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Background <p>This research studies the vibration and stability behavior of a rotating multistep drill bit conveying internal fluid with the effects of warping and a complex non-axisymmetric cross-section. The drill bit is modelled as a twisted Euler-Bernoulli beam with two helical internal fluid channels. Torsional warping is included by means of a dimensionless Prandtl stress function to correctly represent the coupling between the axial, bending and torsional deformations due to the complex geometry of the cross section.</p> Methods <p>Using Hamilton's principle, the governing equations of motion are obtained by taking into account the kinetic energy of the structure and the internal fluid as well as the strain energy of the drill bit. The equations are discretized using the assumed mode method. </p> Results <p>The results from the analyses are verified against the COMSOL Multiphysics simulations, and there is good agreement. Natural frequencies, mode shapes and stability limits for a series of rotational speeds, internal fluid velocities, helix angles and the fluted length ratios were studied under both clamped-free and clamped-clamped boundary conditions.</p> Conclusion <p>The results show that internal fluid flow and rotation have a significant effect on the reduction of natural frequencies and stability margins, whereas clamped and partly embedded configurations will provide better stability. The influence of the helix angle is limited; while warping and cross-sectional complexity play a notable role in the correct prediction of the dynamic response of internally cooled drill bits.</p>

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Frequency and Stability Analysis of Fluid Conveying Rotating Multistep Drilling Bit

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Ali Faez Hasan,
  • Morteza Dardel,
  • Hamid Baseri

摘要

Background

This research studies the vibration and stability behavior of a rotating multistep drill bit conveying internal fluid with the effects of warping and a complex non-axisymmetric cross-section. The drill bit is modelled as a twisted Euler-Bernoulli beam with two helical internal fluid channels. Torsional warping is included by means of a dimensionless Prandtl stress function to correctly represent the coupling between the axial, bending and torsional deformations due to the complex geometry of the cross section.

Methods

Using Hamilton's principle, the governing equations of motion are obtained by taking into account the kinetic energy of the structure and the internal fluid as well as the strain energy of the drill bit. The equations are discretized using the assumed mode method.

Results

The results from the analyses are verified against the COMSOL Multiphysics simulations, and there is good agreement. Natural frequencies, mode shapes and stability limits for a series of rotational speeds, internal fluid velocities, helix angles and the fluted length ratios were studied under both clamped-free and clamped-clamped boundary conditions.

Conclusion

The results show that internal fluid flow and rotation have a significant effect on the reduction of natural frequencies and stability margins, whereas clamped and partly embedded configurations will provide better stability. The influence of the helix angle is limited; while warping and cross-sectional complexity play a notable role in the correct prediction of the dynamic response of internally cooled drill bits.