## 1 Introduction  
Wear is one of the main factors affecting the reliability and service life of mechanical equipment. In the process of mechanical equipment operation, the wear debris produced by the continuous rubbing of friction pairs is collected in the oil system and circulates with the oil. The wear state of a machine can be directly reflected by the debris in the lube oil [1]. As a consequence, the detection of wear debris is significant in identifying abnormal wear conditions for the fault diagnosis and life prediction of mechanical equipment. There are a lot of methods used for wear debris detection, such as optical methods, acoustic methods, capacitive methods, inductive methods, etc. With the maturity of image processing technology, optical methods [2; 3; 4; 5] are widely used for extracting visual features of wear debris. This method can easily detect debris greater than 5 \(\upmu\)m. However, the lube oil may gradually become nontransparent during the operating process, which causes difficulties in obtaining clear pictures and leads to the incorrect counting and sizing of wear debris. Overlapping wear debris and air bubbles in the oil will also have great impacts on the results. Additionally, acoustic methods [6; 7; 8] and capacitive methods [9; 10; 11; 12] are used in debris detection. However, a common defect of the above three mentioned methods is that it is impossible to distinguish ferrous and non-ferrous debris, which is important for judging the source of wear. However, the inductive method has a simpler structure, which is a prominent advantage, and can distinguish between ferrous and non-ferrous debris [13]. Thus, the inductive method is widely used in on-line wear debris monitoring. [PERSON] et al. [14] applied the sensor to the online wear monitoring of aerospace engines. [PERSON] et al. [15] applied the sensor to monitor the fatigue damage process of rolling bearings and determined a physically meaningful debris limit for a deteriorating rolling element bearing. [PERSON] et al. [16] applied the sensor to online wear of full-scale wind turbine gearboxes rated at 750 kW, and the gearbox was tested in three conditions: running-in, healthy, and damaged. Studies indicate that abnormal wear debris size is above 10 \(\upmu\)m [17]. An inductive debris sensor that is currently successful on the market is MetalSCAN from GasTOPS, which can detect 65 \(\upmu\)m ferromagnetic debris. However, because it applies a 3-D solenoid structure [13], MetalSCAN does not have the ability to detect wear debris of a size smaller than 65 \(\upmu\)m [18], which is vital to identifying abnormal wear conditions. To solve this problem, [PERSON] et al. [19, 20] developed a 2-layer planar coil based inductive sensor that is capable of detecting 50 \(\upmu\)m ferromagnetic debris in a 1.2 mm diameter pipe. After they used the parallel inductance-capacitance (LC) resonance method so that the sensor could detect 20 \(\upmu\)m wear debris from a microfluid channel that is 1.2 mm in diameter [21]. [PERSON] et al. [22] proposed a sensor that adopts a circular excitation and two semicircular sensing coils. It can measure ferromagnetic and non-ferromagnetic debris as small as 120 \(\upmu\)m (D) and 210 \(\upmu\)m (D) in a 34 mm-diameter pipe, but the induction coils may invade into the inside of the oil path, which will increase the flow resistance of lubricating oil and adversely affect the lubrication of the equipment. [PERSON] et al. [23, 24] developed a radial inductive debris detection sensor that could effectively detect 81 \(\upmu\)m ferromagnetic debris in a pipe with a 20 mm diameter, but the magnetic field strength inside the pipe is about 100 \(\upmu\)T, and the induced voltage signal is weak. In order to improve detection accuracy, an inductive debris sensor based on a high-gradient magnetic field that can detect wear debris of a size greater than 25 \(\upmu\)m in lube oil in our previous work, was proposed [25].