Development of the Coupled Smoothing Technique λS-FEM for Mechanical Analysis of Twist Drills

A coupled smoothing technique, λ S-FEM, is introduced to improve the accuracy of numerical simulations in the mechanical analysis of twist drills. This method combines the edge-based smoothing finite element method (ES-FEM) with the node-based smoothing finite element method (NS-FEM). The λ S-FEM model is designed to evaluate the mechanical properties of twist drills made from tungsten carbide (WC), titanium nitride (TiN) coatings, and high-speed steel (M35), providing a theoretical basis for lifespan estimation and wear prediction. Linear tetrahedral elements construct the smoothing domain, and optimized weighting parameters balance and combine the smoothed strains from ES-FEM and NS-FEM. This integration enhances the accuracy of solutions for displacements, stresses, and strain energies, constructing stiffness matrices with optimal precision. The method’s feasibility is demonstrated through numerical case studies involving flange and shell extractor components. Analyses of straight shank twist drills compare displacement and stress magnitudes across FEM, S-FEM, and λ S-FEM under various degrees of freedom (DOF). Results show λ S-FEM significantly reduces errors, particularly with coarse meshes, validating its practical application in solving engineering challenges.