Abstract
A new method of measuring reversible permeability is described. The method is not limited by the need to employ laminated specimens of material, since allowance is made for eddy-current effects within the specimen. Measurements were made on solid-bar specimens of two types of rail steel at a frequency of 5 kHz. The results cover biasing field strengths between 160 and 170kA/m.
Measurement of reversible permeability using solid (nonlaminated) specimens
R. Langman, Dip.Tech.(Elec.Eng.)
Indexing terms: Eddy currents, Permeability measurement, Steel
the ratio of the change of flux density to the change of field producing it, i.e. A.8//z0A//, is the incremental permeability ju,A . Bb and Hb are referred to as the biasing-induction and
Hale Waihona Puke List of principal symbols B = flux density, T H = magnetic field strength, A/m /JL0 = primary magnetic constant, H/m fxr = relative permeability /xA = incremental/reversible permeability PepA = apparent permeability R — search-coil radius, m rs = specimen radius, m a = single currenf-loop radius, m p = resistivity, Qm / = frequency, Hz o) = angular frequency, rad/s y/2\K = depth of pentration, m Introduction The requirement of measuring the permeability of solid specimens of steel arose from the development of an eddycurrent-type crack detector1 for use on steel rails. The detector consists of an( exciting coil carrying high-frequency current that induces eddy currents in the metal surface. The action of the induced currents can be likened to the secondary coil of a transformer, the exciting coil being the primary. The impedance of the primary depends on the magnitude of the eddy currents, which, in turn, depend on the metal in which they flow (and also on the proximity and dimensions of the exciting coil). When the metal surface is cracked or pitted, the flow of eddy current is obstructed, and this shows as a change of impedance of the excitation winding. It has been shown by Hammond2 that the distribution of eddy currents in a metal surface owing to a single flat-turn excitation coil is governed by a dimensionless factor represented by [jLcoa2lp. Study of this instrument therefore creates the need to measure [x for rail steel. Most methods of measurement rely on the use of laminated specimens to avoid eddycurrent effects. This approach cannot be adopted in this instance, since the metal under study is nonlaminated. A new method of measurement had to be devised. Permeability A ferromagnetic material has several permeabilities, and methods of measurement are determined by the particular permeability required. In this Section the definitions of permeability are discussed, so that the one relevant to the action of the crack detector can be found; this, in turn, determines the method of measurement. Fig. 1 shows the relationship between B and 7/for an initially unmagnetised specimen. The relative permeability [ir is defined as the ratio Bb/fjL0Hb. With increasing field strength, /xr increases to a maximum and then decreases. When the magnetic field in the specimen is kept constant and an additional field is alternated between limiting values,
1
Hb Fig. 1
H
B\H curve for ferromagnetic material
2
biasing-field strengths, respectively. It can be seen that JUA is less than fxr; but there is no simple relationship between the two quantities. The incremental permeability depends not only on Hb, but also on the amplitude of A/f; its value as A # tends to zero is called the reversible permeability JJLR. Note that, by definition, when Hb is zero, fxR — fjur (although, of course, it is not possible to measure \x.r at zero field strength). Sims3 discusses other factors influencing [MA; these include not only the amplitude of &.H but also its waveform. From the description of the crack detector, the yc in the expression \ioia1\p is the incremental permeability /u.^ with Hb=0. For the proposed crack-detection work, A// would be of the order of 200 A/m. Preliminary tests showed that /xA did not change measurably when AH was varied between 10 and 250A/m, and thus it is reasonable to assume that, at incrementalfieldstrengths of these amplitudes, the incremental and reversible permeabilities are equal. In the rest of this paper /xA will be used to denote reversible permeability. As stated, for normal operation of the crack detector, Hb would be zero, but it was deemed useful to measure values of /nA for a range of values of Hb, since this situation could occur in practical cases. Values of reversible permeability were then required at various biasing-field strengths for rail steel. With this in mind, methods of measurement are discussed in the following Section. Method of measurement of {xA The BjH curve of Fig. 1 is conveniently obtained using a laminated toroid of the specimen steel. A uniformly wound exciting winding produces a known field strength in the toroid; a search coil gives the change of flux on reversal of the magnetic field, and hence the flux density. Laminations are necessary to reduce currents that would 1887 3