DETERMINATION OF OSCILLATOR CIRCUIT PARAMETERS OF A MATHEMATICAL MODEL OF THE DYNAMICS OF THE CUTTING PROCESS WITH A METAL CUTTING TOOL

Abstract

Objectives. The development of a mathematical dynamic system model is necessary for analysing vibrational motion during the metal cutting processes. The mathematical model of the dynamic system is considered to be defined if the system parameters that unambiguously determine its state are known and the alteration of its state over time is specified. Considering the above mentioned, each study of vibrational motion must be preceded by a determination of the parameters of the oscillator circuits of the mathematical model. The working part of the metal cutting tool consists in a shank having a complex profile, which makes such calculations very difficult to carry out. There are no sufficiently rigorous and, at the same time, acceptable formulae for engineering practice in the literature data. Therefore, data on the characteristics of the metal cutting tool – in particular, its stiffness and moment of inertia – scatter significantly. The aim of the study is to obtain calculated dependences that meet these requirements and determine the limits of their applicability for different cutting tool diameter ranges. Methods. Approaches referring to the theory of elasticity are used for the calculations. Results. Engineering formulae for the calculation of stiffness and polar moment of inertia of the metal cutting tool are obtained; in particular, three- and four-blade taps with straight flutes as well as drills. It is established that to increase the dynamic stability of the metal cutting tool, it is necessary to increase the moment of inertia of the section. This can be achieved by increasing the diameter of the core.As the flute helix angle increases, the stiffness of the tool decreases significantly. High stiffness of the metal cutting tool can be achieved by employing a flute with a variable helix angle. Conclusion. The calculated dependences allow the parameters of the Machine-Device-Tool-Part (MDTP) system to be set with an acceptable accuracy when analysing metal processing dynamics using metal cutting tools. The influence of the sharpening angles on the moment of inertia is demonstrated; the account given for the latter will significantly increase the reliability of the results of the analysis of the process dynamics.