Influence of linear vibration on the errors of three-axis FOGs in the measurement while drilling systems

At present, the single-axis FOG has a good anti-vibration performance when being tested with the linear vibration table. However, when the three FOGs are installed into the Initial Navigation System orthonormal, the anti-vibration performance of the FOGs becomes deteriorated. This paper discovers that the sampling rate of the gyros is a critical factor that influences their anti-vibration performance greatly. When the FOGs-based MWD is vibrating linearly, the MWD also involve with an angular vibration which is given rise by the linear vibration. This angular vibration has the same frequency with the linear vibration. As the angular sensor, the FOGs installed in the MWD can sense this angler vibration. According to the Nyquist sampling theorem, a continuous signal should be sampled at a rate greater than 2 times the maximum frequency of the signal. If the sampling rate of the FOGs is lower than 2 times of the maximum frequency of angular vibration, their measurements couldn't recover the real vibration signal accurately which will result in a drift. In this paper, this phenomenon is explained theoretically. And the quantitative relation between the linear vibration and the effect on FOGs is established for the first time. In order to validate this innovative idea, a 10 Hz frequency linear vibration of the MWD was simulated using trajectory generator. This continuous vibration signal was sampled by inertial sensors with different sampling rate (1 KHz, 20 Hz and 12.5 Hz). When the sampling rate of the FOG installed in the MWD was lower than 2 times of the vibration frequency, the measurements of the FOGs drifted 0.25°/h. While the sampling rate was greater than 2 times of the vibration, it barely drifted. Additionally, three linear vibration experiments were performed under the condition of the lab. The fix-frequency vibration along Y axis verified that the linear vibration truly incur the angular vibration with same frequency. The linear sweep-frequency vibration along X axis verified that with the higher sampling rate, the error of FOGs measurements was reduced dramatically. The random vibration along Z axis proved that the attitude errors were reduced more than 50% when the FOGs sampling rate was greater than 2 times of the maximum frequency of the vibration.