Study on several key problems in shock calibration of high-g accelerometers using Hopkinson bar

Accepted Manuscript Title: Study on several key problems in shock calibration of high-g accelerometers using Hopkinson bar Author: Kangbo Yuan Weiguo Guo Yu Su Yunbo Shi Jingyu Lei Hui Guo PII: DOI: Reference:

S0924-4247(17)30285-6 http://dx.doi.org/doi:10.1016/j.sna.2017.02.017 SNA 10000

To appear in:

Sensors and Actuators A

Received date: Revised date: Accepted date:

20-7-2016 15-2-2017 15-2-2017

Please cite this article as: K. Yuan, W. Guo, Y. Su, Y. Shi, J. Lei, H. Guo, Study on several key problems in shock calibration of high-g accelerometers using Hopkinson bar, Sensors and Actuators: A Physical (2017), http://dx.doi.org/10.1016/j.sna.2017.02.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights 1. The pulse shaping techniques for shock calibration of accelerometers were investigated intensively. 2. The findings of pulse shaping technique guide the choice of projectile in linearity calibration of accelerometers. 3. A novel calibration method for dynamic linearity of accelerometers was proposed.

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4. The efficiency and practicality of the newly proposed method was evaluated.

5. A measuring range from thousands of g to nearly 300,000 g can be achieved by this

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method.

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Study on several key problems in shock calibration of high-g accelerometers using Hopkinson bar Kangbo Yuana, Weiguo Guoa,*, Yu Sub, Yunbo Shic, Jingyu Leia, Hui Guoa School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China.

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Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

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School of Instrument and Electronics, North University of China, Taiyuan 030051, China

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Abstract: In this paper we studied several key problems in the shock calibration of high-g accelerometers, in which the Hopkinson bar system was employed as the loading and testing device. Firstly, in order to generate a strain pulse (the excitation signal in shock calibration) with high amplitude and a wide frequency bandwidth, the pulse shaping techniques by adjusting the geometry of projectile were numerically investigated. It was found that a smaller degree of taper at the front end of the projectile causes lower amplitude and wider duration of the acceleration pulse. The findings in studying pulse shaping technique could guide the choice of the projectile’s geometry in the dynamic linearity calibration of accelerometers. Secondly, a novel method of the dynamic linearity calibration for accelerometers was proposed and verified by experimental tests. In the calibration process, we employed a single-barrel gun instead of the double-barrel gun (proposed in earlier studies) to launch two coaxial cylindrical projectiles, such that the synchronous impact of the two projectiles can be easily achieved in practice. Lastly, the efficiency of this developed calibration method was discussed in details. The calibration system used in this study is able to achieve a testing range from thousands of g to nearly 300,000 g. Keywords: Shock calibration; Accelerometers; Hopkinson bar; Pulse shaping; Dynamic linearity

_______________________________________ *Corresponding author: [email protected]

1. Introduction 1.1. General

There exists a class of high-g accelerometers that can measure up to very high shock acceleration in the order of 106 m/s2. These accelerometers are used to measure motion in fields of earthquake measurement, crash safety testing, equipment relating to nuclear power generation, ships, space and aeronautical equipment, micro-motion devices and the like. In order to maintain the accurate measurement, it is necessary to periodically calibrate these

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accelerometers. In the development of high-g accelerometers calibration techniques, modified Hopkinson bar system has been widely used. Starting from 1960s [1], the Hopkinson bar technique began to be applied to the calibration of accelerometers for that the excitation signal with high-g and a wide frequency bandwidth is able to be achieved by using the Hopkinson bar. Still [2] developed an operational system for accelerometer calibration in the range from 10,000 to over 100,000 g. In his design, an acceleration pulse was obtained by

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axially impacting a parabolically pointed projectile into an aluminum mitigator, which is attached to one end of a long slender bar. Based on one-dimensional theory of elastic wave,

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the input acceleration for the accelerometer can be derived from the strain of the bar, which is measured by strain gauges. Ueda and Umeda [3] proposed a similar method to evaluate the

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dynamic characteristics of accelerometers under high acceleration levels (103-105 m/s2) and a wide frequency bandwidth (1-70 kHz). With the modification of the apparatus and the

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development of pulse shaping technique, higher accelerations are able to be achieved in a number of research groups. Togami et al. [4] developed a split Hopkinson bar technique to evaluate the performance of accelerometers that measure pulses with the peak amplitudes

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between 20,000 g and 120,000 g. Bateman et al. [5] used a laser vibrometer in the Hopkinson bar as a calibration reference. They achieved an acceleration calibration of 70,000 g and claimed ±5% accuracy. The modified Hopkinson bar system proposed by Li et al. [6] is able

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to calibrate the acceleration in a range from 5,000 g to 200,000 g. In their experiment, a

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half-sine strain pulse was obtained by impacting a conical-tip projectile into the end of the calibrating bar. Foster et al. [7] modified the conventional Hopkinson bar apparatus to produce relatively-long-duration pulses by using a longer steel striker bar and two annealed copper pulse shapers. They obtained acceleration pulses of 10,000 g in amplitude and 0.5 ms in duration. In the general field of measurement technology, accurate measurement cannot be achieved unless linearity is established [8]. Linearity of an accelerometer is essential in both static and dynamic measurement. Therefore, the establishing of adequate dynamic linearity is one of the key aspects in dynamic measurement using accelerometers. In the earlier practices of dynamic linearity calibration [8, 9], based on the Hopkinson bar system, the calibration apparatus was introduced with two cylindrical coaxial projectiles launched by a double-barrel gun. However, this calibration system for dynamic linearity of accelerometers was left in the theoretical stage because there were problems in actual testing. 1.2. Objectives In view of the developmental state so far, two key problems in the shock calibration of accelerometers through Hopkinson bar technique are pending further investigation. Firstly, 3

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for the sake of controlling the calibration range, the pulse shaping techniques in shock calibration need to be studied systematically. Secondly, the calibration method of dynamic linearity introduced by reference 8 and 9 remains to be validated. Pulse shaping techniques and the control of impact momentum allow creation of half-sine acceleration pulses with a wide range of amplitudes and durations [2]. Several types of the projectile were utilized in the shock calibration of accelerometers through Hopkinson

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bar technique enumerated as above [1-9]. It is noticed that the projectile’s geometry has an influence on the strain waveform, which further affects the amplitude and frequency

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bandwidth of the obtained acceleration pulse. Therefore pulse shaping can be achieved in the calibration system by adjusting the projectile’s geometry. Related researches were conducted

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through both numerical approaches [10, 11] and experimental testing [12, 13]. Kumar et al. [10] showed that the design of a tapered striker bar is able to lengthen the duration of the

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incident stress wave without abrupt increase in the magnitude of the incident stress. The stress oscillation can be eliminated as well. Baranowski et al. [11] presented a parametric study of the striker bar’s design variables in the split Hopkinson pressure bar system, which

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influence the shape and peak magnitude of the pulse in the incident bar. Cloete et al. [12] used a conical striker in a dynamic compression test. They achieved an incident stress pulse with an initial jump followed by a gradual increase that matches the specimen’s hardening

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rate, resulting in a uniform strain rate process. Li et al. [13] obtained a half-sine strain wave

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by using a tapered striker to investigate the relation between the diameter of the split Hopkinson pressure bar and the critical loading rate for rock failure. The aforementioned studies are quite successful on their own merits. However, these investigations are not systematical and pertinent to the shock calibration system of accelerometers. Therefore, one of the main tasks in this work is to find out the correlation between the projectile’s geometry and the resultant excitation signals during the shock calibration of accelerometers. The findings in studying pulse shaping technique could guide the choice of the projectile’s geometry in the calibration of linearity. Since the calibration of linearity should be conducted over a constant frequency bandwidth in a round of calibration, it is necessary to choose the proper geometry of projectile to ensure the same width of the excitation signals. Moreover，the pulse shaping could be conducted by using the pulse shaper, which had been studied in depth by other researchers [14-15]. However, the results of their researches showed that using pulse shaper would lead to the change of pulse width. So using pulse shaper was not appropriate in the linearity calibration of accelerometers, and it would not be discussed in this paper.

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In the calibration method of dynamic linearity introduced by reference 8 and 9, two cylindrical coaxial projectiles were employed. During the calibration process, the elastic-wave pulse was generated in the calibrating bar by impacting the end surface of the calibrating bar with the two coaxial cylindrical projectiles separately and then simultaneously (or at a prescribed time interval). However, when the two coaxial cylindrical projectiles are launched simultaneously, it is a challenge to ensure that the two projectiles impact the

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calibrating bar at the same time using the double-barrel gun. In this paper, we propose a practical shock calibration method for the dynamic linearity of accelerometers. In the

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calibration process, two coaxial projectiles are simultaneously launched by a single-barrel gun instead of a double-barrel gun. In such a way, it can be assured that the two projectiles

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impact the end surface of the calibrating bar at the same time. Furthermore, the high flexibility of the sectional area of the two projectiles brings more convenience to cover a

2. The pulse shaping techniques

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2.1. The principle of shock calibration method

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wide range of acceleration in the dynamic linearity calibration of accelerometers.

Fig. 1 shows a schematic of the basic components used in the shock calibration of the accelerometers. In this system, specifically shaped projectiles were widely adopted to attain

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the proper excitation signals for accelerometers [1-7]. An aluminum shaper is attached to the

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impact end of the calibrating bar. It is used to protect the end surface of the bar from damage due to the impact by the projectile with a pointed end. When the projectile impacts the end of the calibrating bar, an elastic compression wave is generated and it propagates to the other end of the bar. The elastic wave can be detected by the strain gauge positioned on the side surface of the metallic calibrating bar and the accelerometer mounted on the other end of the bar successively. It is assumed that the wave propagates in the bar with no attenuation or distortion and it gets reflected perfectly at the end surface of the bar where the accelerometer is mounted. According to the theory of one-dimensional elastic wave propagation [16, 17], the compression wave reaches the end free surface of the bar and gets reflected as a tension wave. The sudden change of the velocity leads to a high acceleration [3]. Provided that the calibrating bar deforms elastically, the velocity of the accelerometer at the end of the bar can be related to the strain in the bar, as

V (t ) = 2Cε (t ) ,

(1)

where t denotes time and C is the velocity of longitudinal elastic wave in the bar. V(t) is the particle velocity, and ε (t ) is the strain in the bar. So the input acceleration (a(t)) of the accelerometer can be calculated based on the information of the strain measured by the strain 5

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gauge: d ε(t ) , (2) dt Therefore, the calibration was conducted by obtaining the integration of the output a ( t ) = 2C

acceleration pulse and then comparing it with the value of 2C ε (t ) [2], or obtaining the d ε (t ) dt

with the output

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differentiation of the strain pulse and then comparing the value of 2C

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acceleration pulse [3]. T

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Stress wave

Vacuum clamp

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Strain gauge

Projectile L

Shaper

Calibrating bar

Accelerometer

Fig. 1. A schematic of the basic components used in the shock calibration of accelerometers.

The typical strain signal measured by the strain gauge and the output acceleration signal measured by the accelerometer are shown in Fig. 2. The acceleration pulse was moved to be left-justified with the strain pulse. It is observed that a strain pulse of almost a half-sine wave is produced in the bar. When the acceleration pulse becomes negative (i.e., the velocity begins to decrease after the peak value is reached), the tension develops at the interface and the accelerometer flies off the bar. Therefore the accelerometer only experiences a calibration pulse of the positive polarity [2]. So the excitation signal for the accelerometer is just the rising edge of the strain pulse. That is to say, the frequency bandwidth of the input acceleration pulse depends on the duration of the rising edge of the strain pulse. According to Eq. (2), the amplitude of the input acceleration is proportional to the time gradient of the rising edge of the strain pulse. 6

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The strain pulses produced in all the studies of the shock calibration method possess the similar shape of the half-sine wave. However, there lacks sufficient comprehension of the generation process of these strain pulses, such as the initiation mechanism and the parameters affecting the amplitude and duration of the waveform. In the next section, the initiation mechanism of the strain wave and the influence of the projectile’s geometry on the strain

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Acceleration pulse

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Strain pulse

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waveform are being investigated with numerical method.

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Fig. 2. The typical strain and acceleration pulses measured during the calibration process.

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2.2. The correlation between geometry of projectile and strain waveform An input acceleration pulse with high amplitude and a wide frequency bandwidth is supposed to excite all the modal frequency of the high-g accelerometers during the calibration. According to Eq. (2) and Fig. 2, the amplitude and duration of the excitation signal depend on the strain waveform produced by the impact from the projectile. Referring to the studies of the Hopkinson bar technique, it is well known that the projectile’s geometry has an influence on the strain waveform. In this section, the correlation between the projectile’s geometry and the stain waveform were studied by establishing a finite element model of the experimental apparatus. In consideration of symmetry of the problem, one quarter of the experimental apparatus’ geometry was modeled in the simulation to simplify the problem and save computational time. As both the projectile and the calibrating bar remain elastic during the test, Hooke’s law for isotropic material was used in the constitutive equations. The elastic module of the projectile and the calibrating bar were taken from the data of conventional steel and Ti-6Al-4V titanium, respectively. Eight-noded hexahedral elements were used for both the projectile and the calibrating bar. The initial velocity was 7

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applied to the entire projectile in the direction of impact. The impact processes were simulated by using the dynamic finite element code (ABAQUS/Explicit). The strain history was monitored by the elements at the surface of the calibrating bar, where the strain gauges were located in real test. To verify the developed numerical model, we conducted both the experimental test and the numerical simulation, wherein a cylindrical projectile of 19 mm in diameter and 200 mm in length was launched with the velocity of 10 m/s to impact a bar with

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the diameter of 19 mm. As shown in Fig. 3, the obtained strain pulses in the experiment and the simulation are in a good agreement. The slight difference in the pulse’s width and

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amplitude results from the material defects and dumping [18], which were not considered in

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the numerical simulation.

Fig. 3. The experimentally and numerically obtained strain pulses for comparison.

The length of the projectiles used in the shock calibration of accelerometers is shorter than the ones used in conventional Hopkinson bar tests. The initiation mechanism of the half-sine strain wave was investigated by using four cylindrical projectiles with varying length in simulation. As shown in Fig. 4, all the four generated waves possess nearly identical rising edge. The wave width gets narrower as the projectile gets shorter. When the length of the projectile is 30 mm, the platform disappears and the strain wave is almost in the shape of a half-sine wave. Only the rising edge of the strain wave is the excitation signal in calibration. Therefore, the relative shorter projectile is suggested to be chosen in order to saving the impact momentum, as long as the shorter projectile is long enough to produce a strain wave possessing the same whole rising edge with the longer projectiles. It is very likely that there 8

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exists a critical projectile length under which the generated strain wave becomes a half-sine wave regardless of the projectile’s geometry. The existence of such critical length was numerically confirmed and the results are shown in Fig. 5. In the results, the strain waves were produced by using projectiles of different geometries. But all the projectiles are of 30 mm in length and 19 mm in maximal diameter. In order to avoid the stress concentration in the simulation process, the pointed ends of the projectiles were modeled with facets of 2 mm

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in diameter. The generated strain waves can be intuitively divided into three groups according to their widths. They are plotted with different colors in Fig. 5. In Group 1, the projectiles

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(denoted by (a), (b) and (c)) possess constant cross-section area and the 90-degree taper (maximum taper degree) at the front end. In Group 2, the projectiles (denoted by (d), (e) and

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(f)) possess the maximum taper degree at the front end, too. But, as the cross-section area decreases along the axis of symmetry, the overall degree of taper in Group 2 is less than

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Group 1. In Group 3, the projectiles (denoted by (g), (h), (i) and (j)) possess less taper degree than the first two groups. Correspondingly, the widths of the waveforms in Groups 1 are narrowest among the three groups. Group 2 comes the second, and Group 3 is the widest.

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Moreover, the rising edge of the strain waves in Group 1 is the steepest, Group 2 comes the second, and Group 3 is the gentlest. The taper degree causes multiple reflection of the pulse back and forth in the projectile, leading to the enlargement of the wave width. In addition, it

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is deduced that the increasing cross-section area along the axis of symmetry of the projectile

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leads to the rise of the amplitude of the strain wave. When there is a rapid increase in the cross-section area, just like the end surface of the cylindrical projectiles of Group 1, the rising edge of the strain wave becomes the steepest, whereas it ought to be vertical in theory. It is the dispersion effect that let the edge rise more slowly in reality. When the cross-section area increases gradually, just like the projectiles of Group 2 and 3, the amplitude of the strain wave rises gradually, resulting in a slow-rising edge of the strain wave.

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L=100mm

L=200mm

L=30mm

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L=50mm

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Fig. 4. Strain waves produced by impact of the cylindrical projectiles with different length.

Fig. 5. Strain waves produced using projectiles of different geometries but the same length of 30 mm.

In order to verify the correlation between the cross-section area of the projectile and the strain amplitude, ten projectiles with different geometries but the same length of 200 mm were utilized in the simulation. In such a way the changing of the strain-wave amplitude can be easily observed. The computed strain waves are shown in Figs. 6. As well known, the strain pulse duration T is proportional to the length of the cylindrical projectile L, as

T=

2L , C0

(3)

where C0 is the velocity of longitudinal elastic wave in the projectile. T is equal to 80 µs after substituting L=200 mm into Eq. (3). The dotted line in Fig. 6a represents the strain wave 10

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produced by impacting a steel cylindrical projectile against a steel bar. The diameter of both the projectile and calibrating bar is 19 mm. So the projectile and the calibrating bar have the same wave impedance. The strain wave is approximately of 80 µs in duration. The solid lines in Figs. 6 represent the strain curves produced by impacting steel projectiles with different geometries against a Ti-6Al-4V titanium bar. It is observed that there are two main parts for each of the corresponding strain history: the first part (Part 1) lies between 110 µs and 200 µs

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(duration of 90 µs) and the second part (Part 2) starts after 200 µs. The wave in the projectile will get reflected at the impacting interface due to the difference in the wave impedance.

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Consequently, the pulse width is enlarged and Part 2 is added to Part 1 in the strain history. By comparing the strain waveforms shown in Figs. 6a-6c, it is concluded that the difference

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in the amplitude of the strain is attributed to the different kinetic energy of the projectiles (different masses) [11]. The theoretical proof is provided in the followings. The impact of two semi-infinite rods is schematically shown in Fig. 7. Suppose the two bars possess separate

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cross-section areas: ϕ1 (diameter D1) and ϕ2 (diameter D2), and their wave impedance is ρ1C1 and ρ2C2, respectively. According to the elastic wave propagation theory, when bar b2 impacts

ρ 2C2ϕ 2 ( ρ1C1V2 ) . ρ1C1ϕ1 + ρ 2C2ϕ 2

(4)

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σ3 =

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bar b1 with a velocity V2, the stress in bar b1 is given by

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Now let ρ1C1 = 22.5 MPa· s/m, ρ2C2 = 40 MPa· s/m, V2 = 20 m/s and D1 = 19 mm, σ3 can be expressed as following:

18000 D22 σ3 = , 8122.5 + 40 D22

(5)

and the corresponding strain ε3 is

ε3 =

18000 D22 , (8122.5 + 40 D22 ) E1

(6)

where E1 is equal to 105,000 MPa. When D2 is equal to 19 mm or 10 mm, ε3 is equal to 2,743

µε or 1,414 µε , respectively. This is in agreement with the amplitude of the strain wave shown in Figs. 6a and 6b. The value of ε3 for the tube-shaped projectile shown in Fig. 6c is equal to 2,545 µε by substituting the corresponding cross-section area into Eq. (4). Again, the theoretical results agree very well with the numerical results. Therefore, the amplitude of the strain wave is positively correlated with the cross-section area (mass) of the projectile with constant section. By comparing the results in Figs. 6a and 6d-6f, it is observed that there exists a correlation between the strain waveform and the projectile’s geometry of a varying cross-section area: as shown in Fig. 6a, the strain waveform of Part 1 is a constant platform;

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for the case in Fig. 6d, there are two platforms in the waveform of Part 1; the waveform shown in Fig. 6e consists of four clear segments; and the strain magnitude increases linearly with time for the case shown in Fig. 6f, wherein the projectile is continuously tapered. In all the four cases, Part 1 and Part 2 of the waveform exhibit a certain level of symmetry. Therefore, the amplitude of the strain wave appears to be positively correlated with the projectile’s cross-section area (mass), which is changing along the axis of symmetry. Figs. 6g

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and 6h show the waveforms generated by using the projectiles of various tapered front ends. The waveform shown in Fig. 6h exhibits a steeper rising edge in comparison with the

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waveform in Fig. 6g. This is attributed to the use of larger taper degree of the projectile in Fig. 6h. In an extreme case, the use of a cylindrical projectile will result in the steepest rising of

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the strain since the projectile has a 90-degree taper. For the case shown in Fig. 6i, the projectile was designed with a conical tip at the front end and a conical pit at the rear end. As

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a result both the rising course and the drop of the strain wave become less steep. The strain wave of almost the shape of a half-sine wave, as shown in Fig. 6j, was generated by using a projectile of the similar shape as used by Li et al. [13].

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Based on the analyses above, the strain pulse with a steeper rising edge and narrower width can be generated by impacting a projectile with a larger taper degree at the front end. In such a way the acceleration pulse possesses higher amplitude and wider frequency bandwidth.

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To confirm this conclusion, tests were conducted on projectiles of two different geometries

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by using such a calibration apparatus. Fig. 8 shows the measured peak acceleration and the corresponding launch pressure for the two different projectiles used in the tests. It is observed that a wider calibrating range of the peak acceleration can be achieved by adjusting the projectile’s geometry. The projectile of a larger taper degree is able to achieve higher amplitude of the acceleration.

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ip t cr us an M d Ac ce pt e Fig. 6. Strain waves and the corresponding geometries of projectile of 200 mm in length. 13

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V2

V1=0 b1

b2 (ϕ2)

(ϕ1) V2

C1

C2

b1

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b2

V3 (σ3)

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Fig. 7. A schematic of the stress-wave propagation after the impact of two semi-infinite bars.

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(a) Large taper projectile

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(b) Small taper projectile

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Fig. 8. The measured peak acceleration and the corresponding launch pressure of the two different projectiles. (a) The cylindrical projectile with a conical tip of large taper degree. (b) The cylindrical projectile with a conical tip at the front end and a conical pit at the rear end (small taper degree).

3. The dynamic linearity calibration methods for high-g accelerometers The measured acceleration will be inadequate if the dynamic linearity of the accelerometer is not established at the high acceleration level (in the order of 106 m/s2). According to IEC 60747-14-4 Ed.1.0 (Discrete semiconductor devices - Part 14-4: Semiconductor accelerometers) [9], assume that the output signal from a target accelerometer is X1(t) and X2(t) when the input acceleration to the accelerometer is x1(t) and x2(t), respectively. The linearity holds if the output from the accelerometer is aX1 (t) + bX2 (t), when the input acceleration to the accelerometer is ax1 (t) +bx2 (t), where a and b are arbitrary constants. When the acceleration being calibrated is over the high-g range, the dynamic linearity becomes distinct from the linearity in static measurement. According to the definition of the linearity, the calibration of dynamic linearity is carried out by obtaining three groups of excitation and output signals of the accelerometers, then calculating the linear fitting constants (a and b) of the excitation signals, and lastly determining whether the linear 14

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fitting constants fit the output signals. The calibration of linearity should be conducted over a certain frequency bandwidth. So the three groups of the acceleration signals should possess the same width in the time domain. That is to say, when the Hopkinson bar is used to produce the excitation signals in dynamic linearity calibration, the rising edges of these strain waves should be the same in duration. The strain waves with different amplitudes but the same duration can be simply generated by

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launching the same projectile with different air pressure. However, it is indicated in Fig. 8 that a wide range of acceleration is difficult to be achieved by using only one projectile. So

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the cylindrical projectiles with different cross-section areas can be used to widen the testing range of acceleration. In consideration of the centering and simplicity of the launching

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apparatus, the cylindrical projectiles (b and c) are selected from Fig. 5 to be used to generate a wide range of the acceleration. The principle of double-projectile system was proposed in

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Refs.8 and 9.

3.1. The evaluation of the existing method

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Based on the earlier studies [8, 9], the experimental apparatus with double-projectile is shown in Fig. 9, in which a concentric double-barrel gun (with the inner and outer tubes) is used to launch the two coaxial cylindrical projectiles. The calibration is conducted in three

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steps. In the first step, only the inner projectile is launched from the inner tube. The impact

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against the end surface of the calibrating bar generates the strain ε1 (t) in the bar and the input acceleration a1 (t). In the second step, the strain ε2 (t) in the bar and the input acceleration a2 (t) are obtained when only the outer projectile is launched to impact the end surface of the calibrating bar. In the last step, the two projectiles are launched together to impact against the end surface of the calibrating bar at the same time or at a prescribed time interval, leading to the strain ε1+2 (t) and the input acceleration a1+2 (t). The following expressions hold as long as linear elastic deformation is maintained in the metal bar:

ε 1+2 (t ) = αε 1 (t ) + βε 2 (t ) , and

(7)

a1+2 (t ) = αa1 (t ) + βa2 (t ) ,

(8)

Where α and β are constants obtained by bilinear fitting of the three groups of the strain pulse detected by the strain gauges. When the inner projectile is first launched, the output signal from the accelerometer is obtained and denoted by g1 (t). Similarly, the output signal is denoted by g2 (t) for the case of the outer projectile and g1+2 (t) for the simultaneous launch of

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the two projectiles. The following relation can be established when the dynamic linearity of the accelerometer holds:

g1+ 2 (t ) = αg1 (t ) + βg 2 (t ) ,

.

(9)

Eqs. (7) and (9) together serve as the basis of the shock calibration of the dynamic linearity of accelerometers. In the test, the accuracy of ε1+2 (t) and g1+2 (t) mainly depends on

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whether the two projectiles are able to impact the end surface of the calibrating bar at the same time. To achieve the same-time impact, the conditions of the two projectiles (e.g., the

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geometry, the launch pressure and the initial position inside the barrel) have to be the same to each other and they need to be consistent in all the steps of the calibration tests [8]. Usually

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the launch of the two projectiles is controlled by a valve controller, as shown in Fig. 9. There are a number of uncertainties that can affect the launch conditions of the projectiles, such as the air tubes length, the gun barrel length, the initial position of the projectiles, the friction

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between the gun barrels and the projectiles, etc. When the two projectiles are launched simultaneously by the double-barrel gun, supposing the maximum acceptable time interval

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( δ ) for the impacts by inner and outer projectiles is 10 µs (in fact 10 µs is too high to ensure the accuracy of the experimental results) and the impact velocity of the two projectiles is denoted by V, the maximum displacement deviation between the two projectiles at the impact

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moment is S=Vδ. A few selected examples of this relation are shown in the table embedded

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in Fig. 9. When V is 40 m/s, the displacement deviation is of 0.4 mm, which is too small to control in tests. We conducted the calibration tests using this system. A typical obtained strain waveform for these tests is shown in Fig. 10. The waveform is separated into two independent pulses. The time interval between the pulses by the inner-projectile impact and the outer-projectile impact is more than hundreds of microseconds. In addition, the cross-section areas of the two projectiles are fixed for the given bore sizes of the two gun barrels. This further limits the flexibility of this method in the shock calibration practice. For this reason we are introducing a new shock calibration method in Section 3.2 to overcome these difficulties.

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Double gun barrel Double projectiles (outer & inner)

Vacuum clamp

Strain gauge

Air chamber1

Calibrating bar

Air chamber2

Accelerometer

Inner gun barrel Outer gun barrel

S

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Valve controller

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The velocity of the two projectiles V

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Bar

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L

Outer projectile (tube)

10

15

S (mm)

0.05

0.10

0.15

20

25

30

35

40

0.20

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0.30

0.35

0.40

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V (m/s)

Inner projectile

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Fig. 9. The schematic of the calibration apparatus with a double-barrel gun holding two coaxial cylindrical projectiles (listed in the table is the displacement deviation between two projectiles with the corresponding impact velocity).

δ

The reflective pulse of inner projectile impacting

The pulse of inner projectile impacting The pulse of outer projectile impacting

Fig. 10. The typical strain pulse in the tests when the two projectiles were launched synchronously using the double-barrel gun. 17

Page 17 of 32

3.2. The newly developed method Using separate barrels to launch the two projectiles is the underlying cause of the asynchronous impact in the shock calibration tests. In this section, we propose a new calibration method by using a single-barrel gun with double-projectile (inner and outer projectiles) as the loading device. The double-projectile is employed and positioned together

ip t

as illustrated in Fig. 11. To prevent sliding between the two projectiles during the launching process, they are fastened by small-size screws near the rear ends. The two projectiles in various assembly modes are launched simultaneously to achieve three rounds of impact for

cr

the input signal: ε1 (t), ε2 (t) and ε1+2 (t), as shown in Fig. 12. We put a position deviation

us

between the two projectiles in the first two impacts while keeping them abreast with each other in the third impact. The inner projectile will impact the calibrating bar earlier than the outer projectile, as shown in Fig. 12a. As long as the position deviation between the two

an

projectiles is sufficiently large, the first half-sine strain wave of ε1 (t) is only a result from the impact of the inner projectile. The second impact (ε2 (t)) is conducted by shifting the outer

M

projectile right to the inner projectile as shown in Fig. 12b. The third impact (ε1+2 (t)) is conducted by aligning the two projectiles at their ends and then performing the impact at the same time, as illustrated in Fig. 12c. In the test, the contact surfaces of the two projectiles

d

were greased to reduce friction. The gun barrel and the calibrating bar were aligned in

Ac ce pt e

advance using a laser beam as a base line. The impact velocity was monitored by measuring the flying time of the projectiles between two laser beams. Fastening screw

Outer projectile

Inner projectile

Calibrating bar

Strain gauge

Accelerometer Vacuum clamp

Light-gas gun Gun barrel

Fig. 11. A schematic of the developed apparatus with double-projectile in a single-barrel gun.

18

Page 18 of 32

(a)

Fastening screws

S Calibrating bar

Single gun barrel Inner projectile Outer projectile (tube)

cr

(b)

ip t

L

us

Calibrating bar

S

L

an

(c)

M

Calibrating bar

L

d

Fig. 12. The three assembly modes of the two coaxial projectiles in each impact.

Ac ce pt e

3.3. Discussion regarding the newly developed method In this section, a series of experiments are carried out to evaluate this newly developed calibration method. The experimental conditions are listed in Table.1. All the steel projectiles used in the tests were launched from a single-barrel gun with the bore size of 19.2 mm. A Ti-6Al-4V titanium rod was selected as the calibrating bar with the length being 1100 mm and the diameter being 30 mm. The position deviation of the two projectiles (used in Imp. 1 and 2) is 4 mm. The fastening screws used in the double-projectile is of 3 mm in diameter.

19

Page 19 of 32

Table.1. The experimental conditions. Projectile

Projectile

geometry

length (mm)

1

30

2

30

Projectile diameter (mm)

Inner projectile

11.14

11.2 (Internal) Outer projectile

30

4

30

19

5

30

19

6

30

19

7

60

8

60

9

60

velocity (m/s)

0.08

19.2

0.08

19.1

0.08

19.8

15.3

0.09

20.9

0.20

27.6

19

0.10

13.5

19

0.16

16.7

19

0.22

19.3

an

us

0.05

d

M

Impact

(MPa)

cr

19 (External)

3

Air pressure

ip t

Impact no.

Ac ce pt e

3.3.1 The influence of the fastening screws on the strain and acceleration pulses As shown in Table 1, the screws were used in Imps. 1-3 to fasten the two coaxial projectiles. Due to the position deviation between the two projectiles in Imps. 1 and 2, the leading projectile will be the first to impact the end surface of the calibrating bar, and then slow down and bound to the opposite direction. The relative motion between the two projectiles will be hindered by the fastening screws. So it is very likely that the fastening screws will affect the first wave in the strain pulse, as well as the input acceleration pulse. According to Fig. 2，the rising edge of the strain pulse in the calibrating bar corresponds to the excitation signal for the accelerometer. Meanwhile, the dynamic linearity of the accelerometer is calibrated by comparing the peak value of the input and output acceleration pulses. It is observed that the peak value of the acceleration occurs at the moment of the maximum time gradient of the strain pulse before the peak value of the strain is reached. Thus, the accuracy of the calibration will not be influenced as long as the fastening screws do not affect the waveform of the strain pulse before the moment of the maximum time gradient. Let us now consider a scenario wherein the inner projectile is the leading projectile, as illustrated in Fig. 13. The target strain pulse (Pulse 1) is generated once the inner projectile 20

Page 20 of 32

impacts the end surface of the calibrating bar. As the elastic compression wave propagates in the inner projectile and reaches the fastening screws, the outer projectile starts to decelerate following the inner projectile due to the presence of the fastening screws. The fastening screws then react and impose an extra compression to the inner projectile, causing another strain pulse (Pulse 2) in the calibrating bar. Therefore, the strain pulse generated in the calibrating bar is the result from the superposition of Pulse 1 and Pulse 2. As long as the

ip t

fastening screws are installed at the rear ends of the projectiles, Pulse 2 will be after the peak value of Pulse 1 (indicated by P in Fig. 13). Even in an extreme case, when the fastening

cr

screws are positioned at the midpoint of the inner projectile, Pulse 2 will initiate at the moment of the peak value of Pulse 1. The presence of the fastening screws still has no

us

influence on the calibration. The same situation applies to the other case wherein the outer

Outer projectile Inner projectile

an

projectile is the leading projectile.

s

M

Calibrating bar

d

Ac ce pt e

Fastening screw

ε

0 ×P

Pulse 1

Pulse 2

Strain pulse

t

t

Fig. 13. The generation of the strain pulse in the calibrating bar by impacting the double-projectile with fastening screws (the inner projectile is the leading projectile).

In order to confirm the analysis above, we conducted both simulation and experimental test to examine the strain pulses for Imps. 1-3. Meanwhile, to evaluate the effect of the friction between the lower surface of the screws and the inner projectile in real test, two extreme contact conditions were considered in the numerical simulations. For the first contact condition, the lower surfaces of the screws were rigidly fixed to the inner projectile. The computation under such contact condition is denoted by Simulation 1. For the other contact 21

Page 21 of 32

condition, the interfaces between the lower surface of the screws and the inner projectile are set to be frictionless, such that the screws do not take any effect. The corresponding computation is denoted by Simulation 2. The experimental and numerical results for Imps. 1-3 are shown in Figs. 14. It is found that the numerical results for the first strain wave are in good agreement with the experimental data regardless of the contact condition adopted. It indicates that the existence of the fastening screws has neglectable influence on the

ip t

calibration. As shown in Figs. 14a and 14b, there is a second strain peak in the strain history of Simulation 1. Such observation is consistent with the analysis outlined in Fig. 13, where

cr

Pulse 2 is caused by the presence of the fastening screws. While in Simulation 2, there is no second peak in the strain history. We did not observe the second peak in the experimental

us

results either. So it can be deduced that the actual contact condition at the impact moment is similar to Simulation 2. That is to say, the fastening screws only play their roles in the

an

launching process. They fall off once the projectiles impact the end surface of the calibrating bar. Based on our observation, the fastening screws did fall off in actual tests due to the

Strain of Simulation 1 Strain of Simulation 2 The second strain Strain of experiment peak of Simulation 1

Ac ce pt e

d

Imp. 1

M

relatively strong impact.

Acceleration of Simulation 2 Acceleration of Simulation 1 Acceleration of experiment

(a) Imp. 1 (the inner projectile is the leading projectile).

22

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Strain of Simulation 1 Strain of Simulation 2 Strain of experiment The second strain peak of Simulation 1

cr

ip t

Imp. 2

Acceleration of experiment

an

us

Acceleration of Simulation 2 Acceleration of Simulation 1

Strain of experiment Strain of Simulation 1

Ac ce pt e

d

Imp. 3 Strain of Simulation 2

M

(b) Imp. 2 (the outer projectile is the leading projectile).

Acceleration of experiment

Acceleration of Simulation 2

Acceleration of Simulation 1

(c) Imp. 3 (the two projectiles impact the bar synchronously). Fig. 14. The comparison of the strain and acceleration pulses in Imps. 1-3 by experimental testing and numerical simulations.

3.3.2 The frequency characteristics of the excitation signals The dynamic linearity of accelerometers cannot be calibrated unless the excitation 23

Page 23 of 32

signals, which are generated by the three rounds of impact (Imp. 1-3) through the double-projectile system, possess the same bandwidth in the frequency domain. In the next we will study the excitation signals in both the time and frequency domains. Presented in the inset of Fig. 15a are the first waves of the strain pulses detected by strain gauges during the Imps. 1-9. These waves produced by the projectiles of 30 mm in length (Imp. 1-6) last for about 33 µs while the ones produced by the projectiles of 60 mm in length (Imp. 7-9) last for

ip t

about 44 µs. The accelerometer will fly off the end of the calibrating bar after the strain-wave’s peak passes it. Thus the excitation signals actually correspond to the rising

cr

edges of the first strain waves, as illustrated in Fig. 15a. It is noticed that the rising edges of all the first strain waves are of about 25 µs in duration. Fig. 15b shows the spectra of the

us

signals plotted in Fig. 15a. The frequency characteristics of all the excitation signals are in a good agreement with each other. It implies that the cross-section，length and impact velocity

an

of a cylindrical projectile have no influence on the frequency characteristics of the excitation signals during the calibration. It rationalizes that two projectiles can be used to calibrate the dynamic linearity of the accelerometers over a certain frequency range. A higher level of

M

acceleration can be achieved under the same launching pressure by using the cylindrical projectiles of 30 mm in length while a better experimental stability can be attained by using

Ac ce pt e

d

the projectiles of 60 mm in length.

Imp. 6

Imp. 9 Imp. 5 Imp. 7 Imp. 3

Imp. 8

Imp. 2 Imp. 1 Imp. 4

(a)

24

Page 24 of 32

ip t cr us an

M

(b) Fig. 15. The excitation signals produced by Imps.1-9 in time (a) and frequency (b) domain.

3.3.3 The testing range of the new calibration system

The testing range of the calibration system is mainly limited by the maximal elastic

d

strain of the calibrating bar and the measuring range of the strain gauge. In this study, a

Ac ce pt e

Ti-6Al-4V titanium rod was used as the calibrating bar in the tests. The extreme compressive elastic strain of Ti-6Al-4V titanium before plastic deformation is 1%. The measuring range of the strain gauge used in this system is 1% as well. The strain in the calibrating bar can be expressed as

∫ ε=

T0

0

a (t )dt

2C

,

(10)

where the T0 stands for the duration of the excitation signal. If the acceleration takes the peak value (denoted by apeak) during the whole acceleration history, the maximum strain in the calibrating bar is given by

ε max =

a peakT0 2C

.

(11)

As shown in Fig. 15a, the duration of the excitation signals is about 25 µs for all the cylindrical projectiles. Thus, the maximum strain in the calibrating bar is less than 0.75 % when the peak acceleration is 300,000 g. Therefore, an acceleration of 300,000 g can be calibrated by using the developed system as long as the impact velocity is sufficiently high. 25

Page 25 of 32

According to the correlation between the strain waveform and projectile’s geometry, the acceleration can be controlled by adjusting the relative cross-section of the two projectiles, such that a wider testing range can be achieved for the calibration. 3.3.4 The influence of attenuation and dispersion of the elastic wave propagation The numerical analysis conducted in Ref. 16 indicated that an elastic wave in a circular

ip t

bar became a plane wave after its front traveled a distance around fifteen times of the diameter of the bar. Therefore, in this study, the inhomogeneity of the strain in the

cr

cross-section of the bar can be neglected at a distance of 450 mm away from the impact end. In order to study the influence of attenuation and dispersion of the elastic wave propagation, a

us

three-dimensional finite element model was employed in this section to simulate the process of Imps. 1-3. As illustrated in Fig. 16, a series of cross-sections were selected along the axis

an

of the calibrating bar. The strain history of three points A, B and C was recorded for each selected cross-section. The peak value of the strain pulses were plotted along the axis of the bar, as shown in Fig. 17. After the elastic wave traveled a distance of 500 mm from the

M

impact end, the relative difference of the strain of the three recording positions in this cross-section was less than 0.5 %. After the strain wave traveled a distance of 450 mm from the impact end, the attenuation of the strain, which results from the lateral disperse of the

d

wave, was already very weak. Therefore, the subsequent propagation of the strain pulse can

Ac ce pt e

be considered being with constant strain amplitude. For convenience purpose, the strain gauges were positioned at the middle length of the calibrating bar, 550 mm away from the impact end.

10mm 20mm 30mm 40mm

Recording positions for strain in each cross-section

The cross-section of calibrating bar

A B C

50mm 100mm 200mm 300mm 400mm

550mm

700mm 800mm 30mm

The direction of strain wave propagation

The calibrating bar

1100mm

Fig. 16. The recording positions for the strain in numerical simulation. 26

Page 26 of 32

an

us

Imp. 1

cr

Imp. 2

ip t

Imp. 3

3.4. Calibration process and results

M

Fig. 17. The peak values of all the strain pulses at different recording points along the calibrating bar.

In this section, the calibration process is introduced by processing the experimental data of Imps.1-3 in Section 3.3. The calibration principle of dynamic linearity is based on Eq. (7)

d

and (9). Since the linear constants α and β will not change after integrating the acceleration

Ac ce pt e

or differentiating the strain, there is no need for such operations in the calibration of dynamic linearity. The three groups of strain pulses (ε1(t), ε2(t), and ε1+2(t)) detected by the strain gauges are shown in Fig. 18. By doing bilinear fitting on the data of the three strain pulses, the values of the linearity parameters in Eq. (7) are determined as α = −0.39 and β = 1.68 , respectively. The calculated strain pulse ε '1+ 2 (t ) is also shown as the dotted curve in Fig. 18, which is represented by the linear combination of ε1(t) and ε2(t), as

ε '1+ 2 (t ) = -0.39ε1 (t ) + 1.68ε 2 (t ) .

(12)

The output signals of the accelerometer (denoted by g1 (t) , g2 (t) and g1+ 2 (t ) ) are presented in Fig. 19. Once the dynamic linearity of the accelerometer is established, Eq. (9) is able to be satisfied with the parameters α= −0.39 and β= 1.68. The calculated acceleration signal g '1+ 2 (t ) is given by

g '1+ 2 (t ) = -0.39 g1 (t ) + 1.68 g 2 (t ) .

(13)

The calculated g '1+ 2 (t ) is plotted and shown in Fig. 19 as well. The smaller nonlinearity equates to the higher linearity. The dynamic nonlinearity of the accelerometer is quantitatively assessed by the relative error between g1+ 2 (t ) and g '1+ 2 (t ) , which is simply 27

Page 27 of 32

given by the relative error between the peak values of g1+ 2 (t ) and g '1+ 2 (t ) , as

Ld =

g '(1+ 2) peak − g (1+ 2) peak g (1+ 2) peak

(14)

,

where Ld describes the level of dynamic linearity of the accelerometer. The quantities

g (1+ 2) peak and g '(1+ 2) peak are the peak values of g1+ 2 (t ) and g '1+ 2 (t ) , respectively. The peak

ip t

value of the accelerometer obtained in the experiment ( g1+ 2 (t ) ) is 21.3563 × 10 4 g, while the one calculated by Eq. (13) ( g '1+ 2 (t ) ) is 20.4128 × 10 4 g. Thus, the dynamic linearity of the

Ac ce pt e

d

M

an

us

cr

calibrated accelerometer is 4.42 %.

Fig. 18. Strain pulses for Imps.1-3. The solid curves are the measured strain histories; while the dotted curve is the calculated strain history according to Eq. (12).

Fig. 19. Acceleration signals for Imps.1-3. The solid curves are the measured acceleration signals; while the dotted curve is the calculated acceleration signals according to Eq. (13). 28

Page 28 of 32

4. Conclusions In this work the shock calibration methods of high-g accelerometers using Hopkinson bar were studied in details. First, the influences of the projectile’s geometry on the amplitude and frequency bandwidth of the excitation signal were investigated systematically through numerical simulation. Then, we proposed a new method to calibrate the dynamic linearity of

ip t

accelerometers by using a double-projectile single-barrel gun system. Conclusions of this study are drawn and summarized as follows.

(1) Proper geometry of the projectiles needs to be selected to produce proper excitation

cr

signals for calibration. A smaller taper degree at the front end of the projectile will lead to lower amplitude and wider duration of the acceleration pulse. The cylindrical projectiles with

us

the maximum front taper degree (90 degree) were employed in the dynamic linearity calibration of high-g accelerometers to generate the excitation signals with a wide frequency

an

bandwidth.

(2) As the amplitude of the acceleration is positively correlated with the cross-section area of a cylindrical projectile, in addition to the control of air pressure, using the dynamic linearity of accelerometers.

M

double-projectile approach is able to widen the testing range of the calibration system for the

d

(3) It was analyzed and experimentally confirmed that the fastening screws have no

Ac ce pt e

effect on the excitation signals in the shock calibration of the dynamic linearity of accelerometers using the developed apparatus in this study. The experimental results imply that the cross-section，length and impact velocity of a cylindrical projectile have no influence on the frequency characteristics of the excitation signals during the calibration. According to the numerical results, the influence of the attenuation and dispersion of the elastic wave during the propagation can be neglected in calibration. (4) The shock calibration method of dynamic linearity of accelerometers developed in this work can be used to achieve a wide acceleration range from thousands of g to nearly 300,000 g. The dynamic linearity of accelerometers can be quantitatively assessed by a relative quantity defined in this paper.

Acknowledgments This research work was supported by the National Natural Science Foundation of China (No. 11372255 and 11572261) and Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX201609).

References 29

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[1] Brown G. Accelerometer calibration with the Hopkinson pressure bar. Instrument Society of America preprint 1963; (49.3): 63. [2] Sill R D. Shock calibration of accelerometers at amplitudes to 100,000 g using compression waves. Endevco Technical Paper TP 1983; 283. [3] Ueda K, Umeda A. Characterization of shock accelerometers using Davies bar and strain-gages. Experimental mechanics 1993; 33(3): 228-233. [4] Togami T C, Baker W E, Forrestal M J. A split Hopkinson bar technique to evaluate the performance of accelerometers. Journal of Applied Mechanics 1996; 63: 353-356.

ip t

[5] Bateman V I, Brown F A, Davie N T. The use of a beryllium bar to characterize a piezoresistive accelerometer in shock environments. Proceedings–Institute of Environmental Sciences, Orlando, FL, 1996. and Shock Waves (in Chinese) 1997; 17: 90-96.

cr

[6] Li Y L, Guo W G, Jia D X, Xu F. An equipment for calibrating high shock acceleration sensors. Explosion [7] Foster J T, Frew D J, Forrestal M J, Nishida E E, Chen W. Shock testing accelerometers with a Hopkinson pressure bar. International Journal of Impact Engineering 2012; 46: 56-61.

us

[8] Umeda A. Method and device for measuring dynamic linearity of acceleration sensor. United States Patent: US2005/0160785 A1; 2005.

[9] IEC/SC47E. IEC 60747-14-4 Ed. 1.0. Dynamic linearity measurement using an impact acceleration

an

generator. 2002: 74-76.

[10] Kumar A, Mies L T S, Pengjun Z. Design of an impact striker for a split Hopkinson pressure bar. J Inst Eng 2004; 44(1): 119-130.

M

[11] Baranowski P, Malachowski J, Gieleta R, Damaziak K, Mazurkiewicz L, Kolodziejczyk D. Numerical study for determination of pulse shaping design variables in SHPB apparatus. Bulletin of the Polish Academy of Sciences: Technical Sciences 2013; 61(2): 459-466. [12] Cloete T J, Van Der Westhuizen A, Kok S, Nurick G N. A tapered striker pulse shaping technique for

d

uniform strain rate dynamic compression of bovine bone. EDP Sciences 2009; 1: 901-907.

Ac ce pt e

[13] Li X, Hong L, Yin T, Zhou Z L, Ye Z Y. Relationship between diameter of split Hopkinson pressure bar and minimum loading rate under rock failure. Journal of Central South University of Technology 2008; 15: 218-223.

[14] R. Naghdabadi, M.J. Ashrafi , J. Arghavani. Experimental and numerical investigation of pulse-shaped split Hopkinson pressure bar test. Materials Science and Engineering A 2012; 539: 285-293. [15] Alireza Bagher Shemirani, R. Naghdabadi, M.J. Ashrafi. Experimental and numerical study on choosing proper pulse shapers for testing concrete specimens by split Hopkinson pressure bar apparatus. Construction and Building Materials 2016; 125: 326-336.

[16] Davies R M. A critical study of the Hopkinson pressure bar. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 1948; 240(821): 375-457. [17] Kolsky H. Stress waves in solids. Vol. 1098. Courier Corporation, 1963. [18] Tanaka K, Kurokawa T, Ueda K. Plastic stress wave propagation in a circular bar induced by a longitudinal impact. Macro-and micro-mechanics of high velocity deformation and fracture. Springer Berlin Heidelberg 1987; 317-3

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Photographs and biographies of all authors

————— from Northwestern Polytechnical University. She now

ip t

Kangbo Yuan obtained her B.Sc

studies for her M.Sc in Aeronautical Engineering, School of Aeronautics, Northwestern Polytechnical University. Her research interest focuses on calibration method and device of

cr

dynamic characteristics of high g accelerometer; dynamic testing and test technology of

————— Weiguo Guo

us

materials and structures; theory, modeling, and simulation of materials and structures.

an

Organization: Northwestern Polytechnical University, China Title: Professor of mechanics Education:

M

MSc，Mechanics of solid, Northwestern Polytechnical University.1995 PhD，Mechanics of solid, Northwestern Polytechnical University. 2007 Current research:

d

1. Dynamic response of metals, composite and foam materials; 2. Failure mechanism, micromechanical and constitutive modeling for materials;

Ac ce pt e

3. Experimental technique research. Memberships:

1. Member of Society of Chinese Mechanics, Material and Aeronautics; 2. Member of Society of the experimental technique in explosion and shock waves.

—————

Yu Su obtained his B.Sc from Peking University, M.Sc and Ph.D. in Solid Mechanics from the Department of Mechanical & Aerospace Engineering, Rutgers University, USA. He worked as a post-doctoral researcher at the University of California San Diego and Rice University, and gained engineering design experience by working as a design engineer at Moffatt & Nichol Engineers and IDC Consulting Engineers in California, USA. He joined Beijing Institute of Technology in 2008. His research interest focuses on numerical modeling of phase transformation in multi-functional and smart materials; experimental characterization of multi-physical behaviors of smart materials and structures.

31

Page 31 of 32

————— Yunbo Shi is the professor in North University of China. He mainly engaged in MEMS,

ip t

micro inertial devices and other aspects of research.

————— Jingyu Lei obtained her B.Sc

cr

from Northwestern Polytechnical University, M.Sc in

Aeronautical Engineering, School of Aeronautics, Northwestern Polytechnical University.

us

Her research interest focuses on measuring method and device of dynamic linearity of high g accelerometer; fatigue fracture and damage characteristics of materials and structures; theory, modeling, and simulation of materials; dynamic testing and test

an

technology of materials

—————

M

Hui Guo obtained his B.Sc from Henan Polytechnic University, M.Sc in Solid Mechanics from the Institute of Systems Engineering, China Academy of Engineering Physics. Since 2014 he studies as a doctoral student at Northwestern Polytechnical University. His

d

research interest focuses on dynamic mechanical behavior of polymer materials in

Ac ce pt e

extreme environment; fatigue fracture and damage characteristics of materials and structures; resist blasting performance of protective structures.

32

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