One of the most difficult aspects of selecting an accelerometer for a particular application is interpreting the accelerometer’s specifications. Often you understand your test requirements well but run into difficulty matching these requirements with available accelerometer models.
Manufacturers of accelerometers frequently contribute to this problem by engaging in a game of specmanship by positioning their products in the best possible light. This often obfuscates the accelerometer’s set of specifications. There exists, then, a need for a comprehensive description and explanation of accelerometer specifications that manufacturers routinely use.
Sensitivity
Sensitivity of the accelerometer, sometimes referred to as the scale factor of the accelerometer, is the ratio of the sensor’s electrical output to mechanical input. A transducer generally is defined as a device that converts one form of energy to another. An accelerometer simply is a transducer that converts mechanical acceleration into a proportional electrical signal.
Typically rated in terms of mV/g or pC/g, it is valid only at one frequency, conventionally at 100 Hz. Since most accelerometers are influenced to some degree by temperature, sensitivity also is valid only over a narrow temperature range, typically 25 ±5°C. Additionally, it is valid only at a certain acceleration amplitude, usually 5 g or 10 g.
Sensitivity sometimes is specified with a tolerance, usually ±5% or ±10%. This assures the accelerometer’s sensitivity will be within this deviation from the stated nominal sensitivity. In almost all cases, accelerometers are supplied with a calibration certificate stating the exact sensitivity within measurement uncertainty limits.
Sensitivity is called the reference sensitivity when referring to the percentage or decibel tolerance band of frequency response specifications. Sensitivity is called the axial sensitivity when discussing transverse sensitivity.
Despite the tight constraints that surround the sensitivity specification, this is the number most frequently used for programming a signal conditioner or data acquisition system. A signal conditioner or data acquisition system uses this number to process and interpret the signal from the accelerometer.
Frequency Response
Similar to the sensitivity specification, frequency response also tells you what the accelerometer’s scale factor is, but with the additional variable of frequency added. Frequency response is the sensitivity specified over the transducer’s entire frequency range, more properly referred to as amplitude response since the phase response is rarely specified.
Frequency response always is specified with a tolerance band relative to the 100-Hz sensitivity or reference sensitivity. The tolerance band can be specified in percentage or decibels, with typical bands being ±10%, ±1 dB, and ±3 dB. In this context, a decibel is defined as:
dB = 20log (Sf /Sref )
where: Sf = sensitivity at a particular frequency
Sref = reference sensitivity
The frequency response specification enables you to calculate how much the accelerometer’s sensitivity can deviate from the reference sensitivity at any frequency within its specified frequency range. For example, assume an accelerometer model has a reference sensitivity of 10 pC/g; that is, calibration results report this number so it is exact within uncertainty limits. Assume its frequency response specification is ±10% from 1 Hz to 6 kHz. Over this frequency range, sensitivity can vary from 9 pC/g to 11 pC/g or 10 ±1 pC/g. At the reference sensitivity frequency of 100 Hz, sensitivity is exactly 10 pC/g, but at any other frequency, it can vary up or down by 1 pC/g.
Accelerometers often come with a calibration certificate stating the exact reference sensitivity. The certificates often do not show the frequency response in tabular form but instead display a plot from the lowest rated frequency to the highest. The plot shows sensitivity deviation in percentage or dB from the reference sensitivity (Figure 1).
Using the technique illustrated in the example, you can estimate the sensitivity at any frequency using this plot. If the plot shows the sensitivity up 2% at 1 kHz, for example, and the reference sensitivity is stated as 10 pC/g, a simple calculation indicates the sensitivity at 1 kHz to be 10.2 pC/g.
Transverse Sensitivity
Transverse sensitivity is the sensitivity of the accelerometer at 90 degrees to the sensitive axis of the sensor (Figure 2). Stated another way, transverse sensitivity is the sensitivity at 90 degrees to the axial sensitivity expressed as a percentage of the axial sensitivity.
Ideally, it would be 0%, but due to manufacturing tolerances, it can be as much as 5%. Values 3% or lower are available on special request. But as the desired value goes lower, it becomes increasingly difficult and more expensive to achieve. Transverse sensitivity is sometimes referred to as cross-axis sensitivity.
Why be concerned about transverse sensitivity? As a user, you want to be assured that the measurement you are taking is only due to acceleration in one direction. If not, making sense of your data would be difficult, if not impossible. Triaxial accelerometers are available for measuring acceleration in three orthogonal directions from the same point.
When an accelerometer is stimulated on a calibration class shaker, every effort is made to ensure the motion is in one direction, with very little transverse motion. In this situation, you may not care that the accelerometer has a high transverse sensitivity since the sensor does not see any motion in that direction.
However, in a real test on a real structure, we know that the motion is in all directions. In this case, a low transverse sensitivity accelerometer is crucial because you want to be assured that the measurement you are getting is only from one direction. In this sense, the contribution of transverse sensitivity to a measurement can be thought of as a noise contributor to the measurement.
Mounted Resonant Frequency
Mounted resonant frequency is the point in frequency in the accelerometer’s frequency response where the accelerometer outputs maximum sensitivity (Figure 3). It is specified in units of hertz. Typical accelerometers exhibit a mounted resonant frequency above 20 kHz although some show as high as 90 kHz.
As the name implies, it is the result of the natural resonance of the mechanical structure of the accelerometer itself. Certainly, if the resonance of the accelerometer were measured in free space, it would be different than if mounted to a structure. However, this is an impractical application for a piezoelectric accelerometer, so the designation mounted is added.
It is not a design goal of manufacturers to produce an accelerometer that has a mounted resonant frequency within a certain tolerance. Instead, mounted resonant frequency is specified as a minimum, ensuring you that this resonant point will not occur below the minimum. As such, mounted resonant frequency is a rough figure-of-merit that sets the upper limit of the frequency bandwidth of the accelerometer.
For piezoelectric accelerometers with an almost completely undamped mechanical structure, the amplitude of the resonant peak can be quite high, resulting in a sensitivity many times higher than the specified reference sensitivity. As such, any vibration at or near the frequency of the resonant peak will be highly amplified, resulting in distorted measurements and corrupted data.
A manufacturers’ design goal, then, is to push the mounted resonant frequency point as high as possible in the accelerometer’s structure, with the intent that the point be well beyond any vibration frequencies in your measurement application. You also have to ensure that no vibration frequency components are at or near the mounted resonant frequency point.
Mounted resonant frequency is specified assuming ideal accelerometer mounting conditions. Just as the manufacturer can influence the mounted resonant frequency point with the accelerometer’s mechanical structure itself, so too can external structural factors that the user controls.
Because mechanical resonance characteristics in general are dependent on material stiffness and damping, it is critical the accelerometer be mounted correctly. Improper mounting generally decreases stiffness and increases damping, causing the resonant peak to decrease in frequency and the width of the resonant rise to increase—the mechanical Q is lowered. The ultimate result of this will, if allowed to degrade enough, affect the frequency response of the accelerometer.
Amplitude Linearity
Amplitude linearity is a measure of how linear the output of an accelerometer is over its specified amplitude range. Sometimes it is called amplitude nonlinearity since it specifies the deviation from perfect linearity. Ideally, an accelerometer would have exactly the same sensitivity at any amplitude point within its specified amplitude range.
But with a real accelerometer, this is not the case. Amplitude linearity specifies how far the accelerometer’s output may differ from this perfect linearity and is only valid at a single frequency.
There are several ways to specify amplitude linearity. The most restrictive is to specify percentage of reading, typically ±1% over the entire full-scale range. This is a close tolerance specification because it means the accelerometer’s sensitivity cannot vary by more than ±1% at any point in the amplitude range.
A much less restrictive way is to specify linearity in a piecewise manner, such as this example: Sensitivity increases 1% per 500 g, 0 to 2,000 g. This means that at the top end of the amplitude range sensitivity can vary as much as 4% from that at the low end of the amplitude range.
Amplitude linearity errors cause signal distortion, particularly in high-amplitude accelerations. In environments where multiple vibration frequencies are present, intermodulation distortion can result, creating frequencies in the instrumentation that were not present mechanically at the accelerometer.
Output Polarity
Output polarity describes the positive or negative direction of the accelerometer’s output signal given a particular direction of the input acceleration. By convention, most accelerometers are specified to have a positive-going output signal if the acceleration is directed into the mounting surface of the sensor (Figure 4).
If in doubt, you can easily verify this. While holding the accelerometer connected to all proper signal conditioning, tap the mounting surface with your finger. Observe which direction the resulting signal goes. If it is a conventional accelerometer, the signal should go positive.
Output polarity of a triaxial accelerometer is slightly less straightforward. In most cases, however, the manufacturer will mark arrows for each orthogonal direction, indicating the direction the acceleration would have to be for a positive-going signal to result.
Interpreting output polarity correctly is critical in some applications. For example, in a modal test on a large structure, it is essential to understand the directions and phase relationships of the acceleration vectors the structure is exhibiting during vibration excitation. Without correctly understanding polarity in the accelerometers, this would be impossible, and incorrect insight into the behavior of the structure would result.
Grounding or Ground Isolation
Accelerometers, being electrical devices, require a signal ground return back to a signal-conditioning device. How this signal ground is handled mechanically and electrically within the sensor must be understood by the user for proper operation. This is specified by the manufacturer. Without this understanding, the potential exists for an improper grounding system in the instrumentation, resulting in ground loops and erroneous data.
There are a number of ways a grounding system can be realized in the design of an accelerometer, often dictated by expected use and market pricing. One of the least expensive methods is to simply connect the system ground to the accelerometer’s casing. This method often is found in laboratory-grade accelerometers using miniature coaxial connectors. To prevent ground loops, manufacturers offer isolated mounting adapters that install between the accelerometer and structure mounting location.
The next method again connects the accelerometer casing to ground but isolates the mounting surface on the accelerometer itself. This usually is done with an isolating material applied to the surface, such as a hard anodized layer. In essence, the isolated adapter is built into the accelerometer.
The ultimate ground isolation method is where the outer accelerometer casing and connector are completely isolated from the internal system ground. This method often is found in industrial-class accelerometers used on jet engines, gas turbines, or industrial process machine monitoring.
Conclusion
Accelerometer users often are confused over accelerometer specifications, particularly when trying to select an appropriate sensor for a specific application or test. It is essential that you have a clear understanding of these specifications and what the limits and implications of these are to your test situation. Without this understanding, there exists a great potential for errors to enter the test data and for wasting a test. Manufacturers, too, have a responsibility to present their product’s specifications in a clear and unambiguous manner.
About the Author
Scott Mayo is a field applications engineer at Endevco. After earning his electrical engineering degree in 1986, Mr. Mayo went to work for Bently Nevada, now part of General Electric, designing accelerometers and proximity displacement sensors used in industrial applications. While a product manager at Bently Nevada, he wrote several sections adopted into the American Petroleum Institute Standard 670 Machinery Protection Systems, Fourth Edition, December 2000. Endevco, a Meggitt group company, 30700 Rancho Viejo Rd., San Juan Capistrano, CA 92675, e-mail: [email protected]
June 2009