【Abstract】An automatic calibration system for the frequency response characteristics of an accelerometer is introduced. The hardware composition of the system and the implementation of signal measurement, acquisition, calculation, recording, display and printing functions are analyzed. 0 Introduction Accelerometers used in vibration analysis and testing need to have their frequency response tested during the development process. Their dynamic performance is calibrated according to the frequency response curve. There are two types of performance calibration: comparison method and absolute method. In the traditional comparison method calibration process, the sinusoidal excitation needs to be manually adjusted, and the response characteristics test is also manually recorded point by point. The whole process is not only labor-intensive, but also produces a large error due to human factors [1]. In recent years, frequency response analyzers that have appeared on the domestic and foreign markets have solved the above problems. They can automatically measure the frequency response characteristics of the signal and store effective data for plotting the response curve. Although these instruments have excellent performance, they have not been widely used in actual work due to their high price. With the popularization of computers, various testing and analysis technologies have developed towards microcomputerization and digitalization. Multiple tasks can be completed using a microcomputer. 1 Working principle and composition of the system The methods for dynamic calibration of accelerometers usually include absolute calibration method and comparison calibration method. The absolute method is often used to calibrate high-precision sensors or standard sensors, while the comparison method is a commonly used calibration method in engineering. The comparison method involves mounting two accelerometers back to back (or on the same rigid bracket), one of which is a reference standard accelerometer whose entire technical performance is known; the other is the sensor to be calibrated. They are excited by the same acceleration a, and the technical performance of the sensor to be calibrated is obtained by the relationship between the outputs of the two sensors. This system is based on the comparison method with a 486 microcomputer as the host and an external A/D and D/A interface board to collect the analog signals output by the sensors. The interface board is the HY8011 interface board produced by Beijing Huayuan Company. The board has a 12-bit 16-channel A/D and D/A output, a 50Hz acquisition pass rate, programmable gain and 8253 timer, etc. Other peripheral devices include power amplifiers, vibration tables and printers, etc. The hardware composition block diagram is shown in Figure 1 [2]. The standard accelerometer and the accelerometer to be calibrated are mounted back-to-back on the vibration table. The sinusoidal excitation of the vibration table is output by the D/A converter on the microcomputer control interface board. The small signal is amplified by the power amplifier to drive the vibration table. At the same time, the signal output by the standard accelerometer is divided into two paths. One path is used to feed back to the vibration table control system to control the acceleration of the vibration table surface to keep it constant. The other path is sent to the computer along with the signal of the sensor to be calibrated[3]. [align=center] Figure 1 System block diagram[/align] When the system is working, the timer interrupt in the microcomputer is turned on, the calculated data transformed according to the sinusoidal law is retrieved, the D/A port is programmed, and the D/A port is converted into an analog quantity to obtain a sinusoidal signal. This signal is amplified by the power amplifier to drive the vibration table, so that the vibration table performs vibration experiments at the expected frequency. The excitation frequency can be easily changed by simply changing the initial value of the timer. The frequency range of the system is designed to be 1 Hz to 15 kHz. The output signals of the two sensors are amplified by a charge amplifier and directly connected to the AD0 and AD1 ports on the HY8011 board. The output voltage value of the accelerometer is measured periodically via A/D conversion. Using a timed triggering method, the two A/D channels can be acquired at a specific frequency angle. When excited by a sinusoidal signal, the sensor's output signal is a sinusoidal signal of the same frequency. Therefore, processing the data from the two channels according to this model yields the amplitudes of the two sinusoidal signals. Similarly, the phase difference between the tested sensor and the standard sensor can be calculated using this model. After measuring this frequency, the computer automatically increases the frequency according to a predetermined step size, continuing the measurement at the new frequency until completion, thus obtaining the amplitude-frequency and phase-frequency characteristics of the sensor. 2. Software Design In previous tests, amplitude measurement, especially the Φ value, was difficult, computationally intensive, and prone to errors. A fixed-point measurement method was typically used, followed by fitting the entire frequency. In this system, the computer automatically generates the excitation signal and automatically records the calculations, thus enabling both fixed-frequency and frequency-sweep operations. According to the Nyquist sampling theorem, as long as f_sample ≥ 2f_modulus, the analog signal can be reconstructed without distortion. The maximum throughput of this interface board's A/D conversion is 50 Hz, but the A/D setup time is 10 μs each time, and two channels are acquired each time. The maximum acquisition frequency of each channel is 25 kHz, so the highest frequency of the analog signal should preferably not exceed 20 kHz. According to the formula V=Asin(ωt+φ), where: V is the voltage measurement value; ω is the vibration frequency of the vibration table; A is the maximum amplitude; φ is the initial offset angle. Then we have: ωt+φ＝arcsin(V/A) (1) For a certain sensor, the two acquisition times are fixed, so the Δφ for the fixed angle is a known quantity, and according to the formula (1), we have: Δφ＝arcsin(V2/A)-arcsin(V1/A) (2) Where: V1 and V2 are the data acquired in two adjacent acquisitions. Multiple points can be measured at each vibration frequency, so the A value in equation (2) can be solved by solving a system of equations. However, directly solving this equation analytically is complex, so this paper uses numerical analysis to find the numerical solution of amplitude A. For equation (2), we also have: Δφ＝arcsin(V4/A)-arcsin(V3/A) Therefore, we have: arcsin(V4/A)-arcsin(V3/A) ＝arcsin(V2/A)-arcsin(V1/A) Let F(A)=arcsin(V4/A)-arcsin(V3/A)-arcsin(V2/A)+arcsin(V1/A) Therefore, the process of solving amplitude A is to solve the equation F(A)=0. Here, we use the iterative method, let A0=max；V1,V2,V3,V4＝, B0=4096 (digital quantity 4096 represents analog voltage 5 V, 2048 represents analog quantity 0 V). Calculate F(Ai) for each value in the interval [A0, B0], and find the A value that minimizes |F(A)| to obtain the amplitude. Calculate the amplitude of multiple sets, calculate the root mean square σ, and then eliminate gross errors according to the range of 3σ. Then calculate the arithmetic mean, which is the amplitude Ai at a certain frequency. In this way, the amplitude-frequency characteristic of the sensor can be measured. The calculation process is shown in Figure 2. [align=center] Figure 2 Flowchart of the calculation module[/align] Similarly, according to formula (1): ωt_standard + φ_standard - ωt_detection - φ_detection = arcsin(V_standard/A_standard) - arcsin(V_detection/A_detection) The variable with the subscript "standard" represents the variable of the standard sensor, and the variable with the subscript "detection" is the characteristic quantity of the sensor to be detected. Because a timed triggering method is used, the interval Δt between each acquisition is fixed, i.e., (t_standard - t_detection) is a fixed value, and ω is the angular frequency of the vibration table. Therefore, Δφ - φ_standard - φ_detection, i.e., the phase frequency function Δφ(ω) of the phase difference between the two sensors, can be calculated. Since the phase frequency function φ_standard(ω) of the standard sensor is known, we have: φ_detection(ω) - φ_standard(ω) - Δφ(ω). Using a computer is very convenient for data acquisition, processing, storage, and maintenance. The acquired data from both channels can be opened and stored in a file, and the calculated amplitude and phase frequency functions can also be stored in a file for easy retrieval and printing. The system software adopts a modular design, with a flexible structure, making it easy to combine, debug, connect, and expand. It is mainly divided into an A/D acquisition module, data processing, display driver, and print driver. The data processing, display driver, and print driver are all compiled using the Borlad C++ software package. The A/D acquisition module requires real-time, dynamic operation and fast response. Therefore, various high-level languages ​​cannot meet the system requirements, and only 8088 macro assembly can be used. The main program software flowchart is shown in Figure 3. [align=center] Figure 3 Main Program Flowchart[/align] To reduce software downtime and provide sampling frequency, the A/D acquisition module is written in assembly language. It utilizes the timer interrupt generated by the 8223 timer on the interface board to trigger A/D conversion in the interrupt service routine, polls and waits for the A/D to finish, reads the A/D conversion result, and stores it sequentially in the storage area. The display driver module sets the screen to graphical mode, which can display Chinese characters and the measured amplitude and phase frequency curves. The print driver module uses a dot matrix method to drive the printer to print out the calculated amplitude and phase frequency curves. 3 Conclusion This system design is relatively reasonable and has an open structure. It can be added or reduced to achieve a suitable configuration according to different requirements. Moreover, the entire system is simple to operate, highly automated, and fast, making it suitable for sensor frequency response characteristic calibration and possessing great promotional value.