Chapter 4 Inductive Sensors 4.1 Variable Magnetoresistance Inductance Sensor 4.2 Inductance Sensor of Differential Transformer 4.3 eddy current inductance sensor  The Working Basis of Inductive Sensors: Electromagnetic Induction  Realization of non-electric measurement by changing coil inductance or mutual inductance classification According to principle: self-inductance and mutual-inductance According to structure: variable reluctance type, trans former type and eddy current type • Characteristic (1) Simple structure: no active electrical contact, long life. (2) High sensitivity: strong output signal, voltage sensitivity can reach hundreds of millivolts pe r millimeter. (3) High resolution: It can sense small mechanical displacement and small angle change. (4) Good repeatability and linearity: within a certain displacement range, the linearity of output characteristics is good and the output is stable. (5) The disadvantage is the existence of AC zero-bit signal, which is not suitable for high-freque ncy dynamic measurement. • ele ctri c sen se cru de Ro ugh deg ree inst ru me nt Proximity switch Non-contact displacement sensor Thickness Sensor •4 4.1 Variable reluctance inductance sensor (self-inductance) 4.1.1 Working Principle Variable reluctance inductance sensor consists of coil, core and armature.The core and armature are made of magnetic conducti ve material. • There is an air gap between the core and the armature, and the • When the armature moves, the air gap thickness Delta changes. motion part of the sensor is connected with the armature. • It causes the change of reluctance in magnetic circuit, which lea • As long as this inductance can be measured, the magnitude and ds to the change of inductance value of inductance coil. direction of armature displacement can be determined.  N (4-1) • Inductance in coil: L   I I • Ohm's law of magnetic circuit: • The air gap is very small. It can be considered that th IN Rm: Total Reluctance of Magnetic Cir  gap is uniform. e magnetic field in the air (4-2) cuit R m • If the loss of magnetic circuit is neglected, the total re luctance of magnetic circuit is 0. (总磁阻 各段导磁体的磁阻  空气间隙磁阻 长度 2 * 空气间隙厚度  )  导磁率 * 截面积 真空导磁率 * 空气间隙截面积 i段导磁体  L1 L2 2 Rm    1 A1 2 A2 0 A0 (4-3) Vacuum permeability, air permeability and relative permeab ility  Vacuum permeability: 4 PI x 10-7 H/m  Relative permeability: ratio of mate rial permeability to vacuum permeabi lity L1 L2 2 Rm    1 A1 2 A2 0 A0 Usually the air gap magnetor esistance is much larger tha n the magnetoresistance of i ron core and armature. Rule (4-3) can be simplified to 2 l1    0 A0 1 A1   2 l2    0 A0  2 A2  2 Rm   0 A0  N L  (4-4) I I IN  Rm (4-6) The simultaneous (4-1), formula (4-2) and formula (4-5) are available. N 2 N 2 0 A0 L  Rm 2 (4-7) N 0 A0 N L  Rm 2 2 • • • 2 When coil turns are constant, inductance L is only a fu nction of reluctance Rm in magnetic circuit. Changing delta or A0 can lead to inductance change. Therefore, the variable reluctance inductance sensor c an be divided into the sensor with variable air gap thic kness Delta and the sensor with variable air gap area A 0. L L N 2 N 2 0 A0 L  Rm 2 L L(   )  L(   ) R R L A Lmax  L  L  196  131  65(mH) 4.1.2 Output Characteristics The relationship between L and delta is non-linear. The characteristic curve is shown in Fig. 5-2. N 2 N 2 0 A0 L  Rm 2 Fig. 4-2 L-delta Characteristics of Variable Gap Voltage Sensors Analysis: When the armature is in the initial position, t he initial inductance is 0 A0 N 2 L0  2 0 (4-8) When the armature moves up delta, the air gap decreases delta, that is, delta=delta 0-delta, and the out put inductance is N 2 0 A0 L0 L  L0  L   2( 0   ) 1   0 (4-10) When delta/0 1 develops (Taylor series):      2      L  L0  L L0 1    0  0   0  3        (4-11) Inductance increment L and relative increment L/L0 can be obtained. (4-12) (4-13) Similarly, when the armature moves down delta with the initial position of the measured body, there are 2         L L0  1   0   0   0   2 L           1  L0  0   0   0       0     0 3        3        (4-14) (4-15) Linear processing of formulas (4-13) and (4-15), i.e. ignoring higher order terms