Reconstruction of shock wave pressure field based on distributed test system

FENG Hao, ZHANG Zhi-jie

(Key Laboratory of Instrumentation Science & Dynamic Measurement (North University of China),Ministry of Education， Taiyuan 030051, China)



Reconstruction of shock wave pressure field based on distributed test system

FENG Hao, ZHANG Zhi-jie

(KeyLaboratoryofInstrumentationScience&DynamicMeasurement(NorthUniversityofChina),MinistryofEducation，Taiyuan030051,China)

A new distributed test system composed of multiple test nodes was designed by adopting storage test technology to test shock waves in explosion field. The advantage of the system is the application of sensor lattice whose rise time is microsecond level, which can quickly response to transient shock wave signals. In order to reduce dynamic response error, shock tube is employed to conduct dynamic calibration on the system. The overpressure peak values of the explosion shock wave collected by sensor lattice were used to construct a shock wave pressure field with B-spline interpolation algorithm.

distributed test system; dynamic calibration; interpolation algorithm; reconstruction

0 Introduction

In the weapons industry field, the process of explosion as well as the performance and evaluation of lethality after the explosion is increasingly scientific and refined[1]. In terms of blasting warhead, blast overpressure is an important tactical and technical indicator. In view of the nonrepeatability feature of transient blast signals, the test system is required not only to respond quickly to transient signals, but also to possess plenty of distributed test points to describe the entire shock wave pressure field. Distributed test system is capable of forming a measurement plane composed of measuring sensors lattice around the test object. It is of great significance for blast overpressure to conduct dynamic calibration using shock tube on each distributed test node.

1 Distributed test system principle

Distributed test system is a measurement network system which links measuring equipment that accomplishes specific functions independently in various regions with computers through local area network and Internet for the purpose of measuring resource sharing, decentralized operation, centralized management, cooperative work, measurement process monitoring and equipment diagnosis[2]. The system has advantages of networking, concurrency, distribution, dynamics, strong fault tolerance, and high reliability compared with traditional test systems. According to the requirements of field transient signal testing, a distributed test system with short-range wireless communication function was designed by adopting data acquisition method of storing first and processing later based on communication technology, wireless sensor network technology and distributed test technology. The system is composed of four parts: sensor array, analog signal conditioning circuit, data acquisition circuit and terminal display module, as shown in Fig.1.

Fig.1 Basic components of distributed test system

Modular design concept is applied to each test point in the system, which includes analog signal conditioning circuit, data acquisition module, wireless communication module and power management module[3]. This design greatly shortens the development cycle of the system, and meanwhile enhances the flexibility and stability of the system. The overall structure of the test points is shown in Fig.2.

Fig.2 Structure diagram of FPGA-based test nodes

During the process of testing explosion shock wave, amplification, filtering and noise reduction and transformation were conducted on the shock wave transient signal obtained by the sensor. Under the clock cycle of field-programmable gate array (FPGA), the analog-to-digital converter (ADC) converted analog signal to digital signal. After A/D conversion, the digital signal was divided into six high and six low and stored into first-in-first-out (FIFO) inside FPGA, and then the data from the FIFO were written on the external synchronous dynamic random access memory (SDRAM) under the control of FPGA. Finally, the data in the SDRAM were uploaded to the PC via universal serial bus (USB) or wireless module, and final display, analysis and processing are completed in the PC.

2 Dynamic calibration of test system

A series of dynamic calibration experiments were conducted to test the reproducibility and linearity of test system in shock wave parameter measurement and the influence on the change of instrument sensitivity caused by environmental conditions[4]. Dynamic calibration methods of the pressure sensor include sine excitation method, half sine excitation method and step stress incentive method. In this paper, the method of shock tube producing step pressure signal was adopted, whose advantages are wide stress amplitude range, wide frequency range, etc.[5]

2.1 Calibration principle of test system using shock tube method

Charge sensitivity of piezoelectric pressure sensor is defined as the ratio of output charge and average overpressure impacted on the surface of the piezoelectric sensor. Shock tube calibration device is composed of gas source, shock tube, speed and pressure sensor and test system, as shown in Fig.3.

Fig.3 Dynamic calibration of test node

Shock tube is composed of high pressure chamber and low pressure chamber. Compressed gas entered into the high pressure chamber of shock tube, which formed a shock wave when high pressure gas expanded into low pressure chamber after the bursting of the diaphragm under certain pressure. The shock wave wavefront pressure is constant and close to the ideal step wave, rushing into the calibrated sensor at supersonic speed. Then the sensor produced a damping oscillation in accordance with the natural frequency under the stimulus of shock wave. The response curve of the sensor system to step stress is shown in Fig.4, from which it can be seen that the rise time of a rapid response sensor is 4 μs.

Fig.4 Response curve of step pressure

Generally, the useful frequency of shock wave signal concentrates in the range of 0-200 kHz in blast tests, therefore, the distributed test points satisfy the requirement on the amplitude frequency and phase frequency of shock wave testing.

2.2 Calibration methods and results

Distributed test system includes a plurality of distributed test points. In order to deeply understand the dynamic characteristics of distributed test points, dynamic calibration should be conducted on each test point. Due to the second-order system characteristic of piezoelectric pressure sensors, the average voltage values inside and outside the inclusive line of pressure curve were adopted to calculate dynamic sensitivity for the sake of avoiding the effect of system overshoot on sensitivity. Each test point of the distributed test system was employed by data acquisition equipment, reducing the system errors brought by the acquisition equipment, obtaining the dynamic sensitivity of each test point in distributed system. The dynamic sensitivity of each test point is shown in Table 1.

Table 1 Dynamic calibration results of distributed test system

3 Shock wave pressure field reconstruction

Common design methods of curves and surfaces include three categories i.e. approximation, interpolation and fitting. Taking shock wave overpressure peak acquired by sensor lattices at distributed test nodes as the interpolation, isobaric curves and surfaces of shock wave pressure field were obtained inversely with numerical interpolation algorithm through Matlab data processing software. Distributed test points are shown in Fig.5.

According to the features of six test points unilateral and sensor lattice equidistant, cubic spline interpolation method was employed as the solution to calculate the explosion shock wave pressure surface.

Fig.5 Explosion field distribution of test system

Cubic spline function is defined as follows:npoints (xi,yi) (i=1, 2, …,n) are on the plane, among whichx1

1)s(xi)=yi(i=1,2,…,n), the function is through sample points.

2)S(xi) is a cubic polynomial in each subinterval[xi,xi+1],

S(x)=ci1(x-xi)3+ci2(x-xi)2+

ci3(x-xi)+ci4.

3)S(x) possesses continuous first and second order derivatives[6].

Cubic spline function interpolation method can sectionally express curves and surfaces, which is more flexible to reflect the local changes. The isobars of shock wave pressure field were obtained through invoking Matlab toolbox as shown in Fig.6. Three-dimensional surface is shown in Fig.7. Based on the multipoint overpressure values selected from the reconstruction surface, the uncertainty is calculated to be less than 2%.

Fig.6 Shock wave pressure field reconstruction

Fig.7 Shock wave pressure field reconstruction based on distributed test systems

4 Conclusion

In this paper, a new type of distributed test system was designed, which is a collection of storage test technology and wireless communication technology. The system has a plurality of test nodes to collect transient shock wave signals. Dynamic calibration experiments of the system reduce the dynamic response errors and improve the reliability. A series of explosive field static explosive power experiments were conducted with the present system. In addition, the pressure field surface well reflects graded distribution of the explosion field pressure. The design method of the present system and the reconstruction method of shock wave pressure field have important reference significance to overpressure peak test of blast field.

[1] MA Jia-lu. Study on the pressure field of the spherical shell structure under blast loading. Harbin: Harbin Institute of Technology, 2010: 1-75.

[2] YAO Juan. The design of software platform of distributed measurement system based on WLAN. TaiYuan: North University of China, 2013.

[3] LIANG Jie. The shock wave test and design of light-triggerring. Taiyuan: North University of China, 2014.

[4] CUI Hai-tao, LIU Qing-min. Dynamic calibration of shock wave pressure measurement system. Experiments and Measurements in Fluid Mechanics, 2004, 18(1): 93-96.

[5] MENG Li-fan, LAN Jin-hui. Principle and application of sensors. Beijing: Publishing House of Electronics Industry, 2007.

[6] FAN Tian-suo, RUI Bing. The realization of spline interpolation based on Matlab. Joumal of Jiamusi University (Natural Science Edition), 2011, 29(2): 238-240.

基于分布式测试系统的冲击波压力场重建的研究

冯 浩， 张志杰

(中北大学 仪器科学与动态测试教育部重点实验室， 山西 太原 030051)

采用存储测试技术设计了一套由多个测试节点组成的分布式测试系统， 此系统可用于爆炸冲击波测试。 该系统采用上升时间为微秒级的传感器点阵， 能够快速响应瞬态冲击波信号。 为减小动态响应误差， 利用激波管对系统进行了动态标定。 在静爆试验中由传感器点阵采集得到的爆炸冲击波超压峰值， 采用三次样条插值算法对冲击波压力场进行了重建， 并对重建结果进行了误差分析。

分布式； 动态标定； 插值算法； 重建

FENG Hao, ZHANG Zhi-jie. Reconstruction of shock wave pressure field based on distributed test system. Journal of Measurement Science and Instrumentation, 2015, 6(1)： 25-29.

10.3969/j.issn.1674-8042.2015.01.005

FENG Hao (fenghao625@163.com)

1674-8042(2015)01-0025-05 doi： 10.3969/j.issn.1674-8042.2015.01.005

Received date： 2014-10-16

CLD number： TP274 Document code： A