This study with dimension testing of hollow objects with MF as an indicator medium. The procedure is schematically made by such way. The test passage of object is filled with MF which, if necessary, can be kept within a pre-set volume by external forces. The information on geometrical parameters of the object wall and passage is provided by electromagnetic probes mounted above the test object and receiving secondary magnetic field. The indicator medium is magnetized either by external magnetic source or by a local source installed within the probe.The probes can be magnetostatic and ponderomotive; paramagnetic and transforming [4]. Detailed information on the shape of passages of complicated geometry obtained by scanning and determining the secondary (induced) field topography is subsequently processed on a computer. A wide range of MF dimension testing problems can be reduced to finding the potential vector A = A_o exp jwt of electromagnetic field induced by a primary source fixed above the tree-layer medium with magnetic permeabilities m and electric conductivities m and electric conductivities m of the m-th layer; m = 1 to 4.

A₀ + k²_m A_0n = µ ₀µ _m i₀

A_0m = A_{0m - 1}, A_0n/n_m = µ_m+1µ^-1_mA_om+1/n_m

Where i ₀ is the volum current density in medium 1; k²_m = - gµ ₀µ _m In practical calculation of the probes the potential vector A_om induced by a thin turn with current I is determined; then, using superposition principle, the unknown quantities are found. For the turn with current

If km = 0; ₁ = {exp[- (Z+h)]}(1+ )(1+y)^-1

for nonmagnetic object with low electrical conductivity (µ_m= 1) x = y ^-2 = exp(-2d ); µ₄ >> 1-x = y ^-2 = ^-1 exp(-2d ). Since for a wide range of MF compositions µ₃ < 10 series expansion

where E_n and K_m are the first- and second-order elliptic integrals;

and the electric intensity E₀ and electromotive force E are related by ₀ If << 1 at d-0 ₀ (µ - 1)d . If , where A₀₁ is the potential vector of the turn located at the height z = -h and M^-1m = k_m = 0.

The calculation of the measuring system path of our probes has shown good agreement, both qualitative and quantitative (-10%) with the measurements. Kerosene-based samples with saturation magnetization M = 22 kA/m (MF = 22) to 66 kA/m (MF = 66) were used as a model MF. Probes Nos. 1 and 3 are transforming, with core diameters D = 3 and 1.1x 10^-3 m, respectively and a working frequency of 200 Hz; probes No. 2 are magnetic, based on the Hall effect, D = 2.8*10^-3 m. The probes can be used to test thickness of plane parallel passages or hollow electrically conducting walls, 0.1 to 10*10^-3 m. In the thickness range 0.1- 1*10^-3m their deviations of (2-5)*10^-5 m were confidentially measured. Dimension testing can also be done with a magnetic soft base. With variable magnetic properties µ₃ there is a range of MF thickness d at h = const or thickness h at d = const when functions ) (h) or (d) are similar. Because of this, using the normalised relations, variability of MF properties can be eliminated and the test sensibility and stability increased. Feasibility of MF dimension test of hollow object can beincreased by using electrically conducting MF and additional capacity probes; by directed change of µ_i and demagnetizing fields of MF volume with the aid of external field source.

Some hydrodynamic and magnetostatic problems connected with using magnetic fluids are solve; losing of MF mass when its moving in object tested; magnetic properties and their stability when magnetic field is applied.

REFERENCES

1. A. R. Baev, P. P. Prokhorenko, et. al., " Inventor's Certificate 641331", Bull. Izobr. (USSR), No. 1, 1979
2. A. R. Baev, P. P. Prokhorenko, et. al., "Inventor's Certificate 930077", Bull. Izobr. (USSR), No. 18, 1982
3. R. L. Bailey, JMMM, Vol. 39, pp. 178, 1983
4. 'Nondestructive Testing Devices Handbook', Moscow, Vol. 2, 1986
5. G. A. Grinberg, Selected Problems of Mathematical Theory of Mag. and Electr. Phenomena, Moscow, 1948