A novel time-rounding-up-based feedrate scheduling method based on S-shaped ACC/DEC algorithm

The round-off error, which is caused by cycle sampling of the interpolation period, affects the interpolation accuracy and motion smoothness of computer numerical control (CNC) machining. To consider the round-off error while restricting the motion parameters within their specified ranges, a time-rounding-up-based feedrate scheduling method is proposed. Firstly, the characteristics of S-shaped acceleration/deceleration (ACC/DEC) algorithm are analyzed by setting the jerk of each section as a variable. The expressions of jerk are derived and some important properties are discovered. According to these properties, it is possible to limit all the motion parameters in their given ranges through increasing the interpolation time and adjusting other motion parameters. Secondly, a new time-rounding-up scheme is designed to guarantee that the total interpolation time of each curve segment is an integer multiple of interpolation period. Then, based on the rounded time, the adjustment principles of the displacement and maximum feedrate are proposed to satisfy the various constraints. Its feasibility is also analyzed. Finally, based on the time-rounding-up scheme and the parameter adjustment principles, a series of feedrate scheduling methods are designed for different situations. For most situations, a non-standard S-shaped ACC/DEC profile can be generated with no round-off error and all the motion parameters can be restricted within their given ranges. A series of simulations and practical experiments are conducted to verify the good performance and applicability of the proposed method.