NURBS Interpolator with Scheduling Scheme Combining Cubic and Quartic S-shaped Feedrate Profiles Under Drive and Chord Error Constraints

Abstract

Traditional S-shaped feedrate profiles only account for the initial and end feedrates during scheduling; they fail to consider whether the feed rate should continuously satisfy the constraints of the chord error in the processing step. To overcome this problem, this paper proposes a feedrate scheduling scheme that processes S-shaped quartic feedrate profiles at the initial stage followed by S-shaped cubic feedrate profiles to ensure machining quality and efficiency. First, the scheme traverses the feedrate points that satisfy the chord error to determine a slope suitable for the jerk of S-shaped quartic feedrate profile, in order to ensure that the increase in the feedrates does not exceed its constraints. Second, an iterative method is used to optimally allocate processing time between the S-shaped cubic and quartic feedrate profiles to optimize processing efficiency. Finally, a method for determining the new maximum feedrate under feedrate interference is discussed. Simulations and experiments are performed to verify the effectiveness of the proposed method relative to other methods. The results reveal that, when using the proposed approach, the processing and running times of the computer are reduced by 39.48% and 118.34%, respectively, as compared with those of other methods. • Combining S-shaped quartic and cubic feedrate profile, and then calculating the optimal time allocation between them. • Ensure that the speed, acceleration and jerk meet the given constraints. • The method avoids the problem when the profile is complex the maximum feedrate can’t be updated and reduces the caculation. • The problem of low machining efficiency caused by uniform motion near the minimum feedrate point is avoided.