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Theoretical Analysis of the Influence of Different Microstructure on Barkhausen NoiseLi Qiang Liu zhiming Miao longxiu Yuan Zuyi
College of Mechanical and electric Engineering,
Northern Jiaotong University Beijing 100044 Chain.
Where Hm is the largest strength of the outer magnetic field, dH/dt is magnetization rate, DF is the increment of magnetic flux density in the magnetization region, s is variance of duration time. Experiments identify that total voltage value etotal in the detective coil is sum of the voltages of continuous Gauss pulses in a magnetization period T. Suppers that interval time and duration time of each Gauss pulse are constants, i.e. s = constant. And so the sum of the Gauss pulses in a magnetization period T is, N = T/t. When the outer magnetic field condition is given, t is constant. The total voltage value is
Where is determined by the condition of outer magnetic field and amplitude value of a Gauss pulse is
The sum of total amplitude value of Gauss pulse in a whole period T is . The number of pulses in T is N. The output of the magnetic-elastic instrument is MP, MP=ku=kGpt, where u is mean value of voltage output of sensor , therefore. We have
Where coefficient of ratio Cr is , in the given condition of magnetization, B, k is constants. s, t are correlated with microstructure of materials. s, t depend on mean free distance
In view of productive machancoim of the BN, it is produced when a 180° magnetic domain wall has suddenly departed from a place pinned by a inclusion or is nearing another inclusion. At last, the magnetic domain wall is pinned by the new inclusion. When the outer magnetic field strength is coming at critical value, i.e. in this strength the domain wall can be departed from the pinning place and will arrive to the next pinning place without any resistance. When the domain wall departed from a pinning place to the next pinning place, the displacement of the domain wall is L. L is called mean free distance of the domain wall. When the domain wall moved from a inclusion to another inclusion, a Gauss pulse is created and the Barkhausen jump is appeared with duration time t0. We define the t0 = L / , where is mean speed of the domain wall movement, L is mean free distance of the domain wall.
The mean speed of the domain wall movement is proportional to the outer magnetic field strength, i. e. = CvHp Where Hp is the minimum strength of the outer magnetic field to take domain wall away from the pinning place and to produce unreversible motion. Cv is the proportional constant. The expression of Hp is
Where mo is initial permeability, Is is saturated magnetization strength. Assume that the inclusion led the domain wall to be pinning is spherical, its diameter is d and its arrangement is a regular and simple cubic lattice. Cubic axes of the inclusion lattice are parallel with easily magnetized axes as shown in Fig. 2.
The domain wall is pinned and stopped in the center of the inclusion. This arises mainly because when energy density of the domain wall is not varied, the domain wall is located in the center of the inclusion and the total free energy of the domain wall is the minimum. Therefore, the domain wall is in the most stable condition.
Now we only consider the area of a simple domain wall in the inclusion lattice. Suppose that the displacement of a domain wall is X, after has punched by an inclusion, the area of the domain wall is:. If r is the energy density of the domain wall, then the energy of the domain wall may be expressed as Er = rS. When the domain wall moves X, then the variation of the domain wall energy per volume is
Under the action of the outer magnetic field, when the domain wall is in the equilibrium state, DE = 0 must be satisfied, i. e. When the outer magnetic field varied, the 180°domain wall have
Where mo is initial permeability. Is is saturated magnetization strength.q is the angle measured from the outer magnetic field axis to the saturated magnetization strength axis, then the critical outer magnetic field strength is
The sign b denotes the volume density of the inclusion , and the static of volume of a inclusion to total volume incorporated the inclusion is defined as
Substituting Eq10 into Eq9, we get
Where d is thickness of the domain wall, . KI is anisotropic coefficient of magnetic grain.
Let the volume of the inclusion is V1,its weight is W1 and its density is p1; the volume except for the inclusion is V2, its weight is W2 and mean density is p2, and so the volume ratio is b, the weight ratio is Z. We get
Since carbides of material vary with tempered temperature, its distribution density value is varied. But its total weight is a invariable value and b is constant. The space of inclusion, a(as shown in Fig. 2) is identical with L, and then, the duration time of a Gauss pulse ,ts is
Owing to the statistical theory, when |X| ³ 3s, the value of a Gauss type function f(x) can be considered as zero, i. e. F(x)=0. Then ts = 6s, we get
When magnetization period of the outer magnetic field is a fixed value, and then the time of producing BN also is a fixed value, i. e. ttotal is a constant. Total number of Barkhausen Jump in the magnetization process is equal to the total number of inclusion led domain wall to be pinned in the sweeping volume of the domain wall. Let the mean free distance of the domain wall motion is L, then n=1/L3, we have
Substituting Eq14 and Eq15 into Eq4, we get MP=CdL. Where the coefficient of ratio. Following from Eq5, we can be known that the output of the magnet-elastic instrument, MP is in proportion to the free distance of the domain wall motion, L.
|Fig 3: MP and tempreing temperature||Fig 4: Coercivity and tempering temperature|
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