Gurzhiy A. Shaping of curvilinear surfaces on machine tools with parallel kinematic structures

The actual scientific problem of providing of the rational shaping of curvilinear surfaces on machine tools with parallel kinematic structures is well-founded and solved. The special procedure was created for realization of the researches. Theoretical researches are founded on the fundamentals of a differential geometry. In experimental researches has been used the designed machine tool-imitator with special measuring apparatuses and equipment. Researches of features of geometrical shaping of curvilinear surfaces on machine tools with parallel kinematic structures are carried out. Methods of an estimation of quality of curvilinear surfaces with use of factors of the first and second normal quadratic forms defined in separate points of a surface are developed. The determined and casual errors of surfaces of a different aspect are established. Influence of kinematic and dynamic properties of the machine tool with parallel kinematic structures on exactitude of shaping of curvilinear surfaces is defined. It is established, that principal causes of errors are inertial loadings in dynamic system of the machine tool at execution of curvilinear trajectories of movement of the tool. It is displayed, that in points of a break of trajectories there are high-frequency oscillating processes of casual character which cause dynamic errors of shaping of a surface. It is confirmed, that cutting process is the reason of formation of errors of the shaping of a surface which depend on width of a cut off stratum and from stiffness of the elastic system of the machine tool.