Numerical and Analytical Calculations for Modeling and Designing Drilling Wicks or Rotary Cutters Based of Functionally Graded Materials

Abstract

Drilling tools or drilling pipes, such as drill bit and mill drill, are often subjected to various forces, including essentially tangential forces, centered on their axis of rotation. The main objective of this work is to find analytical and numerical solutions of the distribution of stress field, deformation, and displacement, when such tools are subjected to such forces. It will be assumed that the instrument in the chosen model in this work is a rotating hollow cylinder constructed from a Functional Graded Material (FGM). Because of the graduation of the FGM, the mechanical and elastic properties such as Young’s modulus, density, and Poisson’s ratio vary in the radial direction according to a power law function. By choosing that the inhomogeneity parameter is between -0.5 and 0.5, we have established the differential equation which describes the equilibrium of the hollow cylinder in rotation under an axial load. The calculations performed have allowed finding an analytical solution which was compared with numerical solutions obtained by using the shooting method and the fourth-order Runge-Kutta algorithm. These analytical and numerical results have shown that the values of tangential stresses are greater than the radial stresses. The radial stresses and tangential and vertical stresses progressively increase with the axial force Fz. The force Fz affects more tangential stresses that the radial stresses. The tangential stress, tangential deformations, and displacements are higher on the inner walls of the cylinder than on the exterior surfaces. The results obtained are very important and can be applied in the modeling and designing wicks and drilling strawberries in order to reduce their rapid wear and damage.