Tom Bishop, P.E.
EASA Senior Technical Support Specialist

The wires that are associated with most motor and generator windings are copper magnet wires. For some special application machines, there are other wire types that have been used, such as Litz wire (very fine woven strands) or lead wire. In this article, we will address some issues relating to magnet wire type conversions and combinations.

The term magnet wire brings to mind the thought that the wire is somehow “magnetic,” which is not the case. The reason for the name is that it is wire used in magnetic coils. Thus, they are coils that make use of electro-magnetism. The two physical types are round and rectangular magnet wire. Strictly speaking, square wire is a form of rectangular wire. Having mentioned round and rectangular wire, we will move on to our first topic: the conver­sion of rectangular to round wire.  

Rectangular to round wire conversions
How do we convert rectangular to round wire, and are there any pitfalls? To convert from rectangular to round wire, we need to determine the wire area of the rectangular wire and then determine the combination of round wires that will yield the same wire area. The cross sections of round and rect­angular wire are of simple geometric shapes, and it appears that the conver­sion should be quite simple. However, the corners of most rectangular (and square) wire are radiused.  

Step #1: Determine gross area
To obtain the rectangular wire area, we first multiply the thickness times the width. If the dimensions are in inches we use thousandths of an inch, or square mils, as units. The value from this calculation is the gross wire area in square mils, before taking the corners into account.  

Step #2: Account for radius factor, if applicable
Most wires have a corner radius (see Figure 1) and the reduction in area at the corners must be subtracted from the wire area (see EASA Techni­cal Manual Section 7.1, Tables 1, 2 and 3). For example, a wire that is 0.144” thick by 0.289” wide (3.66 mm x 7.34 mm) will have a corner radius of 0.031” (0.79 mm), which necessitates a reduction in wire area of 838 square mils (0.541 mm2). Following through with the math, the gross wire area of the 0.144 x 0.289 wire in square mils is 144 x 289, or 41616 square mils (26.8 mm2). Subtracting the radius fac­tor area of 838 square mils, the result is a net wire area of 40778 square mils (41616-838, or 26.3 mm2). The effect of the corner radius is that the actual wire area in this example is about 98% (40778/41616 x 100%) of the gross area. A useful rule of thumb when the corner radius is not known is to multiply the thickness times width value by 0.98 to obtain the wire area.  

Note: Some small wires have rolled corners providing a full rounded edge, which does not reduce the gross wire area; the net area is equal to the gross. For example, wires with a thickness of 0.062” (1.57 mm) or less that conform to NEMA Magnet Wire MW 1000 will have a full rounded edge.  

Step #3: Determine circular mil area if converting to round wire
To convert from rectangular to round wire, we also need to know the “circular mil area” of the rectangular wire. That value is obtained by multi­plying the net wire area in square mils by the conversion factor 1.2732 (see Figure 1). Applying this multiplier to our example wire, the circular mil area of the 0.144 x 0.289 wire is 51,919 circu­lar mils (40778 x 1.2732). Although the conversion process is straightforward. it can be confusing. The two steps that are most problematic are remembering to convert the rectangular wire thick­ness and width to mils and to obtain the gross wire area in square mils (not circular mils) before subtracting the value associated with the radius factor. 

Step #4: Determine round wire equivalent, if applicable
Having converted the rectangular wire area to circular mils, the next mathematical step is to determine a round wire combination that provides an equivalent wire area. Note the term “mathematical step” in the last sen­tence. Before doing the actual conver­sion, we need to consider the geometry of a rectangular wire winding versus a round wire winding. Simply put, the round wire winding of equivalent area will require more slot space than its rectangular predecessor. To visualize the situation, think of a circle inside a square, with the length of the sides of the square equal to the diameter of the circle. The circle touches each side of the square, but there are spaces inside the corners of the square. The circle in this case has 0.8754 the area of the square. That is about a 12.5% reduc­tion in area.  

Fortunately, the round wires do not stack uniformly on top of and alongside each other, but tend to nest between each other. In most cases the round wire area must be reduced about 5-10% if the form coil winding had minimal separators and bottom sticks, which is still a significant reduc­tion in wire area. Make certain that the reduced wire area will not result in winding overheating, and increase the insulation rating at least one class higher than the original, e.g., from class B to class F or H.  

If the original winding is a medium-voltage form coil stator winding being redesigned to low voltage random wound, such as from 4000 to 460 volts, the slot insulation requirement will be much lower, and the round wire versus rectangular wire area per amp can be increased. Low-voltage stator, wound rotor and armature form coil windings that will remain at the low voltage level will need to be assessed for the effect of any wire area per amp reduction. Also, armature wire fit in the commutator risers will need to be assessed. EASA’s technical support team can assist you with these evaluations.  

Metric and AWG wire conversions
One of the effects of globalization is that motors built with AWG wires may be used in countries that use metric wires, and vice versa. When taking winding data, always use a micrometer to measure wire size. Do not use a wire gauge. The wires in a motor may be metric, AWG full-size, or AWG half-size. Further, if the motor was manufactured outside of North America, the original wire is almost certainly metric.  

If the wire is metric and only AWG wire is available, how do we proceed? First, as noted above, measure the wire with a micrometer. Next, look up the closest wire size on a magnet wire table, such the applicable one in Section 7 of the EASA Technical Manual (see Figure 2). For example, if the wire measures 0.039” (0.99 mm), the closest metric size is 1.0 mm (0.0394”). In some cases the wire will need to be measured to the 4th decimal place (0.000x”) to determine the metric wire size. Also, view the table in the EASA Technical Manual and note that metric wire sizes are the millimeter dimension.  

Using our example, we note that the 1.0 mm diameter wire is a metric gage 1.0. The nearest AWG wire size is #18, with a diameter of 0.0403” (1.02 mm). The wire area of #18 AWG is about 4.5% greater than the 1.0 metric wire. Inserting coils in a stator, wound ro­tor or armature may be more difficult. However, do not reduce turns because that will affect the motor performance. Among the effects of reducing turns are increased magnetic flux densities, no load current, starting current, and core losses.  

If the wire is used in a DC shunt field coil, the larger wire will reduce winding resistance. That will increase the ampere-turn strength of the coil if the supply voltage is constant. The increased field coil strength could reduce armature speed, necessitating a slight overvoltage on the armature to attain rated speed. A combination of a full AWG wire size for the inside part of the coil and a half-size AWG wire for the outer part of the coil may be needed to match the original coil ampere-turn strength. Contact EASA technical support for this type of conversion.

If the scenario is reversed, that is, we only have metric wire and the winding as received has AWG wire, how do we proceed? The answer is to follow the same steps given above, using AWG values for the original and metric wires for the conversions.

Wire size combinations
For practical and economic rea­sons, service centers stock a limited range and quantity of wire sizes. Con­sequently, changes in wire combina­tions are sometimes necessary when rewinding motors and generators. A good practice is to use no more than two different wire sizes that are not more than one full AWG or metric wire gauge apart. Using wire combi­nations wider than that can result in the smallest wire gauge wire(s) being melted and thus open when a connec­tion is brazed. For example, if a com­bination of 2#17 AWG wires and 1#20 AWG wire is used, the smaller wire has only 70% of the diameter of the larger wire, and half the area. The dif­ference in proportions can lead to the #20 AWG wire becoming open during the connection process. The resulting loss of total wire area reduces the wire area per amp (CMA) and increases winding heating, consequently reduc­ing winding thermal life.  

How should we change wire combinations? Let’s use an example of a winding that has 3#12 AWG and 1#12.5 AWG wires to illustrate the method. Few service centers would stock #12 wire, and far fewer might have #12.5 wire on hand. Further, the stiffness of the large diameter wire makes manual coil insertion difficult. A combination of wire sizes smaller than #12 is more practical.

The larg­est wire size commonly stocked is 14 AWG, which is also relatively stiff, thus many winders would prefer us­ing a combination of wires with the largest being 15 AWG, or 1.5 mm if using metric wire. In general, sizes from approximately 15 AWG to 18 AWG (1.5 mm to 1.06 mm) yield the best use of slot space. Much larger wire sizes tend to leave a lot of air space, while a large number of paral­lel smaller wires tend to have more film coating as a proportion to the total slot fill. When considering use of a larger wire size, check that the slot opening is wide enough to allow easy insertion without scuffing the wire insulation.  

The first step in the conversion is to determine the total wire area, which is 25427 circular mils in this case. Next, we calculate various com­binations of #15 and #16 wires until we closely match the original wire area. A combination of 3#15 and 6#16 wires has a circular mil area of 25260, matching the original circular mil area within 1%. A combination that is slightly larger is 4#15 and 5#16 wires, with an area of 25940 circular mils, or about 2% more than the original wire area. If slot space allows, that would be the better choice because it is larger in area than the original.  

If the new wires will be metric sizes proceed in the same manner as with AWG wire, determining a com­bination of smaller diameter wire sizes that match the original wire area, preferably within 2%. To put the original wire in metric size perspec­tive, the #12 AWG has a diameter of 2.05 mm, and the #12.5 AWG diam­eter is 1.94 mm. If we select 1.5 mm and 1.4 mm wires, the combination of 6-1.4 and 5-1.5 metric wires has an area of 25204 circular mils, which is within 1% of the original wire area. A wire combination that is larger than the original by less than 1% is 5-1.4 and 3-1.5 metric wires. That would be the preferred combination with slightly greater wire area than the original.

Categories: AC motors, Stators/windings, Design/theory/application, Wire

Tags: Windings Magnet wire

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