Real-time Adaptive NURBS Interpolation Algorithm Based On Limited Acceleration Of Singular Axis

Traditional CNC systems only provide linear and circular interpolation. As a result, a parametric curve must be discreted into a large number of small linear segments in accordance with the required accuracy in CAD/CAM system before machining. This method exist many disadvantages, such as huge amount of data, poor processing, low efficiency and so on.Existing NURBS curve interpolation algorithm is based on the smooth transition of the synthetic acceleration, ignoring whether the axis acceleration beyond the allow acceleration and deceleration of the motor. Therefore, a new real-time adaptive NURBS interpolation algorithm based on axis acceleration limit is proposed in the paper, which aims at restricting the chord error, axis feedrate and axis acceleration in the permission range simultaneously. The proposed algorithm make sure the correctness and accuracy of the interpolation, and reduce the impact and vibration of the machine tools. Specifically, this paper involves the following aspects:(1) Pre-processing:Firstly, all of the extreme curvature points on the NURBS curve are found out, and then judge whether they are sensitive points. Secondly, The NURBS curve is divided into some segments by sensitive points. In order to obtain a smooth feedrate profile, a certain number of curve segments must be calculate in the Look-ahead module before interpolation.(2) Feedrate profile plan:A new algorithm of calculating maximum allowable feedrate constrained by the axis acceleration and chord error is deduced in this paper by seeking the relationship between the axis acceleration and feedrate. The proposed algorithm not only ensure the chord error, but also restrict the axis acceleration.(3) Look-ahead processing:In order to slow down promptly and meet the need of chord error and axis acceleration, a look-ahead module is designed to calculate the deceleration points from each sensitive point reversely, using the proposed algorithm.(4) The second-order Taylor series expansion algorithm is adopted in parameter densification, which reduce the fluctuation of actual feedrate effectively. In order to decrease the amount of calculation and increase the computational efficiency, the De Boor recursive algorithm is used for real-time interpolation.Finally, MATLAB simulations are performed to verify the correctness and feasibility of the proposed algorithm.