Application of finite-length displacement sensors to precision torque measurements of a tail rotor transmission tube

It is theoretically possible to place long fiber-optic displacement sensors on structures that are generally loaded and still maintain the ability to exactly discriminate signals of interest. The chief advantage of finite-length fiber-optic sensors is that the sensitivity of the measurement scales not only with the maximum strain along the path but the length of the sensor as well. One consequence of this scaling property is that `smart' structures incorporating such a measurement approach could be sensitive yet still have low maximum strains. In other words, the sensitivity of the measurement is partially decoupled from the stiffness of the structure. This theoretical result is true for simple prismatic structures composed of a linear elastic homogeneous material with arbitrary end loading, and with perfectly positioned displacement sensors. A model tail rotor torque tube has been constructed and verifies the essential elements of the analysis. Unfortunately, the use of long displacement sensors effectively integrates signals of interest along the measurement paths and is thus susceptible to accumulated manufacturing errors. These errors are evident both by a decrease in sensitivity to the load intended to be measured and a response of unintended loads. For a simple construction technique certain manufacturing errors were modeled and provide theoretical limits to the performance of a torque tube incorporating finite length sensor paths. Elements of the error model are confirmed by experiments on model torque tubes instrumented on the surface with various finite length sensor topologies. Finally, an extension of this work to sensors embedded in a composite structure is also discussed.