Mathematical modeling of antifriction material diffusion during ultrasonic machining

This paper presents a mathematical model of antifriction material (graphite) diffusion into the surface layer of a metal workpiece during ultrasonic machining. Unlike classical approaches based on Fick’s second law for bulk diffusion, the proposed model is founded on the Fisher equation, which describes grain boundary diffusion under conditions of intense plastic deformation and nanocrystalline structure formation. An analytical expression for calculating the penetration depth of the coating has been derived, taking into account the contact zone temperature, activation energy of diffusion, contact spot geometry, ultrasonic vibration frequency, machining parameters (workpiece rotation speed, transverse feed), and material properties. Numerical summation methods have been implemented to account for the impulsive nature of loading and heat accumulation from individual indenter impacts. The influence of technological parameters on the thickness of the formed layer has been analyzed: it has been established that reducing the rotation speed and transverse feed increases the diffusion depth due to an increase in the number of overlapping contact spots and exposure time per surface point. Simulation results enable prediction of the antifriction layer thickness and optimization of ultrasonic hardening modes to achieve desired tribological characteristics. The model can be applied in designing coating deposition processes in mechanical engineering.

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