Feasibility study of determining axial stress in ferromagnetic bars using reciprocal amplitude of initial differential susceptibility obtained from static magnetization by permanent magnets

An electromagnetic method for determining axial stress in ferromagnetic bars is proposed. In this method, the tested bar is under the static magnetization provided by permanent magnets. The tested bar do not have to be magnetized up to the technical saturation because reciprocal amplitude of initial differential susceptibility (RAIDS) is adopted as the feature parameter. RAIDS is calculated from the radial magnetic flux density Br Lo = 0.5 at the Lift-off Lo = 0.5 mm, radial magnetic flux density Br Lo = 1 at the Lift-off Lo = 1 mm and axial magnetic flux density Bz Lo = 1 at the Lift-off Lo = 1 mm from the surface of the tested bar. Firstly, the theoretical derivation of RAIDS is carried out according to Gauss' law for magnetism, Ampere's Law and the Rayleigh relation in Rayleigh region. Secondly, the experimental system is set up for a 2-meter length and 20 mm diameter steel bar. Thirdly, an experiment is carried out on the steel bar to analyze the relationship between the obtained RAIDS and the axial stress. Experimental results show that the obtained RAIDS decreases almost linearly with the increment of the axial stress inside the steel bar in the initial elastic region. The proposed method has the potential to determine tensile axial stress in the slender cylindrical ferromagnetic bar.