Method of Mathematical Model Development to Study Vibration Resistance of Non-Rigid Shaft Linear Turning

This article is devoted to the mathematical modeling of vibration resistance of non-rigid shaft linear turning. The relevance of the study is based on the occurrence of vibration in machining non-rigid shafts, which are so intense that they force to significantly reduce the cutting mode, and to resort to multi-pass processing; they lead to premature cutting tool wear and, as a consequence, reduce the productivity of the part machining on metal-cutting machine-tools. In this regard, the purpose of this article is the establishment of appropriate mathematical models which describe the vibrations of the machine-tool elastic system under the influence of dynamic cutting forces generated during machining. The article presents methods of constructing a mathematical model closed to the process of non-free machine-tool dynamic system cutting at turning non-rigid shafts. The model takes different ways of mounting the workpiece on the machine-tool into account including the use of the damper. The basic theoretical principles to build a generalized mathematical model closed to the process on non-free machine-tool dynamic system cutting are substantiated herein. The regions of stability border for different types of technological equipment are revealed by the mathematical model developed. These mathematical models give an opportunity to reflect the complex processes that occur in a closed lathe dynamic system objectively to a greater degree. The article may be useful for engineers, scientists and students of engineering courses.