Measurement of torque with shear stress sensors

A downhole torque measurement tool, comprising:

• a lower cylindrical sub having a box end and a pin end;
• an upper cylindrical sub having a box end, a pin end and an inner bore with an inner surface extending between the box end and the pin end,
• wherein the box end of the upper cylindrical sub is connected to the pin end of the lower cylindrical sub;
• wherein the lower cylindrical sub comprises an outer cylindrical shaft having a hollow cavity extending parallel to a longitudinal axis of the outer cylindrical shaft and an inner cylindrical shaft positioned within the hollow cavity and extending parallel to the longitudinal axis of the outer cylindrical shaft, the outer and inner cylindrical shafts each having a common end coupled together and forming a unitary structure at the box end of the lower cylindrical sub;
• and
• wherein the inner cylindrical shaft has an extended end that extends a length greater than a length of the outer cylindrical shaft at the pin end of the lower cylindrical sub such that the extended end of the inner cylindrical shaft extends into the bore of the upper cylindrical sub and forms an annular space;
• a flexible coupling positioned within the annular space and at least partially encircling the extended end of the inner cylindrical shaft, the flexible coupling coupled to the extended end of the inner cylindrical shafts;
• and
• a micro-electro-mechanical-system (MEMS) shear stress sensor positioned within the annular space on the inner surface of the upper cylindrical sub and in contact with the flexible coupling, wherein relative positional displacement between the inner and outer shafts produces shear stress in the flexible coupling that is measured by the MEMS shear stress sensor.