0 Introduction When a suspension shaft rotates, even slight disturbances can cause minute and unstable vibrations, affecting its normal motion. Therefore, non-interference testing of the vibration displacement of a suspension shaft is extremely difficult. If a vibration sensor with high sensitivity, good stability, and strong anti-interference capability is also required, implementation becomes even more challenging. Currently, research on non-contact vibration sensors mainly focuses on eddy current vibration sensors and laser sensors. However, eddy current vibration sensors are easily affected by nearby electromagnetic interference and temperature, while laser sensors are expensive and have poor stability. Considering that capacitive sensors have a simple structure, high sensitivity, and good dynamic characteristics, fully meeting the requirements of the operating environment, this paper designs a high-precision suspension shaft vibration measurement sensor and implements digital vibration signal processing during the measurement process. 1 Overall Design Principle The design of the suspension shaft vibration measurement sensor includes several major parts: the design of the capacitive sensor, the selection of the oscillation circuit, the sampling of the photoelectric encoder, the implementation of the difference frequency counting, and the intelligent control by the microcontroller. Its basic principle is as follows: First, the change in vibration displacement is converted into a change in capacitance using a conductive dielectric capacitance sensor. Since the capacitance sensor is a capacitor element in the oscillation circuit, the change in capacitance will cause a change in the output frequency of the oscillator. At the same time, another capacitance sensor is selected as a temperature compensation sensor, and a frequency signal is also obtained through the oscillator. The sampling of the vibration signal is achieved by the constant rotation angle sampling of the photoelectric encoder. With the cooperation of the photoelectric encoder, gate circuit and microcontroller hardware and software, the two high-frequency signals are input into the difference frequency counter to obtain the count value within a fixed time interval. The count value is sent to the C8051F020 microcontroller for storage and processing, and the count difference is obtained and converted into the magnitude of vibration displacement. The block diagram is shown in Figure 1. 2 Sensor Development 2.1 Measurement Circuit The vibration displacement measurement circuit of the suspension shaft consists of two parts: on the one hand, the change in vibration displacement of the suspension shaft is converted into a change in capacitance using a conductive dielectric capacitance sensor; on the other hand, the constant angle sampling of the rotation of the suspension shaft is achieved using a reflective photoelectric encoder to ensure the sampling accuracy. 2.1.1 Design of Conductive Dielectric Capacitance Sensor The capacitance C can be changed by changing the area S of the capacitor plates and the distance d between the plates. A variable-gap capacitive sensor was selected to measure the vibration displacement of the suspension shaft. To ensure the sensor converts changes in vibration displacement into corresponding changes in capacitance, maintaining a single-valued function relationship between the two, and guaranteeing that the actual motion of the suspension shaft remains unchanged under rotation and external disturbances, the conductive dielectric sensor uses the suspension shaft itself as the moving electrode of the capacitor, and copper, whose coefficient of thermal expansion is minimally affected by temperature, as the stationary electrode. Furthermore, the sensitivity, linearity, and parasitic capacitance of the capacitive sensor were fully considered in the design. Two capacitive sensors were used: one for measurement and one for temperature compensation. Each capacitive sensor is composed of two capacitors connected in series, thus solving the connection problem of the capacitive sensor wires and reducing the influence of parasitic capacitance. Let the capacitance of the capacitor sensor used for measurement be C, and the capacitance of the capacitor sensor used for temperature compensation be C0. The specific parameters of the design are as follows: The initial installation plate spacing of the two capacitors is x0=25μm; the thickness of the insulating material is d1=10μm; the coverage area of ​​each plate is A=0.5 cm2; the range of vibration measurement is -25～25μm (that is, the plate spacing z range is 0～50μm); ε0=8.85×10-12 F/m, εr=2.3ε0, and its structural diagram is shown in Figure 2. First, the relationship between the plate spacing and the vibration displacement Δx is x-x0=Δx (1). Since each capacitor sensor is composed of two capacitors connected in series, considering the thickness of the insulating film on the plate surface, the capacitance C of the measuring capacitor sensor and the capacitance C0 of the temperature compensation capacitor sensor are 2.1.2 Using photoelectric encoder to realize equal rotation angle sampling. The photoelectric pulse encoder is a rotary pulse generator that converts mechanical rotation angle into electrical pulses and can be used as a position detection and speed detection device. The design utilizes a reflective photoelectric encoder to achieve high-precision constant-angle sampling. Its output is a pulse signal, with the number of pulses related to the rotational displacement. The rotational speed of the suspended shaft is 50 rad/s. The photoelectric encoder uses constant-angle (2°) interval sampling, so each sampling period is approximately t = 111 μs, meaning the photoelectric encoder outputs a pulse signal with a frequency of 9 kHz. The continuous vibration signal conversion process of the suspended shaft is continuous signal → discrete signal. According to signal sampling theory: if the continuous signal f(t) has a finite bandwidth, its highest frequency is fm, then the signal f(t) can be uniquely represented by equally spaced sampled values, and the lowest sampling frequency is fs = 2fm, i.e., fs ≥ 2fm. Since the sampling frequency of the photoelectric encoder is fs = 9 kHz, the highest frequency fm that the sensor can measure for the suspended shaft vibration is < 4.5 kHz. 2.2 Signal Processing Circuit: The oscillator, frequency counter, control circuit, and microcontroller together constitute the signal processing system. Utilizing the functional relationship between the vibration displacement and frequency signal of the suspension shaft, the sensor measurement results are converted into a frequency signal through a specially designed oscillation circuit. A difference frequency counter is used for control counting, and then processed by a microcontroller to finally obtain the magnitude of the suspension shaft's vibration displacement. 2.2.1 Selection of the Oscillator Circuit: The capacitance change output by the capacitive sensor is converted into a frequency value that is easy to measure by an oscillator. Moreover, given a capacitance of tens of pF, the oscillator needs to output an oscillation frequency as high as 30 MHz. An asymmetric oscillation circuit can be used, and its structure is shown in Figure 3. Inverters G1 and G2 are selected from 74HC04 chips (hex inverters). RS is a protection resistor; after hardware circuit debugging, RS = 20.3 kΩ. Rf is the feedback resistor, which is also the delay element of the entire oscillation circuit. Its resistance value directly affects the oscillation frequency; therefore, the feedback resistor parameter Rf must be reasonably determined. Since the relationship between the electrode spacing of the capacitive sensor and the oscillation frequency is: the larger the electrode spacing, the higher the oscillation frequency of the oscillator, and the larger the counter's count value. To ensure the accuracy of the measurement results, the counter's count value should reach approximately 90% of the full scale when the electrode spacing is at its maximum. This design uses a serial input/12-bit parallel output differential frequency counter with a counting range of 0 to 2^12. The counting time ΔT should be slightly less than the sampling period of 100 μs. The parameter determination process for Rf is as follows: 2.2.2 Implementation of Differential Frequency Counting The differential frequency counter uses a frequency counting method. An external crystal oscillator obtains the sampling reference signal and the counting reset signal through a gating circuit. After the rising edge of the sampling reference signal, the counter is enabled, and the counting module begins counting the input frequency signal. The counting time is exactly ΔT. The counting reset signal is used to reset the counting module at the beginning of each measurement. The sampled data result is latched on the rising edge of the counting reset signal, and the result of the previous measurement is cleared. During counting, considering the temperature compensation of the capacitive sensor, a differential frequency counting method with two counters is adopted. On the other hand, the counter itself has a counting error of ±1 due to the asynchrony between the sampling time and the counting pulse. In addition, the differential frequency counter is composed of two counters, which further increases the counting error. Therefore, the key is to eliminate the influence of this error. Assume that the capacitances C and C0 of the two capacitor sensors are output by the oscillator at frequencies f and f0 respectively, i.e., f = f(D) + f(t), (7) f0 = f(t), (8) where f(D) is the frequency change caused by vibration displacement; f(t) is the frequency change caused by ambient temperature. Thus, the difference frequency output of the difference frequency counter can eliminate the influence of ambient temperature on the measurement result Δf = f - f0 = f(D) (9) The working principle of the difference frequency counter is to count the two frequency signals respectively within the counting time ΔT, and the number of pulses measured are n and n0 respectively, then n - n0 = (f - f0) ΔT, (10) where n - n0 is the difference between the two counters. Thus, as long as a reasonable counting time ΔT is obtained, the counting difference between the two frequency signals can be obtained. In the design, ΔT is determined by the output pulse of the single-chip microcomputer counting photoelectric encoder. Since the sampling time interval of the photoelectric encoder is about 111μs, in addition to counting, time must be reserved for recording and calculating the count value within one sampling period. Therefore, ΔT=100μs<111μs is selected. According to equation (10), the relationship between the reading difference of the counter and the frequency is that the start and stop signals of the frequency counter are controlled by the microcontroller. When the microcontroller start control signal GEP is high, the frequency counter starts to wait for counting. The measured frequency signal of the frequency counter is controlled by two AND gates. When each sampling period arrives, that is, after the microcontroller receives the photoelectric encoder pulse e1 as the rising edge, the microcontroller detects the output frequency signals osc11 and osc21 of the two oscillators respectively, waits for the first rising edge of the osc11 and osc21 signals, and sends control signals f1 and f2 respectively to start the AND gate, so that the frequency counter receives the corresponding frequency signal and counts. At the same time, the corresponding internal counter of the microcontroller starts timing, and the timing time is ΔT. After the timing interval ΔT expires, the microcontroller closes the gate of the corresponding input signal of the difference frequency counter, reads the count value of the difference frequency counter, and clears the counter. Once both counters have completed counting, the microcontroller begins digital processing of D1 and D2. The difference frequency counter uses a synchronous locking method with the measured frequency signal and the timing control signal, counting the two frequency signals separately, thus eliminating the ±1 counting error. The oscillator output is a high-frequency signal; therefore, the time interval between the first rising edge of the two frequency signals within one sampling period is not large. This means that the ΔT interval counting of the two frequency signals can be completed within each sampling period, thus realizing the entire difference frequency counting function. The timing sequence of the difference frequency counter is shown in Figure 4. In the figure, 1 is the start/stop control signal CEP of the microcontroller, 2 is the output signal e1 of the encoder, 3 is the frequency signal osc11 of the measuring sensor, 4 is the control signal f1 of AND gate 1, 5 is the frequency signal osc12 counted by counter 1, 6 is the frequency signal osc21 of the temperature compensation sensor, 7 is the control signal f2 of AND gate 2, and 8 is the frequency signal osc22 counted by counter 2. 2.2.3 Data processing Since the vibration displacement of the suspension shaft and the output count value of the microcontroller are in a single-valued function relationship, the software program written by the C8051F020 microcontroller is used to convert the count difference into the vibration displacement to realize the storage and analysis of the vibration displacement. Among them, the vibration displacement is stored in 2 bytes. The positive and negative values ​​of the vibration displacement are determined by the carry bit of the subtractor. It is stored in an independent unit. 00H is set to indicate that the vibration is positive and 01H is set to indicate that the vibration displacement is negative. The relationship between the vibration displacement and the difference between the counter can be derived and calculated by combining equations (2), (3), (6), and (11) as shown in Table 1. 3. Conclusion The suspended shaft vibration measurement sensor can measure vibration displacement with a vibration frequency less than 4.5 kHz and a vibration range of -25 to 25 μm. It achieves the measurement of vibration displacement during rotation, while avoiding interference with the sensor's own motion characteristics. Furthermore, the hardware employs differential frequency measurement and photoelectric encoder control for angle sampling, combined with software data processing, which significantly improves measurement accuracy. It eliminates the influence of power fluctuations in the sensor conditioning circuit, ambient temperature changes, and distributed capacitance, and also shields against electromagnetic interference, ensuring the reliability of the measurement results. This makes it suitable for application in special measurement and control environments.