A Generalized Linear Mathematical Model of Cutting Part Movement in Deep Hole Machining

Five types of oscillations of the cutting part of a tool for deep drilling are considered. Using the Lagrange equations of the second kind, a system of five linear differential equations has been compiled. After the transition to Laplace’s images and performing algebraic transformations, the system has been transformed to a system of ten equations, which take into account changes in the velocities and stresses in the mechanical system considered. An example of obtaining an expression for engineering calculation of oscillations of specific system parameters, determined by the methods of linear algebra and the theory of functions of a complex variable, is given.