Air Bearing Shaker for Precision Calibration of Accelerometers

Transcription

1 Air Bearing Shaker for Precision Calibration of Accelerometers NOMENCLATURE Jeffrey Dosch PCB Piezotronics 3425 Walden Avenue, Depew NY DUT Device Under Test S B DUT sensitivity to magnetic field [(m/sec 2 )/Gauss] B Magnetic flux density [Gauss] Bˆ Gradient of magnetic flux density [Gauss/meter] x Displacement [meter rms] ABSTRACT This paper presents the design, construction, and performance testing of a new air-bearing shaker for precision accelerometer calibration in a production environment. The new shaker incorporates a number of novel features. A porous ceramic air bearing provides high stiffness to lateral loading. A Lorentz force electrical spring minimizes the low frequency waveform distortion that is typically associated with non-linear deformation of metal or elastomer flexures. Finally, a beryllium armature provides high stiffness, low mass, and high resonant frequency. INTRODUCTION The shaker is the traditional weak link when calibrating accelerometers. Undesired shaker characteristics, such as excessive transverse motion, waveform distortion, stray magnetic fields, electrical cross-talk, ground loops, and insufficient excitation levels will adversely influence the accelerometer s response, resulting in degraded calibration accuracy. It follows that when making high accuracy measurements a reliable, high fidelity calibration shaker is one of the most important components in the entire measurement chain. For over 25 years the gold standard shaker for precision calibration is the electrodynamic shaker with beryllium armature. One manufactured version of this shaker utilizes a beryllium armature in an air-bearing suspended by elastomer flexures. This shaker exhibits good distortion characteristics and generates acceleration with minimal transverse motion over a wide frequency range. Although the shaker is well suited to the metrology laboratory, the shaker exhibits less desirable features for routine calibration in a production environment. Positioning of the armature in the gap via the elastomeric flexures is cumbersome and must be re-adjusted depending on the mass of the DUT. The single piece armature has a fixed mounting thread and without the use of adaptors it is not easily configured for the large variety mounting configurations encountered in production testing. Finally, the achievable acceleration level is often not sufficient for testing of more massive accelerometers at high frequency. Larger sized calibration shakers from a structural test pedigree are commonly used for routine calibration of accelerometers. These electrodynamic shakers typically provide a more robust solution and higher force output in comparison to the beryllium laboratory shaker. However, the distortion characteristics and especially the transverse motion are not sufficient for high frequency accelerometer calibration. The motivation for the development of the Model 396C1 and shakers was a robust shaker for routine calibration of accelerometers with the precision of the laboratory beryllium shaker. SHAKER DESCRIPTION In this section the main components of the 396C1/C11 air-bearing shakers are described. Shaker components are labeled in the illustrations of Figures 1 and 2. As with traditional electro-dynamic shakers, force and resulting armature displacement is generated as current in a coil interacts with a magnetic field. In the 396C1/C11 shaker the armature has two coils labeled AC Coil and DC Coil (Figure 2). As in the traditional electro-dynamic shaker the AC coil provides dynamic force and

2 displacement in response to the amplifier s control signal. The AC Coil is located within the magnetic circuit air gap in a region of high and relatively constant magnetic flux density. Additionally, there is a DC coil located just outside the gap in a region where the magnetic flux density is decreasing linearly with distance from the gap. This is region labeled L in Figure 3b. A constant DC current is supplied to the DC Coil. As the armature displaces a force is produced in the DC Coil in proportion to displacement. Thus the DC Coil acts as an electrical spring which in combination with the air-bearing eliminates the need for mechanical flexures to support of the armature. The air-bearing assembly is composed of the armature fitted within a tight-tolerance porous air-bearing. The airbearing is supplied with filtered shop air at a pressure between 3 and 6 psi. The extremely small gap between the armature and air-bearing is maintained at about 2 to 4 microns. Air film stiffness is inversely proportional to gap and this close fitting gap provides the armature with a high lateral stiffness. Silicone rubber o-rings on the armature provide over-range stops and prevent the armature from displacing beyond its maximal displacement range of 1 cm peak to peak. The armature assembly is composed of two pieces: the main body and a beryllium insert. A quartz reference accelerometer is located within the removable beryllium insert and back-to-back calibration is performed by comparing output from the device-under-test (DUT) against output from the quartz reference. The beryllium insert assembly is removable for calibration at an off-site calibration laboratory. Or by utilizing a transfer standard the internal reference can be calibrated without removal of the beryllium insert from the armature. The two-piece armature assembly provides a number of advantages over a single piece armature. The armature insert is electrically isolated from the armature body providing means for the armature body earth ground to be isolated from the DUT signal ground. Variations of the calibrated insert can be manufactured with a variety of mounting threads allowing direct calibration of special thread configurations without the need for adaptors. The armature body is fabricated from aluminum in the Model 396C1 and beryllium in the Model. Beryllium is used because of its extremely low density, high stiffness, high resonant frequency (high speed of sound), and good structural strength (Table 1). It is also exceptionally expensive. For more cost sensitive applications, the 396C1 uses a hard-coated aluminum in place of the beryllium armature with the trade-off of lower resonant frequency and higher armature mass. Table 1. Properties of materials used for shaker armatures. Material Modulus Density c E ρ E ρ (GPa) (kg/m 3 ) (m/s) Beryllium Aluminum Titanium Alumina (ceramic) SHAKER PERFORMANCE In this section aspects of shaker performance such as transverse motion, acceleration level, and the influence of extraneous magnetic field are presented. The function of a calibration shaker is to generate uniform axial acceleration with minimal waveform distortion, heating, and most importantly minimal transverse acceleration. Transverse motion directly influences calibration accuracy. For example, take the case of a shaker exhibiting acceleration magnitude in the transverse direction equal to the shaker s axial acceleration magnitude. This is not an unrealistic value. A shaker exhibiting 1% transverse motion or greater is not uncommon when driving at a frequency corresponding to a flexure or armature resonance. Taking the accelerometer s sensitivity to be 5%, a worst-case calibration error due to the influence of 1% transverse motion would be 1 x.5 = 5%. Transverse motion of the 396C1/C11 and two benchmark shakers was tested. The benchmark shakers chosen for comparison are: (1) a 5 lb shaker and (2) a laboratory shaker with a one-piece beryllium armature. This shaker is identified in this paper as Be Lab. The 5 lb calibration shaker is from a structural test pedigree with a large 7cm diameter x 13cm long aluminum armature suspended via metal flexures. Calibration is performed with this shaker by mounting a back-to-back reference standard to the top surface of the armature. This type of shaker has the advantages of ruggedness and high force capability. The Be Lab shaker is of the

3 type that has for years been the de facto precision shaker for use in precision metrology laboratories. The shaker has a one-piece beryllium armature 5 cm diameter x 8 cm long. The armature is held via adjustable elastomer suspensions in a loosely fitted air bearing. Back-to-back calibration can be performed using a piezoceramic reference accelerometer internal to the armature. The three air-bearing shakers are compared in Table 2. Table 2. Shaker characteristics. Shaker Armature Armature ass y Mass (g) Resonant Frequency (khz) (Material) Beryllium C1 Aluminum Be Lab Beryllium Transverse motion was measured using a small tri-axial accelerometer (PCB Piezotronics Model 356A11) mounted to a 3 gram tungsten mass representing the DUT. Data was obtained for frequencies up to 2 khz. The accelerometer s specified performance is rated to only 1 khz. Reasonableness of the data to 2 khz was verified comparing data obtained by the tri-axial accelerometer against data obtained via a scanning laser vibrometer (Polytec FV 56). Figure 4 shows typical transverse performance obtained from the 5 lb shaker. Also displayed in this Figure is the limit for transverse motion as recommended by the ISO Calibration Standard [1]. For frequencies less than 2kHz the shaker transverse motion was found to be within the recommended limit. However, above 2kHz there are frequencies where transverse motion exceeds 25% meaning that acceleration in the transverse is direction is actually larger than acceleration in the desired axial direction. Figure 5 shows typical transverse response of the 396C1,, and Be Lab shakers taken to 2 khz. The two shakers with beryllium armatures, and Be Lab exhibit similar low transverse motion of less than 1% to 15 khz. Between 15kHz and 2kHz the transverse motion is higher but still less than 3%. The 396C1 with aluminum armature exhibits low transverse motion of less than 1% to 1kHz. Between 1kHz and 15kHz the transverse motion is higher but still less than 3%. Uniformity of motion at the mounting surface is of importance when performing laser referenced primary calibration. With laser calibration it is desired to determine acceleration level at the DUT mount at the center of the armature. However, in taking a measurement with a laser vibrometer this point is obscured by the DUT and cannot be measured directly. Instead the center point motion is interpolated from at least two other measurements taken on the armature surface (Figure 6). If shaker motion is uniform, all points on the surface will experience equal acceleration and interpolation error will be zero. A measure of motion uniformity was obtained by taking measurements with a scanning laser vibrometer (Polytec Model OFV 56) directed at a pair of diametrically opposed points 1 cm from armature center (Figure 6). Figure 7 displays the percent difference in acceleration magnitude between these two points as a function of frequency. Below 1 khz the 396C1 shows a difference in acceleration of less than 1.5%. Above 1kHz, because of armature resonance, there are a number of frequencies where the difference exceeds 1%. For the below 2 khz the difference in acceleration between the diametrically opposed points is shown to be less than 1.5%. Above 2kHz the exhibits larger differences between the diametrically opposed points, but not to the level found in the 396C1. The influence of acceleration uniformity was demonstrated by laser calibration of the beryllium insert containing a quartz reference accelerometer, over the range 5 Hz to 5 khz. Although routine calibration is rarely performed beyond 15 khz, calibration of the reference to 5kHz is needed for utilizing the reference for resonant search of the DUT. The same beryllium reference insert (Model 8A199 SN 154) was installed in both the 396C1 and shakers and calibrated by laser vibrometer. Acceleration was determined by averaging two diametrically opposed laser measurements taken at points 1 cm from the center of the insert. Results of the calibration are displayed in Figure 8. Over the entire calibration range, the trend of the calibration data obtained from each shaker is similar. However, above 1 khz the 396C1 exhibits a number of glitches in the response. These glitches correspond to resonant frequencies where the difference between the two laser measurements is excessive.

4 Although it is not a general concern, there are situations where the shaker magnetic field may influence the DUT output. Shakers of the structural test pedigree are generally large and the mounting surface is far from the magnetic circuit air-gap. In compact, high frequency shakers such the 396C1/C11 and the Be Lab shaker, the mounting surface is close to the magnetic circuit and the magnetic field will be larger compared to the structural test shaker. Thus, if a DUT exhibits high magnetic sensitivity, the magnetic influence errors will be exaggerated when calibrated using a compact shaker in lieu of a large structural test shaker. However, most modern piezoelectric accelerometers are relatively insensitive to magnetic influence. DUT magnetic sensitivity is expressed in terms of an equivalent acceleration for given magnetic flux input. The error due to magnetic field is then in proportion to the DUT magnetic sensitivity, S B, the flux density gradient, Bˆ, and dynamic displacement, x : a error = S Bx ˆ [m/s 2 rms] (1) B Here the error is expressed as the apparent acceleration caused by the dynamic displacement of the DUT in a magnetic field. The acceleration error is in proportion to displacement x, so when present, the problem of magnetic sensitivity is usually observed only at the lowest frequencies where displacement is large. The typical magnitude of this error is best appreciated by an example. At the 396C1/C11 mounting surface the flux density is equal to about 7 Gauss and the gradient is 216 Gauss/meter. Based on a typical DUT magnetic sensitivity of 1e-6 (m/s 2 )/Gauss, Eq. (1) is used to calculated the influence magnetic field on calibration uncertainty at a number of frequencies (Table 3). As can be observed from the Table, the influence of magnetic sensitivity is negligible for this example. Table 3: 396C1/C11 contribution of magnetic sensitivity to calibration uncertainty: Bˆ = 216 Gauss/meter, S B = 1e-6 (m/s 2 )/Gauss Error (% of axial acceleration) Acceleration level can influence calibration accuracy especially when testing low sensitivity accelerometers that need a large acceleration level to achieve good signal to noise ratio. Shaker acceleration can be limited by excessive distortion, coil heating, or insufficient voltage from the power amplifier. The 396C1/C11 shakers were designed to achieve an acceleration level of 1g rms. This is usually adequate for most accelerometer testing, with the understanding that at low frequency the acceleration will be limited by armature stroke. Shaker acceleration response of the 396C1,, and the Be Lab shakers is illustrated in Figure 9. In this plot the acceleration per volt input is displayed as a function of frequency. Over the mid-range of frequencies the acceleration response decreases with frequency. This is attributed to the increase in impedance (Figure 1) due to coil inductance. Low impedance is desirable because shaker force is proportional to current. To achieve a given current, a coil with high impedance will need a high voltage that may be beyond the level that can be practically supplied by a standard laboratory power amplifier. SUMMARY Models 396C1 and high performance calibration shakers have been designed and developed. The utilizes an all beryllium armature assembly. The 396C1 utilizes a less costly aluminum armature with beryllium insert with the trade-off of some high frequency performance above 1 khz. These shakers have been shown to exhibit many of the performance attributes of the laboratory standard beryllium shaker, while providing a more robust package, ability to generate larger acceleration levels, and adaptability to variety of thread mounting configurations necessary for the production environment. REFERENCES [1] ISO :23(E), Methods for the calibrations of vibration and shock transducers Part 21: Vibration calibration by comparison to a reference transducer, ISO International Organization for Standardization, 23.

5 FIGURES Figure 1. Model 396C1/C11 shaker. Figure 2. Model 396C1/C11 cross section view.

6 8 7 Flux density (Gauss) L Distance (cm) (a) Figure 3. (a) Lines of flux in magnetic circuit. (b) Flux density along line line a-b. (b) Transverse Motion (% of axial) Shaker response ISO recommended limit Figure 4: Transverse acceleration of a 5 lb shaker.

7 Transverse Motion (% of axial) ISO recommended limit 35 Be Lab C Figure 5: Air bearing shaker transverse acceleration. A DUT B INSERT ARMATURE Figure 6. Laser directed at positions A and B in laser calibration of DUT.

8 Acceleration Difference (%) C Figure 7. Acceleration difference between 2 diametrically opposed points on armature mounting surface. 22 Sensitivity (mv/g) C Figure 8. Accelerometer s response to 5kHz. 8A199 Beryllium insert installed in 396C1 and shaker

9 Acceleration (g/v) Be Lab 396C Figure 9. Shaker acceleration response. Impedance (Ohm) "Be Lab" Figure 1. Shaker impedance E. Kemper Rd., Cincinnati, OH USA calibration@modalshop.com