Modeling the Tribological Properties of Polymer Coatings Based on Phenylone With Copper (Ii) Complex Modifiers Using Matlab

Purpose. This study is dedicated to designing and evaluating antifriction polymer coatings based on phenylone C2, an aromatic polyamide with high thermal stability, modified with copper (II) complexes of the composition [Cu(HL)X₂]₂, where HL represents derivatives of benzimidazole-2-thiocarboxylic acid arylamides. The research aims to model the tribological behavior of these coatings, focusing on the effects of sliding speed, specific load, and modifier concentration, to improve the performance and durability of friction units in mechanical engineering applications under high-load conditions typical of industrial machinery. Methods. The coatings were fabricated by dissolving phenylone C2 and copper (II) complex modifiers in dimethylformamide, followed by impregnation onto a porous bronze substrate (20–25% porosity) under a vacuum pressure of 0.00001 MPa for 30 minutes. The coated samples were cured at 420 K for 1.5 hours and then at 723 K for 2 hours to ensure complete hardening. Tribological testing was conducted using an SMT-2010 friction machine in a block-on-disk configuration, lubricated with I-40A industrial oil (GOST 20799-88). Tests spanned sliding speeds of 0.15 to 1.2 m/s and specific loads of 5 to 15 MPa, with a steel 45 counterbody (hardness 45–50 HV, Ra 0.4–0.63 μm). Friction coefficients were measured with an accuracy of ±0.001, and wear rates were determined gravimetrically with a precision of ±0.01 mg/m after 10-hour test cycles. Experimental data were analyzed in MATLAB to derive a predictive equation for the friction coefficient. Results. Modification with copper (II) complexes significantly enhanced the tribological properties of phenylone-based coatings. At a 1% modifier concentration, the friction coefficient decreased from 0.080 to 0.045, and wear resistance improved by 60%, with coating No. 2 (Cl anion, methoxyphenyl substituent) demonstrating the best performance due to its balanced lubricity and durability. MATLAB processing yielded the equation f(V,P)=0.0335+0.0095⋅V+0.0005⋅P, accurately describing the friction coefficient’s dependence on sliding speed (V, m/s) and specific load (P, MPa) with a maximum deviation of less than 5%. Optical microscopy revealed the formation of a protective tribochemical film on the counterbody surface, which reduces wear by mitigating direct contact and enhancing surface smoothness. Conclusions. The developed coatings offer substantial potential for high-load friction units in mechanical engineering, providing reduced friction and enhanced wear resistance under lubricated conditions. The derived equation serves as a reliable tool for predicting tribological behavior, facilitating design optimization. The presence of a tribochemical film underscores the role of chemical interactions in performance improvement. Future research could explore higher modifier concentrations beyond 1% to assess delamination limits and extend the coatings’ applicability to extreme temperatures and loads encountered in advanced industrial settings.