Low Frequency Accelerometer Calibration

Reference Sensor Limitations

Historically, the limiting factors in low frequency accelerometer calibration were a combination of the limited stroke length of electro-dynamic shakers providing limited acceleration levels at declining low frequencies, and the limited resolution of the piezoelectric reference accelerometer in the presence of the sensor’s rising electric noise floor. By adopting and applying proven technologies in a novel combination, it is now possible for improved simplicity and reduced measurement uncertainties of dynamic vibration calibration at very low frequencies. The commercially available combination of a high accuracy optical displacement reference and ultra-long stroke (>250 mm stroke) calibration grade linear actuator has created a new standard in ultra-low frequency calibration.


The discussion of historical issues with low frequency calibration often centers on the topic of stroke. A precision calibration grade air bearing exciter used for a broad bandwidth accelerometer calibration typically has a maximum displacement of around 10mm. At 1 Hz (Hertz), this maximum displacement translates to an acceleration level of 20 milli-g which is in the low frequency noise floor of most lightweight structural testing accelerometers. Conventional wisdom used to be to address this by adding “a little more displacement.” Often calibration labs would add a “long stroke” (typically 100 mm) electro-dynamic exciter to create a dedicated low frequency calibration setup. This modification would help by raising milli-g calibration excitation acceleration levels at 1 Hz to a more measureable 0.2 g level with the longer stroke. With sufficient cycles, and averaging the 100 mm stroke, it was possible to help resolve an adequate signal-to-noise ratio for a sensitive vibration Sensor-Under-Test (SUT) and piezoelectric reference accelerometer combination in the 1 Hz range and the high tenths of a Hertz. However, the additional cycles for averaging are extremely inefficient and costly in terms of time at frequencies of well below 1 Hz. Even at optimal speeds, the cycle time for a .2 Hz to 10 Hz calibration can be on the order of a half hour or more.

The Innovation

To improve calibration in the extremely low frequency range of tenths of a Hertz, a new approach was needed. First, the patent pending application of an optical encoder such as the dynamic calibration reference, provides an extremely high resolution reference measurement that is not frequency dependent. By ensuring high resolution displacement measurements regardless of frequency or stroke length, the reference methodology is no longer fighting noise due to falling acceleration levels on the low end. At 0.1 Hz, the net effect of switching to a high resolution optical displacement reference is roughly equivalent to using a piezoelectric acceleration reference with a 10,000 V/g sensitivity. This provides the capability for tenths of a Hertz calibration capability with near laser primary type uncertainties.

Improvements within the new low frequency calibration methodology also link to form deeper benefits. In addition to providing the dynamic vibration reference, the optical encoder also provides feedback control for managing the position of the transducer carriage when used in either horizontal or vertical operation. This feedback and active control method avoids the mechanical nonlinearities of historical solutions employing a flexure based suspension or rubber bands. With real-time position feedback and control implementation, when compared to the calibration frequencies, the smart stroke algorithm provides near instantaneous response to amplitude and frequency instructions of the controller. With virtually no overshoot or ringing, frequencies can be set and control amplitudes reached in a fraction of a cycle, which saves massive amounts of time when calibrating in the fractional Hertz range.

Further Innovation

Once the vibration reference resolution was so drastically improved, the stage was also set for the next innovation in exciter technology. Noting that a number of forward thinking national laboratories were considering, or had already moved to, linear positioning technology for their lowest frequency needs, linear motors proved to be rugged, extremely reliable and very inexpensive in the high precision CNC manufacturing environment. These design and performance benefits showed promise to supplant many of the historical electro-dynamic shaker limitations in the ultra-low frequency range. The single most obvious benefit in linear motor based actuators is the ease of creating significantly longer stroke which generates more acceleration extending the useful low frequency range for microvolt resolution piezoelectric accelerometers, as well as capacitive or resistive DC response MEMS accelerometers. As in most precision air bearing calibration exciters, the ultra long stroke linear motor design incorporates air bearings for support stiffness, eliminating traditional flexure distortion and drastically reduces transverse motion. Each of these improvement factors contribute to the near laser primary uncertainties of the new system.

Continuing to link the benefits of a digital excitation and measurement solution, smart calibration signal processing further reduces uncertainties. Operating with a discrete fourier transform (DFT) processing method ensures inherently excitation frequency bin-centered processing and eliminates measurement errors from other frequency inputs like mechanical distortion or uncorrelated ambient noise. Since the excitation signal is controlled to be periodic with the sampling, no windowing is needed for the DFT technique and thus eliminates another common measurement error from windowing called “spectral leakage.”

Improved Return on Investment

As noted at the August NCSLi in Washington D.C., we should not forget there is also a business side to metrology. Like the architectural axiom of “form follows function,” calibration is not all about the technology and technical uncertainty. Calibration involves cycle time and human resources, and as a piece of service providing hardware, should have a definable return-on-investment (ROI). One of the largest opportunities for improved ROI in the low frequency world is reducing cycle time of a complete frequency sweep. In this case, the ultra-low frequency linear motor based calibration grade actuator allows for smart stroke control and tremendous optimization in calibration cycle time. As noted previously, this real time speed of the control loop ensures accurate generation of the next frequency within a fraction of a cycle. This optimum control allows for a huge time savings in the calibration cycle time when compared to traditional reference accelerometer signal based control that needs multiple cycles (often 5 – 10 cycles) for hunting/stabilizing of the controlled drive frequency/amplitude. Time savings can be anywhere from 2 to 10x depending on your traditional means of low frequency calibration processing. From the ROI point of view, higher calibration system throughput ultimately means reduced operator time and costs for a fixed quantity of sensors or more capacity for generating revenue in the business model of a metrology service lab.


The combination of optical and digital technology (optical encoder reference, linear motor actuation, smart control and innovative digital signal processing) creates a string of benefits driving an elegant advancement in an age old problem area. Unlike the application of radically new technology, by selecting proven technologies in a novel combination, the resulting ultra-low frequency calibration system risks are reduced, uncertainties are improved and functionality is enhanced in a simple, reliable, affordable manner.