## Shock vibration compensation of MEMS north finder

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hamousi
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### Shock vibration compensation of MEMS north finder

The borehole north finding system based on MEMS north finder needs to overcome the complex environment in borehole north finding. Shock vibration is one of the main factors affecting the accuracy of borehole north finding by MEMS north finder. When shock vibration occurs, the core component of MEMS gyro is sensitive not only to the horizontal component of earth rotation, but also to the angular velocity component generated by shock vibration interference. Therefore, in order to improve the precision of borehole north finding while drilling, it is necessary to compensate the error of MEMS north finder under shock vibration.

1.The influence of vibration on borehole north finding

When the drill bit is drilling, it will not only cause the tilting of the base of north seeker, but also cause high frequency interference due to shock vibration. In practice, the situation is very complicated, MEMS gyroscope will be sensitive to other signals in addition to the Earth's angular rate component, such as drilling the base Angle to produce additional angular speed. The final output of a MEMS north seeker consists of a superposition of many signals. In this section, the Angle vibration of drilling bit is taken as the main research object, and the error caused by it is analyzed. Bit drilling will make the transverse roller and pitch axis of MEMS north finder do different angular vibration, the specific characteristics are as follows:

In Formula 1, Bm and rm represent the vibration amplitude of the MEMS north seeker around the pitch axis and transverse roller axis, where is the vibration frequency, then the influenced angular velocity brought about by the drilling bit is:

On the basis of two-position north finding, the output after adding only vibration error is:

The north finding Angle obtained by the above formula 3 is:

The above equation 4 is approximated by the first expansion of Taylor's formula

Among them, it belongs to the north-seeking error introduced by drill bit drilling. As can be seen from formula 4, when the sensitive axis of the gyroscope approaches north or south, it approaches 1 and has the smallest impact on error; when it approaches east-west, it approaches 0 and has the greatest impact on error. At present, there are two main ways to reduce downhole vibration errors while drilling: The first is to install shock insulation material at the bit to physically buffer and reduce the impact of shock and vibration on the north finding accuracy of MEMS gyroscope. This method will cause the volume of the whole north finding system to increase and affect the drilling of the bit; The second method is to reduce the impact of shock vibration by means of algorithm compensation, such as using an accelerometer that can sense angular velocity and disturbance angular velocity at the same time to compensate the gyroscope output signal, but the accuracy of this method is affected by the accuracy of the accelerometer. This paper presents a method based on multi-resolution analysis to solve the effect of bit vibration on the accuracy of the north seeker.