4th Chemnitz Parallel Kinematics Seminar, Devel-opment Methods and Application Experience of Parallel Kinematics, Chemnitz, April 20-21, 2004, Tagungsband S. 277-290
The processing time TP in a milling task is ideally determined by the machine programm which contains especially the trajectory of the tool and the demanded feed. In normal CNC programs the feed is not continuously differentiable unlike the velocity of a real machine axis. A change of the velocity is determined by the acceleration capabilities of the drive and the dynamic of the power supply. In state of the art machining the most commonly used digital servo motors obtain higher dynamic capacities than the driven mechanical components can bear without unacceptable loss of accuracy. The acceleration and jerk is limited by means of the controller. In high speed cutting the feed forward control includes this dynamic parameters in predetermining the desired trajectory as a function of time. This limitations lead to a time delay between the desired and the achieved trajectory. The retardation depends on the acceleration demands represented by the agility of the velocity histogram and is directly correlated to the kinematic. The scope of this paper is to examine the processing time TP of different parallel and hybrid kinematic mechanisms due to the dynamic parameters. TP is calculated on the assumption of a limited acceleration and a constant jerk. It can be reduced not only by the better acceleration capabilities and the velocity transform of PKMs often mentioned in the literature, but also by the nature and number of acceleration events. Hybrid kinematic mechanisms can decrease Tp by superposing the velocities of the subkinematics. Further on the smoothing feature of the trace splitting algorithm reduces the acceleration demands for the substructures and the process time can be reduced up to 10% without changing the velocity demand by the cutter path. The paper presents algorithms and numerical results for both pure 2D and 3D parallel kinematics and hybrid kinematic machines.