Research on CNC acceleration and deceleration control method of the hyperbola based on the tangential vector

Presently, Computer Numerical Control (CNC) systems have not fully optimized the performance in velocity planning and interpolation for hyperbolas. This paper proposes a novel CNC acceleration and deceleration (Acc/Dec) control method for hyperbolas based on the tangent vector of the curve. In the velocity planning phase, the curve is segmented into hyperbolic sections and the tangent vector is derived from parametric equations of the hyperbola. Subsequently, the composite accelerations of these segments are calculated using the tangent vectors to ensure that every point within these segments avails the permissible maximum acceleration. This allows a faster and shorter distance response to velocity variations. The velocity is integrated considering the angle, and velocity clamping conditions are implemented to generate different time-velocity curves. Simulations and experiments are conducted on two contour profiles to validate the effectiveness of the proposed method. The results indicate that the directional properties of the tangent vector significantly streamline the interpolation process of the hyperbolas. Compared with the traditional linear interpolation method, the machining efficiency of two contour profiles are increased by 8.2492% and 5.2523% while ensuring the machining accuracy. The proposed method is straightforward and efficient, satisfying the developmental requirements of contemporary high-velocity, high-precision CNC machine tool processing.