(untitled) (Journal of Mathematics Mechanics and Computer Science, 2022)
The motion of drill strings is modeled in the drilling of geotechnological wells in the mining industry by the Lumped-Parameter Method (LPM). This method is widely used in structural mechanics and is most justified in modeling dynamic systems with a variable structure. On the example of horizontal drilling of geotechnological wells, longitudinal vibrations of a drill string with a static compressive load at the left end are considered [1]. The contact interaction of the drill string with the borehole walls and the inertia force of the bit on the destructible rock at the right end of the string are taken into account. The analysis of the column splits number, which specifies the dimension of the system of discrete equations, is carried out by verifying the obtained results with the previously known data [1]. For verification, the developed C# software was used, allowed to determine the error of the column splits in comparison with the test data. The optimal number of the drill string splits in terms of "implementation time - calculation error" by the LPM was identified. The numerical implementation of the model is conducted by the fourth-order Runge-Kutta method. In connection with the increase in the implementation time of the program code due to the increase in the dimension of the system, the numerical algorithm is optimized using the parallel programming tools. The expediency of this optimization is analyzed.