Abstract
S -shape acceleration and deceleration are the most widely used flexible acceleration and deceleration method in the current CNC system, but its velocity solution equation contains irrational terms, which create a more complicated solution process. When analyzing the solution process of the S -shape acceleration and deceleration directly, using a traditional numerical solution method, the phenomenon of “solving the interval jump” arises, which is the main reason for low efficiency and poor stability of the solution. According to the S -curve profile and solution, the concept of separating the curve profile recognition from the velocity solution was proposed, and a method of quickly identifying the interval of the solution location was introduced. Through the method mentioned above, the complete acceleration and deceleration curve parameters can be obtained through a one-time plan and a one-time solution, and the solution efficiency and stability are guaranteed; solving the Newton problem depends too much on the initial value of Newton velocity, which not only retains the speed advantage of the Newton method but also uses the downhill factor to ensure its convergence. Through the simulation comparison and analysis, the efficiency, stability, and universality of the method are verified.
Highlights
The ability of acceleration and deceleration is an important index in evaluating the performance of CNC systems, which directly affects the processing efficiency and quality of CNC equipment
The CNC equipment must be able to move from the current position point to the position point quickly and accurately, while ensuring the smooth operation of the equipment and avoiding impact, out of step, over the range, or oscillation
The two algorithms are simple in programming, good in real-time performance, and high in processing efficiency, but they all have the problems of abrupt change and discontinuity of the acceleration curve, which makes them not suitable for high-speed and high-accuracy machining [5]
Summary
The ability of acceleration and deceleration is an important index in evaluating the performance of CNC systems, which directly affects the processing efficiency and quality of CNC equipment. The planning of NURBS curve interpolation velocity based on S-shape acc/dec has become a hot research topic, and the solution mainly adopts the matching displacement by changing the velocity step by step [18, 19].The main idea of this method is to use the assumed key velocity value to calculate the corresponding displacement, match it with the actual displacement, and determine the curve profile according to the matching situation. In order to reduce the complexity in S-shaped acc/dec curve planning and solutions, some scholars introduced the artificial intelligence algorithms such as genetic algorithms [20] and particle swarm optimization algorithms [21]. Focusing on the disadvantages of low efficiency and poor stability of traditional algorithms, a more concise, efficient, and stable general solution was proposed In this method, the curve profile planning and velocity solution were completely separated. After obtaining the interval of the velocity solution, the modified Newton method was introduced, which can make full use of the Newton method to accelerate up to the convergence speed, and at the same time, the downhill factor guarantees the convergence of the iteration
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