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Computation modeling of drill bits : a new method for reproducing bottom hole geometry and a second-order explicit integrator via composition for coupled rotating rigid bodies


A new, highly adaptable, framework for the simulation of bit dynamics is introduced. The new software, dubbed Three Dimensional Bit Dynamics (TDBD), is implemented as object- orientated code and designed to meet current and future research needs. The software uses a triangulated mesh to represent the bit and rock surface geometry. A novel method for updating the rock surface as the bit drills is presented. This method uses information from both the bit and rock surface to allow for general motion of the bit (including whirl). It also limits the number of operations required to maintain the shape quality of the elements in the rock surface mesh. This method avoids the costly operation of removing elements and remeshing the resulting hole. A derivation of the equations of motion of a roller cone bit is presented as an example of coupled rotating rigid bodies. The equations are derived using the virtual power method which naturally handles the constraint between the bit body and the cones. A state-of-the-art numerical integrator is applied to the equations to produce an algorithm suitable for use in a bit dynamics software application. The integrator is a composition of adjoint first order integrators (reminiscent of the approach used earlier in Reference [47] to derive an explicit midpoint Lie method). It maintains the properties of the original three degree-of-freedom integrator: second order convergence, symplecticness, remarkable accuracy, and momentum conservation. This algorithm can be applied to other applications where rotating rigid bodies are coupled through an axis that allows rotation. The force model from Reference [33], used for calculating the forces on a bit resulting from rock removal, is implemented within the framework and used to evaluate the software. The weight-on-bit and torque-on-bit are compared to laboratory data. Two polycrystalline diamond compact (PDC) bits are used to calibrate the force model and a third is run in the software to "predict" the laboratory data

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