Three-axis computer numerical control machining centers are commonly used in machining due to their simple operations. When machining curved surfaces, the 3-axis CNC machining centers use interpolation line segment to fit the curved surfaces. The quality of the machined surface is affected by the length of the interpolation line segment. Sharp corners are formed at the junction of straight segments. The appearance of sharp corners will lead to increased stress concentration. To study the relationship between machined surface quality and interpolation straight line, this paper establishes the mathematical model of surface topography in ball-end milling multi-curved surfaces by a 3-axis milling center with considering the acceleration and deceleration controls. Based on the surface topography model, the stress concentration factor is analyzed in machining curved surfaces with different lengths of interpolation lines. The results show that the stress concentration factor decreases with the increase of the central angle when the length of interpolation lines and the radius of curvature are kept in constant, while decreases with the increase of the radius of curvature when the length of the interpolation lines and the central angle are held on. Moreover, the stress concentration factor increases as the length of the interpolation lines increases when the radius of curvature and the central angle are kept in constant. A method for selecting proper length of interpolation lines based on the stress concentration is proposed. In addition, the quality of the machined surfaces can be improved through the optimization of the tool path.
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