Research of Probability-Based Tunneling Magnetoresistive Sensor Static Hysteresis Model

Tunneling magnetoresistive (TMR) sensors have broad application prospects because of their high sensitivity and small volume. However, the inherent hysteresis characteristics of TMR affect its applications in high accuracy scenarios. It is essential to build a model to describe the attributes of hysteresis of TMR accurately. Preisach model is one of the popular models to describe the behavior of inherent hysteresis for TMR, whereas it presents low accuracy in high-order hysteresis reversal curves. Furthermore, the traditional Preisach model has strict congruence constraints, and the amount of data seriously affects the accuracy. This paper proposes a hysteresis model from a probability perspective. This model has the same computational complexity as the classic Preisach model while presenting higher accuracy, especially in high-order hysteresis reversal curves. When measuring a small amount of data, the error of this method is significantly reduced compared with the classical Preisach model. Besides, the proposed model’s congruence in this paper only needs equal vertical chords.

NORMALIZED PARAMETERS OF A MAGNETORESISTIVE SENSOR IN BRIDGE CIRCUITS

Magnetoresistive sensors are considered as part of bridge circuits for measuring magnetic field strength and electric current value. Normalized or relative expressions are introduced to change the resistance of the sensor and the measured bridge voltage to increase the information content of the regime to provide the possibility of comparing the regimes of different sensors. To justify these expressions, a geometric interpretation of the bridge regimes, which leads to hyperbolic straight line geometry and a cross ratio of four points, is given. Upon a change in the sensor resistance, the bridge regime is quantified by the value of the cross ratio of four samples (three characteristic values and the current or real value) of voltage and resistance. The cross ratio, as a dimensionless value, is taken as a normalized expression for the bridge voltage and sensor resistance. Moreover, the cross ratio value is an invariant for voltage and resistance. The proposed approach considers linear and nonlinear dependences of measured voltage on sensor resistance from general positions.

Measurements of the Magnetic Field Variations Related with the Size of V-Shaped Notches in Steel Pipes

Gas and oil pipeline networks require periodic inspections to detect cracks or notches that can cause industrial accidents and environmental contamination. For these inspections, the metal magnetic memory (MMM) method could be used as a non-destructive testing (NDT) technique, which does not need expensive equipment and high-skilled operators. However, more investigations are required to quantify the size and shape of defects in ferromagnetic pipes using the MMM signals. We present experimental measurements of MMM signals around five small V-shaped notches of an ASTM-A36 steel pipe using a three-axis magnetoresistive sensor. The V-shaped notches have different values of depth (500 µm, 1000 µm, 1500 µm, 2000 µm and 2500 µm) and width (1000 µm, 1500 µm, 2000 µm, 3000 µm and 3500 µm). We measured the variations of tangential and normal MMM signals around these defects and their relationships with the size of each defect. The first V-notch defect (500 μm depth and 1000 μm width) registers variations of the tangential and normal MMM signals of 14.32 μT ± 1.62 μT and 27.95 μT ± 1.14 μT, respectively. On the other hand, the fifth V-notch defect (2500 μm depth and 3500 μm width) has variations of the tangential and normal MMM signals of 68.75 μT ± 1.10 μT and 71.37 μT ± 0.72 μT, respectively. The MMM method could be used for real-time monitoring of V-shaped notches in steel pipes. This method does not require special treatment of steel pipes.