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# Calibration and Linearity

## Why is My 1G or 10G Calibration Good at 100 + G?

Article written by Bob Sill & Mike Lally

Another common question I hear, “Is my accelerometer calibration valid for an acceleration level other than what I calibrated at?”  The common reason for the question is that automated accelerometer calibration systems traditionally calibrate the various frequency choices at constant acceleration levels like 1G or 10G, yet users can be using the sensors in ranges of hundreds, thousands or tens of thousands of G’s. The answer for most accelerometers is a definite yes, although it is useful to examine the definition of its full scale range...

...The extremely good linearity characteristics of piezoelectric accelerometers (<1% nonlinearity full scale) are a function of the piezoelectric accelerometer sensing crystal properties coupled with the high mechanical preload of the sensor element design.  The structural integrity of a properly designed piezoelectric accelerometer sensing element (via preloading of the crystal with a through stud or shape memory ring) ensures the measurement of dynamic events as small as a few micro G’s with a range as high as 1000s of G’s.  The dynamic range of the piezoelectric sensors is on the same order as the dynamic range of 24 bit analog to digital converts (functionally around 120 dB).  This ideal dynamic range is, however, reduced somewhat by the coupling electronics, such that the noise floor of the electronics imparts a lower limit to the dynamic range, and the supply rails force an upper limit. In addition, some designs highly stress the piezo element, to the point that nonlinearities on the order of 10% can be seen. An example is that the linearity is sometimes specified as 1% per some number of G's, such as 1% per 10,000G's up to a full scale of 100,000G's.

Other sensing mechanisms are inherently nonlinear, such as in variable capacitance vibration sensors. The capacitance is inversely proportional to the gap of the moving plate (C=kA/d). If the term d in the denominator changes by +/-50%, the resultant change in C is a highly nonlinear -33%/+100%. Even by reducing the full scale change of d to 10%, and making a differential mode (which cancels the first order nonlinearity) residual nonlinearity is still on the order of 1-2%. Although servo feedback accelerometers often use capacitance sensing, they maintain excellent linearity by forcing the moving plate to stay at the midpoint, and actually not move at all.  Bridge accelerometers, such as piezoresistive MEMS sensors can have nonlinearity below 1%, particularly if they are fully active. Having both compressive and tensile gauges in a differential mode also brings the cancellation of nonlinear terms.

Why is 1 or 10G used historically? It seems to be a coincidental choice of the unit of measure (the G), the physics of reasonably sized electrodynamic shakers, and the number of fingers on human hands. If we had 8 fingers, we would likely use 8 G's as a standard, [though of course it would be called 10 (base 8)].

Most of these nonlinear terms only come into play when the sensing elements are significantly stressed, which normally will not happen in the low levels attained on calibration shakers. So another question that comes up regarding “How would I generate those high G levels anyway?”  The answer lies in a shift of excitation method.  Moving from sinusoidal excitation to transient impact, G levels are no longer dependant on stroke length of the exciter but rather dependent on the amplitude and width of the impact pulse.  By stiffening the contact interface of an impact while still providing a small amount of damping to eliminate high frequency ringing, extremely high G levels can be created on a controlled repeatable basis.  Pneumatically controlled excitation is used to generate mid-to-high level accelerations in the 1,000 to 10,000 G range where a Hopkinson bar setup is used to generate acceleration levels in extremely high 50,000 to 100,000 G level range.  With these high G excitation methods, various amplitude points can be measured across the upper ranges of both standard and shock accelerometers.   These high G levels are typical of impact or blast events like automotive crashes, ballistics and pyrotechnic separation of space structure stages. Check out a short application paper on shock & vibration calibration and our previous newsletters for more discussion on shock cal.