## Theories and Methods  
### Sensor Type and Measurement Principle  
Displacement measuring methods could be categorized into contact and non-contact types based on whether the measuring probe is in touch with the object to be measured or not. The non-contact type has a wide range of applications due to its many advantages. For example, there is no disturbing or destruction of the object nor the measuring instruments. There are several types of non-contact displacement sensors and Table 1 lists those that are commonly applied. Each type of sensor has its own advantages and disadvantages. For example, the laser displacement sensor has high measurement accuracy and range, while it demands certainenvironmental conditions. Through comprehensive comparisons, the eddy current displacement sensor is employed in this work with regard to the actual operation conditions. Figure 3 gives a measurement schematic of an eddy current sensor. Based on the electric eddy current effect [23], the sensor could accurately detect the distance between the measured body, namely the target in the schematic, which must be a metallic conductor, and the coil in a probe through the change in electrical signal in the circuits. This method has the advantages of high sensitivity, strong anti-interference ability, non-contact measurement, fast response speed, and being free from oil and water and other factors [18; 24; 25]. One sensor could measure the displacement to a metal surface on one side. The measuring range is limited. In order to measure the spacing between two surfaces, two opposite sensors could be used. Figure 4 gives the measuring principle for the displacement between two sides, i.e., \(H\). For probe 1, the distance to the surface at side 1, namely \(h_{1}\), as shown in the diagram, could be acquired. And, in a similar way, the \(h_{2}\) could also be measured. As long as the distance between the two oppositely installed probes, i.e., \(h_{3}\), is known, the final spacing \(H\) could be given by \(H=h_{1}+h_{2}+h_{3}\). It is worth noting that, in order to gain the \(H\), a standard platform with a similar structure and known accurate spacing must be prepared. This is the calibration station \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Type** & **Measurement Range** & **Resolution** & **Linearity/Error Value** & **Characteristics** \\ \hline \multirow{3}{*}{1} & Capacitive sensor & & & & Low cost, low power consumption, small positioning space, susceptible to environmental interference [18] \\  & [17] & 0.05–20 mm & 0.0007–0.03\% & 0.2–0.5\%FS & \\ \hline \multirow{3}{*}{2} & Laser displacement & & & & High measurement accuracy, wide range, noise interference can easily lead to data distortion \\  & sensor [19] & 0–18 mm & 0.1 \(\mu\)m & 0.02\%FS & \\ \hline \multirow{3}{*}{3} & Fiber optic & & & & Wide measuring range, immune to electromagnetic interference \\  & displacement & 0–200 mm & 0.06 mm & 0.16 mm (error) & \\  & sensor [20] & & & & Rapid response, corrosion resistance, high precision, susceptible to temperature influence \\ \hline \multirow{3}{*}{4} & Grating & & & & Rapid response, corrosion resistance, high precision, susceptible to temperature influence \\  & displacement & 0–90 mm & 2.9 \(\mu\)m & - & \\ \hline \multirow{3}{*}{5} & Eddy current & & & & Small size, high measurement accuracy [18] \\  & displacement & 2–50 mm & 0.3 \(\mu\)m & 0.2\%FS & \\ \cline{1-1}  & sensor [22] & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Commonly used non-contact displacement sensors with ordinary parameters. Figure 3: Schematic diagram of an eddy current sensor. that is discussed later. What is more, the measured result is highly relevant to the metal material. A fixed distance to different metals will be measured to vary greatly. Therefore, the eddy current sensor itself must be calibrated. If the metals are different, the calibration process of the corresponding sensors should be based on the specified material.