Synergetic approach to study forming path stability of the end cutdown milling by side faces (case of high speed cutting)

The work objective is to consider the stability problem of steady-state paths of the elastic deformational tool displacement under the longitudinal end milling. The authors analyze the case of high speed cutting in contrast to the previously discussed stability problems that analyze the case of slow movements for which the system parameters can be considered frozen in the equations in variations relative to the stationary path. In this case, the stability analysis must consider the linearized system in variations with periodically varying coefficients. With speeding-up the tool rotation in many cases there is a parametric self-excitation of oscillations. Therefore, the main attention is paid to studying the parametric excitation conditions of a dynamic endmilling system. It is shown that the parametric excitation condition is affected by the technological cutting modes, both the tool rotation frequency and the tool geometry which determines the matrix angular coefficients of the cutting forces orientation. Examples of stability areas depending on changes in the system settings are given.