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Large-amplitude vibrations in drilling often occur at frequencies near multiples of the rotation frequency, even when these are much lower than the system’s first natural frequency. These vibrations are responsible for out-of-round, “lobed” holes. A simplified model of the mechanics of this phenomenon is presented in this paper. The model includes cutting and “rubbing” forces on the drill, but inertia and damping of the tool are neglected at low speeds. This quasi-static model remains dynamic because of the regenerative nature of cutting; the force on each cutting element depends on both the tool’s current position and its position at the time of the previous tooth passage. Characteristic solutions, including unstable retrograde “whirling” modes, are found in terms of eigenvalues and eigenvectors of a discrete state-transition matrix. These unstable modes correspond closely to behavior observed in drilling tests.

A quasi-static model of reaming is developed to explain oscillation of the tool during cutting and the resulting roundness errors in reamed holes. A tool with N evenly-spaced teeth often produces holes with N+1 or N−1 “lobes.” These profiles correspond, respectively, to forward or backward whirl of the tool at N cycles/rev. Other whirl harmonics (2N cycles/rev, e.g.) are occasionally seen as well. The quasi-static model is motivated by the observations that relatively large oscillations occur at frequencies well below the natural frequency of the tool, and that in this regime the wavelength of the hole profile is largely independent of both cutting speed and tool natural frequency. In the quasi-static approach, inertial and viscous damping forces are neglected, but the system remains dynamic because regenerative (time-delayed) cutting and rubbing forces are included. The model leads to an eigenvalue problem with forward and backward whirl solutions that closely resemble the tool behavior seen in practice.

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Pressure measurements are made by measuring Bragg grating peak splitting caused by transverse strain differences in the core of a single mode side hole fiber. The side holes and not the fiber exterior are pressurized, demonstrating the ability to use the side holes as a pressure conduit so that pressure measurements can be made in a thermally and mechanically stable environment. Geometrical and residual stress-based birefringence stemming from partial side hole collapse during the drawing process allows measurements to be made near atmospheric pressures. Peak fitting techniques are used to determine peak separation to sub-pm levels despite substantial peak overlap. IntroductionFiber optic pressure sensors have attracted attention in recent years because they are passive, immune to electromagnetic interference, intrinsically safe, multiplexible and corrosion resistant. These advantages make them good candidates for high range pressure sensing in hostile environments. Fiber Bragg grating sensors are intrinsically sensitive to both strain and temperature, and thus are useful for making simultaneous measurements of temperature and pressure-induced strain. Traditional Bragg grating sensors based on axial strain, however, are plagued by high temperature and pressure cross-sensitivity. Previous work with Bragg gratings in single mode side