A comparison of low-shock and centrifuge calibrations using piezoresistive accelerometers

This paper describes the degree of equivalence between low-shock and centrifuge calibrations up to 10 000 m s−2 against three types of piezoresistive accelerometer: an undamped sputter gauge type, a damped sputter gauge type and an undamped semiconductive type. The complex sensitivity in the low-shock calibration and the DC sensitivity in the centrifuge calibration are well consistent within each expanded uncertainty in the frequency domain, together with the vibration calibration using the second-order transfer function. In addition, the preliminary uncertainty budget in the centrifuge calibration facility is also indicated, and distinctly estimated from the viewpoint of the mechanical parts and accelerometers.


Introduction
For more than fifty years, the Japanese automobile industry has been using centrifuge calibration for piezoresistive accelerometers, which function linearly up to 10 000 m s −2 , according to a de facto standard method that is documented internationally as ISO 16063-17 [1]. As vibration calibration can generate acceleration of only as much as several hundred metres per second squared, the Japanese automobile industry uses centrifuges instead to generate high acceleration, which corresponds to a plateau waveform at 0 Hz. That is to say, the centrifuge calibration can be considered as an optimum facility for the easy evaluation of the linearity of piezoresistive accelerometer DC sensitivity . In contrast, the European and American automobile industries use low-shock calibrations with half-sine waveforms, which include broadband frequency components depending on the duration of a shock pulse. Lowshock calibration, which follows both the linearity and the frequency response of accelerometers, is regarded to be more appropriate than the centrifuge method from the viewpoint of complying with actual shock testing. For this reason, some national metrology institutes (NMIs) have developed primary low-shock calibration facilities [2][3][4][5]. Although one lowshock pilot comparison has been conducted internationally among Asian-Pacific NMIs [6], no international comparison has been made between low-shock and centrifuge calibrations.
Recently, an international conformity assessment was demanded from the perspective of worldwide harmonization of ISO documentation. To assure measurement reliability in car crash tests, ISO 6487 specifies the traceability and measurement uncertainty of vibration, shock and centrifuge calibrations [7]. In addition, equivalence in both the static and dynamic response of the sensors is required. Hence, the equivalency of the low-shock and centrifuge calibrations of three Metrologia A comparison of low-shock and centrifuge calibrations using piezoresistive accelerometers types of piezoresistive accelerometer is investigated here as a collaboration between Kyowa Electric Instruments (KYOWA) and the National Metrology Institute of Japan (NMIJ). Figure 1 is a photograph of the low-shock calibration facility at NMIJ. The facility is equipped with two heterodyne laser interferometers based on He-Ne laser light (λ = 632.8 nm) as the length standard, in compliance with ISO 16063-13 [8]. The two heterodyne laser interferometers, which integrate the optical heads of a commercial laser Doppler vibrometer (LV-1800; Onosokki Co., Ltd), are used to monitor two different positions on the mounting plane of the accelerometer under calibration. The two laser light beams are pointed at axial-symmetrical distances from the sensitive axis of the accelerometer to measure the shock motion on the reference mounting plane. Since the difference between the acceleration measurements of these two points ranges from 0.1% to 0.8%, two heterodyne laser interferometers are required to calibrate the mean shock sensitivity of the accelerometer precisely. The dynamic momentum of a shock is generated by a rigid collision between two metallic bodies that are supported by an air bearing with a 10 µm air gap [3] and an interface element called a pulse shaper. Figure 2 shows a typical shock waveform; the peak value is roughly 3000 m s −2 with a duration of 0.5 ms. The left side of figure 2 shows the acceleration waveform measured by two heterodyne laser interferometers with a carrier frequency of 80 MHz; the right-hand side of figure 2 is the output voltage waveform of the damped accelerometer. The time difference between the peaks of the measured acceleration and voltage waveforms is 25 µs, which is two-hundredths of the duration of the shock. The low-shock calibration facility generates unipolar pulses with a peak value of 10 000 m s −2 and was able to calibrate the shock sensitivity of an accelerometer with an expanded uncertainty of 0.6% in 2011 [9]. Currently, an expanded uncertainty of 0.4% has been realized following some improvements, including a change to the laser interferometer [10]. In ISO 16063-13, the shock sensitivity S sh is defined as the ratio of the two peak values:

Low-shock calibration facility
where A p is the peak value of the input acceleration applied to the accelerometer, and V p is the peak value of the accelerometer output signal. To obtain smooth waveforms, a digital fourth-order Butterworth low-pass filter with a cutoff frequency of 5 kHz is applied to both the input-acceleration and accelerometer-output waveforms.

Centrifuge calibration facility
The centrifuge calibration facility manufactured by KYOWA comprises a turntable, a signal conditioning unit, and other mechanical parts. It can generate a maximum static centrifuge acceleration of 10 000 m s −2 in compliance with ISO 16063-17. Recently, KYOWA developed a new centrifuge calibration facility with a removable bridge amplifier type of signal conditioner, which enables the temperature response characteristics of the bridge amplifier themselves to be inspected. The voltage ratio sensitivity of piezoresistive accelerometers can be evaluated by independently considering the characteristic of the bridge amplifier. The expanded measurement uncertainty with a coverage factor k = 2 is estimated as roughly 1.0%. The 32 kg aluminum turntable has a radius r = 0.2 m, a maximum rotational frequency of 2135 rpm, and is supported by an air bearing with an air gap of several micrometres. The devices under test are symmetrically placed at either two or four opposing positions relative to the rotational axis of the turntable (see figure 3). Figure 4 shows a schematic of the centrifuge facility. The bridge amplifier is attached to the upper side of the turntable and rotates with it. External power is supplied to the bridge amplifier via a signal transmitter (revolving transformer). The accelerometers receive their excitation voltage from the bridge amplifier, which comprises a digitizer that transmits a digitized version of the accelerometer signal to a personal computer via the signal transmitter. The noise level of this digitized signal to a full scale is typically 0.05%. The noise level of 7264B-2000 T is 0.05 mV V −1 peak to peak, and that of ASD-B-1KV and ASE-A-500 is 0.002 mV V −1 when there is no input centrifuge acceleration.
This centrifuge facility gives the sensitivity S ce of an accelerometer as where V is the output DC voltage from the accelerometer, and A is the centrifuge DC acceleration A = ω 2 r , where ω is the angular speed (a rotary encoder counts each rotation). Figure 5 shows the operational sequence used for centrifuge calibration using this facility. Firstly, the two accelerometers for the balancing purpose are set symmetrically on the turntable so that they output positive voltages. In the case of a single accelerometer, a dummy mass is used on the opposite side of the turntable for balancing purposes. After a burn-in test of several tens of seconds for zero voltage determination, the rotational speed is ramped up in 20% increments toward the specified centrifuge acceleration, after which it is ramped down in 20% decrements. Next, the accelerometers are remounted in the opposite direction to the reference surface so that they provide an (opposite) negative voltage output, and the same 20% up-and-down ramp is repeated. Finally, the hysteresis, linearity and average sensitivities of the positive and negative voltage outputs are derived.

Piezoresistive accelerometers under test
We prepared three types of piezoresistive accelerometer, as follows, to evaluate the consistency between the sensitivities determined by dynamic and static high acceleration calibrations.
In this comparative research, a 10 V bridge voltage is supplied by the bridge amplifier to each accelerometer. As each bridge amplifier in both the shock and centrifuge facilities is independently calibrated, the measurand to be compared is the voltage sensitivity ratio mV/V/(m s −2 ) of accelerometers with 10 V supplied. Each of the above accelerometers covers a flat sensitivity of less than 1 kHz and is used worldwide in car crash tests.     to 10 kHz using the NMIJ vibration calibration facility [11]. Actually, the voltage signals from the accelerometers in car crash tests are recorded by a data logger through a low-pass analog filter with a cutoff frequency of roughly 1600 Hz, in accordance with ISO 6487 standards. Thus, the static and dynamic calibrations normally become comparable in the case of flat frequency accelerometer responses of less than 1 kHz.
In order to further understand the mechanical characteristics of each accelerometer, a second-order transfer function of the resonant frequency f 0 and the damping factor δ is investigated as a mass spring damper model [12]. That is, the sensitivity can be written for a sinusoidal excitation with a certain frequency f as follows, and the phase shift with S 0 denoting the sensitivity at 0 Hz. Each mechanical characteristic of the three accelerometers is derived from an approximation between the measured frequency response and the transfer function (see table 1.) The approximation result is calculated using a solver algorithm from the EXCEL software; the 7264B-2000 T is an accelerometer with high sensitivity and a low damping factor, and the ASE-A-500 has a high damping factor that can suppress resonant effects in acceleration measurement. Figure 7 presents the relative difference of each accelerometer based on the sensitivity at 100 Hz. The accelerometer 7264B-2000 T has stable, high-sensitivity furnishing differences lower than 0.1% up to 1 kHz at least. The accelerometers ASD-B-1KV and ASE-A-500 can also be regarded as having almost flat sensitivity up to 1 kHz, despite the sensitivity presenting a dispersion within 1%. Figures 8(a) and (b) stand for the relative gain and phase shift measured for three settings of bridge amplifier. In figure 8(a), the relative gain normalized by the gain at 100 Hz with different three settings is shown, and each gain at 100 Hz is enclosed by parenthesis. These results mean that the bridge amplifier does not affect the difference of each shock waveform in the three accelerometers.    In low-shock calibrations, it was preferable to fix the shock durations to suppress the waveform change by the frequency response of the accelerometer, and the frequency content of the shock pulse was dominant from several hundred Hz to several kHz. Nevertheless, the non-negligible linearity from 2000 m s −2 to 10 000 m s −2 is estimated to be roughly 1% for the accelerometer 7264B-2000 T. In contrast, the centrifuge calibration facility can evaluate the DC sensitivity of the accelerometers. If the dynamic acceleration contains abundant high-frequency components over the flat frequency response (typically less than 1 kHz) of the accelerometer, the complex sensitivity at the discrete frequencies noted in ISO 16063-13 will possibly be straightforward [13]. Because of this, the shock and complex sensitivities refer to the sensitivity of the accelerometer in the time and frequency domains, respectively. However, considering the measurement uncertainty, measured spectral region, or accelerometer specification, even the shock sensitivity of damped ASE-A-500 accelerometers with a larger phase shift is feasible for comparison, and less sensitive to shock durations of more than roughly 0.5 ms. Also, the methodology of shock sensitivity is widely accepted in the calibration certificates of accredited laboratories and in the international interlaboratory comparisons carried out by NMIs [6]. Tables 2-4 give the numerical values that are plotted in figures 7-9. To compare the individual results of the lowshock and centrifuge calibrations, the difference with respect to a certain acceleration is calculated as

Comparison of results from low-shock and centrifuge calibrations
where D is the degree of equivalence in %, S ce is the centrifuge sensitivity and S sh is the shock sensitivity. The shock sensitivity S sh is a reference value that consists of the Japanese national length, time and voltage standards. As the length standard, a non-stabilized He-Ne laser source with a wavelength of 632.8 nm is used. A rubidium time base and DC voltage generator calibrated by accredited Japanese laboratories are used to assure the time and voltage standards. Here, all the shock sensitivities of ASD-B-1KV and ASE-A-500 are obtained using the original shock sensitivity of the acceleration measuring chain (a combination of the accelerometer and bridge amplifier) and the gain of the bridge amplifier at 160 Hz. On the other hand, the shock sensitivities of 7264B-2000 T are given with a 10 V power supply and no gain. In the case of ASD-B-1KV and 7264B-2000 T, all the values of the low-shock, centrifuge and vibration calibrations are well consistent within a deviation of less than 0.3%. However, only the low-shock calibration of ASE-A-500 generates a constant difference of 0.9% beyond the measurement uncertainty of 0.4%, compared with centrifuge and vibration calibrations. This means that all the centrifuge and vibration calibrations are comparable in the three accelerometers. Also, a nonlinear subtractive sensitivity decrease was only observed in

Uncertainty budget of centrifuge calibration
The uncertainty budget of the three accelerometers in centrifuge calibration is under investigation, but has been preliminarily estimated in table 5. The centrifuge calibration facility can achieve a small and stable uncertainty. However, the dominant uncertainty component is the temperature effect, which is given as a change in the sensitivity or zero voltage of the accelerometers. Owing to the heat generation from the drive motor in rotational operation, the temperature of the accelerometers increases by 1.5 °C during centrifuge calibration. Currently, although the assured expanded uncertainty is subject to the temperature effect of accelerometers, some improvements in the centrifuge calibration facility are being investigated with the view of suppressing temperature increase in the future.

Dependence of shock sensitivity on damping factor
In order to investigate the dependence of shock sensitivity on the damping factor, the actual shock duration is calculated using a difference equation based on equations (3) and (4). Then, a known input waveform of 100 peak value is prepared with a pulse width of 0.6 ms, corresponding to a shock duration of 0.47 ms, which is a time width between two points at 10% peak acceleration in the shock pulse [14]. Figure 12 presents three kinds of waveforms: one is an input waveform (grey line) and the other two output waveforms are based on a resonance frequency of 10 kHz with damping factor of 0.05 (black line) and 1.0 (black dashed line). The output waveform with a resonance frequency of 10 kHz and a damping factor of 0.05 has a slightly increased peak value with a negligible time delay due to the low-damped characteristic. Another waveform is generated with a time delay of several tens µs by the high damping factor, but the resonant perturbation after the shock pulse is not observed. Figure 13 indicates the dependence of shock sensitivity on the resonance frequency and damping factor in the case of a pulse width of 0.6 ms. Since the estimated damping factor of ASE-A-500 is the largest and closest to 0.707 of the presented damping factors in table 1, then little or no resonance is excited by external forces. The approximation of figure 6(b) is carried out against the sensitivity, and a damping factor of 0.67 is obtained, as shown in table 1. In this case, with the damping factor of 0.67, a constant time delay L = φ ( f ) /2πf is observed in the high-frequency range. In order to explain the constant time delay using the same second-order transfer function as equation (3), a dead time is added to the numerator as follows: where ω = 2πf denotes the angular frequency. Then, for the function of the phase shift it follows that    where ∠ stands for an argument and the dead time L corresponds to 3.72 ms. Meanwhile, the 0.707 damping factor acts as a threshold, which decreases the shock sensitivity. In figures 9 and 11, ASD-B-1KV and 7264B-2000 T, with a low damping factor of less than 0.1, show comparable sensitivity regarding vibration, shock and centrifuge calibrations. In contrast, the difference between two sensitivities in the shock and centrifuge calibrations of ASE-B-500 can be explained by the high damping factor. Figure 14 presents the frequency response of the three accelerometers based on the spring damper model, as indicated in table 1, and the frequency components (dotted line) of a shock pulse with a pulse width of 0.6 ms. Since the sensitivity of the accelerometer ASE-B-500 does not increase in the high-frequency range, as shown in figure 6(b), and decreases from several kHz, it is estimated that the shock sensitivity also drops to a lower value.

Approach to centrifuge calibration from complex sensitivity in low-shock calibration
In order to compare the shock sensitivity with the complex sensitivity precisely, both the time and frequency domains should be analysed using the same shock pulse. Up to now, some similar research has been attempted to determine the complex sensitivity at each discrete frequency using the fast Fourier transform [13,15]. For this purpose, a rectangular window from 2.0 ms to 7.0 ms is applied to a shock pulse (see figure 2). Normally, the low-shock calibration facility records the measurement data at 10 ms, in which the trigger is given at 3.0 ms by the rising edge of the voltage output signal from the accelerometer. Table 6 presents a results comparison of the shock and complex sensitivities, using each shock pulse at a peak acceleration of around 4000 m s −2 for three kinds of accelerometers. Since the basic frequency becomes 200 Hz by a window length of 5.0 ms, complex sensitivities from 200 Hz to 600 Hz are obtained. The average complex sensitivity is given by the three complex sensitivities, and the difference between the shock and average complex sensitivities is also evaluated. Then, all the average complex sensitivities at 4000 m s −2 are close to the measurement values obtained in the centrifuge and vibration calibrations (see figures [15][16][17]. Moreover, the difference between the two sensitivities determined by low-shock and centrifuge calibrations can be well explained. Nevertheless, the sensitivity of 7264B-2000 T in low-shock calibration decreases toward the high acceleration region; this may be an inherent characteristic of 7264B-2000 T and is still under investigation.

Summary and outlook
The consistency of the dynamic and static calibration results for three types of piezoresistive accelerometer was investigated using a low-shock calibration facility at NMIJ and a centrifuge calibration facility at Kyowa Electric Instruments. The low-shock calibration facility was used to evaluate the shock sensitivities of the three types of piezoresistive accelerometer in the time domain, and all the sensitivity differences in both calibration facilities were compared at the same acceleration. As a result, these differences ranged from 0.2% to −0.9%. The shock sensitivity is given on the basis of a physically unclear definition in ISO 16063-13. Nevertheless, the shock sensitivity is an important measurand in various industries for establishing the momentary maximum power acting on products in the time domain.
In order to understand the dynamic characteristics of the three types of accelerometer from the viewpoint of the frequency domain, the frequency response of each of the three accelerometers is investigated. Using this, the dependence of the shock sensitivity on the damping factor is calculated. Furthermore, assessment of the consistency of complex sensitivity in low-shock calibration has also been confirmed compared to the centrifuge and vibration calibrations in the frequency domain. These results support the technical validity of static calibration as required by ISO 6487. For future experimental comparisons of different types of sensor between dynamic and static calibrations, a large and diverse set of data must be investigated from the viewpoint of both the time and frequency domains.