Abstract:

To solve the problem of planning acceleration and deceleration time of the asymmetric S type speed curve with the beginning and the end speed non zero, acceleration curve is divided into seven time segments and speed and displacement equations are obtained. Construct square function which has argument of derivative of acceleration and the convex feature according to the monotonic change of simplified high order equation transformed from speed and displacement equations. The time segment of derivative of acceleration is obtained by the Newton Iterative and then modified by the principle of efficiency optimization and speed and acceleration limitations. The time segment of acceleration is obtained by solving quadratic equation in one variable and also modified by principle of efficiency optimization and speed and acceleration limitation. And at last the time segment of constant speed is obtained by solving one order equation in one variable. This algorithm solves the problem of the complexity of traditional planning of asymmetric S type acceleration and deceleration time and provides a simple, efficient acceleration and deceleration time planning algorithm. Through simulation and experiment, the efficiency of this algorithm is increased by 10.8%, the interpolation efficiency is increased by 3.39%, and the interpolation accuracy meets the requirements and the algorithm is proved to be simple, efficient and meets the requirements of CNC with high speed and high precision.

Key words: asymmetric S-type acceleration and deceleration control, monotonic function, Newton iteration, time planning