XU Peng

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

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Effect of projectile head style on highgacceleration waveform of Hopkinson bar calibration system

XU Peng

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

The freestyle Hopkinson bar is a kind of main high g loading equipment utilized widely in calibration of high g accelerometer and other high shock conditions. The calibration experiment of accelerometer was conducted. With one-dimension stress wave theory, ANSYS/LS-DYNA software and experiment, the effect rules of the projectile’s front-head style and the accelerometer’s mounted base’s length on acceleration waveform were analyzed. The results show that the acceleration duration inspired from Hopkinson bar is almost equal to the rising edge time of perfect half sine stress wave, and it is independent to the mounted base’s length. Moreover, the projectile’s front-head style is a main affecting factor, and the projectiles with less conical degrees will produce the lower amplitude and longer acceleration duration.

Hopkinson bar; highgacceleration; stress wave; waveform adjustment

0 Introduction

High g accelerometers have been widely used in acceleration time signal measurements, especially in projectile penetration and explosion dispersion. Because of good reproducibility and convenient operation, a freestyle Hopkinson bar becomes a kind of main high g loading equipment in acceleration calibration[1-3]. In order to gain desired acceleration waveform, relevant means are taken. Forrestal in Sandia Lab in USA adopted a aluminum bar with a length of 0.254 m and Flat ends to coaxially impact a aluminum incident bar with a length of 1.829 m, and plexiglass or copper adjusting pad was placed between two bars. But the acceleration waveform is more similar to rectangle signal, which is very different from the signal commonly used in calibration[4]. The projectile’s shape and length were changed to adjust the incident stress wave’s rising edge of Hopkinson bar[5-7]. Many factors can affect acceleration waveform, such as projectile head style, impact velocity, adjusting pad’s material and thickness, and so on. In this paper, theory analysis, numerical simulation and calibration experiment on freestyle Hopkinson bar have been used to investigate the effects of the projectile’s front-head styles and the accelerometer’s mounted base’s length on accelerometer’s inspiring waveform, and conclusion is significant to the waveform regulation in accelerometer calibration test on Hopkinson bar.

1 Experimental principle and test methods

The experiment setup is shown in Fig.1. In this experiment, a freestyle Hopkinson bar with 1.6 m length and 16 mm diameter made of TC4 titanium alloy is used as a high g shock acceleration generator. A projectile with a certain type conical tip is launched by compressed air to axially impact the adjusting pad made of aluminum alloy. The adjusting pad and accelerometer mounted base are placed respectively on two ends on Hopkinson bar with grease and a vacuum collar, a evaluated accelerometer is attached to the end of a titanium alloy mounted base with M5 bolt, and the reflecting grating is axially glued on the base’s surface, thus the mounted base, accelerometer and grating are kept an ensemble (called flying object) during the impact process.

Fig.1 Sketch of experiment setup

When impacted, an approximate half sine shape elastic stress wave is generated and then it propagates axially in the incident bar. When the compressive stress wave reflects into a tensile one on the free surface of the titanium alloy mounted base and the sum of stress at the interface between bar and base become tensile, the flying object separates axially from the incident bar with certain waveform acceleration, then it is caught by a soft material catcher. By means of grating interference technique, the accelerating course of flying object is directly acquired and recorded from basic quantity and unit (time and length) with high accuracy. According to Doppler effect, the velocity of the base is linearly proportional to Doppler frequency shift, therefore, the base’s acceleration can be calculated by means of derivation of the velocity. Moreover, by comparing the base’s acceleration and accelerometer’s output, calibration can be completed.

2 Theoretical analysis of base’s acceleration duration

In order to investigate the relation between acceleration duration and stress wave rising edge, a right propagating perfect half sine compressive stress wave is assumed in Hopkinson bar, as shown in Fig.2.

Fig.2 Stress wave in Hopkinson bar

The equation of incident stress waveσiat the interface between Hopkinson bar and mounted base is

wheret0is half-sine stress wave duration.

The reflective tensile stress waveσrform ? (from?) right free end is

wherelis length of accelerometer’s base andcis the velocity of stress wave.

Therefore, the sum of stress at the interface between the base and the bar is

Ifσ=0，

The base’s acceleration durationtais described by

In Eq.(4), the base’s acceleration duration is equal to rising edge of half sine stress wave, and is independent of the base’s length. In order to obtain desired acceleration waveform, the rising edge of stress wave in bar can be modified by certain modes.

3 Numerical simulation of acceleration calibration course

3.1 Finite element model

ANSYS/LS-DYNA software is used to simulate the operation process of acceleration calibration with Hopkinson bar. For the axial symmetry of the whole structure，the plane finite element model of the whole structure is established, including the projectile (see Fig.3), adjusting pads, Hopkinson bar and the mounted base, with plane 162 axial-symmetrical element. Lagrange algorithm is selected and the nodes ony-axis are constrained into zero displacement.

Fig.3 Shapes of the projectiles

In order to avoid the aberration of element and control the standard of acceleration waveform, the elements are refined in the interface between the projectile and the adjusting pads. The total solution time is estimated with stress wave propagating time from one end to the other of the bar. The wave velocity in TC4 Hopkinson bar is 5 100 m/s and the bar’s length is 1.6 m, therefore, the propagating time is almost 314 μs. Moreover, considering the required time that the stress wave reflects back and forth in base and the base flies from the bar’s end, the total solution time is assumed to be 700 μs. The impact velocity of the projectile is 15 m/s.

3.2 Material model

Table 1 Material model parameters of 35CrMnSiA and 2A12

4 Simulation results

The rigid acceleration-time curve of the base is shown in Fig.4 and stress wave-stress curve is shown in Fig.5. Comparison of the acceleration duration and the rising edge time of stress wave at middle point is shown in Table 2.

In Fig.4, the different shapes of projectile’s head-ends have tremendous effect on base’s acceleration-time curve.

Table 2 Acceleration duration and stress wave rise time

The amplitude of acceleration caused by projectile 1# is the largest, while its duration is the shortest. The amplitude of acceleration caused by projectile 3# with the smallest conical degree is the smallest, and its duration is the longest. It can be seen from Table 2 that the base’s acceleration duration is nearly equal to stress wave rise time and the simulation results agree with the above theoretical analysis.

Fig.4 Rigid acceleration of the base caused by three kinds of projectile’s head-ends

In Fig.5, there are great distinctions between the stress waves at bar’s middle point caused by different projectile’s head-ends. The stress wave rising edge caused by projectile 1# is very steep, stress amplitude is very high, and the high frequency oscillation arises in trailing edge. With the decrease of conical degree, the stress wave rising edge caused by 3# projectile with small conical degree becomes very gentle, the stress amplitude is very small, and the trailing edge is relatively smooth.

Fig.5 Stress wave at half point of Hopkinson bar caused by three kinds of projectile’s head-ends

5 Calibration test

In calibration experiments, the free-style Hopkinson bar (see Fig.6) and three types of projectiles (see Fig.7) are utilized. The piezoelectric accelerometer B&K8309 is chosen to be calibrated, and its installation resonance frequency is 180 kHz in factory specification. Figs.8-10 give the tested output signals of accelerometer caused by projectiles from 1# to 3#.

Fig.6 Free-style Hopkinson bar

Fig.7 Projectile with different heads

Fig.8 Tested acceleration-time curve by projectile 1#

Fig.9 Tested acceleration-time curve by projectile 2#

Fig.10 Tested acceleration-time curve by projectile 3#

Because the head end of 1# projectile is plane, it can load rapidly when impacting Hopkinson bar, and its acceleration duration is only 38.6 μs. In contrast, the acceleration duration of 2# projectile with 45 degree taper is 95 μs, and 3# projectile with smaller taper has 190 μs acceleration duration. The impacted adjusting pads are shown in Fig.11. The impacted deformation arises at local central position and the dent becomes deeper with the taper of projectile head decreasing. As the projectiles with small conical degree head ends have small impact area, thus the local stress at impact point is very high, and the plastic deformation and the plastic stress wave with slower propagating velocity are produced. Because the impact energy is dissipated, the loading rate becomes slower, the loading duration becomes longer, and the stress wave rising edge in bar is gentle. When the local high amplitude plastic stress wave with slower velocity propagates forward, the stress amplitude will reduce with the increase of the impact area.

Fig.11 Impacted adjusting pads

6 Conclusion

When the high g accelerometer is calibrated with free-type Hopkinson bar, the required different wave-style acceleration signals can be gained by exactly design of projectile’s head-ends.

1) With one-dimension stress wave theory, the mounted base’s acceleration duration inspired from free-type Hopkinson bar is almost equal to the rise-edge time of perfect half sine stress wave. In order to gain the desired inspiring acceleration signal, the method of controlling stress waveform must be considered.

2) The head-ends’ shapes of the projectiles have great effect on acceleration-time curves. The projectile with small conical can produce smaller acceleration amplitude and wider duration. In order to get the acceleration with larger amplitude, the projectile with flat head-end has to be taken.

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彈頭形狀對(duì)Hopkinson桿校準(zhǔn)系統(tǒng)高g值加速度波形的影響

徐 鵬

(中北大學(xué) 儀器科學(xué)與動(dòng)態(tài)測(cè)試教育部重點(diǎn)實(shí)驗(yàn)室， 山西 太原 030051)

自由式Hopkinson桿是一種主要的高g值加載設(shè)備， 已經(jīng)被廣泛應(yīng)用于高g值加速度計(jì)校準(zhǔn)和其它高沖擊環(huán)境中。 介紹了自由式Hopkinson桿校準(zhǔn)的加速度計(jì)試驗(yàn)， 應(yīng)用一維應(yīng)力波理論和ANSYS/LS-DYNA軟件以及試驗(yàn)手段， 分析了子彈頭部形狀， 加速度計(jì)安裝座長(zhǎng)度等因素對(duì)加速度波形的影響。 結(jié)果表明： 自由式Hopkinson桿產(chǎn)生的加速度持續(xù)時(shí)間等于理想半正弦應(yīng)力波前沿， 并與安裝座長(zhǎng)度無關(guān)； 子彈頭部形狀對(duì)加速度波形影響較大， 頭部錐度小的子彈產(chǎn)生的加速度幅值較低、 持續(xù)時(shí)間較寬。

Hopkinson桿； 高g值加速度； 應(yīng)力波； 波形調(diào)節(jié)

XU Peng. Effect of projectile head style on highgacceleration waveform of Hopkinson bar calibration system. Journal of Measurement Science and Instrumentation, 2015, 6(1)： 1-6.

10.3969/j.issn.1674-8042.2015.01.001

XU Peng (xptj1972@163.com)

1674-8042(2015)01-0001-06 doi： 10.3969/j.issn.1674-8042.2015.01.001

Received date： 2014-10-11

CLD number： TJ410 Document code： A