Capacitance (C) is determined by the overlapping area of ​​the plates (S), the plate separation distance (d) and the dielectric constant (ε) of the material between the plates. In a typical system, the capacitive probe acts as one on the board and the target under test acts as the other. The dielectric properties of the material within the gap typically remain constant with the area of ​​the probe; therefore, the only variable causing a change in capacitance is the probe-to-target distance [2]. Using the following method, the system converts this changing capacitance into a linear voltage proportional to the probe gap.

capacitive sensor

The amplitude modulation amplification system is introduced into the aperture measurement of small deep holes, and the open-loop gain of the measurement circuit is greater than 95 db. Formula 1 where Cs is the standard capacitance (F); Us US fixed amplitude power supply (V), the voltage offset must be less than 0.01 %; U is the amplification system output voltage (V); d is the distance between the electrode and the workpiece (m); S is the overlapping area of ​​the electrodes (m2); ε dielectric constant; k proportionality coefficient, and (2). Therefore, in equation (1), the system converts this changing capacitance into a linear voltage proportional to the probe gap (d)

To maintain a highly linear response, it is important to establish a uniform electric field in the gap. In order to achieve this goal, this paper adopts the "protection" detection method. By design, the probe ring is completely surrounded by a guard ring that is precisely driven at the same potential and phase as the probe's sensing area. This not only eliminates any external effects of noise, but also reduces the "streaking" of the magnetic field on the target being measured. In this way a linearity exceeding 0.1% of the full-scale measurement range can be obtained. The structure of the gauge head is shown in Figure 2.

Gauge head structure

1.4.1 Principle of non-contact capacitive sensor for aperture measurement

1.4.2 Eccentricity

1.4.3 Principle of drive cable

As shown in Figure 6, the system consists of a stepper motor, a two-dimensional positioning device, a CCD camera, a probe, a rectifier filter circuit, a data acquisition card, an image acquisition card and a motor drive card. The two-dimensional size positioning device, clamp, stepper motor and CCD camera are fixed on the workbench. Clamps are used to secure ring gauges, sensors and workpieces. The two-dimensional positioning device is used to adjust the X and Y position of the sensor. The stepper motor is used to adjust the vertical position of the workpiece so that the aperture is at different depths measured by the sensor. A CCD camera is used to photograph the tops of the cylindrical fixed head and sensor head to produce a magnified image, thus initially aligning their centers. Processing circuitry is used to eliminate stray capacitance noise and convert the different diameter values ​​into a linear digital output voltage that is displayed on the front panel and transmitted to the computer. The computer software performs data processing and data storage.

Structure of the measuring system

The system can use four different specifications of capacitive sensors to measure the aperture value ranges of four series: Ф2.4mm, Ф2.92mm, Ф3.5mm, and Ф7mm. Each series of sensors is calibrated using four standard rings with different known diameter values. By measuring the voltage values ​​of four different diameters, linear fitting is performed to obtain the slope k and intercept b of the linear function. Therefore, the relationship between voltage and aperture is y = kx b, where x is the voltage and y is the aperture. Then by measuring the output voltage, the pore diameter of the workpiece can be calculated accordingly. The system is controlled by LabView software. The system can automatically perform measurements

This experiment takes the Φ3.5mm series in the system as an example. The capacitive aperture measurement sensor and Φ3.5mm series standard ring are shown in Figure 7. In the calibration experiment, the diameter of the standard ring is approximately 3.5 mm. The results are shown in Table 1. We then measured these standard ring gauges again using the above calibration results in Table 1 to obtain the indicated error of the standard ring gauge. The results are shown in Table 2.

Table 1 Calibration experimental data of Φ3.5mm series sensors

sensor probe

Standard ring gauge

Tab.2 indicates the error measurement of the standard ring gauge

As can be seen from Table 2, the indicated error for this family of systems ranges from 0.002 µm to 0.076 µm, with an average of 0.039 µm. Since the calibration error is caused by the error in the nominal value of the standard ring gauge, the calibration error makes it impossible to further enhance the effect of the system indicating the error. In order to obtain the repeatability measurement standard deviation and measurement uncertainty of the standard ring gauge, we conducted ten measurements on the standard ring gauge with a nominal value of Φ3.5101 mm. The results are shown in Table 3.

Table 3 Repeatability measurement of standard ring gauge Φ3.5101 mm

In Tab.3 we can see that the repeatability metric standard deviation is 0.082 µm and the measurement uncertainty is 0.246 µm. In the workpiece measurement experiment, a workpiece with a diameter of about 3.5mm and a length of about 50mm is taken as an example. The above coefficient calibration results are used for the measurement system. The results are shown in Table 4.

Tab.4 Measurement results of workpiece

As can be seen from the data in Table 4, the measurement result of the inner diameter of the workpiece is Φ3499.47 µm, the maximum value is Φ3499.68 µm, the minimum value is Φ3499.32 µm, and the processing tolerance is 0.36 µm. The system's diameter measurements and machining tolerances are consistent with previous measurements.