Look-ahead is one of the most significant functions of modern computer numerical control (CNC) systems and look-ahead algorithms are directly related to the machining efficiency and motion stability of a CNC machine tool. For decades, the look-ahead algorithm based on S-shape acceleration and deceleration (Acc/Dec) has been widely adopted, which however is too complex and time-consuming for real-time requirements. This article proposes a nested adaptive look-ahead algorithm to deal with these weaknesses. Based on the jerk symmetry in S-shape Acc/Dec, a velocity planning model is designed, and an approximation algorithm to the equivalent acceleration profile is proposed to improve model solution efficiency. Analytical solutions are given in the two main stages of velocity curve construction and checking. Taking the machining of continuous micro-segments as an example, the complete fast nested look-ahead algorithm with machining verification is provided. Machining results show that global optimal motion efficiency can be obtained with the proposed algorithm, while computation cost is less than 30% that in the traditional method. This algorithm can meet the real-time requirements to look-ahead in modern CNC systems and even in high-speed high-precision CNC systems. The analytical results given in this article are of general significance for the solution of an S-shape Acc/Dec model, and the algorithm should be applicable to look-ahead planning of continuous micro-segments, conic and even parametric curves such as non-uniform rational B-spline (NURBS).

In motion control systems driven by stepping motors, reference word interpolation is usually used with a constant period, which inevitably results in vibration caused by quantization errors and interpolation spare. An interpolator with adaptive random-period is proposed: with the adaptive random-period interpolator, the high-frequency energy excitation from stepping motor driving signals can be greatly dispersed and the desired trajectory and feed profile can be realized through the mutual restriction between the velocity and the displacement. Simulation results show that the adaptive random-period interpolator can effectively improve the velocity excitation, resonant excitation and motion accuracy.

Based on the index of motion stability for stepping motor systems, according to the module of constant acceleration-deceleration motion planning, a conception of optimal interpolation period was proposed both in single-axis motion and multi-axis motion, and the selection rules were given theoretically. Theoretical analyses and machining experiments have shown that precision, effi-ciency and stability restrict mutually in CNC machining. To achieve the best motion stability and ma-chining quality, the mentioned parameters should be selected suitably when designing machine tools or selecting machining parameters. The proposed interpolator has already been applied to nonmetal-carving machines with an in-house developed open CNC.