Vibration correction error (VRE) is the response of the accelerometer to ac vibration (rectified to dc), which is taken as the abnormal deviation of the accelerometer misalignment. In applications such as the inclinometer, this is a significant source of error because the accelerometer's dc output is the target signal, and any misalignment change can be misinterpreted as a change in inclination, resulting in errors all the way down, which can lead to misfiring of the safety system, platform stabilization, or over-compensation of the drill mast alignment mechanism.
VRE is highly dependent on the vibration characteristic curve experienced by the accelerometer, and may vary depending on the vibration mode applied to the accelerometer. Vibration correction has many mechanisms, two of which are discussed in this paper.
The first mechanism is asymmetric orbits. Gravity produces a static 1 g (9.8 m/s2) acceleration field, and when the accelerometer sensitive axis is aligned vertically, its measurement range will be offset. When the sensor with a full range of 2 g is aligned with the gravity acceleration, only 1 g of peak vibration can be measured, otherwise the response will be clipped. The mean value of a symmetric excitation signal greater than 1 g will not be zero because the level will be clipped in the direction of the additional 1 g acceleration.
FIG. 1. Vibration correction diagram for accelerometers with a full range of + / - 2 g due to asymmetric clipping
In figure 1, an exciting vibration signal is applied to a 2 g full range sensor. When the vibration is 0.3 g RMS (between 300 and 600 samples), there is no observable deviation from the misalignment. However, when the vibration is 1 g RMS (between 600 and 1000 samples), VRE is about -100 mg.
VRE can be modeled as an average offset of a truncated distribution, limited by the accelerometer's full range range. When a sensor is subjected to random vibration in a 1 g field, the input excitation signal can be modeled as a normal distribution of average value = 1 g and standard deviation sigma = X, where X represents the root mean square value of the input vibration amplitude. The sensor output is modeled as a double-truncated normal distribution, and the lower and upper bounds of the output values are -r and +R respectively, where R is the maximum range of the sensor. The average value of the double-truncated normal distribution is calculated as follows:
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