# Small Displacement Measuring System Based on MEMS Accelerometer

Authors: Wei-meng Niu; Fang Li-qing; Zi-yuan Qi; De-qing Guo
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

In order to intelligently measure the displacement of moving objects, a small displacement measuring system based on MEMS (microelectromechanical system) accelerometer is designed. Firstly, the principle and error of displacement measurement using acceleration signal are deeply analyzed. The method of fitting polynomial extremum with better correction effect is selected in the time domain to eliminate the trend term error caused by the DC component, which is the main source of error. Real-time correction algorithm is added to the time-domain integral of acceleration. On the hardware circuit, the measurement module, control module, storage module, and power module of the system are designed, respectively. Finally, the system-integrated packaging scheme is designed, which enables the system to complete the real-time acceleration measurement, velocity and displacement calculation, and data storage of the motion carrier. Through simulation experiments, it is found that the system has good antioverload capability, and the displacement measurement average accuracy can reach 0.96%, which has very important engineering significance.


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## Body

## 1. Introduction

With the development of MEMS technologies, MEMS accelerometers are penetrating more and more high-end applications such as aerial navigation, earthquake detection, and gravity measurement [1–3]. Due to various new measurement principles and introduction of hybrid assembly technology, the MEMS accelerometer has the characteristics of small size, light weight, and strong impact resistance, and its output signal resolution, signal-to-noise ratio, and other parameters are greatly improved at the same time. The continuous innovation and development of MEMS technology has made MEMS accelerometers gradually replace traditional mechanical structure sensors, and MEMS accelerometers have been widely used in aviation navigation, home electronics, mechanical manufacturing, medical chemistry, and other military and civilian fields [4–6]. People are increasingly working on the measurement and control technology of motion vectors based on MEMS accelerometers.In the existing ranging methods, the techniques of transmitting signals based on ultrasonic waves, lasers, and so on are relatively mature, and the accuracy of the distance is high [7, 8]. However, such measurements must rely on feedback from external objects and are not suitable for the situations where the reflected signal is weak or has no target reference point. Therefore, people have proposed the theory of nonreference displacement measurement. The method of measuring displacement by using accelerometer is low in cost, easy to use, and mature in technology, so it is a method with more research and more common applications.The technology of displacement measurement and control by using accelerometer has been developed for a long time. The method of acceleration integral is mainly divided into time-domain method and frequency-domain method. The integral method in the time domain mainly includes the trapezoidal formula method, the Simpson formula method, and the Newton method. Its main disadvantage is that it will produce a large trend term error [7, 8]. Through long-term exploration and research, people have deeply analyzed the causes of the trend term error and proposed a method to eliminate the trend term by using the fitting polynomial extremum method. The method was applied to the shaking table test of simple signal and achieved good results [9]. At the same time, for the influence of initial velocity and initial displacement on the integration result, researchers proposed high-pass filtering and deaveraging methods to reduce the error and verified them in the bridge vibration displacement test [10, 11]. The frequency-domain integration method of directly performing FFT on the signal can effectively remove the noise signal error that is difficult to be removed in the time-domain integration, but this method is sensitive to low-frequency error, and the low frequency is also the frequency band with poor sensor accuracy. The cutoff algorithm and the low-frequency attenuation algorithm have achieved good results in processing of low-frequency interference signals [12, 13]. The comparison test of uniform sinusoidal signal, seismic signal, and actual bridge vibration signal shows that when the signal processing method is properly selected, the low-cost accelerometer can achieve high precision and can be used as a supplement to the on-site visual inspection [14]. In practical applications, the traditional French railway track is equipped with three depth accelerometers and geophones. The acceleration signal is processed by a variety of high-order Butterworth filters and trapezoidal formula integration in the time domain to obtain displacement, which has quite consistent results compared with the displacement obtained in LVDT recording. It is found that the accelerometer can give consistent displacement results for each analyzed depth, which verifies the integration method for displacement determination [15].However, these applications aimed at small displacements caused by vibration, and the processing and analysis of acceleration signals are performed offline. The measurement system is large in size, and some have long cables for data transmission. This paper studies a small displacement measurement system based on the principle of accelerometer displacement measurement and control. The system adopts a small convection, high overload, and stable thermal convection MEMS accelerometer to collect the acceleration during the motion of the carrier and selects a DSP (digital signal processor) with excellent performance to process signals for acceleration acquisition, real-time distance calculation, and data storage. It is verified by simulation test that the average accuracy of this system reaches 0.96%, which has very important engineering significance.


## 2. Working Principles

### 2.1. Acceleration Integral Algorithm

Both the frequency-domain method and the time-domain method have their own advantages and disadvantages. Due to the real-time limitation of the integral of the distance system, the frequency of the deceleration signal of the motion carrier is difficult to know in advance, so the frequency domain method is not suitable. Therefore, the acceleration integral algorithm is designed by the trapezoidal formula method in the time domain [16]. For the inevitable trend term error in the time domain, the error processing algorithm is designed based on fitting polynomial extremum method according to the literature [9].According to the calculus relationship between acceleration and displacement, the relationship of acceleration, velocityvt, and displacement st at any time from t0 can be expressed as follows:(1)st=∫t0tvtdt+st0,vt=∫t0tatdt+vt0.In the discrete domain, the formula for calculating velocity and displacement using the trapezoidal formula method is (n > 1) as follows:(2)vn=∑k=1nak+ak−12Δt=v0+12a0+an⋅Δt+a1+a2+⋯an−1⋅Δt,(3)sn=∑k=1nvk+vk−12Δt=12v0+vn⋅Δt+v1+v2+⋯vn−1⋅Δt.According to equations (2) and (3), it can be concluded that the moving displacement of the target object in one direction at time “n” is(4)sn=n⋅v0⋅Δt+n−1⋅a1+n−2⋅a2+...an−1⋅Δt2+14a0+an⋅Δt2.It can be concluded from equation (4) that the real-time displacement result of the target object can be obtained by using the real-time acceleration of the MEMS accelerometer output and the initial velocity v0 of the object motion. To simplify the calculation process, the algorithm is designed in an iterative manner.(5)vn=vn−1+an+an−12⋅Δt,(6)sn=sn−1+vn+vn−12⋅Δt=sn−1+vn−1⋅Δt+14an−1+an⋅Δt2.From equations (5) and (6), it is possible to use the last measured acceleration a[n − 1] and the operation results vn−1 and sn−1 and measure the acceleration an in real time. Then, the real-time motion displacement sn of the object and the real-time motion velocity vn can be obtained.


### 2.2. Polynomial Fitting Algorithm

In engineering practice, the acceleration signal contains various interference signals from the environment, which will cause serious trend term error in the integral result. These errors can be effectively removed by polynomial fitting. Assuming that a DC error term is generated during acceleration acquisition, the actual measured acceleration can be expressed as(7)at=ft+ε.The error trend termε⋅Δt+γ occurs every time the velocity is integrated in the time domain. The secondary error trend term 1/2ε⋅Δt2+γ⋅Δt+δ appears in each displacement integral, and the measurement error increases continuously (γandδ are the integral constants generated after one and two integrals, respectively).In order to eliminate the influence of this error, suppose there is a minimum sum of squares of the differences between the polynomialymt and data point (ti,vi) (i = 0, 1, 2,…, n−1), and the trend term error is fitted by least-squares method:(8)ymt=∑k=0mpktk∈ϕ.In equation (8), m is the highest-order coefficient, pk is the polynomial coefficient, and Φ is the set of polynomials whose highest order does not exceed m, resulting in the following equation:(9)min=I=∑i=1n−1vi−ymt2=∑i=1n−1vi−∑k=0mpktik2.It can be seen from equation (9) that as long as a set of coefficients pk is found, such that the function I takes the minimum value, the integral trend term can be determined. According to the condition of the multivariate function to obtain the extremum, the following equation can be obtained:(10)∂I∂pj=2∑i=0n−1vi−∑k=0mpktiktij=0,∑i=0n−1vitij=∑k=0m∑i=0n−1tik+jpk.Expressed as a rectangle formula,(11)n∑i=0n−1ti⋯∑i=0n−1tim∑i=0n−1ti⋯∑i=0n−1tim+1⋯∑i=0n−1tim∑i=0n−1tim+1⋯∑i=0n−1ti2mp0p1⋯pm=∑i=0n−1vi∑i=0n−1viti⋯∑i=0n−1vitim.It can be proved that the coefficient matrix in equation (11) is a positive definite matrix, and there is a unique solution. If pk is solved, the polynomial ymt can be obtained. Then, the corresponding velocity and displacement signals under the algorithm can be obtained.Since the trend term error of the velocity is a polynomial, the velocity calculation formula can be written as(12)vi′=vi−p1t+p0.In the above formula,vi′ is the corrected speed and vi is the acquired speed. In order to minimize the amount of chip computing and realize real-time calculation of the system, it is assumed that the sampling frequency of the sensor is fs, and time t can be expressed as(13)t=ifs,i=0,1,2,…,n−1.First, calculate three data matrices:Bn, Cn, and Dn, where Bi=i/fs, Ci=∑i=0n−1i/fs, and Di=∑i=0n−1i/fs2; then, the solution of the linear equations can be expressed as(14)p0=Di∑i=0n−1vi−Ci2∑i=0n−1BivinDi−Ci2,p1=n∑i=0n−1Bivi−Ci∑i=0n−1vinDi−Ci2.Substitute the result into equation (12) to get accurate velocity value.Solving the displacement can remove the trend of error based on the corrected velocity signal, and the process is the same.


## 2.1. Acceleration Integral Algorithm

Both the frequency-domain method and the time-domain method have their own advantages and disadvantages. Due to the real-time limitation of the integral of the distance system, the frequency of the deceleration signal of the motion carrier is difficult to know in advance, so the frequency domain method is not suitable. Therefore, the acceleration integral algorithm is designed by the trapezoidal formula method in the time domain [16]. For the inevitable trend term error in the time domain, the error processing algorithm is designed based on fitting polynomial extremum method according to the literature [9].According to the calculus relationship between acceleration and displacement, the relationship of acceleration, velocityvt, and displacement st at any time from t0 can be expressed as follows:(1)st=∫t0tvtdt+st0,vt=∫t0tatdt+vt0.In the discrete domain, the formula for calculating velocity and displacement using the trapezoidal formula method is (n > 1) as follows:(2)vn=∑k=1nak+ak−12Δt=v0+12a0+an⋅Δt+a1+a2+⋯an−1⋅Δt,(3)sn=∑k=1nvk+vk−12Δt=12v0+vn⋅Δt+v1+v2+⋯vn−1⋅Δt.According to equations (2) and (3), it can be concluded that the moving displacement of the target object in one direction at time “n” is(4)sn=n⋅v0⋅Δt+n−1⋅a1+n−2⋅a2+...an−1⋅Δt2+14a0+an⋅Δt2.It can be concluded from equation (4) that the real-time displacement result of the target object can be obtained by using the real-time acceleration of the MEMS accelerometer output and the initial velocity v0 of the object motion. To simplify the calculation process, the algorithm is designed in an iterative manner.(5)vn=vn−1+an+an−12⋅Δt,(6)sn=sn−1+vn+vn−12⋅Δt=sn−1+vn−1⋅Δt+14an−1+an⋅Δt2.From equations (5) and (6), it is possible to use the last measured acceleration a[n − 1] and the operation results vn−1 and sn−1 and measure the acceleration an in real time. Then, the real-time motion displacement sn of the object and the real-time motion velocity vn can be obtained.


## 2.2. Polynomial Fitting Algorithm

In engineering practice, the acceleration signal contains various interference signals from the environment, which will cause serious trend term error in the integral result. These errors can be effectively removed by polynomial fitting. Assuming that a DC error term is generated during acceleration acquisition, the actual measured acceleration can be expressed as(7)at=ft+ε.The error trend termε⋅Δt+γ occurs every time the velocity is integrated in the time domain. The secondary error trend term 1/2ε⋅Δt2+γ⋅Δt+δ appears in each displacement integral, and the measurement error increases continuously (γandδ are the integral constants generated after one and two integrals, respectively).In order to eliminate the influence of this error, suppose there is a minimum sum of squares of the differences between the polynomialymt and data point (ti,vi) (i = 0, 1, 2,…, n−1), and the trend term error is fitted by least-squares method:(8)ymt=∑k=0mpktk∈ϕ.In equation (8), m is the highest-order coefficient, pk is the polynomial coefficient, and Φ is the set of polynomials whose highest order does not exceed m, resulting in the following equation:(9)min=I=∑i=1n−1vi−ymt2=∑i=1n−1vi−∑k=0mpktik2.It can be seen from equation (9) that as long as a set of coefficients pk is found, such that the function I takes the minimum value, the integral trend term can be determined. According to the condition of the multivariate function to obtain the extremum, the following equation can be obtained:(10)∂I∂pj=2∑i=0n−1vi−∑k=0mpktiktij=0,∑i=0n−1vitij=∑k=0m∑i=0n−1tik+jpk.Expressed as a rectangle formula,(11)n∑i=0n−1ti⋯∑i=0n−1tim∑i=0n−1ti⋯∑i=0n−1tim+1⋯∑i=0n−1tim∑i=0n−1tim+1⋯∑i=0n−1ti2mp0p1⋯pm=∑i=0n−1vi∑i=0n−1viti⋯∑i=0n−1vitim.It can be proved that the coefficient matrix in equation (11) is a positive definite matrix, and there is a unique solution. If pk is solved, the polynomial ymt can be obtained. Then, the corresponding velocity and displacement signals under the algorithm can be obtained.Since the trend term error of the velocity is a polynomial, the velocity calculation formula can be written as(12)vi′=vi−p1t+p0.In the above formula,vi′ is the corrected speed and vi is the acquired speed. In order to minimize the amount of chip computing and realize real-time calculation of the system, it is assumed that the sampling frequency of the sensor is fs, and time t can be expressed as(13)t=ifs,i=0,1,2,…,n−1.First, calculate three data matrices:Bn, Cn, and Dn, where Bi=i/fs, Ci=∑i=0n−1i/fs, and Di=∑i=0n−1i/fs2; then, the solution of the linear equations can be expressed as(14)p0=Di∑i=0n−1vi−Ci2∑i=0n−1BivinDi−Ci2,p1=n∑i=0n−1Bivi−Ci∑i=0n−1vinDi−Ci2.Substitute the result into equation (12) to get accurate velocity value.Solving the displacement can remove the trend of error based on the corrected velocity signal, and the process is the same.


## 3. Design of Distance Measuring System

### 3.1. Design of System Hardware Circuit

The system consists of a power module, a storage module, a control module, and an acceleration measurement module. The block diagram of overall design is shown in Figure1.Figure 1
Structure diagram.When the system starts to work after receiving the trigger signal, the power module supplies power to each module. Two seven-cell batteries are able to meet the voltage requirements. In order to highlight the miniaturization and integrated design features, a small Li-con battery was designed specifically for the system, and its external dimensions are shown in Figure2. The storage capacity of the battery is not less than 55 mAh. After the Marshall hammer test, the rated voltage is between 3.7 V and 4.2 V after more than 50,000 g overload. After the test on the access board, the discharge current is about 100 mA and the working time of voltage above 3.7 V is about 90 s∼150 s, which has reached the power supply requirements under special conditions. The battery is packaged in a heat-shrinkable tube to provide a certain cushioning effect with almost no increase in volume.Figure 2
Li-con battery shape.The measurement module starts working after it is energized. The module uses a three-axis thermal convection MEMS accelerometer MXC4005XC whose interior has no movable mechanical parts so that it has good antioverload performance. Under the impact of 200,000 g, the sensing performance is basically unchanged. In order to obtain as much experimental data as possible, an acceleration sensor is placed in the center of both sides of the board. Sensors’ communication selects the I2C (Inter-Integrated Circuit) bus mode. The data flow processing method was adopted to collect and process the acceleration signal. After one acquisition being completed, acceleration data were sequentially stored and calculated immediately.The control module obtains the acceleration signal by accessing the measurement module. This module selects TI company’s DSP-TMS320C28xx series as the core of microprocessor. Compared with ARM chip, this kind of processor adopts an improved Harvard structure and has a built-in high-speed multiplier and an enhanced multistage pipeline, which can meet the real-time integration and polynomial fitting algorithm of this control system. After the distance is solved, the acceleration signal and the calculation result are saved to the storage module through the SPI (Serial Peripheral Interface) protocol.The storage module selects ferroelectric memory FM25V20A. It was recent introduction of a nonvolatile memory that combined low power consumption and high performance This module is designed to realize the offline observation of the carrier flight state and the working condition of this system during the test phase. After the test is completed, the acceleration data in the storage module is uploaded to the computer for analysis and judgment.In order to protect the board and make full use of the space during the test, SolidWorks was used to design the package for the system. The housing is produced by 3D printing technology, as shown in Figure3. The package housing can fix the orientation and position of the board, providing support and protection. At the same time, the housing also has a card slot for power supply, which is convenient for installing the power module. In Figure 3, the circular plate is the measuring module and the square plate is the storage module. The two separate designs are designed to facilitate retaining only the circular measuring plate when the data is not required to be observed, thereby sufficiently reducing the volume of the system.Figure 3
System package design.


### 3.2. Design of System Software

The DSP-based control program is written in the CCS (Code Composer Studio). The main tasks of the program include IIC protocol data reading, real-time integration distance and error processing, SPI and SCI (serial communication interface) data transmission. When the system is powered, the DSP first initializes the processor, sensors, and memory and reads the acceleration data from the sensor through an internal interrupt instruction. Then, the acceleration integral algorithm is executed to calculate the velocity and displacement, and the trend term error of the discrete data is eliminated according to the polynomial extremum method. The acceleration signal and the calculated velocity and displacement data measured in real time are saved to the storage module. The stop of the measurement and control program may be according to the actual setting of the application. The end of the program may be caused by the impactor circuit when the carrier reaches the target point or the solution distance reaches a preset value to issue a stop signal. The read program is used to transfer the test data to the computer after the test is finished. The software flow chart is shown in Figure4.Figure 4
Software flow chart. (a) Read program flow chart. (b) Measurement program flow chart.
(a)
(b)


## 3.1. Design of System Hardware Circuit

The system consists of a power module, a storage module, a control module, and an acceleration measurement module. The block diagram of overall design is shown in Figure1.Figure 1
Structure diagram.When the system starts to work after receiving the trigger signal, the power module supplies power to each module. Two seven-cell batteries are able to meet the voltage requirements. In order to highlight the miniaturization and integrated design features, a small Li-con battery was designed specifically for the system, and its external dimensions are shown in Figure2. The storage capacity of the battery is not less than 55 mAh. After the Marshall hammer test, the rated voltage is between 3.7 V and 4.2 V after more than 50,000 g overload. After the test on the access board, the discharge current is about 100 mA and the working time of voltage above 3.7 V is about 90 s∼150 s, which has reached the power supply requirements under special conditions. The battery is packaged in a heat-shrinkable tube to provide a certain cushioning effect with almost no increase in volume.Figure 2
Li-con battery shape.The measurement module starts working after it is energized. The module uses a three-axis thermal convection MEMS accelerometer MXC4005XC whose interior has no movable mechanical parts so that it has good antioverload performance. Under the impact of 200,000 g, the sensing performance is basically unchanged. In order to obtain as much experimental data as possible, an acceleration sensor is placed in the center of both sides of the board. Sensors’ communication selects the I2C (Inter-Integrated Circuit) bus mode. The data flow processing method was adopted to collect and process the acceleration signal. After one acquisition being completed, acceleration data were sequentially stored and calculated immediately.The control module obtains the acceleration signal by accessing the measurement module. This module selects TI company’s DSP-TMS320C28xx series as the core of microprocessor. Compared with ARM chip, this kind of processor adopts an improved Harvard structure and has a built-in high-speed multiplier and an enhanced multistage pipeline, which can meet the real-time integration and polynomial fitting algorithm of this control system. After the distance is solved, the acceleration signal and the calculation result are saved to the storage module through the SPI (Serial Peripheral Interface) protocol.The storage module selects ferroelectric memory FM25V20A. It was recent introduction of a nonvolatile memory that combined low power consumption and high performance This module is designed to realize the offline observation of the carrier flight state and the working condition of this system during the test phase. After the test is completed, the acceleration data in the storage module is uploaded to the computer for analysis and judgment.In order to protect the board and make full use of the space during the test, SolidWorks was used to design the package for the system. The housing is produced by 3D printing technology, as shown in Figure3. The package housing can fix the orientation and position of the board, providing support and protection. At the same time, the housing also has a card slot for power supply, which is convenient for installing the power module. In Figure 3, the circular plate is the measuring module and the square plate is the storage module. The two separate designs are designed to facilitate retaining only the circular measuring plate when the data is not required to be observed, thereby sufficiently reducing the volume of the system.Figure 3
System package design.


## 3.2. Design of System Software

The DSP-based control program is written in the CCS (Code Composer Studio). The main tasks of the program include IIC protocol data reading, real-time integration distance and error processing, SPI and SCI (serial communication interface) data transmission. When the system is powered, the DSP first initializes the processor, sensors, and memory and reads the acceleration data from the sensor through an internal interrupt instruction. Then, the acceleration integral algorithm is executed to calculate the velocity and displacement, and the trend term error of the discrete data is eliminated according to the polynomial extremum method. The acceleration signal and the calculated velocity and displacement data measured in real time are saved to the storage module. The stop of the measurement and control program may be according to the actual setting of the application. The end of the program may be caused by the impactor circuit when the carrier reaches the target point or the solution distance reaches a preset value to issue a stop signal. The read program is used to transfer the test data to the computer after the test is finished. The software flow chart is shown in Figure4.Figure 4
Software flow chart. (a) Read program flow chart. (b) Measurement program flow chart.
(a)
(b)


## 4. Test of Live Shot

### 4.1. Design of the Test

In order to test the working performance of the system, the motion carrier is simulated by means of launching a light air gun. The light-gas gun is a simulation test device that launches a simulated projectile in the form of a gas burst impact. Its structure is shown in Figure5. Its body length is 12.7 m, and there is a recycling bin at the exit for recycling simulated bombs. The velocity of the simulated bomb can be controlled by changing the launch pressure.Figure 5
Light-gas gun test device structure.Under the premise of not exceeding the sensor range, this simulation test sets two emission pressures of 0.8 and 1.8 MPa, respectively, and fired two rounds of shots. When the projectile is packaged, the measuring disc is placed in the fuse hood, the storage module is placed in the bomb body, and the military structure glue is used for the body potting. This material slowly expands and solidifies after 48 hours and has a certain elasticity, which can support and buffer the whole system. After the shooting is completed, the projectile is cut open and the storage board is taken out. The data are transmitted to the computer through the USB serial port for analysis.


### 4.2. Result of the Test

In this test, the switch wire in the simulated bomb is taken out, and when the simulated bomb enters the recovery bin, the lead wire breaks and the system stops working. Read the acceleration, velocity, and displacement data in the memory board of the computer and use MATLAB to plot as shown in Figure6. The results of the four shots are shown in Tables 1 and 2.Figure 6
Measurement result curve. (a) Acceleration plot for the first shot. (b) Acceleration plot for the third shot. (c) Velocity integral curve. (d) Displacement integral curve.
(a)
(b)
(c)
(d)Table 1
Measurement result of velocity.
Times
Launch pressure (MPa)
Gun muzzle velocity (m/s)
Measuring velocity (m/s)
Error (%)
First shot
0.8
23.0741
22.8976
0.76
Second shot
23.4025
23.2534
0.65
Third shot
1.5
34.5947
34.7046
0.34
Fourth shot
34.7425
34.8411
0.28Table 2
Measurement result of displacement.
Times
Launch pressure (MPa)
Body length (m)
Measuring distance (m)
Error (%)
First shot
0.8
12.7
12.47233
1.79
Second shot
12.59807
0.81
Third shot
1.5
12.62027
0.63
Fourth shot
12.76764
0.53


### 4.3. Data Analysis

As can be seen from the above graph, the operation process of the carrier recorded by the memory board is substantially the same as the actual operation. Although the installation and potting of the entire system is optimized as much as possible, the acceleration signal still has a certain DC component. After the polynomial fitting method is used to remove the influence of the trend term, the average error of the velocity value obtained by the measurement system compared with the velocity measurement value of the light-gas gun is 0.51%. The average error of the displacement value compared with the length of the light pipe of the light-gas gun is 0.96%. The main reason for the analysis error is that the correction method of polynomial fitting cannot completely remove the influence of trend term error, and the actual motion environment is more complicated. The installation accuracy of the measurement system and the vibration of the motion carrier will produce effects greatly.


## 4.1. Design of the Test

In order to test the working performance of the system, the motion carrier is simulated by means of launching a light air gun. The light-gas gun is a simulation test device that launches a simulated projectile in the form of a gas burst impact. Its structure is shown in Figure5. Its body length is 12.7 m, and there is a recycling bin at the exit for recycling simulated bombs. The velocity of the simulated bomb can be controlled by changing the launch pressure.Figure 5
Light-gas gun test device structure.Under the premise of not exceeding the sensor range, this simulation test sets two emission pressures of 0.8 and 1.8 MPa, respectively, and fired two rounds of shots. When the projectile is packaged, the measuring disc is placed in the fuse hood, the storage module is placed in the bomb body, and the military structure glue is used for the body potting. This material slowly expands and solidifies after 48 hours and has a certain elasticity, which can support and buffer the whole system. After the shooting is completed, the projectile is cut open and the storage board is taken out. The data are transmitted to the computer through the USB serial port for analysis.


## 4.2. Result of the Test

In this test, the switch wire in the simulated bomb is taken out, and when the simulated bomb enters the recovery bin, the lead wire breaks and the system stops working. Read the acceleration, velocity, and displacement data in the memory board of the computer and use MATLAB to plot as shown in Figure6. The results of the four shots are shown in Tables 1 and 2.Figure 6
Measurement result curve. (a) Acceleration plot for the first shot. (b) Acceleration plot for the third shot. (c) Velocity integral curve. (d) Displacement integral curve.
(a)
(b)
(c)
(d)Table 1
Measurement result of velocity.
Times
Launch pressure (MPa)
Gun muzzle velocity (m/s)
Measuring velocity (m/s)
Error (%)
First shot
0.8
23.0741
22.8976
0.76
Second shot
23.4025
23.2534
0.65
Third shot
1.5
34.5947
34.7046
0.34
Fourth shot
34.7425
34.8411
0.28Table 2
Measurement result of displacement.
Times
Launch pressure (MPa)
Body length (m)
Measuring distance (m)
Error (%)
First shot
0.8
12.7
12.47233
1.79
Second shot
12.59807
0.81
Third shot
1.5
12.62027
0.63
Fourth shot
12.76764
0.53


## 4.3. Data Analysis

As can be seen from the above graph, the operation process of the carrier recorded by the memory board is substantially the same as the actual operation. Although the installation and potting of the entire system is optimized as much as possible, the acceleration signal still has a certain DC component. After the polynomial fitting method is used to remove the influence of the trend term, the average error of the velocity value obtained by the measurement system compared with the velocity measurement value of the light-gas gun is 0.51%. The average error of the displacement value compared with the length of the light pipe of the light-gas gun is 0.96%. The main reason for the analysis error is that the correction method of polynomial fitting cannot completely remove the influence of trend term error, and the actual motion environment is more complicated. The installation accuracy of the measurement system and the vibration of the motion carrier will produce effects greatly.


## 5. Conclusion

This paper first analyzed the advantages and disadvantages of traditional distance control technology, introduced the development of MEMS technology and the excellent performance of MEMS accelerometer, and then introduced the development and application status of the technology of displacement measurement and control by accelerometer. In view of the shortcomings of existing technologies was proposed a small displacement measurement system based on MEMS accelerometer. The error analysis of the principle of displacement measurement of the accelerometer was carried out. According to the time-domain method of acceleration integral, the principle of polynomial fitting to remove trend term is designed. Select a DSP dedicated to digital signal processing as the embedded processing core. The hardware circuitry and packaging scheme of each module are designed based on the principles of miniaturization, software, and intelligence. Through simulation experiments, it is found that the performance of MEMS accelerometer can accurately and stably measure the acceleration of the motion carrier and provide reliable data support for the calculation of displacement and velocity. The data error obtained by the test is less than 1%, the displacement measurement is 0.96%, and the integral velocity error is 0.51%, which satisfies the requirements of engineering application within the error range. However, in actual use, it is subject to installation errors, ambient temperature, and noise. Subsequent work will quantify the laws of temperature displacement measurements.



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*Source: 3470604-2019-10-31.xml*