OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 Based on the above, the purpose of this work is is to create a theoretical and probabilistic model of material removing during fi nishing and fi ne grinding, which allows, taking into account the relative vibrations of the abrasive tool and the workpiece, to trace the patterns of its removal in the contact zone. The research methods The presence of mutual oscillatory movements of the abrasive tool and the workpiece being processed is a characteristic feature of the grinding process. Oscillatory movements arise due to the imbalance of the rotating parts of the machine, vibrations coming from outside, self-oscillations that accompany the cutting process. The frequency of forced oscillations for grinding machines according to P.I. Liashcheritsyn is 150–350 Hz, the frequency of self-oscillations is 300–900 Hz [1]. The presence of relative oscillatory movements of the grinding wheel and the workpiece leads to a change in the size and shape of the contact zone, to a distortion of the trajectories of the relative movement of the tops of abrasive grains in the material being processed, to a change in the current depth of microcutting, Figure 1. Relative displacements in the direction of the center line of the grinding head and the workpiece, regardless of the reasons that caused it, can be described by the equation: cos( ) i i yi i Y A , (1) where i A , i , yi – amplitude, cyclic frequency and initial phase of deviations f t ; – contact time of the surface with the tool. The current value of the microcutting depth z t depends on the radius vectors of the workpiece r and a wheel R, center-to-center distance A (see Fig. 1). For the most protruding grains, it can be determined by the equation: 2 2 ( ) ( ) f f e z D d z t z t t d D D , (2) where D, d are the diameters of the tool and the workpiece, respectively, e D is the equivalent diameter, z is the distance of the workpiece section to the main plane. When the workpiece rotates, the section of the machined surface passes in the contact zone from point A to point B. The depth of cut in the absence of vibrations changes monotonously (line 1) from zero to f t and from f t to zero, the current contact time is determined as u z V . For point A z L , 0 , for point B z L , 2 u L V . Fig.1. Infl uence of vibrations on the depth of microcutting during internal grinding
RkJQdWJsaXNoZXIy MTk0ODM1