MINIMIZING MEASUREMENT UNCERTAINTY IN CALIBRATION AND USE OF ACCELEROMETERS

This paper summarizes techniques and equipment used to minimize measurement uncertainty in the calibration of accelerometers. Background is given on the physics of vibration and design of accelerometers. Although referring primarily to comparison calibrations using sinusoidal vibration, the topics of shock and absolute calibration methods are included. Physics being universal, the topics should be just as pertinent to accelerometer use in the field as they are in the wellcontrolled laboratory. INTRODUCTION The paper was written to inform the reader about acceleration, accelerometers and their calibration, and to instill a healthy respect of the challenge of making reliable and accurate measurements (with any instrument, not just acceleration transducers). Mistakes are easy to make, and can be costly. With study and understanding, expensive mistakes might be avoided, and usually the biggest uncertainties are minimized. There are three sections: First is a short summary of the “Do’s and Don’t’s” in accelerometer calibration. Then, a more lengthy second section discusses the physics of acceleration, accelerometers and calibration techniques. The final section describes the sources of uncertainty summarized in the first section, the reasons behind the “Do’s and Don’t’s,” and techniques for estimation of uncertainty. This is not a comprehensive listing of all the sources of uncertainty possible, nor of all the techniques useful for field application. More thorough coverage can come from many sources [1-5]. Instead the paper is intended to be brief and practical on each of the many topics. The difficulties are that the number of parameters in shock and vibration measurements is very large, and many of the parameters interact. Since most parameters go nonlinear at some extreme, the results can be chaotic, with wildly varying outcomes caused by seemingly minor input variations. Two themes should stand out concerning measurement uncertainty. First, is quality: The best results are obtained with accelerometers and signal conditioning that have the best features for the application. Second is technique: Lack of good methods, understanding, or poor control of the pertinent parameters can result in poor results from even the best instruments. Another point is made on calibration accuracy: The overall uncertainty of an accelerometer used in the field can be no better than the uncertainty of its calibration in the laboratory. Overall uncertainty combines the uncertainties of all parameters, including those of the calibration. A note of caution is advised when applying the results of a calibration, good or otherwise: The quality of a transducer should not be judged from a limited calibration, but rather from a thorough characterization. In a high quality calibration, numerous subtle performance parameters are controlled to establish the probable value of perhaps just one parameter, such as acceleration sensitivity. “Good” calibrations are possible on otherwise lousy accelerometers, since the controlled laboratory conditions could mask the characteristics that might cause problems in the field. On the other hand, an excellent transducer may seem to have poor performance with sloppy calibration. The following is a summary of recommendations for good calibration technique: Minimizing measurement uncertainty in calibration and use of accelerometers DO’S AND DON’TS OF ACCELEROMETER CALIBRATION 1. General mounting Keep surfaces flat and clean Use recommended mounting torque (don’t guess; use a calibrated torque wrench) Assure full contact on transducer mounting surface Use couplant, such as oil (improves response at high frequencies, and prevents surface damage during mounting) Mount for calibration as it will he used in the application, if possible (examples, actual cable and connec¬tors, insulating mounting studs, adapting fixtures, etc.) Don’t nick or gouge surfaces Don’t overtorque (may damage shaker or transducer) Don’t undertorque (results in poor frequency response, or possible damage during shock) Don’t use more mounting interfaces than necessary Don’t use fixtures or cables which are larger or more massive than acceleration source can handle to provide good quality input 2. Mounting with studs Use recommended mounting studs (with shoulder flange and correct thread length to prevent “bottoming out” in transducer) Don’t use too large a flange (it must fit completely in recess, otherwise transducer may be seated only on rim of shoulder) 3. Mounting with adhesives Use recommended adhesives, such as cyanoacrylate instant-setting Use appropriate solvents and procedures to remove adhesives (Note: many solvents may cause cancer) Don’t remove adhesively mounted units with the shock of a hammer blow or by twisting them off Never use razor blade or sandpaper to remove adhesives 4. Fixtures Keep fixtures stiff and light, balancing trade-offs of amplitude and acceleration quality (due to maximum mass the exciter can take), with the required frequency response. Beryllium is best but is expensive, and particles are toxic if inhaled Design fixtures so mounting surfaces call be easily lapped Don’t orient the inertial center of mass of accelerometer (or overall center of gravity of fixtures) off the centerline of motion 5. Cables “Finger tighten” only. (Exception: Sonic miniature connectors have hex flats. Use only supplied tools and recommended torque) Use only “noise treated” cable for high impedance piezoelectric accelerometers (unless they have low impedance output internal electronics) Connections in cabling must have complete and continuous shielding Use same cable or clamping technique during calibration as used in application, if possible Don’t use tools to tighten connectors. Don’t overtighten Don’t kink or knot cables, or overtighten cable clamps (insulation or noise treatment can be damaged) Don’t attempt to splice or repair noisetreated cable Don’t use damaged cables (even if damage is only suspected) DO’S AND DON’TS OF ACCELEROMETER CALIBRATION 6. Cable strain relief Clamp the cable if possible on the same structure the transducer is mounted Use free cable loop length 10 to 20 times cable diameter between transducer connector and first clamp Make sure clamp is at least 5 times wider than cable, to prevent tight bend radii and motion of inner conductors Don’t tie down cable rigidly with a short, straight path, or with any preload. There should be no axial forces Don’t subject cable or connector to forces caused by relative motion between the transducer and the stationary end. Some transducers respond to cable-induced forces Don’t use long loops. Whipping may cause cable noise, forces and fatigue 7. Grounding Prevent ground loops: Ground signal conditioning at one point only. (Example, if using Endevco model 2270 with grounding nut shorting its shield to the case of a single ended test unit, that becomes the common point. Test and reference charge convertors should then stay isolated) For adhesive mounting, measure insulation and connect grounding accordingly as above Don’t add extra ground paths (“just to be sure its grounded”) Don’t use damaged insulating mounting studs (verify isolation) Don’t inadvertently ground a differential bridge by connecting to single ended conditioning (unless bridge excitation is floating) 8. Signal conditioning Check that frequency response, slew rates, overload recovery, and filters are appropriate (check anti-aliasing requirements for digital sampling) Measure bridge excitation voltage at the connector (use sense lines to correct for lead resistance) Don’t use direct voltage reading of piezoelectric devices; instead use charge convertors Don’t use large input capacitances (such as from long cables) without knowing the effect on noise and frequency response (use remote charge convertor with piezoelectric transducers in very noisy conditions) 9. Excitation sources Be sure motion is pure, partcularly at the reference frequency For shock or vibration, maintain alignment so motion has minimal cross axis input and rotation For shock, don’t use pulse durations too long or too short, which have frequencies outside the useful bandwidth of either channel. If this is not possible, keep frequency response of both channels as similar as possible 10. General calibration goals Avoid frequencies at which there is distortion due to resonances, or those at which there is more than 10% transverse motion Use a standard for a frequent (daily) check of system accuracy, and record trend Choose gain range and acceleration amplitude to provide optimum signal-to-noise ratio (use full dynamic range of data acquisition if possible) Control and/or record pertinent parameters, and know the effect each has on the calibration (Examples: Temperature, humidity, line voltage, grounding configuration, gain settings, etc.) Maintain traceability of all calibration equipment used, and establish and maintain calibration intervals Don’t use a reference transducer above approximately 20% of its resonance without good knowledge of the effect that the mass of the test transducer and fixtures has on the frequency response [and sometimes sensitivity] of the reference transducer Don’t interchange equipment without knowing the effect of the change on the entire system Don’t hesitate to call the transducer manufacturer with performance questions, particularly to learn what parameters may affect the measuremerits, or whether there are any peculiarities (such as “minor” resonances) Don’t trust any measurement unless you can prove its validity and know its uncertainty BACKGROUND: ACCELERATION Definitions The position of an object is established with respect to some fixed reference, and the displacement or translation (given in meters, m) measures its change in position. If the position changes during a period of tune, the object has velocity (given in meters per second, m/s). Velocity is a vector quantity, which means it is a parameter with magnit