A method, system, and computer-readable medium related to control of mud motors in drilling systems, of which the method includes measuring an eccentricity of rotation of a rotor in a stator of a mud motor using a rotor-position sensor, determining a torque of the mud motor based in part on the eccentricity, and selecting a fluid flow rate, a pressure, or both of fluid delivered downhole, through the mud motor, based in part on the determined torque.

A method, system, and computer-readable medium related to control of mud motors in drilling systems, of which the method includes measuring an eccentricity of rotation of a rotor in a stator of a mud motor using a rotor-position sensor, determining a torque of the mud motor based in part on the eccentricity, and selecting a fluid flow rate, a pressure, or both of fluid delivered downhole, through the mud motor, based in part on the determined torque.

In at least one general aspect, an inductive sensor can include a shaft having an axis of rotation, and a rotor physically coupled to the shaft and including a rotor coil. The rotor and the rotor coil can be aligned along a plane orthogonal to the axis of rotation. The inductive sensor can include a stator including a stator layer, an excitation coil, and an eccentricity receiver coil where the excitation coil and the eccentricity receiver coil are physically coupled to the stator layer.

Systems and methods for measuring displacement parameters of rotating shafts and couplings are disclosed. In some aspects, a measurement system includes a shaft extended in a longitudinal direction and a target wheel configured to rotate with the shaft. The target wheel includes sensor targets circumferentially distributed around the target wheel. Some of the targets are slanted in the longitudinal direction and some of the targets are parallel to the longitudinal direction. The measurement system includes a sensor array including at least three sensors mounted radially around the shaft and configured to detect the sensor targets as the target wheel rotates with the shaft. The measurement system includes a controller configured to receive sensor signals from the sensors and determine, based on the sensor signals, at least an axial displacement measurement of the shaft in the longitudinal direction and a radial displacement measurement of the shaft.

Systems and methods for measuring displacement parameters of rotating shafts and couplings are disclosed. In some aspects, a measurement system includes a shaft extended in a longitudinal direction and a target wheel configured to rotate with the shaft. The target wheel includes sensor targets circumferentially distributed around the target wheel. Some of the targets are slanted in the longitudinal direction and some of the targets are parallel to the longitudinal direction. The measurement system includes a sensor array including at least three sensors mounted radially around the shaft and configured to detect the sensor targets as the target wheel rotates with the shaft. The measurement system includes a controller configured to receive sensor signals from the sensors and determine, based on the sensor signals, at least an axial displacement measurement of the shaft in the longitudinal direction and a radial displacement measurement of the shaft.

Apparatus and methods can be conducted in a multi-pipe structure to determine eccentricity of one or more pipes of the multi-pipe structure. A tool having a center axis as a symmetry axis of the tool can be used in which receivers are arranged as a number of pairs of receivers around the center axis of the tool. Each receiver of a pair can be disposed opposite the other receiver of the pair with respect to the center axis such that each pair is symmetrical with respect to the center axis of the tool. Eccentricity of one or more pipes of the multi-pipe structure can be determined based on the received responses at the receivers of the pairs.

Apparatus and methods can be conducted in a multi-pipe structure to determine eccentricity of one or more pipes of the multi-pipe structure. A tool having a center axis as a symmetry axis of the tool can be used in which receivers are arranged as a number of pairs of receivers around the center axis of the tool. Each receiver of a pair can be disposed opposite the other receiver of the pair with respect to the center axis such that each pair is symmetrical with respect to the center axis of the tool. Eccentricity of one or more pipes of the multi-pipe structure can be determined based on the received responses at the receivers of the pairs.

Systems and methods for measuring displacement parameters of rotating shafts and couplings are disclosed. In some aspects, a measurement system includes a shaft extended in a longitudinal direction and a target wheel configured to rotate with the shaft. The target wheel includes sensor targets circumferentially distributed around the target wheel. Some of the targets are slanted in the longitudinal direction and some of the targets are parallel to the longitudinal direction. The measurement system includes a sensor array including at least three sensors mounted radially around the shaft and configured to detect the sensor targets as the target wheel rotates with the shaft. The measurement system includes a controller configured to receive sensor signals from the sensors and determine, based on the sensor signals, at least an axial displacement measurement of the shaft in the longitudinal direction and a radial displacement measurement of the shaft.

Systems and methods for measuring displacement parameters of rotating shafts and couplings are disclosed. In some aspects, a measurement system includes a shaft extended in a longitudinal direction and a target wheel configured to rotate with the shaft. The target wheel includes sensor targets circumferentially distributed around the target wheel. Some of the targets are slanted in the longitudinal direction and some of the targets are parallel to the longitudinal direction. The measurement system includes a sensor array including at least three sensors mounted radially around the shaft and configured to detect the sensor targets as the target wheel rotates with the shaft. The measurement system includes a controller configured to receive sensor signals from the sensors and determine, based on the sensor signals, at least an axial displacement measurement of the shaft in the longitudinal direction and a radial displacement measurement of the shaft.

Apparatus and methods can be conducted in a multi-pipe structure to determine eccentricity of one or more pipes of the multi-pipe structure. A tool having a center axis as a symmetry axis of the tool can be used in which receivers are arranged as a number of pairs of receivers around the center axis of the tool. Each receiver of a pair can be disposed opposite the other receiver of the pair with respect to the center axis such that each pair is symmetrical with respect to the center axis of the tool. Eccentricity of one or more pipes of the multi-pipe structure can be determined based on the received responses at the receivers of the pairs.