The surface hardened steel is used in a large-sized ball bearing part or the gear part in a large-sized heavy industrial machine, etc. The inspection of the surface hardened depth is important in the intensity or the guarantee of quality of these parts. Especially, since the size of the hardened steel parts in a large-sized heavy industrial machine is large, the destructive inspection using the Vickers hardness tester, etc. is made difficult. Therefore, the non-destructive inspection method is needed for the evaluation of its hardened depth. The maximum permeability and the conductivity of the hardened domain are smaller than the non-hardening domain inside the steel [1]. Therefore, the electromagnetic non-destructive methods for detecting the surface hardened depth by the difference of flux density inside the surface hardened steel are proposed [2], [3]. In this paper, the high sensitivity inspection method using the detecting of the magnetic field on the surface of the hardened steel is investigated. The detection sensitivity of this proposal technique is higher than the method [3]of detecting the flux density inside the hardened steel. The magnetic field is estimated by 3-D nonlinear finite element method (FEM) taking account of the electromagnetic characteristics of the layers with and without hardening. Moreover, the optimal design of the search coil in the proposal sensor for raising detection sensitivity is carried out using the evolution strategy method [4]. The usefulness of this proposal inspection method is shown also from comparison with an experimental verification. Inspection method and modeling of magnetic properties Fig.1shows the 1/2 domain of the proposed the inspection model for detecting the surface hardened depth inside the hardened SCM440 steel plate. The proposal electromagnetic sensor is composed of a magnetic yoke of lamination of silicon steel plates with an alternating exciting coil, and a search coil for the detecting of the magnetic field on the surface of the hardened steel. As for a search coil in this sensor, the $x -$direction of the magnetic field $( B_{x})$on the surface of the steel plate is detected. The width $( Sw)$, length $( Sl)$and height $( Sh)$of the search coil are 9.4mm, 6mm and 1.2mm, respectively. The distance (lift-off: $L_{o})$between the yoke of the sensor and the surface of the hardened steel is equal to 0.5mm. The exciting frequency and ampere-turns are 15Hz and 126AT, respectively. Fig.2shows the initial magnetization curves of the layer with and without hardening inside the SCM440 steel. And, since the conductivities of the steel plate with and without hardening are $3.61\mathrm {x} 10 ^{6}\mathrm {S} /\mathrm {m}$and $3.98\mathrm {x} 10 ^{6}\mathrm {S} /\mathrm {m}$, the permeability and conductivity are decreased with the increase of the hardness. The flux density and eddy current density are analyzed by 3-D electromagnetic FEM taking account of the initial magnetic curves and conductivities of the layers with and without hardening inside the steel. Moreover, the initial magnetic curve and conductivity in the layer between the hardened layer and non-hardened layer in the steel are calculated by interpolation using the electromagnetic property of each layer. Inspection of surface hardened depth in steel plate Fig.3shows the distribution of flux density inside surface hardened steel plate when the hardened depth is 0mm and 3mm, respectively. This figure denotes that since the permeability and conductivity in surface hardened domain is decreased the flux density in the surface domain in the steel plate is decreased when the hardened depth is increased. Fig.4shows the effect of the surface hardened depth on the value of the change rate of $B_{x}$in the search coil. The figure denotes that $B_{x}$is increased when the hardened depth is increased. This is, because the $B_{x}$from the impression magnetic field is increased since the permeability and conductivity in surface domain of the steel plate is decreased when the hardened depth is increased. As for $B_{x}$in the search coil, the calculated result is in agreement with measurement. In this research, comparison of the detection sensitivity of the inspection method [3]by the detecting of the flux density $( B_{z})$inside the magnetic yoke as shown in Fig.5, and this proposal method by the detecting of the magnetic field $( B_{x})$on the steel is investigated. In this model of Fig.5, a magnetic closed loop is formed between the sensor and the steel, and the flux density in the steel is detected with a search coil of the yoke. Fig.6shows the comparison result of absolute values of $B_{x}$and $B_{z}$for the detecting of the hardened depth of the surface hardened steel by experiment. This figure denotes that the detection sensitivity of the proposal method by $\vert B_{x}\vert $is higher than the method by $\vert B_{z}\vert $. Optimal design of search coil The optimal dimension of a search coil for detecting the magnetic field $B_{x}$in the proposal sensor is determined using the evolution strategy [4]. Fig.7shows the inspection result in the optimal search coil form determined by the evolution strategy. The width $( Sw)$, length $( Sl)$and height $( Sh)$of the optimal search coil are 20.36mm, 6mm and 1.8mm, respectively. The inspection result by the initial search coil model as shown in Fig.1is also shown in this figure. This figure denotes that the detection sensitivity of the optimal search coil is increased from the initial model. The optimal search coil is the form which detects more magnetic fields on the steel plate distributed between the magnetic poles of the magnetic yoke.