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The quality of permanent magnets is defined by several parameters such as Br, Hci, BHmax, permeability (μ) and reversible temperature coefficients of induction and coercivity. All these are measured parameters. Engineers designing devices for use at other than room temperature or in the presence of a demagnetizing field also use a characteristic describing the quality of the intrinsic curve. This calculated value, Hk, is too little understood and alternative definitions of curve quality are appearing. The Past: Prior to the late 1950s commercial magnet materials fell into two general categories: magnet steels and alnico. When measured, the Normal and the Intrinsic curves were very similar and only the Normal curve was routinely utilized. Even for alnico 8, where moderate differences between the curves are evidenced, the Intrinsic curve is successfully ignored as the Normal curve provides for conservative calculations. That point on the Intrinsic or Normal curves where the straight line deviates to a curve is called the “knee.” If the magnet were to operate below the knee, significant irreversible loss would occur. The earliest ceramic magnets did not exhibit true straight line (square loop) properties so a need existed to describe just how square the curve was. Motor designers were eager to push these magnets to their limits and also wished to know where approximately 10 percent knockdown would occur, especially on leading and trailing edges which would reduce motor cogging. James Ireland [1] proposed a quantity he called Hx, which was obtained from a horizontal line drawn at 0.8 x Br with a vertical dropped to the H axis from the horizontal line’s intersection with the Intrinsic curve (Figure 1). Later authors adjusted the determination of Hx starting with a value of 0.9 • Br. One such reference is Parker and Studders, Permanent Magnets & Their Application, in 1962 and 1964. Six years later Rollin J. Parker wrote a greatly updated text for the magnet industry, Advances in Permanent Magnetism [3], 1990, in which he too refers to this definition of Hx. Glenn R. Gaster of Indiana General and later 3M Corp. was also a proponent of a quantity called Hx. However, he modified the definition as follows; the line drawn from the 0.9 • Br point on the B axis was not a horizontal line, but slopes downwards at the Intrinsic Recoil slope. Where it intersects the intrinsic curve, a vertical is dropped to the H axis. That value of H is called Hx (Figure 2). Sometime prior to 1981 and continuing thereafter, several authors referred to the Hx value as Hk. One interpretation is that the “k” refers to “knee” of the intrinsic curve. These early writings referring to Hk include papers in the International Workshops on Rare Earth Magnets and Their Applications [5][6][7] (1981 and 1985) and the MMPA Permanent Magnet Guidelines [4] from 1988. The Present: Despite almost total lack of reference to Hk in textbooks on magnetism, it remains a useful quantification of intrinsic curve shape. The one exception found to-date is in Magnetism II [2] (du Tremolet de Lacheisserie, D. Gignoux and M. Schlenker) pp.13-14. They refer to Hk (in SI units it is μ 0Hk) as the “maximum working field… defined as the reverse field for which the magnetization is reduced by 10 percent.” In 2008, Stan Trout wrote [8] that [Hk] is “better than Hci”, which, interpreted means it is more informative about showing when a magnet will start to suffer loss of flux. By definition Hk is always less than Hci. If one were to divide Hk by Hci, the resulting number represents how “square” the intrinsic curve is. For a perfectly square curve, this squareness ratio [7] would be 1. For high quality rare earth and ferrite magnets typical values range from 0.90 to 0.95 though occasionally SmCo may be as low as 0.85. The Future: Is the current definition of Hk adequate? One difficulty arises with very high coercivity materials such as the “EH” grades of neo with Hci values greater than 30,000 Oe (2,390 kA/m). A recoil permeability slope of 1.05 produces an intrinsic recoil slope of 0.05. For example, for a Br of 11,000 gauss, 0.9 • Br = 9,900 gauss or a “drop” of 1,100 gauss. Calculating H=1,100 / 0.05 = 22,000 oersted. What this indicates is that no matter how high Hci is, or otherwise how good the demagnetization curve is, Hk will have a maximum value of 22,000 Oe and the squareness ratio will be low. Even with a recoil slope of 1.035, the maximum Hk is 31,400 Oe (2500 kA/m). M. Katter [9] has proposed a revision of the Hk definition to the IEC (International Electrotechnical Committee), an international standards organization. Katter’s revised definition (Figure 3) requires analysis and plotting only slightly more difficult than the traditional Hk method while retaining the primary purpose; identifying the value of H where the knee occurs. In fact, with some amplification it is what Glenn Gastner had proposed some 23 years ago. It also allows for variable sensitivity by specifying how much lower than the Intrinsic curve the new line will be drawn (Figure 3). Note also, that the frequently observed minor drop in induction as the curve moves away from the B axis is ignored in the calculation resulting in a more accurate assessment of squareness. One calculates the slope of the intrinsic curve between points A and B. A is located at H=20 percent of Hci and B is located at H=70 percent of Hci. Then a parallel line is plotted at some percentage lower than points A and B. In the example shown here, lines are drawn at 95 and at 90 percent of the intrinsic curve. The values of H at the intersections would be referred to as Hr,95 and Hr,90 respectively. This procedure can be performed automatically when making hysteresisgraph measurements or manually with a calculator and straight edge on a printed demagnetization curve. This method also accommodates the slight shifts in recoil slope that take place at elevated temperatures, producing a better estimate at high temperature. Like the standard Hk calculation, it does place a greater performance burden on lower Br materials: 90 percent of a smaller number produces a smaller drop in either the horizontal or the recoil slope lines used to obtain Hk or Hr. One alternative is to calculate a fixed drop, say 0.2 Tesla. The resulting intersection point could then be called Hr,0.2. Whatever is finally decided it seems that curve shape and the describing value will finally see the attention and respect it deserves. Steve Constantinides is director of Technology for Arnold Magnetic Technologies Corp. Steve solicits and performs research, engineering and project work associated with Arnold Magnetic Technologies’ permanent and soft magnetics businesses. He is a graduate of Alfred University in Ceramic Engineering. Prior experience includes 12 years with Corning, Inc. involved with glass ceramics, combustion systems design and manufacturing management systems. He can be reached at SConstantinides@ArnoldMagnetics.com. Click here for reuse options!
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When (hard) ferrite magnets, also known as ceramic magnets, were developed in the mid to late 1950s they began to dominate the market for permanent magnets due to their low material cost and good magnet properties. By the mid 1960s ferrite magnets had made significant inroads into loudspeaker and motor applications. Ferrite magnets also had an interesting and useful characteristic, the Normal curve under most conditions was very close to a straight line – at least to the maximum energy point. Due to this, ferrite became known as a “straight line” material. Engineers working with the Intrinsic curve, referred to ferrite magnets as a “square loop” material. Today, one can hear either expression used. The relevance is that as long as the operating point of the magnet remains within the linear portion of the Normal (or Intrinsic) curve, the magnet will suffer little to no irreversible loss in magnetic output.© 2011 Webcom Communications Corp.