EVALUATION OF THE VIBRATION STABILITY OF A TECHNOLOGICAL SYSTEM AS A PREREQUISITE FOR ENSURING THE ACCURACY OF PRECISION HOLE MACHINING

Abstract

The article presents an evaluation of the vibration stability of a technological system for machining precision conical holes with unilateral cutting tools. The relevance of the study is linked to the influence of the system’s dynamic state on the accuracy of hole-shape generation, form deviations, and the quality of the machined surface. Precision conical holes are considered as a representative object of investigation, since their geometry is sensitive to transverse tool displacements, variation in the actual uncut chip thickness, and cutting-force vibrations. The technological system is represented as the interaction of an equivalent elastic system and the cutting process. The cutting process is described by a first-order dynamic element, and the equivalent elastic system by a second-order oscillatory element. The frequency response of the conditionally open-loop system is obtained as the product of the corresponding characteristics. The computational-graphical procedure was implemented in the Scilab environment, which ensured automated determination of the real and imaginary components and construction of the corresponding hodographs. For different machining conditions and workpiece materials, amplitude-phase frequency characteristics were constructed. It was established that the cutting-process gain coefficient and the time constant affect the shape and scale of the hodographs. Evaluation of vibration stability via the Nyquist criterion for all considered conditions, the hodographs remain close to the origin of the complex plane and do not encircle the critical point (–1; i0), confirming the vibration-stable state of the system. From a metrological viewpoint, vibration stability is regarded as a prerequisite for stable formation of measured machining results: dimensional accuracy, conical profile, form deviations, and surface quality. The proposed approach can be used as a preliminary stage of analysis for determining the conditions that ensure the accuracy of precision hole machining.