\frac{r}{R_t}\right)}^{n-1}*\cos ?\left(n.Math..Math.?\right)$ [00002]$B_{?}^I=\begin{array}{c}{B}_{\mathrm{rem}}*n\\ n-1\end{array}*\left(1.Math.{\left(\begin{array}{c}{R}_t\\ R_o\end{array}\right)}^{n-1}\right)*{\left(\begin{array}{c}r\\ R_t\end{array}\right)}^{n-1}*\sin ?\left(n.Math..Math.?\right)$ Region-II (n > 1): [00003]$B_r^{\mathrm{II}}=\frac{B_{\mathrm{rem}}*n}{n-1}*\left(1-{\left(\frac{r}{R_o}\right)}^{n-1}\right)*\cos ?\left(n.Math..Math.?\right)$ [00004]$B_{?}^{\mathrm{II}}=\begin{array}{c}{B}_{\mathrm{rem}}\\ n-1\end{array}*\left(1.Math..Math.{n?\left(\begin{array}{c}r\\ R_o\end{array}\right)}^{n-1}\right)*\sin ?\left(n.Math..Math.?\right)$ The flux density in Region-III is zero.

TABLE-US-00002 TABLE 2 Equations for Halbach array for outer flux. Region-III (n < ?1): [00005]$B_r^{\mathrm{III}}=\frac{B_{\mathrm{rem}}*n}{n-1}*\left(1-{\left(\frac{R_t}{R_o}\right)}^{1-n}\right)*{\left(\frac{R_o}{r}\right)}^{1-n}*\cos ?\left(n.Math..Math.?\right)$ [00006]$B_{?}^{\mathrm{III}}=-\frac{B_{\mathrm{rem}}*n}{n-1}*\left(1-{\left(\frac{R_t}{R_o}\right)}^{1-n}\right)*{\left(\frac{R_o}{r}\right)}^{1-n}*\sin ?\left(n.Math..Math.?\right)$ Region-II (n < ?1): [00007]$B_r^{\mathrm{II}}=\frac{B_{\mathrm{rem}}*n}{n-1}*\left(1-{\left(\frac{R_t}{r}\right)}^{1-n}\right)*\cos ?\left(n.Math..Math.?\right)$ [00008]$B_{?}^{\mathrm{II}}=-\frac{B_{\mathrm{rem}}}{n-1}*\left(1-{n?\left(\frac{R_t}{r}\right)}^{1-n}\right)*\sin .Math..Math.\left(n.Math..Math.?\right)$ The flux density in Region-I is zero.

TABLE-US-00003 TABLE 3 Equations for a dipole Halbach array for inner flux. Region-I: [00009]$B_r^I=B_{\mathrm{rem}}*\ln ?\left(\frac{R_o}{R_t}\right)*\cos .Math..Math.\left(?\right)$ [00010]$B_{?}^I=-B_{\mathrm{rem}}*\ln ?\left(\frac{R_o}{R_t}\right)*\sin .Math..Math.\left(?\right)$ Region-II: [00011]$B_r^{\mathrm{II}}=B_{\mathrm{rem}}*\ln ?\left(\frac{R_o}{r}\right)*\cos .Math..Math.\left(?\right)$ [00012]$B_{?}^{\mathrm{II}}--.Math.B_{\mathrm{rem}}*\left(\ln ?\left(\frac{R_o}{r}\right)-1\right)*\sin .Math..Math.\left(?\right)$ The flux density in Region-III is zero.

[0025] The resulting flux density distribution given by these equations for the case of a quadrupole (n=2) for inside-directed flux are shown in FIG. 2. The inner and outer radii (R.sub.i 004 and R.sub.o 005) of the permanent magnet material are arbitrarily chosen as 100 mm and 150 mm, respectively, as an example.

[0026] The flux density distribution in the inner circle, i.e. the inside of the Halbach array shows a standard 2-D quadrupole field, given by: B.sub.r=const*r*cos(?) and B.sub.?=?const*r*sin(?) with 0?r?R.sub.i. As can be seen from the equations in Table 1, the flux density inside of the permanent magnet material itself is more complicated. The complete radial dependence of the radial and azimuthal field component for Regions-I, -II and -III are shown in FIG. 3.

[0027] The flux density in Region-I is a precise quadrupole field, represented by a linear increase of B.sub.r and linear decrease of B.sub.? from the center to the inner boundary of the permanent magnet material (see FIG. 4 left and middle). The total field in this region shows a linear rise. In the adjacent Region-II, B.sub.r is decreasing from its maximum value at the start of Region-II to zero; the azimuthal component shows a linear rise from a pedestal value to a maximum at the border to Region-III. The total field shows a complex dependence on radius, first falling than increasing, given by the opposite radial dependence of B.sub.r and Bo in this region.

[0028] The resulting flux density distribution described by the equations in Table 2 for the case of a quadrupole (n=2) for outside-directed flux are shown in FIG. 5. As can be seen in that figure, the flux density in Region-I is zero and the flux from Region-II extends towards the outside into Region-III.

[0029] For both cases, the inside-directed and outside-directed Halbach array, the radial distributions further depend on the radial thickness of the permanent magnet material. As can be seen by the equations in Tables 1 to 3, all flux densities obey the same multipole order as given by the magnetization (Equation 1), and no terms of a different multipole order are present. Although, the resulting flux density distributions, shown in FIG. 2 and FIG. 3 are rather complex, they result from the simple sinusoidal magnetization given be equation 1.

Manufacturing of Permanent Magnets:

[0030] Permanent magnets with high energy products like neodymium-iron-boron magnets are produced with a modified powdered metallurgical process which requires the following manufacturing steps. See FIG. 7 for an exemplary process.

Preparing the Powdered Metal

[0031] The appropriate amounts of neodymium, iron, and boron are heated to the melting point under vacuum. The vacuum prevents any chemical reaction between air and the melting materials that might contaminate the final metal alloy. Once the metal has cooled and solidified, it is broken up and crushed into small pieces, which are then ground into a fine powder.

Pressing

[0032] The powdered metal is placed in a die that has the approximate shape of the finished magnet. A magnetic field is applied to the powdered material to line up the powder particles. While the magnetic force is being applied, the powder is pressed from the top and bottom with hydraulic or mechanical rams to compress it to within about 0.125 inches (0.32 cm) of its final intended dimensions.

Heating

[0033] The compressed, powdered metal is removed from the die and placed in an oven for sintering which fuses the powder into a solid piece. The process usually consists of three stages. In the first stage, the compressed material is heated at a low temperature to slowly drive off any moisture or other contaminants that may have become entrapped during the pressing process. In the second stage, the temperature is raised to about 70-90% of the melting point of the metal alloy and held there for a period of several hours or several days to allow the small particles to fuse together. Finally, the material is slowly cooled down in controlled, step-by-step temperature decrements.

Annealing

[0034] The sintered material undergoes a second controlled heating and cooling process known as annealing. This process removes residual stresses within the material and strengthens it.

Finishing

[0035] The annealed material is very close to the finished shape and required dimensions. A final machining process removes any excess material and produces a smooth surface. The material is then given a protective coating to seal the surfaces.

Magnetizing

[0036] Up to this point, the material is just a piece of compressed and fused metal powder. Even though it was subjected to a magnetic force during pressing, that force didn't magnetize the material, it simply lined up the loose powder particles. To turn it into a magnet, the piece is placed between the poles of a powerful electromagnet and oriented in the desired direction of magnetization. The electromagnet is then pulsed, typically for a few milli-seconds to several Tesla. The resulting magnetic force aligns the magnetic domains within the material and transforms the piece into a permanent magnet. The remanent flux density, B.sub.rem, achieved in the magnetization process depends on the field strength of the magnetizer. For neodymium-iron-boron field strengths of more then 60 kOersted are needed to achieve the highest possible values of B.sub.rem. A 2D coil configuration for an embodiment of a magnetizer is shown in FIG. 6 which depicts a coil configuration for the magnetizer comprising of two inner and two outer DH/DDH coils placed concentrically to magnet ring with center radius R.sub.h. Coils at R1&R4 are coupled to generate angular field at R.sub.h. Coils at R2&R3 are coupled to generate radial field at R.sub.h.

Quality Control

[0037] Each step of the manufacturing process is monitored and controlled. The sintering and annealing processes are especially critical to the final mechanical and magnetic properties of the magnet, and the variables of time and temperature are therefore closely controlled.

Single Step Manufacturing of Halbach Arrays:

[0038] As has been pointed out herein, manufacturing Halbach arrays out of pie-shaped pieces with appropriate magnetization direction requires machining of permanent magnet material. The required machining process is complex and expensive due to the hardness and brittleness of the sintered permanent magnet material and the presence of strong magnetic forces.

[0039] A recently disclosed manufacturing process of manufacturing so-called permanent magnet wire disclosed in patent application PCT/US17/25212 filed Mar. 30, 2017, herein incorporated by reference, enables manufacturing of pie-shaped permanent magnets of any length with arbitrary magnetization direction. In case of neodymium-iron-boron, the prepared fine powder is inserted into tubes of a non-magnetic metal, e.g. stainless steel or titanium, which allows unhampered penetration of magnetic flux of the final magnet wire. Using a swaging process the tubes are shaped and reduced in size to the required cross section. The swaging process compresses the powder under an external magnetic field that aligns the crystals. The final resulting cross section of the tubes can be circular, rectangular, pie-shaped or other. The tubes are then sintered with the appropriate temperature profile. After cooldown, the tubes are magnetized with the required orientation of the field direction. For the application in Halbach arrays the disclosed process eliminates the costly machining process of permanent magnet material and significantly facilitates the assembly of tube-shaped, long Halbach arrays.

[0040] With the powder-in-tube process no annealing and machining of the sintered magnets is needed, and no further surface coating, as required for conventional permanent magnets, is required.

[0041] The powder-in-tube process described here can be modified to enable single-step manufacturing of flux-directed assemblies (Halbach arrays) of such as, for example, doughnut shape or in the form of linear structures. For dough-nut shape assemblies the magnetic powder, e.g. neodymium-iron-boron, is filled into the radial gap of two concentric tubes of appropriate diameter and length. As for the permanent magnet wire the tube must be non-magnetic to allow unhampered penetration of magnetic flux of the final product. The powder is compressed while exposed to a magnetic field that aligns the magnetic particles in the direction needed in the final flux direction. The field direction as a function of azimuth is determined by Equation 1. After sintering and cool-down the dough-nut shaped structures are magnetized. The magnetizer, described in the following, imprints the correct field directions as needed for the flux-directed assembly. The resulting Halbach arrays for inside- or outside-directed flux have the ideal continuous magnetization directions which cannot be achieved with arrays assembled out of a given number of pie-shaped segments. The described manufacturing process significantly reduces manufacturing cost of Halbach arrays. Given by the mechanical strength of the concentric tubes being used, the resulting assemblies can be highly robust as needed for example for electrical machines operating at high RPM. Due to the continuous variation of the magnetization direction, which is not possible with an assembly of separate pie shaped segments, the performance of the single-step Halbach arrays is superior to that available in the prior art.

[0042] The disclosed manufacturing process of flux-directed assemblies is applicable to any magnetic powder material and not limited to neodymium-iron-boron. Novel, non-rare-earth materials currently under development are directly applicable. As shown in equation 1, the field of the magnetizers should not have any dependence on the radius. While any multiple field with order n greater than 1 has a radial dependence, this is overcome by using a magnetization filed that is higher than the saturation magnetization of the material being magnetized. For NdFeB this can be as high as 7 Tesla. However, using pulsed magnetic fields this can be achieved.

Magnetizer Coil Design:

[0043] The 2-D field generated inside and outside of an ideal cos n? coil of radius R is given by Beth's current sheet theorem.sup.2,

[00013]$B_{i.Math..Math.n}?\left(z\right)=-\frac{{?}_0.Math.J_n}{2}.Math.{\left(\frac{z}{R}\right)}^{n-1}$$B_{\mathrm{out}}?\left(z\right)=\frac{{?}_0.Math.J_n}{2}.Math.{\left(\frac{R}{2}\right)}^{n+1}$

where ? represents the multipole order, z=re.sup.?? the complex coordinate and J.sub.n the current density in the current sheet. The current density J.sub.n can be expressed as number of ampere-turns I in the

[00014]$\frac{?}{2.Math.n.Math.}$

section of the coil and is given by J.sub.n=nI/R. Replacing current density with ampere-turns in above relation gives,

[00015]$B_{i.Math..Math.n}?\left(z\right)=-\frac{{?}_0.Math.\mathrm{nI}}{2}.Math..Math.\frac{z^{n-1}}{R^n}$$B_{\mathrm{out}}?\left(z\right)=\frac{{?}_0.Math.\mathrm{nI}}{2}.Math.\frac{R^n}{z^{n+1}}$

The 2-D magnetic field in a region between two concentrically placed cos n ? coils with radius R.sub.a and R.sub.b (R.sub.b>R.sub.a) and currents I.sub.a and I.sub.b is given by,

[00016]$B?\left(z\right)=\frac{{?}_0.Math.n}{2}.Math.\left(\frac{I_a.Math.R_a^n}{z^{n+1}}-\frac{I_b.Math.z^{n-1}}{R_b^n}\right)$

Noting z=re.sup.?? and B(z)=B.sub.y(r,?)+iB.sub.x(r, ?)=e.sup.?i?(B.sub.r(r, ?)?iB.sub.?(r, ?)), the radial and angular component of the resulting magnetic field are given by,

[00017]$B_r?\left(r,?\right)=\frac{{?}_0.Math.n}{2}.Math.\left(\frac{I_a.Math.R_a^n}{r^{n+1}}-\frac{I_b.Math.r^{n-1}}{R_b^n}\right).Math.\cos .Math..Math.n.Math..Math.?$$B_{?}?\left(r,?\right)=\frac{{?}_0.Math.n}{2.Math.}.Math.\left(\frac{I_a.Math.R_a^n}{r^{n+1}}+\frac{I_b.Math.r^{n.Math..Math.1}}{R_b^n}\right).Math.\sin .Math..Math.n.Math..Math.?$

[0044] At any given radius r a purely radial field with cos n? variation is generated, if relations R.sub.aR.sub.b=r.sup.2 and I.sub.a=?I.sub.b are simultaneously satisfied. In that case the resulting B.sub.?(r, ?)=0 everywhere on a circle of radius r. On the other hand, a purely angular field with sin n? variation is generated on circle of radius r if relations R.sub.aR.sub.b=r.sup.2 and I.sub.a=I.sub.b are simultaneously satisfied.

[0045] Design for single step magnetization fixture is based on cos n? coils. The actual implementation of such coils can be based on AML patent technologies including Double-Helix (DH), Direct-Double-helix (DDH) or Constant-cosine-theta (CCT) coil configurations. The single step magnetization process requires four cos n? coils to independently control radial and angular magnetization of a ring magnet. Such a system can produce both internal and external Halbach field configurations.

[0046] A 2-D coil configuration for the magnetizer comprising of two inner and two outer DH/DDH coils placed concentrically to magnet ring with center radius R.sub.h as show in FIG. 6. Coils at R.sub.1 & R.sub.4 are coupled to generate purely angular field with sin n? variation at R.sub.h. They have same number of Amp-turns I.sub.14. Coils at R.sub.2 & R.sub.3 are coupled to generate radial field with cos n? variation at R.sub.h and have number of same number of Amp-turns I.sub.23. The field at center radius R.sub.h of magnet ring is given by,

[00018]$B_r?\left(?\right)=+{?}_0.Math.{\mathrm{nI}}_{23}.Math.\frac{R_2^n}{r_h^{n+1}}.Math.\cos .Math..Math.n.Math..Math.?$$B_{?}?\left(?\right)=?{?}_0.Math.{\mathrm{nI}}_{14}.Math.\frac{R_1^n}{r_h^{n+1}}.Math.\sin .Math..Math.n.Math..Math.?$

[0047] The amplitude of the radial and angular field components can be made identical by satisfying relation I.sub.14R.sub.1.sup.n=I.sub.23R.sub.2.sup.n, as required for Halbach magnet ring configuration. Further all four coils can be coupled to have same current amplitude I.sub.0 by adjusting number of turns in coil 1 & 4 N.sub.14, and coils 2 &3 N.sub.23 such that the relation

[00019]$\frac{I_{23}}{N_{23}}=\frac{I_{14}}{N_{14}}=I_0$

is satisfied. The current direction in each magnetizer coil will depend on the remanent magnetization required for the ring magnet.

[0048] Direct Helix (DH), Direct Double Helix (DDH) and Canted Cosine Theta (CCT) coil configurations offer highest field uniformity, i.e. for a sufficiently long coil higher-order components are highly suppressed. DDH coils can sustain very high current densities and therefore enable coils with very low inductance, which is needed to achieve the required high field strength in the magnetizer. Since the remanent field achieved in the magnetization process depends on the magnetizer field strength, this field strength should be uniform throughout the permanent magnet material. This can be realized by choosing the magnetizer field strength in the saturation region.

Other Materials:

[0049] The manufacturing processes of flux-directed magnet assemblies, described above, are not limited to the use of magnetic powders like neodymium-iron-boron or samarium-cobalt, but any other magnetic powder. Also, the recently disclosed manufacturing of permanent magnet wire described in international application PCT/US17/25212, filed in the United States Receiving Office on Mar. 30, 2017, which is herein incorporated by reference in its entirety, would benefit from the magnetizer described in this disclosure. Un-magnetized pie-shaped permanent magnet wires can be assembled to Halbach arrays and the then magnetized as a complete assembly. In this case, no magnetic forces must be overcome in the assembly process, and the individual wires can be welded together before magnetization. Welding already magnetized wires could destroy the existing magnetization by exceeding the Curie temperature of the magnetic material. Likewise the present method would benefit the manufacture of dual rotor synchronous machines as described in international application PCT/US17/25214, filed in the United States Receiving Office on Mar. 30, 2017, which is herein incorporated by reference in its entirety,

Example Process and Magnetizer for a Motor Rotor:

[0050] FIG. 7 provides photos of example configuration for a motor rotor including the resultant flux-directed magnetic field of using two, magnetizer coils (FIG. 8). FIG. 9 provides the 2D D analysis of the magnetized rotor having a flux-directed field configuration.