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A new quasi-elliptical cylindrical (QEC) fiber optic gyroscope (FOG) for petroleum logging is proposed for the special condition of the borehole diameter limitation in inclinometer while drilling (IWD). Due to the thermally induced nonreciprocal phase shift in fiber coil, the three-dimensional (3-D) temperature transient effects mathematical model and finite element model of QEC fiber coil are established by quadrupole (QAD) winding method, which are based on the Shupe effect of fiber coil and used to analyze the influence of structural parameters of QEC fiber coil on Shupe error. Combined with the actual working environment of FOG, the numerical simulation of QEC fiber coil is done to analyze the Shupe error in the fiber coil at certain temperature gradient quantitatively. It also verifies the correctness of model building comparing with the experimental results. The results show that when the fiber length, the number of fiber coil and the radius of fiber coil are fixed, the thermal error rate of QEC fiber coil is 40% to 50% smaller than that of FOG fiber coil.

The design of structure and simulation analysis of thermal effect on small fiber optic gyroscope in inclinometer while drilling