Error effect of executive elements movement of the lathe tool on forming motion paths

Introduction. Any metal-cutting machine has errors of the executive elements movement depending on its geometric accuracy and state. These errors change the forming motions indirectly, through their transformation by the dynamic cutting system with account for the elastic deformations of the tool and the workpiece. Materials and Methods. Laws of the relation between the executive elements and forming paths for the longitudinal cutting case are considered. All deformation displacements are counted off from the independent coordinate system anchored to the carrier system of the machine which is considered to be absolutely rigid and non-deforming. Research Results. A mathematical transformation model consisting of two elastic-deformation subsystems on the part of the tool and workpiece that interact through the dynamic link generated by the cutting process is proposed. This model allows for the errors of the executive elements movement. They are specified by the kinematic disturbances and spindle wavering, and a workpiece in the space. Discussion and Conclusions. Therefore, as opposed to the known studies, it is shown how the mathematical formulation and parameters of the dynamic link generated under the cutting process are changed depending on the kinematic and other types of disturbances. Two types of disturbances are fully considered: those inducing speed variations of the tool motion relative to the workpiece in the direction to the caliper mobility, and disturbances in the form of oscillating displacements in the orthogonal direction to the feed velocity attitude. These disturbances are generated as radial and axial spindle wavering, and as speed variations of the longitudinal feed and variations of the caliper position relative to the ideal rotation axis of the part. It is shown, that the law of the disturbance transformation into the forming movements trajectories depends on the frequency content of the disturbances. The examples are provided, and the conclusions about the transformation properties are made. In particular, it is shown that the speed variations in the direction to the longitudinal feed with the frequency equal to or multiple of the spindle rotation frequency in no way image into the forming movement trajectories.