Study on the Shupe error of the elliptic fiber coil

In this work, the fiber optic gyroscope (FOG) with an elliptic fiber coil (EFC) is applied to the inertial measurement of petroleum well trajectory for the special condition of the borehole diameter limitation in the inclinometer while drilling (IWD). The three-dimensional (3D) Shupe error mathematical model and finite element model of the EFC are established by the quadrupole symmetrical technique, which is based on the Shupe effect of fiber coil. Then, the simulation experiments and the temperature experiments of the EFC are carried out to verify the correctness of the mathematical model. Under this prerequisite, the influence of the structure parameters of the EFC on the Shupe error is analyzed. In order to compare the rotation rate error between the EFC and the circular fiber coil (CFC), the temperature experiments of the EFC and the CFC are carried out with the same temperature excitation when the fiber length, the layers of fiber coil, and the radius of fiber coil of the EFC are the same as those of the CFC. The results show that the bias stability of the EFC is 35% to 39% smaller than that of the CFC before the temperature compensation, and after the temperature compensation, the bias stability of the EFC is 49% to 70% smaller than that of the CFC.