A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk

In this paper, the problem of optimal feedrate planning along a curved tool path for 3-axis CNC machines with the acceleration and jerk limits for each axis and the tangential velocity bound is addressed. It is proved that the optimal feedrate planning must be “Bang–Bang” or “Bang–Bang-Singular” control, that is, at least one of the axes reaches its acceleration or jerk bound, or the tangential velocity reaches its bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of the curve parameter u. The explicit formula for the velocity function when a jerk reaches its bound is given by solving a second-order differential equation. Under a “greedy rule”, an algorithm for optimal jerk confined feedrate planning is presented. Experiment results show that the new algorithm can be used to reduce the machining vibration and improve the machining quality.     

Contour error reduction for free-form contour following tasks of biaxial motion control systems

In modern machining applications, reduction of contour error is an important issue concerning multi-axis contour following tasks. One popular approach to this problem is the cross-coupled controller (CCC). By exploiting the structure of CCC, an integrated control scheme is developed in this paper and an in-depth investigation on the issue of contour error reduction is also conducted. The proposed motion control scheme consists of a feedback controller, a feedforward controller, and a modified contour error controller (CCC equipped with a real-time contour error estimator). In addition, a fuzzy logic-based feedrate regulator is proposed to further reduce the contour error. The proposed feedrate regulator is designed based on the real-time estimated contour error and the curvature of the free-form parametric curves for machining. Several experiments are conducted to evaluate the performance of the proposed approach. Experimental results demonstrate the effectiveness of the proposed approach.