The mathematical model of the elastic machine system has been developed, and describes the dynamic processes that occur during the frictional hardening of cylindrical surfaces of parts using a tool with transverse grooves on its working part, which forms a surface hardened metal layer with nanocrystalline structure. Transverse grooves on the working part of the tool increase the intensity of deformation of the surface layer in the contact area of the tool-part and the oscillating processes of the system. Differential equations that describe this process are based on Lagrange equations of the second kind. Based on the solution of the model’s the systems of equations, it is possible to determine the velocity and magnitude of displacement of a special device with autonomous drive of the tool, tool and treatment part during machining, reaction of device supports and spindle unit.
Mathematical model of dynamic processes during frictional hardening of the cylindrical surfaces of parts
