Calibration technique for airborne vibration sensors based on actuators

Addressing the challenge of in-situ calibration for onboard vibration sensors in aircraft installations, we propose an online calibration method based on actuators. Leveraging the inverse piezoelectric effect, we employ piezoelectric actuators mounted on the vibration sensors to calibrate vibration signals. Experimental results demonstrate that the influence of the actuator on the energy transfer of the measured sensor’s vibration signal during the calibration process can be negligible, meeting the calibration accuracy requirements of onboard vibration sensors. Through validation experiments, we determine the excitation coefficients of the actuators at different frequencies, subsequently obtaining the sensitivity of the vibration sensors equipped with actuators. The results reveal that within the frequency range, the relative error of sensitivity remains within ±3%, satisfying the relevant calibration requirements. Therefore, the actuator-based online calibration technique offers an efficient means of calibrating onboard vibration sensors, carrying significant practical value.


Introduction
In the realm of flight testing, vibration sensors find indispensable applications in modal testing, monitoring bearing vibrations in turbofan engines, and measuring propeller vibrations, among other critical functions.These sensors play a pivotal role in elucidating the strength and stiffness of aircraft structures and monitoring aircraft status during flight by measuring vibrational parameters [1,2] .Furthermore, vibrational parameter measurements are instrumental in detecting faults in aircraft engines and other components, as well as conducting structural health monitoring [3,4] .Flight testing environments are often harsh, characterized by extreme temperatures, intense vibrations, and electromagnetic interference, among other challenges [5] .These conditions can potentially impact the sensors on board aircraft, resulting in reduced accuracy or malfunctions [6] .The performance of vibration sensors directly influences the safety and reliability of the entire aircraft.Hence, calibration of vibration sensors before flight is imperative.
Presently, onboard vibration sensors are calibrated in laboratory environments.Standard vibration systems generate mechanical vibration signals, and sensors mounted on these systems detect mechanical vibrations and output electrical signals.Sensor-measured vibration signals are obtained through data analysis.There have been several studies on calibration techniques for aircraft vibration sensors.Among them, Garg [7] et al can calibrate the acceleration level at frequency f by performing a discrete Fourier transform on the voltage and displacement signals received by a laser interferometer and then checking the spectral components at the frequency.Varanis [8] et al used standard accelerometers to calibrate the vibration sensors at different frequencies.Yan et al [9] designed a closed-loop calibration system (i.e., the device automatically adjusts the excitation signal and samples and analyzes the real-time data) to improve the calibration accuracy and efficiency of vibration sensors.Yang et al [10] investigated a monocular vision-based calibration method for low-frequency vibration sensors to determine the frequency characteristics of the vibration sensors through calibration.Although these methods can calibrate the sensors, they have some defects, such as low accuracy and complicated operation.Additionally, repeated disassembly and reassembly of vibration sensors can lead to sensor damage, affecting the progress of flight tests.
To address these issues, this paper presents an online calibration method for onboard vibration sensors.We begin by introducing the principle of onboard vibration sensor calibration based on actuators, followed by laboratory validation.Experimental results indicate that during the calibration process of vibration parameters, the influence of actuators on the energy transfer of the tested sensors' vibration signals can be negligible, meeting the calibration accuracy requirements for onboard vibration sensors.

Experimental procedure
Exploiting the inverse piezoelectric effect of piezoelectric ceramics, we devised a piezoelectric actuator that serves a dual purpose: as an integral component for mounting vibration sensors on aircraft and as an excitation source for the vibration parameter testing system's online calibration.In the calibration state, an alternating current voltage signal of a specific frequency is applied to the actuator.Leveraging the principle of the inverse piezoelectric effect, the output end of the actuator generates alternating mechanical vibrations, serving as the excitation source for the vibration sensor.The sensors convert vibration signals into electrical signals, complete the data acquisition through the KAM-500 collector, and finally calculate the vibration signal value based on the code value output from the computer.Comparing it with the vibration signal value of the standard generator, the calibration of the sensor can be realized.The principle of online calibration of vibration sensors is shown in Figure 1.In this case, the core of the actuator is a piezoelectric ceramic, which produces the phenomenon of charge separation or charge reorganization when stimulated by external mechanical stress or electric field.Its working principle can be explained by the mathematical formulation of the linear piezoelectric effect, which is known as the piezoelectric equation, and the piezoelectric equation can be expressed as follows.

D d E + gT < ≥≥
(1 Where D is the potential shift in the piezoelectric ceramic, d is the piezoelectric coefficient, which indicates the piezoelectric properties of the piezoelectric ceramic, E is the mechanical stress applied to the piezoelectric ceramic, and G is the temperature.Based on the inverse piezoelectric effect, the piezoelectric ceramic sheet will deform when a voltage signal of a certain range is input for the actuator.Therefore, the actuator can be used as an excitation device for vibration sensor calibration. The specific impact of an actuator on the transfer of vibrational quantities can be ascertained through experimental methodologies.In order to do so, the actuator is co-installed with a calibrated, onboard sensor onto a standardized vibration platform for calibration purposes.The calibrated results are then compared with those obtained from the sensor when calibrated independently.For this study, the ICP-type vibration sensor, model 355B12, was selected.As shown in Figure 2, the standardized vibration platform utilized in this investigation was the CS-18MF medium-frequency vibration system manufactured by Spectra GmbH, Germany.The actuator (model E53B, XinMingTian Co., Ltd.) under investigation possesses a diameter of 9 mm and a mass of 12 grams.To commence our analysis, we shall initially scrutinize the influence of the actuator on the linearity of amplitude in the onboard sensor.In this investigation, the 355B12 sensor was selected, and the vibration frequency was held constant at 160 Hz.Subsequently, measurements of the sensor's output voltage were conducted at various acceleration levels, and the results are tabulated in As shown in Figure 3 (a) and (b), the effect of the actuator addition on the amplitude linearity error of the vibration sensor is small and can be ignored.The effect on the frequency response of the vibration sensor is mainly larger in the low-frequency stage, which is related to the characteristics of the CS-18MF intermediate-frequency shaker.As the frequency of the vibration signal increases, the error of its frequency response shows a decreasing trend.Both the amplitude error and the frequency error meet the requirements of GJB1692 for the calibration of test flight test instruments.It can be seen that in the process of vibration parameter calibration, the effect of the actuator on the energy transfer of the vibration signal of the measured part can be ignored.Subsequently, the calibrated sensor with sensitivity S is fixed on the actuator, and a standard sinusoidal signal U is input to the actuator, and the sensor senses the mechanical vibration signal and outputs a voltage signal V.The excitation coefficient C of the actuator is thus found to be: The piezoelectric on-board vibration sensor 7259B-25 with a sensitivity of 2.53 mV/m/s2 was selected to derive the excitation coefficients of the actuator at different frequencies as shown in Table 3.
Table 3 Table 4 shows the values of the sensitivity error of the added actuator sensor at different frequencies.Figure 4 illustrates the curve depicting the relative error in sensor sensitivity, as a function of frequency.Notably, this curve reveals a gradual decline in sensitivity relative error with increasing frequency, consistently maintaining itself within the confines of ±3%.This adherence to precision criteria, as outlined in JJG 233-2008 for vibration sensor calibration, underscores the sensor's compliance with calibration regulations.Hence, the sensor augmented by actuators satisfies both inspection protocols and the requisites for in-flight vibration sensor applications.These actuators can serve as dynamic exciters, facilitating real-time calibration of onboard vibration sensors and their respective testing systems.

Conclusion
The present study introduces a novel aircraft-borne vibration sensor calibration technique based on the utilization of piezoelectric actuators, designed to counteract the influence of flight test environments on vibration sensor performance.Employing the inverse piezoelectric effect by installing piezoelectric actuators onto the vibration sensors, online calibration is realized.In rigorous laboratory experiments, we thoroughly investigate the impact of these actuators on sensor performance, encompassing parameters such as amplitude linearity and frequency response.Our experimental results unequivocally demonstrate that the influence of actuators on the transmission of vibration signal energy to the tested sensors can be negligibly small during the process of vibration parameter calibration.Furthermore, the calibration errors meet the stipulated standards, affirming the viability of this actuator-based aircraft-borne vibration sensor calibration technique.In summary, this research presents an actuator-based calibration methodology for aircraft-borne vibration sensors, holding great promise for widespread application, and promising to enhance the safety and data accuracy of flight testing endeavors.

Figure 1 .
Figure 1.Schematic Diagram of Onboard Vibration Sensor Calibration Based on Actuators.The principle of online calibration of vibration sensors is shown in Figure1.In this case, the core of the actuator is a piezoelectric ceramic, which produces the phenomenon of charge separation or charge reorganization when stimulated by external mechanical stress or electric field.Its working principle can be explained by the mathematical formulation of the linear piezoelectric effect, which is known as the piezoelectric equation, and the piezoelectric equation can be expressed as follows.

Figure 2 .
Figure 2. Vibration Sensor Based on Actuator on the Vibration Platform.To commence our analysis, we shall initially scrutinize the influence of the actuator on the linearity of amplitude in the onboard sensor.In this investigation, the 355B12 sensor was selected, and the vibration frequency was held constant at 160 Hz.Subsequently, measurements of the sensor's output voltage were conducted at various acceleration levels, and the results are tabulated in Table1, as presented below:Table1.Effect of the actuator on the amplitude linearity of the transducer.

Figure 4 .
Figure 4. Sensitivity error of the added actuator sensor at different frequencies.

Table 1 ,
as presented below:

Table 1 .
Effect of the actuator on the amplitude linearity of the transducer.effect of the actuator on the frequency response of the sensor is analyzed, and the acceleration is fixed at 2 g.The output voltage of the sensor at different frequencies is measured, and the test results are shown in Table2.

Table 2 .
The effect of the actuator on the frequency response of the sensor.
Figure 3. (a) amplitude linearity error and (b) frequency response error.

.
Excitation coefficients of actuator at different frequencies.By varying the excitation coefficient C, at distinct frequencies for the retrofitting of the 355B12 vibration sensor with actuators, one can readily ascertain the sensitivity S2, of the sensor.Here, S1 denotes the sensitivity of the sensor obtained through meticulous laboratory calibration in the absence of any actuation, and W represents the relative error in sensor sensitivity.

Table 4 .
Sensitivity errors of added actuator sensors at different frequencies.