Eddy current testing - effective permeability

Effective magnetic permeability frequency
On a long straight cylindrical conductor of radius r, magnetic permeability u, and electrical conductivity γ, a solenoid coil is tightly wound. When an alternating current is passed through the solenoid, an alternating magnetic field is generated in the cylindrical conductor, and the distribution of the magnetic field on the cross section of the cylindrical conductor is uneven due to the skin effect. The people then proposed a hypothetical model: the cylindrical conductor has a constant uniform magnetic field across the entire section, and the two magnetic permeability changes radially in the cross section. The magnetic flux produced by it is equal to the actual physical location in the cylindrical conductor. Magnetic flux.

Thus, a constant magnetic field and varying magnetic permeability are substituted for the actually changing magnetic field and constant magnetic permeability, and the entire varying magnetic permeability is called the effective magnetic permeability.

Eddy current detection similarity
The effective permeability is a parameter that depends entirely on the frequency ratio, and the effective permeability determines the distribution of eddy currents and magnetic field strengths in the specimen. Therefore, the distribution of eddy currents and magnetic fields in the test piece changes as the frequency ratio changes.

Theoretical analysis and derivation can prove that the distribution of eddy current and magnetic field strength in the test piece is only a function of the frequency ratio. Thus, the similarity rate of eddy current detection can be obtained: for two different test pieces, the geometrical distributions of effective permeability, eddy current density and magnetic field strength are the same as long as the corresponding frequency ratios are the same.

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