George P. Gogue
Joseph J. Stupak, Jr.
1. INTRODUCTION AND PURPOSE
A large number of magnets are magnetized in a uniform field along a straight-through axis. While fixtures used for radially-oriented and other specially shaped fields must be designed for the specific magnet shape (and often, for the material properties as well), fixtures used for straight-through magnetization are able to handle a variety of tasks. Straight-through magnetizing fixtures are of two basic types, the solenoid (Figure 1) (which may or may not have steel backing), and the C-frame (Figure 2). Of these, the C-frame is heavier, more expensive and takes up more space. Why then, would anyone prefer this type of fixture? The purpose of this paper is to explore the advantages and disadvantages of each type, and to present considerations for a choice between them, for particular applications. Complete design criteria for these designs is not however, within the scope of this paper.
Figure 1: Solenoid
Figure 2: C-frame
2. BASIS OF COMPARISON
Although both authors have had considerable experience with magnetizing fixtures, it was felt that in order to make a fair comparison between these two types it would be necessary to actually construct and test two fixtures, one of each type, of "equivalent" performance and to back up the results with such calculations and finite-element models as might be necessary. The problem then immediately presented is to decide what is meant by "equivalent". First, it seemed necessary for the fixtures to have the same internal volume, since only material within that volume could be magnetized, and since the magnetic energy supplied by the system is proportional to the volume integral of the field strength squared.
In addition, the winding should be equivalent, i.e. the same length of the same size of wire. The electrical resistances of the two fixtures would then be the same, although the number of turns on each would vary because of differences in shape. Beyond that, the fixtures were designed to shapes which were representative of usual practice, with proportions which were known to be good compromises between the competing requirements these fixtures must meet. In order to reduce time and cost, and to simplify experimentation however, both fixtures were made smaller than most of those in general use.
3. FIXTURE DIMENSIONS
a. The solenoid used in this comparison was wound on a Delrin bobbin, using 90 turns of AWG #14 round copper wire, .0641 inch, diameter bare, .0659 inch, diameter insulated. The clear bore of the bobbin was .775 inch, diameter and the wire coil length was 1.80 inch, long, for an internal working volume of .849 cubic inches. The coil itself was .815 inch ID and 1.438 inch OD. Measured with an ESI video bridge, the resistance at 20 Hz was .0740 ohm, as built, and the inductance was 107.7 microhenry. The assembly weight was found to be 188 gm, almost all of which was copper conductor.
b. The C-frame (Figure 2) was made of laser-cut laminations of 24 gage (.024 inch) mild steel, with a gap .464 inch wide and a cross section of 1.44 inch by 1.50 inch With .030 inch plastic faces over the pole ends and .005 inch bond joints, the remaining gap was .394 inch, for an internal working volume of .851 cubic inches. A winding of 29 ft 9.5 inch of AWG #14 round copper wire was wound near and on both sides of the gap, a total of 49 turns. The measured resistance at 20 Hz (ESI video bridge) was .0726 ohm and the inductance (at 10 mA) was 464.9 microhenry. The assembly weight was about 10.5 lb (4765 gm), about 25 times that of the solenoid. Of this weight, about 96% was accounted for by the pole steel.
4. FIRST-ORDER CALCULATIONS
The designer of a magnetizing fixture intended for general use wants to get the most useful magnetizing volume possible, in order to magnetize the largest part possible, or perhaps the largest number of smaller parts at once. The field strength H must be sufficient to completely coerce the magnets to full strength. In order to minimize heating and to keep the design within the limits of the magnetizer (pulse generator), the ratio of field to current (H/i) should be as large as possible. It seems reasonable then to compare the two fixture configurations on the basis of field strength times volume (HxV), at the same current and winding.
The field strength of an infinitely long, thin-walled solenoid is zero outside the coil, uniform and axially-directed everywhere within the coil and is therefore of magnitude:
H = field strength (coercive force)
n/l = coil turns per unit length
i = current in the coil conductor
If the coil is formed of a conductor of length c, the number of turns will be:
c = coil conductor length (in the coil segment of interest)
D = coil diameter
note: the conductor diameter is assumed to be negligibly small, compared to D.
The volume, with the coil in length l, is:
V = internal volume of the coil
The product of volume times field strength for length l of the infinite solenoid is therefore:
For a thin-walled solenoid of finite length (Figure 3), the solution for H on the axis is a vector pointing along the axis of magnitude:
Figure 3: Solenoid cross-section
For a solenoid of finite length, the coercive force-volume product is:
HxV = kcDi/4
k=(1/2)(cos J + cos K)
angles J and K are defined as shown in Figure 3.
The magnetomotive force around the C-frame magnetic path is:
mmf = ni
The field strength in the gap, if the mmf drop in the steel pole structure is negligible and fringing effects may be neglected, is:
H = coercive force in the gap
= gap length
If the cross-section of the fixture at the gap is square with sides of length W, the number of turns of conductor (of negligible diameter) of length c is:
n = c/4W
n = number of turns
c = conductor length
W = width of side of pole cross-section at the gap
The working volume within the gap is:
V = gap space volume
c. Ratio of H-V product
The H-V product for a C-frame fixture was calculated (approximately) as cWi/4, whereas the value for a finite solenoid was found to be kcDi/4.
The ratio of these two, which may serve as a rough measure of the comparative effectiveness of the two designs, is:
R = W/kD
W = average side of the C-frame gap
k=(1/2)(cos J + cos K)(see Figure 3)
D = solenoid average diameter
Following is a computation of this ratio for the two test fixtures:
The average side of the C-frame gap is (1.44 inch + 1.5 inch)/2 = 1.47 inch
The average diameter of the coil is (.815 inch + 1.438 inch)/2 = 1.1265 inch
Therefore k = (.848 + .848)/2 = .848
R = W/kD
= 1.47/(1.1265 x .848)
R = 1.54
5. CALCULATIONS VS. MEASUREMENTS
Applying the above calculations to the two fixtures, for the solenoid, the field strength in the center of the coil is calculated to be:
H = (n/l )i(1/2)(cos J + cos K)
n = 90 turns
l = 1.8 inch
(1/2)(cos J + cos K) = .848
The permeability of free space (or air) is 1 gauss/oersted, and 1 oersted = 2.02 amp-turns per inch.
The flux-density at the coil center, in gauss/amp of current, is thus calculated as:
B/amp = (90/1.8) X .848/2.02
B = 20.99 gauss/amp
The flux-density determined by finite-element-analysis and confirmed by measurement at other accessible points, is 20.8 gauss/amp.
The field intensity for the C-frame is calculated approximately as:
H = mmf/l(g)
= 49 turns/.464 inch
= 105.6 amp-turns/inch
B = 105.6/2.02 X 1 gauss/oersted
= 52.3 gauss/amp
The actual value, found by direct measurement at the center of the C-frame gap, was 44.6 gauss. The rather large difference is accounted for by the spreading out of the flux lines near the center of the gap, as they pass outward, expanding sideways from one pole face, through the center and then converge toward the opposite pole face.
Nonetheless, the ratio of the center measurements, 44.6 gauss/20.8 gauss = 2.14, is quite large, and is larger than was predicted by the simplified analysis. The difference is due to the fact that the entire gap region of the C-frame is accessible, while the average diameter of the solenoid lies within the actual coil; the accessible volume is less than that which would be calculated based on it.
6. USEFUL MAGNETIZING VOLUME
How much of the total volume within a fixture may actually be used for magnetization, without significant loss of strength or variation? The field at the end of a solenoid is much less than in the middle (half or less) and the field at the edge of the gap of a C-frame fixture is also somewhat reduced. The absolute value of the coercivity is not what is needed but rather only the component in the preferred direction of the material to be magnetized.
It would not seem reasonable to base comparisons of the effectiveness of fixtures based on the maximum field reached within the magnetizing space, as one type might have a high field in a small region, at the expense of the rest. It was decided therefore, again somewhat arbitrarily, to use as a basis of comparison the volume of space within a fixture which had a component of magnetization in the preferred direction which was at least 90% of the (arithmetic) average field within the space.
(c) with sleeve and poles
Figure 4: Solenoid flux-plots
On this basis, it was found that all the solenoid variations had much more limited useful volume than the C-frame. A solenoid without steel structure, Figure 4a, had a useful volume of about 66% of the total. Adding a steel sleeve outside, Figure 4b, increased the peak field about 4% but the useful volume decrease to about 56%. Adding steel poles at each end, as well as the backing sleeve, Figure 4c, increased the peak field over the plain solenoid by 17% but decreased the useful volume fraction to 52% of the total. The C-frame, Figure 5, on the other hand, had a much more even field; 95% of the volume within the gap had field strengths within 90% of the average. These figures are for fields well below saturation, however.
Figure 5: C-frame flux-plot
7. OTHER CONSIDERATIONS
When a strong pulse of electrical current is passed through a solenoid (with no surrounding permeable pole structure), large magnetic forces act on the conducting wire. These forces are directed such as to crush the coil axially toward the center, while expanding the coil loops outward radially. These forces may be thousands of pounds per square inch of area, enough to cause structural failure in some cases. Bonding the coil to an outer steel structure adds to overall strength, while the permeability of the steel reduces the forces on the coil. If the steel sleeve is very highly permeable and unsaturated, almost no force remains on the coil. The sleeve must be laminated, however, or eddy currents may prevent rapidly changing flux from penetrating it.
The C-frame design provides good anchoring means for the windings. Its shape makes laminating relatively easy, compared to the solenoid.
A C-frame is naturally a better fit to parts which are short in the direction of magnetization compared to their cross-sectional dimensions. Modern, low-permeability magnet materials of high
coercivity are more efficient when made in these shapes. Older materials, such as the Alnico family and others, have high flux-density, relatively high permeability and correspondingly less coercivity. These parts must be long and thin, to prevent self-demagnetization and they naturally fit a solenoid better. For the most part, these magnet materials magnetize at lower field intensities than do the newer types, and so maximum performance is less critical.
It may be easier to load and unload parts either through the end (solenoids) or from the sides (a C-frame), depending on circumstances. After the pulse decays (usually on the order of milliseconds), a solenoid which is not steel-encased has no attraction for the magnet, which is therefore, easily removed. Parts magnetized in a C-frame, on the other hand, may be difficult to remove because of high magnetic forces, and may break during removal if fragile.
Parts which are not restrained may sometimes be violently expelled from either type of fixture, although the solenoid type has somewhat more difficulty in this regard than the C-frame. Parts which are off-center may be pulled inward, flying out the other end ballistically, or may be repelled outward by eddy currents. Solenoids sometimes react against the field of a just-magnetized part, resulting in a high force on the solenoid itself as well as an opposite force on the part. Parts placed off-center in a C-frame may be accelerated inward toward the center, then fly out the opposite side (as the pulse subsides), at right angles to the direction of magnetization.
8. FIXTURE BEHAVIOR AT VERY HIGH FIELDS OF SHORT DURATION
The magnetizing pulse must be short, in order to achieve the very high fields necessary to magnetize some high-energy materials without overheating the fixture or part. Exposed to these high, fast-changing fields, fixtures may saturate in magnetically permeable regions, be limited by eddy currents through any electrically conductive part, including the part to be magnetized itself, and may have increased apparent resistance, either by "reflection" of resistance from eddy currents or by the phenomenon known as "skin effect" in the conductors. Solenoids without metal backing or flux-carrying material are immune to saturation and eddy currents in those parts but may still be affected by skin effect. In addition, they may experience structural problems at very high fields.
Mild steel saturates completely at about 20,500 gauss. This is more than enough to magnetize ferrite materials, but high-energy materials such as samarium-cobalt and neodymium-iron may require much higher fields. Vanadium-permandur saturates at a still higher field intensity, about 24,000 gauss (including the coercive force component). This material contains high percentages of nickel and cobalt, and is very expensive (about $38 per pound at present). Its cost is often justified in very high-field fixtures, however, as an increment of field strength is many times more difficult to obtain above saturation than below it.
For a typical C-frame fixture, the coil layout on each side of the gap may be approximately equivalent to a one-radius spacing between two concentrated windings. The field in the center of such a pair of coils is:
H = .716 ni/r
r = coil radius
n = total number of turns (both coils)
It can be seen, then, that the penalty for the open space between the coils, when operated above the saturation level of the pole material, is not very great compared to the other advantages offered by this construction, since the field of a solenoid with windings uniformly distributed over this length, assumed to be of length r to the coil centerlines, plus 3/8 r to each side, for a total length of 1.75 r, would be at the center:
l/D = 1.75/2 = .875
H = .753 ni/l
The C-frame construction of magnetizing fixture is significantly larger, heavier and more expensive than a solenoid, but offers in return a more efficient use of the magnetizing pulse generator, a more uniform field and possibly other advantages for use with large pieces of highly permeable material such as Alnico and may have advantages for use with fragile parts and in other special circumstances.